TSTP Solution File: SWV852-1 by SPASS---3.9
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- Process Solution
%------------------------------------------------------------------------------
% File : SPASS---3.9
% Problem : SWV852-1 : TPTP v8.1.0. Released v4.1.0.
% Transfm : none
% Format : tptp
% Command : run_spass %d %s
% Computer : n014.cluster.edu
% Model : x86_64 x86_64
% CPU : Intel(R) Xeon(R) CPU E5-2620 v4 2.10GHz
% Memory : 8042.1875MB
% OS : Linux 3.10.0-693.el7.x86_64
% CPULimit : 300s
% WCLimit : 600s
% DateTime : Wed Jul 20 21:45:23 EDT 2022
% Result : Timeout 299.64s 300.36s
% Output : None
% Verified :
% SZS Type : -
% Comments :
%------------------------------------------------------------------------------
%----No solution output by system
%------------------------------------------------------------------------------
%----ORIGINAL SYSTEM OUTPUT
% 0.12/0.13 % Problem : SWV852-1 : TPTP v8.1.0. Released v4.1.0.
% 0.12/0.14 % Command : run_spass %d %s
% 0.14/0.35 % Computer : n014.cluster.edu
% 0.14/0.35 % Model : x86_64 x86_64
% 0.14/0.35 % CPU : Intel(R) Xeon(R) CPU E5-2620 v4 @ 2.10GHz
% 0.14/0.35 % Memory : 8042.1875MB
% 0.14/0.35 % OS : Linux 3.10.0-693.el7.x86_64
% 0.14/0.35 % CPULimit : 300
% 0.14/0.35 % WCLimit : 600
% 0.14/0.35 % DateTime : Thu Jun 16 04:58:50 EDT 2022
% 0.14/0.35 % CPUTime :
% 299.64/300.36
% 299.64/300.36 SPASS V 3.9
% 299.64/300.36 SPASS beiseite: Ran out of time.
% 299.64/300.36 Problem: /export/starexec/sandbox/benchmark/theBenchmark.p
% 299.64/300.36 SPASS derived 79966 clauses, backtracked 0 clauses, performed 7 splits and kept 31475 clauses.
% 299.64/300.36 SPASS allocated 198265 KBytes.
% 299.64/300.36 SPASS spent 0:05:00.00 on the problem.
% 299.64/300.36 0:00:00.06 for the input.
% 299.64/300.36 0:00:00.00 for the FLOTTER CNF translation.
% 299.64/300.36 0:00:02.40 for inferences.
% 299.64/300.36 0:00:00.00 for the backtracking.
% 299.64/300.36 0:4:55.27 for the reduction.
% 299.64/300.36
% 299.64/300.36
% 299.64/300.36 The set of clauses at termination is :
% 299.64/300.36 94371[7:SpL:10.0,93902.0] || c_lessequals(v_Procs,c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* -> .
% 299.64/300.36 93902[7:Res:652.1,87829.0] || c_lessequals(v_Procs,c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* -> .
% 299.64/300.36 93931[7:Res:90130.1,93904.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),v_x),v_x)** -> .
% 299.64/300.36 14491[0:Res:526.1,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(v,w)) c_Finite__Set_Ofinite(v,u) -> c_lessequals(w,c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.64/300.36 94233[7:SpL:10.0,93907.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> .
% 299.64/300.36 93907[7:Res:89344.1,87829.0] || equal(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> .
% 299.64/300.36 94101[7:Res:90130.1,93922.0] || equal(hAPP(c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(u,tc_bool)),v_x),v_x)** -> .
% 299.64/300.36 93933[7:Res:3282.1,93904.0] || equal(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),v_Procs)** -> .
% 299.64/300.36 14364[0:Res:526.1,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(v,w)) c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),w,u)*.
% 299.64/300.36 93932[7:Res:27207.1,93904.0] || equal(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),v_x)** -> .
% 299.64/300.36 94103[7:Res:3282.1,93922.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(u,tc_bool)),v_Procs)** -> .
% 299.64/300.36 94102[7:Res:27207.1,93922.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(u,tc_bool)),v_x)** -> .
% 299.64/300.36 93922[7:SpL:10.0,93904.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(u,tc_bool)),v_x))* -> .
% 299.64/300.36 10791[0:SpR:353.0,376.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(x,v),w)),tc_fun(v,tc_bool))*.
% 299.64/300.36 93904[7:Res:526.1,87829.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),v_x))* -> .
% 299.64/300.36 87829[7:Res:74701.0,11883.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool))))* -> .
% 299.64/300.36 87712[7:Res:72664.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v_x,v_x))),w,t_a)*.
% 299.64/300.36 86342[0:SpR:86109.1,36264.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(u,v_x)))*.
% 299.64/300.36 7462[0:Res:364.1,437.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(x,w),v),w)*+ -> c_Finite__Set_Ofinite(u,w).
% 299.64/300.36 86148[0:SpR:86109.1,36471.0] || equal(u,v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),v,t_a)*.
% 299.64/300.36 86147[0:SpR:86109.1,36407.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),v))*.
% 299.64/300.36 93330[7:SpR:78167.0,85556.1] || equal(c_Set_Oinsert(v_x,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> c_lessequals(v_x,hAPP(v_x,v),tc_bool)*.
% 299.64/300.36 85556[4:SpR:3229.1,85419.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(v_x,hAPP(hAPP(u,v_x),v),tc_bool)*.
% 299.64/300.36 5878[0:SpR:584.0,300.1] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_Orderings_Obot__class_Obot(u)),hAPP(v,c_Orderings_Obot__class_Obot(u)))**.
% 299.64/300.36 83230[7:SpR:10463.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w),v_x),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.36 83229[7:SpR:9911.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w),v_x),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.36 82198[7:SpL:78597.0,46860.0] || equal(c_Set_Oinsert(v_x,u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))*+ -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.36 82187[7:SpR:78597.0,36600.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,w)),v_x))*.
% 299.64/300.36 5876[0:SpR:584.0,341.0] || -> c_lessequals(hAPP(u,v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u,x,y,z),v),tc_fun(w,tc_bool))*.
% 299.64/300.36 82185[7:SpR:78597.0,36599.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,v)),w),v_x))*.
% 299.64/300.36 92670[7:SpR:78167.0,82151.1] || equal(c_Set_Oinsert(v_x,u),c_in(t_a))**+ -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,v)))*.
% 299.64/300.36 82151[7:SpR:78597.0,3317.1] || equal(c_in(t_a),u) -> hBOOL(hAPP(hAPP(u,v_x),c_Set_Oinsert(v_x,v)))*.
% 299.64/300.36 82134[7:SpR:78597.0,43177.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(v_x,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w,t_a)*.
% 299.64/300.36 5227[0:Res:288.1,348.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x) -> equal(c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x)),c_Suc(w))**.
% 299.64/300.36 82133[7:SpR:78597.0,42583.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(v_x,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w))*.
% 299.64/300.36 92117[7:SpR:79101.0,36687.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(u,t_a),hAPP(c_in(v),v_x)),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 92132[7:SpL:79101.0,36406.0] || c_lessequals(hAPP(hAPP(c_in(u),v_x),v_x),v,tc_bool)* -> hBOOL(v).
% 299.64/300.36 92116[7:SpR:79101.0,36264.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_in(v),v_x),v_x)))*.
% 299.64/300.36 5022[0:SSi:4984.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),w,tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Oinsert(u,v),w),w).
% 299.64/300.36 92048[7:SpR:79101.0,36471.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_in(u),v_x),v_x)),v,t_a)*.
% 299.64/300.36 92047[7:SpR:79101.0,36407.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_in(u),v_x),v_x)),v))*.
% 299.64/300.36 92094[7:SpR:79101.0,10813.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_in(w),v_x)),v_x))*.
% 299.64/300.36 92131[7:SpL:79101.0,2674.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_in(u),v_x),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.36 4019[0:Res:448.2,54.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u).
% 299.64/300.36 92050[7:SpR:79101.0,36605.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_in(u),v_x),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 79101[7:Res:78199.0,279.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(c_in(v),v_x)),hAPP(c_in(v),v_x))**.
% 299.64/300.36 79073[0:Res:78077.0,279.0] || -> equal(hAPP(c_Set_Oinsert(v_Procs,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.64/300.36 78747[4:Res:78665.1,45899.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname)),v_x)** -> hBOOL(hAPP(u,v_x)).
% 299.64/300.36 834[0:SpR:301.1,415.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(u),v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.64/300.36 91289[0:Rew:91288.1,44588.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(u)),v)**.
% 299.64/300.36 91292[0:Rew:91288.1,91058.2] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.36 91291[0:Rew:91288.1,91059.2] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Olattice(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.36 91263[0:SSi:91161.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.36 90278[4:SpL:78660.1,70390.0] || equal(hAPP(u,v_x),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* -> .
% 299.64/300.36 90134[4:SpR:78660.1,267.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u))*.
% 299.64/300.36 90593[4:Rew:336.0,90499.0,538.0,90499.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))*.
% 299.64/300.36 90020[4:SpR:78660.1,36605.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool))*.
% 299.64/300.36 26480[0:SpR:524.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool))* -> c_lessequals(u,v,tc_fun(w,tc_bool)).
% 299.64/300.36 90584[4:Rew:88.1,90495.1] class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Otop__class_Otop(u),v_x) -> hBOOL(c_Orderings_Otop__class_Otop(u))*.
% 299.64/300.36 90582[4:Rew:302.1,90478.1] class_Lattices_Obounded__lattice(u) || equal(c_Orderings_Otop__class_Otop(u),v_x) -> hBOOL(c_Orderings_Otop__class_Otop(u))*.
% 299.64/300.36 90580[4:Rew:365.1,90459.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),v_x) -> hBOOL(c_Orderings_Obot__class_Obot(u))*.
% 299.64/300.36 90579[4:Rew:397.1,90458.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(u),v_x) -> hBOOL(c_Orderings_Otop__class_Otop(u))*.
% 299.64/300.36 26231[0:SpL:338.0,333.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),v)* -> c_Finite__Set_Ofinite(w,v).
% 299.64/300.36 90130[4:SpR:78660.1,423.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(u,v_x))*.
% 299.64/300.36 90404[4:Obv:90403.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBK(v_x,u,v),w,t_a)*.
% 299.64/300.36 78660[4:Res:9268.0,78632.1] || equal(hAPP(u,v_x),v_x) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),u),u)**.
% 299.64/300.36 89539[7:SpL:78590.1,418.0] || equal(c_Set_Oinsert(v_x,t_a),u) equal(u,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.36 26183[0:SpR:524.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),v)),hAPP(c_Set_Oinsert(w,u),v))**.
% 299.64/300.36 89344[7:SpR:78590.1,267.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u))*.
% 299.64/300.36 89673[7:MRR:89672.1,3591.0] || equal(c_COMBK(u,tc_bool,tc_Com_Opname),c_Set_Oinsert(v_x,t_a))** -> hBOOL(u).
% 299.64/300.36 89230[7:SpR:78590.1,36605.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool))*.
% 299.64/300.36 78590[7:MRR:73362.1,78524.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),u),u)**.
% 299.64/300.36 25984[0:SpL:339.0,332.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),v)* -> c_Finite__Set_Ofinite(x,v).
% 299.64/300.36 78407[7:SpL:78167.0,58248.0] || equal(c_COMBK(v_x,u,v),c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_x,w),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.36 78350[7:SpR:78167.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,u),v,tc_fun(w,tc_bool)),v_x),v_x,tc_bool)*.
% 299.64/300.36 78099[0:MRR:78098.0,820.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.36 75153[7:Res:1145.0,71908.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_x,u,v),tc_Com_Opname,tc_fun(w,tc_bool)),v_x))*.
% 299.64/300.36 14196[0:Res:176.0,527.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(u,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),x))*.
% 299.64/300.36 88347[7:SpL:55036.1,88286.0] || equal(u,c_HOL_Ouminus__class_Ouminus(hAPP(v_x,v_x),tc_bool))* equal(u,c_Orderings_Otop__class_Otop(tc_bool)) -> .
% 299.64/300.36 88344[7:SpL:54996.1,88286.0] || equal(hAPP(v_x,v_x),u)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**+ -> .
% 299.64/300.36 88660[7:SpL:23912.0,88086.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x) hBOOL(c_HOL_Ominus__class_Ominus(u,v_x,tc_bool))* -> .
% 299.64/300.36 87880[7:Res:87822.0,72021.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(t_a,tc_bool)),v_x),hAPP(v_x,v_x))** -> .
% 299.64/300.36 12998[0:Res:168.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,v),t_a)*+ -> c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a) c_Hoare__Mirabelle_Otriple__valid(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,v),t_a)*.
% 299.64/300.36 88278[7:Res:88170.0,70856.2] || equal(u,c_HOL_Ominus__class_Ominus(v,hAPP(v_x,v_x),tc_bool))*+ hBOOL(u)* -> .
% 299.64/300.36 88677[7:SpL:78167.0,88086.1] || equal(c_Set_Oinsert(v_x,u),v_x)**+ hBOOL(c_HOL_Ominus__class_Ominus(v,v_x,tc_bool))* -> .
% 299.64/300.36 88086[7:SpL:3229.1,88022.0] || equal(v_x,u) hBOOL(c_HOL_Ominus__class_Ominus(v,hAPP(u,v_x),tc_bool))* -> .
% 299.64/300.36 88524[7:SpL:10.0,87838.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** -> .
% 299.64/300.36 8306[0:SSi:8238.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* -> c_lessequals(u,v,tc_fun(x,tc_bool)).
% 299.64/300.36 87838[7:MRR:87837.1,826.0] || equal(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> .
% 299.64/300.36 88263[7:SpR:55036.1,88170.0] || equal(u,c_HOL_Ouminus__class_Ouminus(hAPP(v_x,v_x),tc_bool))*+ -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))*.
% 299.64/300.36 88114[7:SpL:55036.1,88100.0] || equal(u,c_HOL_Ouminus__class_Ouminus(hAPP(v_x,v_x),tc_bool))* equal(u,v_x) -> .
% 299.64/300.36 87890[7:MRR:87873.1,826.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(t_a,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.36 8176[0:SSi:8113.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool))*.
% 299.64/300.36 88098[7:SpL:55036.1,88022.0] || equal(u,c_HOL_Ouminus__class_Ouminus(hAPP(v_x,v_x),tc_bool))*+ hBOOL(u)* -> .
% 299.64/300.36 88276[7:Res:88170.0,72021.1] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(v_x,v_x),tc_bool),hAPP(v_x,v_x))** -> .
% 299.64/300.36 88342[7:SpL:15569.0,88286.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(v_x,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.36 88286[7:MRR:88273.1,826.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(v_x,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.36 7227[0:SpR:351.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_COMBK(v,w,x),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.64/300.36 88170[7:SpR:414.0,87889.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(v_x,v_x),tc_bool),tc_bool))*.
% 299.64/300.36 88100[7:Res:78665.1,88022.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(v_x,v_x),tc_bool),v_x)** -> .
% 299.64/300.36 1439[0:Res:448.2,437.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,u) -> c_lessequals(v,w,tc_fun(u,tc_bool))* c_Finite__Set_Ofinite(w,u).
% 299.64/300.36 88022[7:SpL:414.0,87988.0] || hBOOL(c_HOL_Ominus__class_Ominus(u,hAPP(v_x,v_x),tc_bool))* -> .
% 299.64/300.36 1006[0:SpL:140.1,134.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),v)** -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.36 87822[7:SpR:15476.0,74701.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(t_a,tc_bool)),v_x),tc_bool))*.
% 299.64/300.36 74701[7:SpR:104.0,71907.0] || -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),v_x))*.
% 299.64/300.36 1005[0:SpL:137.1,134.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),v)** -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.36 74399[7:MRR:74261.1,6340.0] || equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(v_x,v)).
% 299.64/300.36 72665[7:Res:10746.0,71881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),hAPP(v_x,v_x)))*.
% 299.64/300.36 72664[7:Res:10745.0,71881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v_x,v_x))),w))*.
% 299.64/300.36 71679[7:SpR:71455.1,36264.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(u,v_x)))*.
% 299.64/300.36 769[0:SpR:524.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v,v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v))**.
% 299.64/300.36 71493[7:SpR:71455.1,36471.0] || equal(u,v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),v,t_a)*.
% 299.64/300.36 71492[7:SpR:71455.1,36407.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),v))*.
% 299.64/300.36 87254[7:MRR:87243.1,820.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v)),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.36 87157[7:Res:82177.0,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v)),v_x),tc_bool))* -> .
% 299.64/300.36 32820[0:MRR:32758.1,124.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.64/300.36 83256[7:SpR:23682.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v),v_x),v_x))*.
% 299.64/300.36 82177[7:SpR:78597.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v))))*.
% 299.64/300.36 82132[7:SpR:78597.0,35192.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(v_x,u),c_in(tc_Com_Opname),t_a,tc_fun(v,tc_bool)),v_Procs))*.
% 299.64/300.36 70737[0:Res:35795.0,70400.1] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(t_a,tc_bool)),v_x))* -> .
% 299.64/300.36 32817[0:MRR:32790.0,366.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.64/300.36 86111[0:Res:36017.0,86011.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.36 86345[0:SpR:86109.1,36588.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x))*.
% 299.64/300.36 86054[0:SpL:351.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)) equal(c_COMBK(u,v,w),v_Procs)** -> .
% 299.64/300.36 86110[0:Res:35795.0,86011.0] || equal(c_HOL_Ominus__class_Ominus(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.36 24483[0:MRR:24481.1,214.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(w,x,tc_fun(u,tc_bool))*.
% 299.64/300.36 86108[0:Res:15482.1,86011.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** equal(u,v_Procs) -> .
% 299.64/300.36 86106[4:Res:78665.1,86011.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v_x)** equal(u,v_Procs) -> .
% 299.64/300.36 86261[0:SpR:86109.1,267.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u))*.
% 299.64/300.36 86150[0:SpR:86109.1,36605.0] || equal(u,v_Procs) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool))*.
% 299.64/300.36 19823[0:SpR:104.0,518.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),v))*.
% 299.64/300.36 86109[0:Res:9268.0,86011.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),u),u)**.
% 299.64/300.36 86011[0:Rew:15476.0,86006.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* equal(u,v_Procs) -> .
% 299.64/300.36 70618[0:SpL:2097.1,70492.0] || hBOOL(hAPP(u,v_x)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.36 85725[4:Rew:23912.0,85656.0] || -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),v_x,tc_bool)*.
% 299.64/300.36 13582[0:Res:526.1,147.1] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x))* hBOOL(hAPP(hAPP(c_in(w),x),v)) -> .
% 299.64/300.36 85486[4:SpR:78507.0,36687.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 78556[7:MRR:27828.1,78524.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 78540[4:MRR:15781.1,78524.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.36 85505[4:SpL:78507.0,2674.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.36 9066[0:Res:341.0,214.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(v,u),x))))*.
% 299.64/300.36 85425[4:SpR:78507.0,10746.0] || -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),tc_bool)*.
% 299.64/300.36 85419[4:SpR:78507.0,10745.0] || -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),tc_bool)*.
% 299.64/300.36 78507[4:Res:77988.0,279.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))**.
% 299.64/300.36 85370[0:SpL:337.0,26240.0] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** -> .
% 299.64/300.36 26240[0:SpL:338.0,418.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.36 78390[7:SpL:78167.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(v_x,u),v_Procs)** -> .
% 299.64/300.36 78389[7:SpL:78167.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(v_x,u),v_x)** -> .
% 299.64/300.36 78282[7:SpR:78167.0,23902.1] || equal(c_Set_Oinsert(v_x,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.36 75156[7:Res:23936.0,71908.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(u,tc_bool)),v_x))*.
% 299.64/300.36 824[0:SpR:365.1,415.0] class_Orderings_Obot(u) || -> equal(c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x,c_Orderings_Obot__class_Obot(u),v,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)))**.
% 299.64/300.36 74858[7:SpR:10463.0,72297.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_in(t_a))**+ -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_x))*.
% 299.64/300.36 74857[7:SpR:9911.0,72297.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(t_a))**+ -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x))*.
% 299.64/300.36 74648[7:SpR:10090.1,71906.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x))*.
% 299.64/300.36 74641[7:SpR:3294.1,71906.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a))**+ -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_x))*.
% 299.64/300.36 819[0:SpR:397.1,415.0] class_Orderings_Otop(u) || -> equal(c_Fun_Ofun__upd(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x,c_Orderings_Otop__class_Otop(u),v,w),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)))**.
% 299.64/300.36 73605[7:SpR:71835.1,9911.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.36 71457[7:Res:36017.0,71221.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 78674[4:Res:78665.1,657.0] || equal(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))),v_x)** -> .
% 299.64/300.36 85001[0:Res:84957.0,11894.1] || equal(hAPP(c_Set_Oinsert(u,v),u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.36 644[0:Res:589.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),v_Procs),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.64/300.36 84957[0:SpR:584.0,77906.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(v,w),v)))*.
% 299.64/300.36 77906[0:Res:423.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oinsert(v,w),x,y,z),v))*.
% 299.64/300.36 83237[7:SpR:351.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBK(u,v,w),x,y),v_x),u))*.
% 299.64/300.36 84903[4:SpL:351.0,78744.0] || equal(u,v_x) -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBK(u,v,w),x,t_a)*.
% 299.64/300.36 24060[0:MRR:24056.2,8517.0] || c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u) equal(c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))** -> .
% 299.64/300.36 78744[4:Res:78665.1,19641.0] || equal(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v)),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a).
% 299.64/300.36 78781[4:Res:78665.1,38139.0] || equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),v_x)** -> hBOOL(u).
% 299.64/300.36 78444[7:SpL:78167.0,21018.0] || equal(hAPP(c_Set_Oimage(u,v,w),v_x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.36 78315[7:SpR:78167.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,u),v_x,v_x,v,w),c_Set_Oinsert(v_x,u))**.
% 299.64/300.36 3088[0:MRR:2455.2,3087.1] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> .
% 299.64/300.36 78677[4:Res:78665.1,262.0] || equal(hAPP(hAPP(c_in(u),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_x)** -> .
% 299.64/300.36 78396[7:SpL:78167.0,3506.1] || equal(c_Set_Oinsert(v_x,u),c_Com_Ocom_OBODY)**+ equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.36 78317[7:SpR:78167.0,9566.0] || -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,w)),v_x),tc_bool)*.
% 299.64/300.36 84749[7:Res:78665.1,84748.0] || equal(hAPP(v_G,v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v_na,v_x)),v_x)** -> c_Hoare__Mirabelle_Otriple__valid(v_na,v_x,t_a).
% 299.64/300.36 3087[0:MRR:2394.2,3086.1] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> .
% 299.64/300.36 84748[7:Res:1012.1,78178.0] || hBOOL(hAPP(v_G,v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v_na,v_x)))* -> c_Hoare__Mirabelle_Otriple__valid(v_na,v_x,t_a).
% 299.64/300.36 78178[7:Res:77996.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,v_x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.36 84598[4:Res:82966.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u)),v,t_a)*.
% 299.64/300.36 84492[4:Res:82965.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x)),v,t_a)*.
% 299.64/300.36 3086[0:MRR:3085.2,394.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> .
% 299.64/300.36 84274[7:SpL:2807.0,78774.0] || equal(u,v_x) equal(hAPP(v_x,v_x),c_HOL_Ouminus__class_Ouminus(u,tc_bool))* -> .
% 299.64/300.36 83257[7:SpR:23912.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v),v_x),v_x))*.
% 299.64/300.36 82966[4:SpR:5924.0,40606.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u)),v))*.
% 299.64/300.36 82965[4:SpR:5924.0,40388.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x)),v))*.
% 299.64/300.36 2936[0:Rew:2934.0,2608.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_in(t_a),v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),u,v),hAPP(c_in(t_a),v_x))**.
% 299.64/300.36 82889[7:Res:15482.1,82846.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),v_x),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.36 82888[7:Res:27219.1,82846.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),v_x),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 82887[7:Res:78665.1,82846.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),v_x),tc_bool),v_x)** -> .
% 299.64/300.36 82184[7:SpR:78597.0,36687.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v)),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 10287[0:Rew:414.0,10277.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Fun_Ofun__upd(u,v,z,x,y))* -> equal(z,w).
% 299.64/300.36 78774[7:Res:78665.1,72021.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x)**+ equal(hAPP(v_x,v_x),u)* -> .
% 299.64/300.36 78767[7:Res:78665.1,71221.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v_x)** equal(u,v_x) -> .
% 299.64/300.36 78284[7:SpR:78167.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,u),tc_Com_Opname,v),v_x)))*.
% 299.64/300.36 78769[4:Res:78665.1,70390.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),u),v_x),tc_bool),v_x)** -> .
% 299.64/300.36 5899[0:SpR:584.0,584.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),z),hAPP(c_COMBS(u,v,x1,x2,x3),z))*.
% 299.64/300.36 78423[7:SpL:78167.0,10885.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_x),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.36 78258[7:SpR:78167.0,24020.1] || equal(c_Set_Oinsert(v_x,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> equal(hAPP(v_x,v_x),v_x)**.
% 299.64/300.36 78528[7:MRR:27861.1,78524.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 78527[4:MRR:23732.1,78524.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.36 5961[0:SpR:351.0,584.0] || -> equal(hAPP(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2),hAPP(u,hAPP(x,x2)))**.
% 299.64/300.36 83273[7:SpR:78167.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),v_x),v_x))*.
% 299.64/300.36 78357[7:SpR:78167.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),v_x),hAPP(u,v_x)))*.
% 299.64/300.36 82845[7:Res:77991.0,11894.1] || equal(hAPP(c_Set_Oinsert(u,v),v_x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.36 78393[7:SpL:78167.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u,v),c_Set_Oinsert(v_x,w))* -> .
% 299.64/300.36 5924[0:SpR:351.0,584.0] || -> equal(hAPP(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2),hAPP(hAPP(u,x2),v))**.
% 299.64/300.36 78323[7:SpR:78167.0,43177.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(v,tc_bool)),w,t_a)*.
% 299.64/300.36 78322[7:SpR:78167.0,42583.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(v,tc_bool)),w))*.
% 299.64/300.36 78253[7:SpR:78167.0,3229.1] || equal(c_Set_Oinsert(v_x,u),v)*+ -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.36 78156[7:SpR:3229.1,77996.0] || equal(hAPP(c_in(u),v_x),v)*+ -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.36 22513[0:SpR:158.0,318.1] || c_Finite__Set_Ofinite(u,v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(w,x,y),hAPP(c_Set_Oimage(z,v,x),u)),y)*.
% 299.64/300.36 78152[7:SpR:3229.1,77996.0] || equal(c_in(u),v)*+ -> hBOOL(hAPP(hAPP(v,v_x),v_x))*.
% 299.64/300.36 82894[7:MRR:82884.1,820.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.36 82846[7:Res:77991.0,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),v_x),tc_bool))* -> .
% 299.64/300.36 77991[7:Rew:584.0,77960.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(v,w),v_x)))*.
% 299.64/300.36 7671[0:Obv:7633.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)*+ c_lessequals(x,v,u)* -> c_lessequals(x,w,u)*.
% 299.64/300.36 82186[7:SpR:78597.0,36588.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,w)),v_x))*.
% 299.64/300.36 82206[7:SpL:78597.0,418.0] || equal(c_Set_Oinsert(v_x,u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.36 82148[7:SpR:78597.0,267.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Set_Oinsert(v_x,u)))*.
% 299.64/300.36 82124[7:SpR:78597.0,36605.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_x,u),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 5880[0:SpR:584.0,309.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(v,w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),w),u)*.
% 299.64/300.36 78597[7:MRR:78251.0,78524.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(v_x,u)),c_Set_Oinsert(v_x,u))**.
% 299.64/300.36 78378[7:SpL:78167.0,33513.1] || c_Finite__Set_Ofinite(v_x,u) equal(c_Finite__Set_Ocard(v_x,u),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.36 78321[7:SpR:78167.0,35192.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,c_in(tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs))*.
% 299.64/300.36 5879[0:SpR:584.0,306.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(v,w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),w),u)*.
% 299.64/300.36 78289[7:SpR:78167.0,38042.1] || equal(c_Set_Oinsert(v_x,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.36 78278[7:SpR:78167.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,u),tc_Com_Opname,v)))*.
% 299.64/300.36 78272[7:SpR:78167.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,u),v_x,tc_Com_Opname,v)))*.
% 299.64/300.36 78265[7:SpR:78167.0,37987.1] || equal(c_Set_Oinsert(v_x,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.36 5075[0:Res:83.0,437.1] || c_Finite__Set_Ofinite(u,v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(w,x,v),hAPP(c_Set_Ovimage(w,x,v),u)),v)*.
% 299.64/300.36 78247[7:SpR:78167.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.36 79136[7:Res:15482.1,79106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_in(u),v_x),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.36 79135[7:Res:27219.1,79106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_in(u),v_x),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 79134[7:Res:78665.1,79106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(u),v_x),v_x),tc_bool),v_x)** -> .
% 299.64/300.36 21894[0:Res:474.0,464.0] || -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(u,w),u,v,x)),hAPP(u,w))**.
% 299.64/300.36 78731[4:Res:78665.1,888.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_x),v_x)** -> .
% 299.64/300.36 78254[7:SpR:78167.0,3283.1] || equal(c_Set_Oinsert(v_x,u),c_in(tc_Com_Opname))**+ -> hBOOL(hAPP(v_x,v_Procs))*.
% 299.64/300.36 78526[7:MRR:27862.1,78524.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 78525[4:MRR:23939.1,78524.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.36 21268[0:Res:474.0,469.0] || -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,hAPP(u,w),v,x)),hAPP(u,w))**.
% 299.64/300.36 79105[7:Res:78199.0,11894.1] || equal(hAPP(c_in(u),v_x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.36 79076[0:Res:78077.0,11894.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.36 78846[4:SpL:54650.0,78780.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))*.
% 299.64/300.36 79139[7:MRR:79131.1,820.0] || equal(hAPP(hAPP(c_in(u),v_x),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.36 15858[0:Res:267.0,277.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oinsert(v,x),y),u,x)))*.
% 299.64/300.36 79106[7:Res:78199.0,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(u),v_x),v_x),tc_bool))* -> .
% 299.64/300.36 78199[7:Rew:584.0,78180.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_in(v),v_x)))*.
% 299.64/300.36 78179[7:Res:77996.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(v_x,u,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v_x,u),v_x,t_a)*.
% 299.64/300.36 78077[0:MRR:78076.0,820.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.36 15630[0:Res:267.0,278.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,w),x),y,u,w)))*.
% 299.64/300.36 78596[7:MRR:78250.1,78524.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_x,u),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.36 78595[7:MRR:78249.1,78524.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_x,u),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 78395[7:SpL:78167.0,3483.1] || equal(c_Set_Oinsert(v_x,u),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.36 78728[4:Res:78665.1,836.0] || equal(hAPP(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_x),v_x)** -> .
% 299.64/300.36 11064[0:Res:124.0,357.1] || c_Finite__Set_Ofinite(u,v) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(w,v,x),u),y,tc_fun(x,tc_bool)),x)*.
% 299.64/300.36 78780[4:Res:78665.1,13945.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),v_x)** -> hBOOL(u).
% 299.64/300.36 78670[4:MRR:78652.2,62518.2] || equal(u,c_Orderings_Obot__class_Obot(tc_bool))* equal(v_x,u) -> .
% 299.64/300.36 78653[4:SpL:2807.0,78632.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x)** hBOOL(u) -> .
% 299.64/300.36 78771[7:Res:78665.1,71853.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(v_x,v_x),tc_bool),v_x)** -> .
% 299.64/300.36 5988[0:SpL:584.0,333.0] || c_Finite__Set_Ofinite(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),u)* -> c_Finite__Set_Ofinite(z,u).
% 299.64/300.36 78748[4:Res:78665.1,1014.0] || equal(hAPP(v_G,v_n(v_na)),v_x)** -> .
% 299.64/300.36 78665[4:Res:9320.0,78632.1] || equal(v_x,u) -> hBOOL(u)*.
% 299.64/300.36 78632[4:SSi:78624.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(v_x,u) hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))* -> .
% 299.64/300.36 78524[4:Rew:23912.0,78512.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool))* -> .
% 299.64/300.36 5986[0:SpL:584.0,527.0] || hBOOL(hAPP(c_COMBS(c_in(u),v,w,x,y),z))*+ -> hBOOL(hAPP(hAPP(v,z),z))*.
% 299.64/300.36 77988[4:Rew:584.0,77926.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))*.
% 299.64/300.36 78167[7:Res:77996.0,279.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),v_x),v_x)**.
% 299.64/300.36 77996[7:Rew:524.0,77946.0,584.0,77946.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),v_x))*.
% 299.64/300.36 5892[0:SpR:584.0,526.1] || hBOOL(hAPP(hAPP(u,v),v))*+ -> hBOOL(hAPP(c_COMBS(c_in(w),u,x,y,z),v))*.
% 299.64/300.36 77504[7:MRR:77497.1,820.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.36 77503[7:Res:9320.0,72390.0] || -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname),v_x))*.
% 299.64/300.36 2429[0:Res:448.2,44.1] class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u).
% 299.64/300.36 72390[7:MRR:70433.0,72294.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname),v_x),tc_bool))* -> .
% 299.64/300.36 2399[0:Res:448.2,48.1] class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u).
% 299.64/300.36 75151[7:Res:7539.0,71908.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),v_x))*.
% 299.64/300.36 74865[7:SpR:351.0,72297.1] || equal(c_COMBK(u,v,w),c_in(t_a))** -> hBOOL(hAPP(u,v_x)).
% 299.64/300.36 801[0:SpR:525.1,415.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v,v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.64/300.36 74788[7:SpL:3229.1,74782.0] || equal(v_x,u) equal(hAPP(u,v_x),v)*+ -> hBOOL(v)*.
% 299.64/300.36 73678[7:SpR:71835.1,351.0] || equal(c_COMBK(u,v,w),c_Set_Oinsert(v_x,t_a))** -> equal(v_x,u).
% 299.64/300.36 72588[7:SpR:584.0,71879.0] || -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),hAPP(v_x,v_x)))*.
% 299.64/300.36 72516[7:SpR:3229.1,71856.0] || equal(hAPP(c_Set_Oinsert(u,v),v_x),w)*+ -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.36 30321[0:Obv:30086.0] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)),u)*.
% 299.64/300.36 72507[7:SpR:3229.1,71856.0] || equal(c_Set_Oinsert(u,v),w)*+ -> hBOOL(hAPP(hAPP(w,v_x),v_x))*.
% 299.64/300.36 71682[7:SpR:71455.1,36588.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x))*.
% 299.64/300.36 71406[7:SpL:351.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)) equal(c_COMBK(u,v,w),v_x)** -> .
% 299.64/300.36 75159[7:Res:7542.0,71908.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),v_x))*.
% 299.64/300.36 29199[0:Obv:29025.0] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v)),u)*.
% 299.64/300.36 73621[7:SpR:71835.1,423.0] || equal(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(u,v))*+ -> hBOOL(hAPP(v_x,u))*.
% 299.64/300.36 76240[7:SpL:135.0,71454.0] || equal(u,v_Procs) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 10470[0:Rew:10463.0,5969.0] || -> equal(hAPP(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.36 10469[0:Rew:10463.0,5968.0] || -> equal(hAPP(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.36 71456[7:Res:35795.0,71221.0] || equal(c_HOL_Ominus__class_Ominus(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 9915[0:Rew:9911.0,5973.0] || -> equal(hAPP(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.36 72734[7:Rew:71835.1,72731.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ equal(c_in(u),v_x)** -> .
% 299.64/300.36 7823[0:Rew:534.1,7822.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)),u)*.
% 299.64/300.36 74966[7:MRR:74965.1,22906.0] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_in(t_a))** -> .
% 299.64/300.36 7820[0:Obv:7806.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v)),u)*.
% 299.64/300.36 71908[7:AED:24.0,71839.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool))* -> hBOOL(hAPP(u,v_x)).
% 299.64/300.36 74783[7:MRR:74769.2,820.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(v_x,v_x),u)* -> .
% 299.64/300.36 6845[0:SpL:328.1,327.0] || c_lessequals(u,v,tc_fun(w,tc_bool))*+ equal(v,u) -> c_lessequals(v,u,tc_fun(w,tc_bool))*.
% 299.64/300.36 74770[7:SpL:2807.0,72021.1] || equal(hAPP(v_x,v_x),c_HOL_Ouminus__class_Ouminus(u,tc_bool))* hBOOL(u) -> .
% 299.64/300.36 72625[7:Res:448.2,71881.0] class_Orderings_Olinorder(tc_bool) || -> c_lessequals(u,hAPP(v_x,v_x),tc_bool)* hBOOL(u).
% 299.64/300.36 5893[0:SpR:584.0,499.0] || -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_COMBS(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w,x,y,z),hAPP(c_Com_Ocom_OBODY,x1)),u)*.
% 299.64/300.36 74782[7:Res:9320.0,72021.1] || equal(hAPP(v_x,v_x),u)*+ -> hBOOL(u)*.
% 299.64/300.36 72021[7:SSi:71993.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(v_x,v_x),u) hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))* -> .
% 299.64/300.36 71909[7:AED:24.0,71845.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(v_x,v_x),u,v),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 4858[0:SpL:1.1,51.1] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ozero__class_Ozero(u),u)*+ -> c_lessequals(v,v,u)*.
% 299.64/300.36 71907[7:AED:24.0,71838.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),v_x))*.
% 299.64/300.36 71906[7:AED:24.0,71837.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),v_x))*.
% 299.64/300.36 4857[0:SpL:4.1,51.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ozero__class_Ozero(u),u)*+ -> c_lessequals(v,v,u)*.
% 299.64/300.36 74387[7:MRR:74023.1,6340.0] || equal(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> .
% 299.64/300.36 74384[7:MRR:74020.1,6340.0] || equal(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> .
% 299.64/300.36 74383[7:MRR:73606.1,52007.0] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> .
% 299.64/300.36 4487[0:SpR:1.1,52.2] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,v,u)*+ -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.36 71608[7:SpR:71455.1,267.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u))*.
% 299.64/300.36 4486[0:SpR:4.1,52.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,v,u)*+ -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.36 4219[0:SpR:299.2,87.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* -> equal(v,c_Orderings_Otop__class_Otop(u)).
% 299.64/300.36 18903[0:Res:463.1,250.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x)*+ -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u)),v,x)*.
% 299.64/300.36 71495[7:SpR:71455.1,36605.0] || equal(u,v_x) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool))*.
% 299.64/300.36 71881[7:AED:24.0,71844.0] || c_lessequals(hAPP(v_x,v_x),u,tc_bool)* -> hBOOL(u).
% 299.64/300.36 12988[0:Res:526.1,501.0] || hBOOL(hAPP(u,v))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,u),t_a)*+ -> c_Hoare__Mirabelle_Otriple__valid(w,v,t_a)*.
% 299.64/300.36 71880[7:AED:24.0,71843.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v_x,v_x)),u,t_a)*.
% 299.64/300.36 71879[7:AED:24.0,71842.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v_x,v_x)),u))*.
% 299.64/300.36 71878[7:AED:24.0,71841.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(v_x,v_x)))*.
% 299.64/300.36 71856[7:AED:24.0,71840.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),v_x))*.
% 299.64/300.36 12554[0:Res:526.1,148.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x))* -> hBOOL(hAPP(hAPP(c_in(w),x),u)).
% 299.64/300.36 7830[0:SSi:7785.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u)),tc_fun(w,tc_bool))*.
% 299.64/300.36 71855[7:AED:24.0,71847.0] || equal(hAPP(v_x,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.36 71853[7:AED:24.0,71846.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v_x,v_x),tc_bool))* -> .
% 299.64/300.36 71455[7:Res:9268.0,71221.0] || equal(u,v_x) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),u),u)**.
% 299.64/300.36 71221[7:Rew:15476.0,71216.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* equal(u,v_x) -> .
% 299.64/300.36 7538[0:Res:341.0,363.0] || -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),u)),tc_fun(v,tc_bool))*.
% 299.64/300.36 70589[7:SpL:2097.1,70491.0] || hBOOL(hAPP(u,v_x)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 70509[0:SpL:3744.1,70504.0] || equal(c_in(tc_Com_Opname),c_in(t_a)) equal(hAPP(v_Procs,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.36 70405[0:Res:3283.1,70070.1] || equal(c_in(tc_Com_Opname),c_in(t_a)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v_Procs,v_x),tc_bool))* -> .
% 299.64/300.36 70983[0:MRR:70969.3,62520.3] || equal(u,c_Orderings_Obot__class_Obot(tc_bool))*+ equal(v,u)* hBOOL(v)* -> .
% 299.64/300.36 7568[0:Rew:339.0,7537.0] || -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x)),tc_fun(w,tc_bool))*.
% 299.64/300.36 70970[0:SpL:2807.0,70856.2] || equal(u,c_HOL_Ouminus__class_Ouminus(v,tc_bool))*+ hBOOL(u)* hBOOL(v) -> .
% 299.64/300.36 70982[0:Res:9320.0,70856.2] || equal(u,v)*+ hBOOL(u)* -> hBOOL(v)*.
% 299.64/300.36 70856[0:SSi:70817.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* hBOOL(u)* hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool))*+ -> .
% 299.64/300.36 70845[0:MRR:70828.2,38129.2] || equal(u,c_Orderings_Obot__class_Obot(tc_bool))*+ hBOOL(u)* -> .
% 299.64/300.36 6582[0:SpL:538.0,327.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v)** -> c_lessequals(w,v,tc_fun(u,tc_bool)).
% 299.64/300.36 70742[0:Rew:351.0,70687.0] || hBOOL(u) hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))* -> .
% 299.64/300.36 70492[0:Res:15482.1,70390.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v_x,t_a),u),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.36 70491[7:Res:27219.1,70390.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v_x,t_a),u),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 1376[0:SpL:26.1,14.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u))** -> equal(c_HOL_Ozero__class_Ozero(u),v).
% 299.64/300.36 70504[0:MRR:70488.1,36591.1] || equal(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),u),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.36 70390[0:Res:267.0,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),u),v_x),tc_bool))* -> .
% 299.64/300.36 70070[0:SpL:15476.0,11883.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)) hBOOL(hAPP(hAPP(c_in(t_a),v_x),u))* -> .
% 299.64/300.36 12983[0:Res:267.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v,t_a).
% 299.64/300.36 65954[0:SpR:65404.1,3283.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.36 70279[0:Obv:70257.1] class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),u)*.
% 299.64/300.36 65893[0:Res:65647.1,146.1] class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v,u)*.
% 299.64/300.36 68748[0:Obv:68549.2] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.36 11883[0:Res:526.1,150.1] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w))* hBOOL(hAPP(hAPP(c_in(v),w),u)) -> .
% 299.64/300.36 67577[0:Rew:67573.3,67572.3] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.36 67418[0:Obv:67222.2] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.36 67118[0:Obv:66921.2] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.36 66670[0:Obv:66633.1] class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.36 6239[0:SSi:6192.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),u,tc_fun(v,tc_bool))* -> equal(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u).
% 299.64/300.36 69643[0:Obv:69642.4] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Obounded__lattice(u) || -> .
% 299.64/300.36 68745[0:Rew:26.1,68744.3] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) || -> equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.36 69350[0:Obv:69349.4] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || -> .
% 299.64/300.36 67573[0:MRR:62705.3,67572.3] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || -> equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.36 1251[0:SpL:73.1,116.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Ogroup__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u))** -> equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.36 69052[0:Obv:69000.5] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || -> .
% 299.64/300.36 67447[0:SpR:1189.2,525.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.36 68749[0:Obv:68697.5] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || -> .
% 299.64/300.36 67446[0:SpR:1189.2,65404.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.36 1250[0:SpL:74.1,116.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Ogroup__add(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.36 68160[0:Obv:68159.4] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Obounded__lattice(u) || -> .
% 299.64/300.36 67416[0:Rew:27.1,67415.3] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || -> equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.36 67872[0:Obv:67871.4] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Obounded__lattice(u) || -> .
% 299.64/300.36 67115[0:Rew:27.1,67114.3] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) || -> equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.36 1189[0:SpR:26.1,88.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),c_HOL_Ozero__class_Ozero(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.36 67420[0:Obv:67368.5] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || -> .
% 299.64/300.36 66692[0:SpR:1188.2,525.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.36 67119[0:Obv:67067.5] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || -> .
% 299.64/300.36 66691[0:SpR:1188.2,65404.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.36 1188[0:SpR:27.1,88.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),c_HOL_Ozero__class_Ozero(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.36 65888[0:Res:65647.1,144.1] class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u)*.
% 299.64/300.36 66188[0:SpL:65404.1,3483.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.36 66459[0:Rew:88.1,66363.1] class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Otop__class_Otop(u),v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_x))*.
% 299.64/300.36 66455[0:Rew:302.1,66346.1] class_Lattices_Obounded__lattice(u) || equal(c_Orderings_Otop__class_Otop(u),v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_x))*.
% 299.64/300.36 1002[0:SpL:73.1,134.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u))** -> equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.36 66453[0:Rew:365.1,66325.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),v_Procs) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(u),v_x))*.
% 299.64/300.36 66452[0:Rew:397.1,66324.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(u),v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_x))*.
% 299.64/300.36 66449[0:Rew:10463.0,66351.0] || equal(c_Orderings_Obot__class_Obot(tc_bool),v_Procs) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_x))*.
% 299.64/300.36 66448[0:Rew:9911.0,66350.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x))*.
% 299.64/300.36 1001[0:SpL:74.1,134.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u))** -> equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.36 65575[0:SSi:65344.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(u,v_x),v_Procs) -> hBOOL(hAPP(hAPP(u,v_x),v_x))*.
% 299.64/300.36 65404[0:SpR:414.0,23593.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v),v)**.
% 299.64/300.36 65647[0:SpR:414.0,65571.1] class_Lattices_Olattice(u) || -> c_lessequals(v,v,u)*.
% 299.64/300.36 28903[0:SpR:10463.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.36 28902[0:SpR:9911.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.36 28748[0:SpR:10463.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.36 28747[0:SpR:9911.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.36 20403[0:AED:24.0,20340.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> .
% 299.64/300.36 28289[0:SpR:10463.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.36 28288[0:SpR:9911.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.36 27987[0:SpR:10463.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.36 27986[0:SpR:9911.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.36 2065[0:SpL:79.0,16.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> equal(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u).
% 299.64/300.36 27958[7:SpL:2267.1,27890.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))*+ equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 27900[7:MRR:27899.1,826.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 27335[7:MRR:22872.2,27297.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.36 27332[7:MRR:13102.2,27297.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.36 2064[0:SpL:81.0,16.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),u).
% 299.64/300.36 26782[0:Res:23997.0,10429.0] || -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.36 24629[0:SpR:525.1,24020.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.36 24576[0:SpR:24020.1,9569.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(hAPP(v_x,v_x),v_x,tc_bool).
% 299.64/300.36 24257[0:SpL:3229.1,23943.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_in(tc_Com_Opname))**+ -> hBOOL(hAPP(v_x,v_Procs))*.
% 299.64/300.36 662[0:Res:589.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(w,tc_bool)),v))*.
% 299.64/300.36 24036[0:SpL:23912.0,3499.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) hBOOL(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.36 24029[0:SpL:23912.0,3484.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Com_Ocom_OBODY)**+ equal(hAPP(c_Com_Ocom_OBODY,u),v_x)** -> equal(v_x,u).
% 299.64/300.36 23957[0:SpR:23912.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.36 23950[0:SpR:23912.0,8376.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))**+ equal(u,v_Procs) -> hBOOL(hAPP(v_x,u))*.
% 299.64/300.36 645[0:Res:589.0,373.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),v_x)**.
% 299.64/300.36 23948[0:SpR:23912.0,3291.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),v_Procs))*.
% 299.64/300.36 23826[0:SpL:23682.0,3698.2] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)))* equal(c_Com_Ocom_OBODY,u) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.36 23811[0:SpR:23682.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),t_a)* hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)))).
% 299.64/300.36 646[0:Res:589.0,71.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),v_x)**.
% 299.64/300.36 63743[0:SSi:63725.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),u),v_x),v)* -> hBOOL(v)*.
% 299.64/300.36 64148[4:SSi:64124.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a))** -> .
% 299.64/300.36 62698[4:MRR:62697.3,52007.0] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v_x,u)* -> .
% 299.64/300.36 679[0:Res:589.0,424.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.36 63740[0:SSi:63711.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(u,c_HOL_Ominus__class_Ominus(v,w,tc_bool))* -> c_lessequals(u,v,tc_bool)*.
% 299.64/300.36 63739[4:SSi:63706.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(u,v)* c_lessequals(v_x,u,tc_bool)* -> hBOOL(v)*.
% 299.64/300.36 63738[4:SSi:63705.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(u,v)* equal(c_Orderings_Otop__class_Otop(tc_bool),u)* -> hBOOL(v)*.
% 299.64/300.36 647[0:Res:589.0,56.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)))**.
% 299.64/300.36 63742[4:SSi:63727.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),v)* -> hBOOL(v)*.
% 299.64/300.36 63741[4:SSi:63726.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),v)* -> hBOOL(v)*.
% 299.64/300.36 4804[0:Obv:4799.0] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,w,u) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(w,u),u),u)*.
% 299.64/300.36 62368[0:Obv:62253.3] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || equal(v,w) -> c_lessequals(v,w,u)*.
% 299.64/300.36 62367[0:SSi:62338.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),u) -> c_lessequals(u,c_HOL_Ominus__class_Ominus(u,v,tc_bool),tc_bool)*.
% 299.64/300.36 4719[0:Obv:4713.0] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),w,u)*.
% 299.64/300.36 63376[0:AED:24.0,63374.3] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || -> .
% 299.64/300.36 62710[0:MRR:62709.2,4691.2] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v)**.
% 299.64/300.36 62726[0:MRR:62725.2,5701.2] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.36 4340[0:Obv:4302.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)*+ c_lessequals(w,v,u)* -> equal(w,v).
% 299.64/300.36 62530[0:MRR:62529.2,24071.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool))*+ equal(v,u)* -> c_lessequals(v,w,tc_bool)*.
% 299.64/300.36 4246[0:Obv:4240.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)*+ equal(w,v) -> c_lessequals(w,v,u)*.
% 299.64/300.36 23757[0:SpR:23682.0,3316.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.36 23754[0:SpR:23682.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.36 23747[0:SpR:23682.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),t_a,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x))*.
% 299.64/300.36 23729[0:SpR:23682.0,651.0] || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.64/300.36 10510[0:Res:168.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) c_Hoare__Mirabelle_Ohoare__valids(v,w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v,w),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),t_a)*.
% 299.64/300.36 23727[0:SpR:23682.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.36 23321[0:Res:212.1,3489.1] || hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))*+ equal(c_Set_Oinsert(u,v),c_in(tc_Com_Opname))** -> .
% 299.64/300.36 19719[0:Res:8366.1,19641.0] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_in(tc_Com_Opname),v_x),u),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_in(tc_Com_Opname),v_x),u,t_a)*.
% 299.64/300.36 18082[0:Res:1145.0,17941.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_Procs,u,v),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))** -> .
% 299.64/300.36 9511[0:Res:434.1,251.1] class_Orderings_Opreorder(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(w,x),v)*.
% 299.64/300.36 62081[2:Res:10196.1,16623.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.36 16623[2:SpR:9936.1,4250.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY) -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.36 15905[0:SpL:2267.1,15828.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))*+ equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.36 15838[0:MRR:15837.1,826.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.36 9510[0:Res:433.1,251.1] class_Orderings_Oorder(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(w,x),v)*.
% 299.64/300.36 61982[0:Rew:2990.0,61927.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.36 61981[0:Rew:3014.0,61926.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.36 15487[0:Rew:15475.0,15466.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.36 13528[0:SpR:10463.0,11030.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_in(t_a))**+ -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.36 8252[0:Res:367.1,426.1] class_Orderings_Obot(u) class_Orderings_Oorder(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)*+ -> c_lessequals(v,w,u)*.
% 299.64/300.36 13527[0:SpR:9911.0,11030.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(t_a))**+ -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.36 11167[0:Res:10684.0,10214.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),v_Procs)**.
% 299.64/300.36 10885[0:SpL:353.0,2674.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.36 8141[0:Res:421.1,427.1] class_Orderings_Otop(u) class_Orderings_Opreorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)*+ -> c_lessequals(w,v,u)*.
% 299.64/300.36 10553[0:SpL:10463.0,3493.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_in(tc_Com_Opname))**+ equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.36 10526[0:SpR:10463.0,3284.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_in(tc_Com_Opname))**+ -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.36 10492[0:Res:678.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_in(tc_Com_Opname),v_x),u,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_in(tc_Com_Opname),v_x),u),v_Procs,t_a)*.
% 299.64/300.36 9974[0:SpL:9911.0,3493.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname))**+ equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.36 7766[0:SpL:88.1,296.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)*+ -> c_lessequals(w,v,u)*.
% 299.64/300.36 9947[0:SpR:9911.0,3284.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname))**+ -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.36 9267[0:Res:9258.0,355.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x),tc_bool))* equal(v_x,u).
% 299.64/300.36 61338[0:Obv:61272.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(u),v) -> c_lessequals(w,v,u)*.
% 299.64/300.36 7761[0:SpL:302.1,296.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)*+ -> c_lessequals(w,v,u)*.
% 299.64/300.36 7597[0:Res:7539.0,1937.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.36 6931[0:Res:652.1,3499.1] || c_lessequals(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* equal(c_in(u),c_in(tc_Com_Opname)) -> .
% 299.64/300.36 57079[0:MRR:57042.2,826.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.36 61046[0:Obv:61015.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(v,c_Orderings_Obot__class_Obot(u)) -> c_lessequals(v,w,u)*.
% 299.64/300.36 7650[0:SpR:301.1,294.2] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)*+ -> c_lessequals(v,w,u)*.
% 299.64/300.36 57078[7:MRR:57041.2,826.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 59525[0:Res:1103.1,15857.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a)* hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),v,x)))*.
% 299.64/300.36 59017[0:Res:1103.1,15629.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a)* hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,v,w)))*.
% 299.64/300.36 60715[0:SpL:10.0,59706.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> c_Finite__Set_Ofinite(u,v).
% 299.64/300.36 5890[0:SpR:584.0,342.0] || -> c_lessequals(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),u),tc_fun(v,tc_bool))*.
% 299.64/300.36 59706[0:MRR:59705.1,379.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** -> c_Finite__Set_Ofinite(v,w).
% 299.64/300.36 59477[0:Res:3282.1,15857.0] || equal(v_Procs,u) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,w)))*.
% 299.64/300.36 59476[7:Res:27207.1,15857.0] || equal(v_x,u) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,w)))*.
% 299.64/300.36 58969[0:Res:3282.1,15629.0] || equal(v_Procs,u) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,u,v)))*.
% 299.64/300.36 5882[0:SpR:584.0,302.1] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.36 58968[7:Res:27207.1,15629.0] || equal(v_x,u) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,u,v)))*.
% 299.64/300.36 60256[0:Rew:2990.0,60201.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x),u)*+ -> .
% 299.64/300.36 60255[0:Rew:3014.0,60200.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),u)*+ -> .
% 299.64/300.36 60371[0:MRR:60370.1,60370.2,12840.1,826.0] class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,tc_bool)) || -> .
% 299.64/300.36 4803[0:Obv:4798.0] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),u)*.
% 299.64/300.36 58170[0:SpL:3229.1,58055.0] || equal(u,v) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),w,x),u)* -> .
% 299.64/300.36 60048[0:SSi:60026.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(w,u)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),w)*+ -> .
% 299.64/300.36 60035[0:SpL:56980.1,60015.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u)*+ equal(v,u)* equal(c_Orderings_Obot__class_Obot(tc_bool),v)* -> .
% 299.64/300.36 60116[0:MRR:60115.1,59987.1] class_OrderedGroup_Opordered__ab__group__add(tc_bool) || -> .
% 299.64/300.36 4718[0:Obv:4712.0] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),v,u)*.
% 299.64/300.36 60015[0:SSi:59996.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v) equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),u)* -> .
% 299.64/300.36 59984[0:Rew:351.0,59960.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),u)** -> .
% 299.64/300.36 57894[0:SpL:2807.0,55910.1] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v,w),x)*+ equal(u,hAPP(x,v_x))* -> .
% 299.64/300.36 4126[0:Obv:4104.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v)** -> c_lessequals(w,v,u).
% 299.64/300.36 57755[0:Obv:57754.3] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Olordered__ab__group__add(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.36 58251[0:Rew:3014.0,58222.0] || equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),hAPP(c_Set_Oinsert(w,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))))* -> .
% 299.64/300.36 21018[0:SpL:317.0,418.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.36 58144[0:Rew:2990.0,58089.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_COMBK(v,w,x))* equal(c_Orderings_Otop__class_Otop(tc_bool),v) -> .
% 299.64/300.36 58143[0:Rew:3014.0,58088.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_COMBK(v,w,x))* equal(c_Orderings_Obot__class_Obot(tc_bool),v) -> .
% 299.64/300.36 58179[0:SpL:525.1,58055.0] class_Lattices_Oupper__semilattice(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> .
% 299.64/300.36 58466[0:SpL:10463.0,58248.0] || equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.36 19883[0:SpL:104.0,332.0] || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(v,w).
% 299.64/300.36 58465[0:SpL:9911.0,58248.0] || equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),u,v),c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.36 58492[0:SpL:23682.0,58248.0] || equal(c_COMBK(v_x,u,v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.36 59552[7:Res:27205.0,15857.0] || -> hBOOL(hAPP(v_x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v_x,v)))*.
% 299.64/300.36 59428[0:Res:660.0,15857.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v_Procs,v)))*.
% 299.64/300.36 15857[0:Res:264.0,277.1] || hBOOL(hAPP(u,v))*+ -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,x)))*.
% 299.64/300.36 58636[0:SpL:2807.0,58188.0] || equal(c_COMBK(u,v,w),c_Fun_Ofun__upd(x,v_x,c_HOL_Ouminus__class_Ouminus(u,tc_bool),y,z))* -> .
% 299.64/300.36 59044[7:Res:27205.0,15629.0] || -> hBOOL(hAPP(v_x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,v_x,u)))*.
% 299.64/300.36 58920[0:Res:660.0,15629.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,v_Procs,u)))*.
% 299.64/300.36 15629[0:Res:264.0,278.1] || hBOOL(hAPP(u,v))*+ -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,u,w)))*.
% 299.64/300.36 58638[0:SpL:3014.0,58188.0] || equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),c_Fun_Ofun__upd(w,v_x,c_Orderings_Otop__class_Otop(tc_bool),x,y))* -> .
% 299.64/300.36 58637[0:SpL:2990.0,58188.0] || equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),u,v),c_Fun_Ofun__upd(w,v_x,c_Orderings_Obot__class_Obot(tc_bool),x,y))* -> .
% 299.64/300.36 58188[0:SpL:414.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v,w),c_Fun_Ofun__upd(x,v_x,u,y,z))* -> .
% 299.64/300.36 58473[0:SpL:351.0,58248.0] || equal(c_COMBK(u,v,w),c_HOL_Ouminus__class_Ouminus(c_COMBK(u,x,y),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.36 10771[0:Res:254.1,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,u),w),v))*.
% 299.64/300.36 58177[0:SpL:524.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x))* -> .
% 299.64/300.36 58493[0:SpL:23912.0,58248.0] || equal(c_COMBK(v_x,u,v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.36 58248[0:Rew:2807.0,58167.0] || equal(c_COMBK(hAPP(u,v_x),v,w),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)))** -> .
% 299.64/300.36 58217[0:SpL:23682.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)))** -> .
% 299.64/300.36 5005[0:Res:421.1,405.1] class_Orderings_Otop(u) class_Orderings_Oorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> equal(c_Orderings_Otop__class_Otop(u),v).
% 299.64/300.36 58351[0:SpL:2990.0,58198.0] || equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),u,v),c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x))* -> .
% 299.64/300.36 58198[0:SpL:351.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v,w),c_COMBK(u,x,y))* -> .
% 299.64/300.36 58247[0:Rew:3014.0,58214.0] || equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))* -> .
% 299.64/300.36 58218[0:SpL:23912.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))** -> .
% 299.64/300.36 4996[0:Res:367.1,405.1] class_Orderings_Obot(u) class_Orderings_Oorder(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> equal(v,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.36 58246[0:Rew:2990.0,58191.0] || equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),u,v),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.36 58245[0:Rew:3014.0,58190.0] || equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))* -> .
% 299.64/300.36 58055[0:EqR:55992.1] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v,w),u)** -> .
% 299.64/300.36 55992[0:SpL:351.0,55174.1] || equal(u,c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v)*+ -> .
% 299.64/300.36 4229[0:SpR:299.2,303.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> equal(v,c_Orderings_Otop__class_Otop(u)).
% 299.64/300.36 57896[0:SpL:3014.0,55910.1] || equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),u,v),w)*+ equal(hAPP(w,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.36 57895[0:SpL:2990.0,55910.1] || equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w)*+ equal(hAPP(w,v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.36 55910[0:SpL:351.0,55174.1] || equal(c_COMBK(u,v,w),x)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(x,v_x))*+ -> .
% 299.64/300.36 57407[0:Rew:15569.0,57365.2] || equal(u,c_Orderings_Obot__class_Obot(tc_bool))*+ equal(v,u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.36 4203[0:SpR:299.2,300.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> equal(c_Orderings_Obot__class_Obot(u),v).
% 299.64/300.36 55804[0:Rew:365.1,55732.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_bool))* -> .
% 299.64/300.36 55625[0:Rew:336.0,55526.0,538.0,55526.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool)*.
% 299.64/300.36 57560[4:MRR:57499.1,52007.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v_x),c_HOL_Ouminus__class_Ouminus(v_x,tc_bool))** -> .
% 299.64/300.36 4122[0:Rew:1409.2,4110.3] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(u),v) -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.36 55477[4:MRR:55440.1,52007.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v_x),tc_bool),v_x)** -> .
% 299.64/300.36 57076[0:MRR:57061.3,11284.0] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),u,tc_bool)* equal(u,c_Orderings_Obot__class_Obot(tc_bool)) -> .
% 299.64/300.36 57008[0:SpR:2807.0,54996.1] || equal(u,c_HOL_Ouminus__class_Ouminus(v,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(v,u,tc_bool),v)**.
% 299.64/300.36 57352[0:SpR:57059.1,2807.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),u).
% 299.64/300.36 57162[0:SpR:56980.1,2807.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Obot__class_Obot(tc_bool),u).
% 299.64/300.36 57059[0:Rew:15569.0,57009.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) -> equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.36 56980[0:SpR:54996.1,11918.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.36 54996[0:SSi:54954.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v) -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(v,tc_bool),u,tc_bool),c_HOL_Ouminus__class_Ouminus(v,tc_bool))**.
% 299.64/300.36 30928[0:Rew:29648.2,30793.2,29758.1,30793.2,14043.2,30793.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.36 55596[0:Rew:365.1,55486.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(v,c_Orderings_Obot__class_Obot(u),tc_bool)*.
% 299.64/300.36 30368[0:Rew:29124.2,30231.2,29241.1,30231.2,13749.2,30231.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.36 55174[0:MRR:55173.2,10475.0] || equal(u,v) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(v,v_x))* -> .
% 299.64/300.36 55713[0:AED:24.0,55694.2] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.36 55605[0:AED:24.0,55574.2] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.36 20384[0:AED:24.0,20319.2] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> .
% 299.64/300.36 55109[0:SSi:55108.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool))*+ equal(v,u)* -> equal(c_Orderings_Obot__class_Obot(tc_bool),v)*.
% 299.64/300.36 54983[0:SpL:54650.0,12591.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(u,tc_bool),tc_bool)*.
% 299.64/300.36 54593[0:SpL:54406.0,12591.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(v,hAPP(u,v_x),tc_bool)*.
% 299.64/300.36 55036[0:SpR:2807.0,54699.1] || equal(u,c_HOL_Ouminus__class_Ouminus(v,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),u)**.
% 299.64/300.36 14043[0:SpR:87.1,543.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.36 54699[0:SSi:54641.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v) -> equal(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(v,tc_bool),tc_bool),u)**.
% 299.64/300.36 54650[0:SpR:2807.0,54449.0] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(u,tc_bool),u,tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_bool))**.
% 299.64/300.36 13749[0:SpR:87.1,544.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.36 54697[0:MRR:54691.1,9595.0] class_OrderedGroup_Oordered__ab__group__add(tc_bool) || -> .
% 299.64/300.36 54449[0:SpR:414.0,54406.0] || -> equal(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(u,tc_bool),tc_bool),u)**.
% 299.64/300.36 54251[0:SpR:135.0,8667.0] || -> equal(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),u)**.
% 299.64/300.36 8667[0:SpR:10.0,117.0] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),u,tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)))**.
% 299.64/300.36 3705[0:SpL:331.0,3483.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.36 52997[0:Res:23739.1,279.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),v_x),v_x)**.
% 299.64/300.36 52856[4:MRR:52841.3,37988.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ equal(c_in(u),v_x)** -> .
% 299.64/300.36 7827[0:SSi:7770.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))*+ -> c_lessequals(w,v,tc_fun(u,tc_bool))*.
% 299.64/300.36 51366[0:SpR:23912.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.36 51305[0:SpR:24020.1,51231.0] || equal(c_Set_Oinsert(u,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> equal(c_HOL_Ominus__class_Ominus(hAPP(v_x,v_x),v_x,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.36 7672[0:SSi:7652.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*+ -> c_lessequals(u,w,tc_fun(v,tc_bool))*.
% 299.64/300.36 37397[0:SpR:3744.1,36687.0] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(u,t_a),v_Procs),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 53772[0:Res:7226.0,469.0] || -> equal(hAPP(c_Option_Othe(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(u),w,v,x)),w)**.
% 299.64/300.36 53771[0:Res:7226.0,464.0] || -> equal(hAPP(c_Option_Othe(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Option_Othe(u),v,x)),w)**.
% 299.64/300.36 7226[0:SpR:456.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Option_Othe(w),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.36 4247[0:SSi:4231.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* -> equal(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))).
% 299.64/300.36 36115[0:MRR:36114.1,826.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.36 34753[0:SpL:34428.0,3483.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.36 33303[0:SpR:23912.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.36 53381[0:Res:1012.1,12982.0] || hBOOL(hAPP(v_G,v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v_na,c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)))))*+ -> c_Hoare__Mirabelle_Otriple__valid(v_na,u,t_a)*.
% 299.64/300.36 12982[0:Res:264.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)*+ -> c_Hoare__Mirabelle_Otriple__valid(u,v,t_a)*.
% 299.64/300.36 31800[7:SpL:524.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v_x)** -> .
% 299.64/300.36 31543[0:Res:23961.0,473.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x)),v_Procs))*.
% 299.64/300.36 25019[0:SpR:524.0,23902.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.36 506[0:Inp] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),y)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),y),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),y),u).
% 299.64/300.36 53243[0:SSi:53160.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x,tc_bool)*.
% 299.64/300.36 23958[0:SpR:23912.0,21893.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u)),v_x)**.
% 299.64/300.36 23956[0:SpR:23912.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),t_a,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.36 53111[0:SSi:53028.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),v_x,tc_bool)*.
% 299.64/300.36 458[0:Inp] || c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,x,y,z,x1))),hAPP(x1,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,x,y,z,x1))),hAPP(y,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,x,y,z,x1))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),x),x1,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),z,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*+ -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),x1,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),y,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.64/300.36 23955[0:SpR:23912.0,21267.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u)),v_x)**.
% 299.64/300.36 23947[0:SpR:23912.0,3285.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs)))*.
% 299.64/300.36 23745[0:SpR:23682.0,11030.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(t_a)) -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.36 23739[0:SpR:23682.0,3284.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),v_x))*.
% 299.64/300.36 457[0:Inp] || c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),x,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),y,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*+ -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,z,w,x1,y,x))),hAPP(x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,z,w,x1,y,x))),hAPP(y,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,z,w,x1,y,x))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),z),x,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x1,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.64/300.36 41491[4:SpR:9924.0,38236.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 32269[0:SSi:32267.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool),v_x)**.
% 299.64/300.36 31495[0:SpL:23912.0,24254.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.36 504[0:Inp] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),y),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),z,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),y),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),z,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v),w)*+ -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),hAPP(y,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(z,u)),tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.64/300.36 31349[0:Res:23961.0,2629.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.36 25048[0:SpR:9924.0,23902.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.36 592[0:Inp] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))+ -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,u)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u))),hAPP(v_Q,u)),t_a)*.
% 299.64/300.36 23953[0:SpR:23912.0,15262.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(t_a)) -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.36 23944[0:SpR:23912.0,3279.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.36 23744[0:SpR:23682.0,10090.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.36 23734[2:SpR:23682.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.36 623[0:Rew:9.0,40.3] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1))))*+ c_Fun_Oinj__on(y,x1,z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> equal(hAPP(c_Fun_Othe__inv__into(x1,y,z,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,u),v)),hAPP(c_Fun_Othe__inv__into(x1,c_Fun_Ocomp(w,y,x,u,z),z,u),v))*.
% 299.64/300.36 23320[0:Res:9258.0,3489.1] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_x),tc_bool))*.
% 299.64/300.36 52509[0:Res:1103.1,38147.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_HOL_Ominus__class_Ominus(c_COMBK(v,w,x),y,tc_fun(z,tc_bool)),t_a)* hBOOL(v).
% 299.64/300.36 52505[0:Res:3282.1,38147.0] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),v_Procs)** -> hBOOL(u).
% 299.64/300.36 624[0:Rew:9.0,230.3] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1))))*+ c_Fun_Oinj__on(y,x1,z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x1,y,z,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Fun_Ocomp(w,y,x,u,z),z,u),v))*.
% 299.64/300.36 52504[7:Res:27207.1,38147.0] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),v_x)** -> hBOOL(u).
% 299.64/300.36 38147[0:Res:11611.0,37920.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),z))* -> hBOOL(u).
% 299.64/300.36 37898[0:SpR:584.0,37799.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,w,x,y),v))*.
% 299.64/300.36 37474[0:SpR:205.1,16814.1] class_Finite__Set_Ofinite_Ofinite(u) || c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u)*+ -> c_Finite__Set_Ofinite(x,w)*.
% 299.64/300.36 228[0:Inp] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*+ c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),y),z),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSemi(x,z)),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.64/300.36 52265[0:SpL:2095.0,35720.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))*+ -> hBOOL(hAPP(v,w))*.
% 299.64/300.36 35720[0:SpR:328.1,26119.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* -> hBOOL(hAPP(x,u)).
% 299.64/300.36 27265[7:SpR:9.0,27207.1] || equal(c_Fun_Ocomp(u,v,w,x,y),v_x)** -> hBOOL(hAPP(u,hAPP(v,v_x))).
% 299.64/300.36 461[0:Inp] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.64/300.36 50366[0:SSi:50273.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)*+ c_lessequals(v,w,tc_bool)* hBOOL(u) -> hBOOL(w).
% 299.64/300.36 52015[4:MRR:24955.3,52007.0] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v_x,c_Orderings_Obot__class_Obot(tc_bool),u)* -> .
% 299.64/300.36 52007[4:Res:24071.1,51862.0] || equal(c_Orderings_Obot__class_Obot(tc_bool),v_x)** -> .
% 299.64/300.36 51862[4:Rew:10463.0,51861.0] || c_lessequals(v_x,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)* -> .
% 299.64/300.36 459[0:Inp] || equal(hAPP(u,hAPP(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,v,w,x))),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,v,w,x))**+ -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(v,x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),u)),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(u,x1),x2,x,y))**.
% 299.64/300.36 40792[4:Res:9566.0,40171.0] || c_lessequals(v_x,hAPP(u,v),tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),u),v))*.
% 299.64/300.36 40244[4:SpR:584.0,38632.1] || c_lessequals(v_x,u,tc_bool) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),u))*.
% 299.64/300.36 39448[4:SpR:3229.1,38615.0] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(v_x,w,x)),y)*+ -> hBOOL(hAPP(y,v_x))*.
% 299.64/300.36 38794[4:SpR:586.0,37987.1] || equal(c_COMBB(u,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(hAPP(u,hAPP(v_x,y)))*.
% 299.64/300.36 233[0:Inp] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(w,x) c_lessequals(hAPP(c_Set_Oimage(y,v,x),u),w,tc_fun(x,tc_bool))*+ c_lessequals(hAPP(c_Set_Oimage(z,x,v),w),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(y,u,v,x) c_Fun_Oinj__on(z,w,x,v) -> equal(c_Finite__Set_Ocard(u,v),c_Finite__Set_Ocard(w,x)).
% 299.64/300.36 38793[4:SpR:585.0,37987.1] || equal(c_COMBC(u,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(hAPP(hAPP(u,y),v_x))*.
% 299.64/300.36 38146[0:Res:11610.0,37920.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Option_Ooption_OSome(x,u)))* -> hBOOL(x).
% 299.64/300.36 51469[0:SpL:8385.1,33513.1] || equal(u,v_Procs) c_Finite__Set_Ofinite(u,tc_Com_Opname) equal(c_Finite__Set_Ocard(u,tc_Com_Opname),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.36 51471[0:SpL:659.0,33513.1] || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) equal(c_Finite__Set_Ocard(v_Procs,tc_Com_Opname),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.36 195[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool))*+ c_lessequals(x,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(y,v,w,z)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(y,w,z),u),hAPP(c_Set_Oimage(y,w,z),x),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,w,z),c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool))))**.
% 299.64/300.36 33513[0:SpL:61.1,290.0] || c_Finite__Set_Ofinite(u,v) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,v),u),v),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.36 32700[0:SpR:414.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ofun__upd(u,v_x,v,w,x),tc_Com_Opname,y),v)))*.
% 299.64/300.36 27284[7:Res:27207.1,33.0] || equal(hAPP(c_Set_Ovimage(u,v,w),x),v_x)** -> hBOOL(hAPP(x,hAPP(u,v_x))).
% 299.64/300.36 51231[0:SSi:51230.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),hAPP(hAPP(c_Set_Oinsert(v,t_a),u),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.36 462[0:Inp] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.64/300.36 26873[0:MRR:26808.0,267.0] || -> equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),u),tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.64/300.36 472[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* hBOOL(hAPP(hAPP(c_in(u),z),hAPP(c_Set_Oimage(w,x,u),y)))* equal(hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),z))*+ -> equal(v,z).
% 299.64/300.36 50575[0:SSi:50531.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)*+ equal(v,c_Orderings_Obot__class_Obot(tc_bool)) hBOOL(u) -> hBOOL(w)*.
% 299.64/300.36 48288[4:SpR:369.0,39064.1] || equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),v_x),w,t_a)*.
% 299.64/300.36 50898[4:Res:48173.1,3499.1] || equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ equal(c_in(w),c_Set_Oinsert(u,v))* -> .
% 299.64/300.36 48173[4:SpR:369.0,39023.1] || equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),w))*.
% 299.64/300.36 622[0:Rew:89.0,222.0] || -> equal(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_x),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))))**.
% 299.64/300.36 46640[4:SpL:351.0,46565.1] || equal(c_COMBK(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ equal(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),u)* -> .
% 299.64/300.36 46413[0:SSi:46378.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool)* hBOOL(u) -> hBOOL(w).
% 299.64/300.36 50576[0:SSi:50532.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Obot__class_Obot(tc_bool))**+ hBOOL(u) -> hBOOL(w)*.
% 299.64/300.36 50351[0:Res:24071.1,46309.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Obot__class_Obot(tc_bool))**+ hBOOL(v) -> hBOOL(w)*.
% 299.64/300.36 223[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oimage(z,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,x,u,y),u,y),w))**.
% 299.64/300.36 46309[0:SSi:46275.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool)* hBOOL(v) -> hBOOL(w).
% 299.64/300.36 44926[0:Res:7539.0,44833.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))),v_x))*.
% 299.64/300.36 43608[4:Res:7539.0,43176.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))),x,t_a)*.
% 299.64/300.36 43372[4:Res:7539.0,42582.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))),x))*.
% 299.64/300.36 620[0:Rew:89.0,189.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,v,tc_fun(x,tc_bool)),u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,w,v,tc_fun(x,tc_bool))))**.
% 299.64/300.36 43266[4:Res:7539.0,42356.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x))),v_x))*.
% 299.64/300.36 43177[4:SpR:410.0,42609.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(w,tc_bool)),x,t_a)*.
% 299.64/300.36 50087[4:Res:48865.1,19641.0] || equal(u,v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,tc_fun(v,tc_bool)),w,t_a)*.
% 299.64/300.36 48865[4:SpR:8385.1,42583.0] || equal(u,v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,tc_fun(v,tc_bool)),w))*.
% 299.64/300.36 497[0:Inp] || -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)))**.
% 299.64/300.36 49871[4:Res:48869.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,tc_fun(v,tc_bool)),w,t_a)*.
% 299.64/300.36 49079[0:SpR:49017.1,10813.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.36 48869[4:SpR:2089.0,42583.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,tc_fun(v,tc_bool)),w))*.
% 299.64/300.36 49657[0:MRR:49656.0,49656.1,219.0,262.0] || -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),w,x)*.
% 299.64/300.36 49342[0:Res:49314.1,279.0] || hBOOL(hAPP(u,v_x)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.36 49343[0:Res:49314.1,527.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.36 49314[0:Con:49297.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)),v_Procs))*.
% 299.64/300.36 49219[4:Res:48882.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(u,tc_bool)),v,t_a)*.
% 299.64/300.36 488[0:Inp] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))*+ -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)),x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)),y))*.
% 299.64/300.36 48882[4:SpR:10063.0,42583.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(u,tc_bool)),v))*.
% 299.64/300.36 49207[4:Res:48879.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(v,tc_bool)),w,t_a)*.
% 299.64/300.36 48879[4:SpR:2095.0,42583.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(v,tc_bool)),w))*.
% 299.64/300.36 49150[4:Res:48880.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w,t_a)*.
% 299.64/300.36 239[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))*+ c_lessequals(y,z,tc_fun(x,tc_bool)) c_Fun_Oinj__on(w,y,x,u) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Fun_Othe__inv__into(y,w,x,u),v)),z))*.
% 299.64/300.36 48880[4:SpR:9987.0,42583.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w))*.
% 299.64/300.36 49017[0:Res:48989.1,279.0] || -> hBOOL(hAPP(u,v_x)) equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.36 49018[0:Res:48989.1,527.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.36 48989[0:Con:48972.1] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname)),v_Procs))*.
% 299.64/300.36 483[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))*+ -> hBOOL(hAPP(y,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,y,u)),w))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,y,u)),x))*.
% 299.64/300.36 42583[4:SpR:410.0,40590.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(w,tc_bool)),x))*.
% 299.64/300.36 42414[4:SpR:584.0,40372.0] || -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x),y),v_x))*.
% 299.64/300.36 619[0:Rew:89.0,179.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))*+ -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,u,tc_fun(y,tc_bool)),w),c_Set_Oinsert(z,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(z,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))))**.
% 299.64/300.36 42357[4:SpR:410.0,40371.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(x,tc_bool)),v_x))*.
% 299.64/300.36 197[0:Inp] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))))**.
% 299.64/300.36 41073[4:Res:12533.1,40323.1] || c_lessequals(u,v,tc_bool)* equal(c_HOL_Ominus__class_Ominus(u,w,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**+ -> hBOOL(v).
% 299.64/300.36 40812[4:Res:12533.1,40171.0] || c_lessequals(u,v,tc_bool)* c_lessequals(v_x,c_HOL_Ominus__class_Ominus(u,w,tc_bool),tc_bool)*+ -> hBOOL(v).
% 299.64/300.36 40606[4:SSi:40564.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),y)))*.
% 299.64/300.36 40388[4:SSi:40345.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v_x)))*.
% 299.64/300.36 224[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(v,x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(v,hAPP(c_Set_Oinsert(w,x),y),x,u) -> .
% 299.64/300.36 39064[4:SpR:3229.1,39040.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),hAPP(u,v_x)),x,t_a)*.
% 299.64/300.36 39057[4:SpR:3229.1,38612.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x)*+ -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.36 39023[4:SpR:3229.1,38611.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(u,v_x)),x))*.
% 299.64/300.36 38881[4:SpR:3229.1,38042.1] || equal(u,v)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)*+ -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(v,v_x),w,t_a)*.
% 299.64/300.36 489[0:Inp] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y)))*+ -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,u,w)),y))*.
% 299.64/300.36 38692[4:SpR:3229.1,37987.1] || equal(u,v)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)*+ -> hBOOL(hAPP(hAPP(v,v_x),w))*.
% 299.64/300.36 47829[0:Res:12463.0,38190.0] || hBOOL(c_HOL_Ominus__class_Ominus(u,v,tc_bool))*+ -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w))*.
% 299.64/300.36 490[0:Inp] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v)))*+ -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,u,w)),y))*.
% 299.64/300.36 38190[0:SSi:38080.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)*+ hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w))*.
% 299.64/300.36 47549[4:SSi:47531.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool),u,tc_bool)* -> hBOOL(u).
% 299.64/300.36 47681[4:Res:47550.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool)),u,t_a)*.
% 299.64/300.36 47550[4:SSi:47532.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool)),u))*.
% 299.64/300.36 484[0:Inp] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))*+ -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)),y))*.
% 299.64/300.36 47158[4:MRR:47157.0,6340.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool)))*.
% 299.64/300.36 47318[4:SSi:47300.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool),u,tc_bool)* -> hBOOL(u).
% 299.64/300.36 47458[4:Res:47319.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool)),u,t_a)*.
% 299.64/300.36 47319[4:SSi:47301.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool)),u))*.
% 299.64/300.36 485[0:Inp] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))*+ -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)),x))*.
% 299.64/300.36 47138[4:MRR:47137.0,6340.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool)))*.
% 299.64/300.36 47109[0:Res:12463.0,38189.0] || hBOOL(c_HOL_Ominus__class_Ominus(u,v,tc_bool))*+ -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u))*.
% 299.64/300.36 242[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))* -> c_lessequals(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool)).
% 299.64/300.36 38189[0:SSi:38077.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)*+ hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v))*.
% 299.64/300.36 38148[0:Res:23997.0,37920.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),u))* -> hBOOL(u).
% 299.64/300.36 46860[0:Res:13387.1,44750.0] || equal(hAPP(c_Set_Oinsert(v_x,t_a),u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))*+ -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.36 46859[0:Res:651.0,44750.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,tc_fun(u,tc_bool)),v_x))*.
% 299.64/300.36 241[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))*.
% 299.64/300.36 44750[0:SpR:329.1,36599.0] || c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(v,v_x)).
% 299.64/300.36 46565[4:SpL:3229.1,46560.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),hAPP(u,v_x))* -> .
% 299.64/300.36 617[0:Rew:89.0,186.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,v,tc_fun(x,tc_bool)),u),c_Set_Oinsert(y,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,w,v,tc_fun(x,tc_bool))))**.
% 299.64/300.36 46560[4:AED:24.0,46558.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))* -> .
% 299.64/300.36 42029[4:SpR:23965.1,38616.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x))*.
% 299.64/300.36 480[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))*+ -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w)))*.
% 299.64/300.36 37989[0:SSi:37948.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w)))*.
% 299.64/300.36 37923[0:SSi:37888.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u)))*.
% 299.64/300.36 37916[0:Res:37799.1,19641.0] || hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,t_a)*.
% 299.64/300.36 37549[0:SpR:351.0,36690.1] || equal(c_COMBK(u,v,w),c_Set_Oinsert(v_x,t_a))**+ -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool))*.
% 299.64/300.36 481[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))*+ -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)))*.
% 299.64/300.36 36802[0:SpR:8498.1,36588.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool))) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x))*.
% 299.64/300.36 45899[0:Con:45882.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname)))* -> hBOOL(hAPP(u,v_x)).
% 299.64/300.36 482[0:Inp] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)))* hBOOL(hAPP(hAPP(c_in(w),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x)))*+ -> hBOOL(hAPP(u,y))*.
% 299.64/300.36 43324[4:SpR:3229.1,43270.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,tc_fun(u,tc_bool)),v)*+ -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.36 38888[4:SpR:525.1,38042.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.36 323[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),y),w,x,tc_fun(u,tc_bool)))**.
% 299.64/300.36 38699[4:SpR:525.1,37987.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.36 45481[4:MRR:45480.0,6340.0] || -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_Com_Opname))*.
% 299.64/300.36 45476[4:MRR:45475.1,6340.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_Com_Opname))*.
% 299.64/300.36 45474[4:MRR:45473.0,6340.0] || -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname))*.
% 299.64/300.36 237[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*+ c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u) -> equal(hAPP(w,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v,w,u,x)),v)**.
% 299.64/300.36 45357[0:Con:45339.2] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.36 45401[7:Res:27205.0,45376.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,tc_bool))*.
% 299.64/300.36 45266[7:EqR:45265.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(u,t_a),v_x),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 487[0:Inp] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))*+ -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)))*.
% 299.64/300.36 45265[7:MRR:45249.1,27205.0] || equal(c_Set_Oinsert(u,t_a),v)*+ -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(v,v_x),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 37394[0:SpR:2097.1,36687.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(v,t_a),u),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 36608[0:SSi:36577.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),u),v_x),v,w),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 36600[0:Res:9569.0,36406.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(v_x,t_a),w)),v_x))*.
% 299.64/300.36 326[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,y,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),tc_fun(w,tc_bool))*.
% 299.64/300.36 44833[0:SpR:329.1,44716.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(v,v_x)).
% 299.64/300.36 44824[0:SpR:538.0,44716.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.36 44716[0:SpR:9987.0,36599.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w),v_x))*.
% 299.64/300.36 593[0:Inp] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))+ c_Hoare__Mirabelle_Otriple__valid(v,v_n(v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,u)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u))),hAPP(v_Q,u)),t_a)*.
% 299.64/300.36 36599[0:Res:9568.0,36406.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v)),w),v_x))*.
% 299.64/300.36 36561[0:Res:448.2,36406.0] class_Orderings_Olinorder(tc_bool) || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v_x,t_a),v),v_x),tc_bool)* hBOOL(u).
% 299.64/300.36 240[0:Inp] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(c_Finite__Set_Ofold(hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),x),y,v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u)))**.
% 299.64/300.36 40794[4:Res:10684.0,40171.0] || c_lessequals(v_x,v_Procs,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs))*.
% 299.64/300.36 36528[0:SpL:3744.1,36406.0] || equal(c_in(tc_Com_Opname),c_in(t_a)) c_lessequals(hAPP(v_Procs,v_x),u,tc_bool)* -> hBOOL(u).
% 299.64/300.36 30[0:Inp] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,hAPP(c_COMBB(c_Set_Ovimage(v,w,x),tc_fun(x,tc_bool),tc_fun(w,tc_bool),y),z),y,tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,z,y,tc_fun(x,tc_bool))))**.
% 299.64/300.36 35900[0:MRR:35899.1,826.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(t_a,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.36 41469[4:SpR:10463.0,38236.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 41468[4:SpR:9911.0,38236.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 40684[4:SSi:40655.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**+ -> hBOOL(u)*.
% 299.64/300.36 90[0:Inp] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,hAPP(c_COMBB(c_Set_Oimage(v,w,x),tc_fun(w,tc_bool),tc_fun(x,tc_bool),y),z),y,tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,z,y,tc_fun(w,tc_bool))))**.
% 299.64/300.36 36486[0:SpR:3744.1,36471.0] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v_Procs,v_x)),u,t_a)*.
% 299.64/300.36 268[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))*+ hBOOL(hAPP(hAPP(c_in(u),x),w))* equal(hAPP(y,v),hAPP(y,x))* c_Fun_Oinj__on(y,w,u,z)* -> equal(v,x).
% 299.64/300.36 36412[0:SpR:3744.1,36407.0] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v_Procs,v_x)),u))*.
% 299.64/300.36 36345[0:SpR:3744.1,36264.0] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(v_Procs,v_x)))*.
% 299.64/300.36 232[0:Inp] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.36 39450[4:SpR:584.0,38615.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),c_COMBK(v_x,x1,x2)))*.
% 299.64/300.36 44114[0:Res:38134.1,19641.0] || hBOOL(u) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),c_COMBK(u,x,y)),z,t_a)*.
% 299.64/300.36 38134[0:Res:10713.0,37920.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_COMBK(u,x,y)),z))*.
% 299.64/300.36 42018[4:MRR:42007.1,6340.0] || equal(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),y)*+ -> hBOOL(hAPP(y,v_x))*.
% 299.64/300.36 358[0:Inp] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,y,tc_fun(v,tc_bool)).
% 299.64/300.36 39033[4:SpR:584.0,38611.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))*.
% 299.64/300.36 38895[4:SpR:414.0,38042.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> c_Hoare__Mirabelle_Ohoare__valids(v,y,t_a)*.
% 299.64/300.36 38706[4:SpR:414.0,37987.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(hAPP(v,y))*.
% 299.64/300.36 231[0:Inp] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool))*+ c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),u),y,tc_fun(w,tc_bool))*.
% 299.64/300.36 38133[0:Res:10712.0,37920.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),c_Option_Ooption_OSome(u,x)))*.
% 299.64/300.36 43849[0:Res:38130.1,19641.0] || hBOOL(u) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),x,t_a)*.
% 299.64/300.36 38827[4:Res:37987.1,33.0] || equal(c_Set_Ovimage(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(hAPP(v_x,hAPP(u,x)))*.
% 299.64/300.36 235[0:Inp] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)+ -> hBOOL(hAPP(x,y))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(x,u,v,w)),hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))))*.
% 299.64/300.36 38826[4:Res:37987.1,371.0] || equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(hAPP(v_x,w))* equal(u,w)*.
% 299.64/300.36 38140[0:Res:12621.0,37920.0] || hBOOL(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,tc_bool))* -> hBOOL(u).
% 299.64/300.36 38131[0:Res:10746.0,37920.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),u))*.
% 299.64/300.36 38130[0:Res:10745.0,37920.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),x))*.
% 299.64/300.36 162[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),hAPP(c_Set_Ovimage(v,u,w),y)),hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))**.
% 299.64/300.36 43611[4:Res:13385.1,43176.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))*+ -> c_Hoare__Mirabelle_Ohoare__valids(u,w,t_a)*.
% 299.64/300.36 43176[4:SpR:329.1,42609.0] || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(v,tc_bool))*+ -> c_Hoare__Mirabelle_Ohoare__valids(u,w,t_a)*.
% 299.64/300.36 507[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),hAPP(c_Set_Oimage(v,w,u),y)),hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))**.
% 299.64/300.36 43437[4:Res:43376.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,tc_fun(u,tc_bool)),v,t_a)*.
% 299.64/300.36 43376[4:Res:651.0,42582.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,tc_fun(u,tc_bool)),v))*.
% 299.64/300.36 42582[4:SpR:329.1,40590.0] || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(v,tc_bool))*+ -> hBOOL(hAPP(u,w))*.
% 299.64/300.36 43271[4:Res:13387.1,42356.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))*+ -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.36 406[0:Inp] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(y,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))* -> equal(u,x) equal(u,y).
% 299.64/300.36 42356[4:SpR:329.1,40371.0] || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(v,v_x)).
% 299.64/300.36 41476[4:SpR:351.0,38236.1] || equal(c_COMBK(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool))*.
% 299.64/300.36 40831[4:SSi:40752.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,u,tc_bool) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 408[0:Inp] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(y,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))* -> equal(w,y) equal(u,y).
% 299.64/300.36 40728[4:Res:448.2,40171.0] class_Orderings_Olinorder(tc_bool) || c_lessequals(v_x,u,tc_bool)* -> c_lessequals(v,u,tc_bool)* hBOOL(v).
% 299.64/300.36 42829[4:Res:40591.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w,t_a)*.
% 299.64/300.36 42609[4:Res:40590.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v),w,t_a)*.
% 299.64/300.36 40671[4:SSi:40640.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_x,u,v),tc_Com_Opname,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**+ -> hBOOL(w)*.
% 299.64/300.36 486[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)))**.
% 299.64/300.36 40601[4:SSi:40566.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),v,w),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 40591[4:Res:9569.0,40105.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w))*.
% 299.64/300.36 42604[4:Res:40590.0,3499.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))* -> .
% 299.64/300.36 42617[4:MRR:42598.1,826.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),c_in(t_a))** -> .
% 299.64/300.36 161[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),w,tc_fun(u,tc_bool)))**.
% 299.64/300.36 42605[4:Res:40590.0,3489.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),c_in(tc_Com_Opname))** -> .
% 299.64/300.36 40590[4:Res:9568.0,40105.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v),w))*.
% 299.64/300.36 40550[4:Res:448.2,40105.0] class_Orderings_Olinorder(tc_bool) || -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v),tc_bool)* hBOOL(u).
% 299.64/300.36 40383[4:SSi:40347.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),v,w),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 315[0:Inp] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,w,x,y)),hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,w,x,y)))* -> equal(hAPP(c_Set_Oimage(u,x,y),v),hAPP(c_Set_Oimage(w,x,y),v)).
% 299.64/300.36 40372[4:Res:9569.0,40016.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),v_x))*.
% 299.64/300.36 40371[4:Res:9568.0,40016.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v)),w),v_x))*.
% 299.64/300.36 40331[4:Res:448.2,40016.0] class_Orderings_Olinorder(tc_bool) || -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),v_x),tc_bool)* hBOOL(u).
% 299.64/300.36 38886[4:SpR:524.0,38042.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.36 221[0:Inp] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_List_Ofoldl(c_COMBC(hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),v),w),v,u,u),c_Orderings_Obot__class_Obot(u),x,u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(x,v),w,v,u))**.
% 299.64/300.36 38697[4:SpR:524.0,37987.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.36 38144[0:Res:11580.0,37920.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs))* -> hBOOL(v_Procs).
% 299.64/300.36 40680[4:SSi:40654.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**+ -> hBOOL(u)*.
% 299.64/300.36 38919[4:SpR:9924.0,38042.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Otop__class_Otop(tc_bool),u,t_a)*.
% 299.64/300.36 180[0:Inp] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(w,u),v),u,u))**.
% 299.64/300.36 38730[4:SpR:9924.0,37987.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),u))*.
% 299.64/300.36 38616[4:Res:10705.0,38471.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,v_x,y,z)),x))*.
% 299.64/300.36 37962[0:SpR:584.0,37921.1] || hBOOL(u) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),u))*.
% 299.64/300.36 82[0:Inp] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.64/300.36 38142[0:Res:12533.1,37920.0] || c_lessequals(u,v,tc_bool)* hBOOL(c_HOL_Ominus__class_Ominus(u,w,tc_bool))*+ -> hBOOL(v).
% 299.64/300.36 41783[4:Res:40094.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v,w),x,t_a)*.
% 299.64/300.36 41070[4:Res:12593.0,40323.1] || equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(u).
% 299.64/300.36 40809[4:Res:12593.0,40171.0] || c_lessequals(v_x,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),tc_bool)* -> hBOOL(u).
% 299.64/300.36 199[0:Inp] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(u,w,v,x))))*+ c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(u,y))*.
% 299.64/300.36 40094[4:SpR:584.0,38566.0] || -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v,w),x))*.
% 299.64/300.36 38613[4:Res:10697.0,38471.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x)),v_x))*.
% 299.64/300.36 40825[4:SSi:40756.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,hAPP(u,v_x),tc_bool) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool))*.
% 299.64/300.36 38898[4:SpR:10463.0,38042.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_bool),v,t_a)*.
% 299.64/300.36 494[0:Inp] || hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),z),t_a)*+ c_Natural_Oevaln(y,w,x,x1)* -> hBOOL(hAPP(hAPP(z,v),x1))*.
% 299.64/300.36 38897[4:SpR:9911.0,38042.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Otop__class_Otop(tc_bool),v,t_a)*.
% 299.64/300.36 38790[4:SpR:336.0,37987.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))*.
% 299.64/300.36 38709[4:SpR:10463.0,37987.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v))*.
% 299.64/300.36 38708[4:SpR:9911.0,37987.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v))*.
% 299.64/300.36 284[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(v,x,u),y)))*+ c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u)* -> hBOOL(hAPP(hAPP(c_in(x),w),y)).
% 299.64/300.36 38236[4:SpR:3229.1,38176.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(u,v_x),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 38183[0:MRR:38085.2,9320.1] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(u,c_HOL_Ozero__class_Ozero(tc_bool),tc_bool)* -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)).
% 299.64/300.36 275[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(z,v)))*+ -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,z,u,tc_fun(x,tc_bool))))*.
% 299.64/300.36 38124[0:Res:10684.0,37920.0] || hBOOL(v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs))*.
% 299.64/300.36 38922[4:SpR:23682.0,38042.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> c_Hoare__Mirabelle_Ohoare__valids(v_x,u,t_a)*.
% 299.64/300.36 38733[4:SpR:23682.0,37987.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(hAPP(v_x,u))*.
% 299.64/300.36 38905[4:SpR:351.0,38042.1] || equal(c_COMBK(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> c_Hoare__Mirabelle_Ohoare__valids(u,x,t_a)*.
% 299.64/300.36 478[0:Inp] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),x))*+ -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,x,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),x)))*.
% 299.64/300.36 38716[4:SpR:351.0,37987.1] || equal(c_COMBK(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(hAPP(u,x))*.
% 299.64/300.36 41096[4:Rew:11167.1,41055.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs)** -> hBOOL(v_Procs).
% 299.64/300.36 40323[4:SpL:11176.1,40016.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) c_lessequals(u,v,tc_bool)* -> hBOOL(v).
% 299.64/300.36 40861[4:Res:10196.1,40808.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(u).
% 299.64/300.36 479[0:Inp] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),x))*+ -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,y,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))*.
% 299.64/300.36 40808[4:Res:12463.0,40171.0] || c_lessequals(v_x,c_HOL_Ominus__class_Ominus(u,v,tc_bool),tc_bool)* -> hBOOL(u).
% 299.64/300.36 40171[4:SSi:40123.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)*+ c_lessequals(v_x,u,tc_bool)* -> hBOOL(v).
% 299.64/300.36 38164[0:SSi:38083.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(u) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 38059[0:Res:448.2,37920.0] class_Orderings_Olinorder(tc_bool) || hBOOL(u) -> c_lessequals(v,u,tc_bool)* hBOOL(v).
% 299.64/300.36 530[0:Inp] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),y),v) -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),v)*.
% 299.64/300.36 40433[4:SSi:40414.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,u,tc_bool)*+ equal(u,c_Orderings_Obot__class_Obot(tc_bool)) -> hBOOL(v)*.
% 299.64/300.36 40262[4:Res:38632.1,19641.0] || c_lessequals(v_x,u,tc_bool) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,t_a)*.
% 299.64/300.36 40105[4:SSi:40071.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),v,tc_bool)* -> hBOOL(v).
% 299.64/300.36 40434[4:SSi:40415.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),c_Orderings_Obot__class_Obot(tc_bool))**+ -> hBOOL(v)*.
% 299.64/300.36 529[0:Inp] || c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),v)* -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),y),v).
% 299.64/300.36 40363[4:Res:24071.1,40016.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),c_Orderings_Obot__class_Obot(tc_bool))**+ -> hBOOL(v)*.
% 299.64/300.36 40374[4:SSi:40351.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 40016[4:SSi:39986.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),v,tc_bool)* -> hBOOL(v).
% 299.64/300.36 398[0:Inp] || c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w),tc_fun(u,tc_bool))* -> c_lessequals(v,w,tc_fun(u,tc_bool)).
% 299.64/300.36 38789[4:SpR:303.1,37987.1] class_Lattices_Obounded__lattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> hBOOL(c_Orderings_Otop__class_Otop(u))*.
% 299.64/300.36 38762[4:SpR:87.1,37987.1] class_Lattices_Oboolean__algebra(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> hBOOL(c_Orderings_Otop__class_Otop(u))*.
% 299.64/300.36 38632[4:SSi:38589.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,u,tc_bool) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v))*.
% 299.64/300.36 399[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),u),hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),v),tc_fun(w,tc_bool))*.
% 299.64/300.36 38631[4:SSi:38586.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,u,tc_bool) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u))*.
% 299.64/300.36 38566[4:SSi:38537.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v)))*.
% 299.64/300.36 38473[4:SSi:38459.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),v_x)))*.
% 299.64/300.36 38923[4:SpR:23912.0,38042.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> c_Hoare__Mirabelle_Ohoare__valids(v_x,u,t_a)*.
% 299.64/300.36 532[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))*.
% 299.64/300.36 38734[4:SpR:23912.0,37987.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> hBOOL(hAPP(v_x,u))*.
% 299.64/300.36 39456[4:Res:38615.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),c_COMBK(v_x,w,x)),y,t_a)*.
% 299.64/300.36 38615[4:Res:10713.0,38471.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(v_x,w,x)),y))*.
% 299.64/300.36 38614[4:Res:10712.0,38471.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(v_x,w)))*.
% 299.64/300.36 533[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))**.
% 299.64/300.36 38139[0:Res:12593.0,37920.0] || hBOOL(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool))* -> hBOOL(u).
% 299.64/300.36 39040[4:Res:38611.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w,t_a)*.
% 299.64/300.36 38612[4:Res:10746.0,38471.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),v_x))*.
% 299.64/300.36 38611[4:Res:10745.0,38471.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w))*.
% 299.64/300.36 354[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),hAPP(c_Set_Oimage(x,w,y),u)),u)**.
% 299.64/300.36 38042[4:MRR:38037.1,6340.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(u,v_x),v,t_a)*.
% 299.64/300.36 38828[4:Res:37987.1,3499.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)*+ equal(c_in(v),u)* -> .
% 299.64/300.36 37987[4:MRR:37926.1,6340.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(u,v_x),v))*.
% 299.64/300.36 38621[4:SSi:38592.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_x,u,v),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 184[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))*+ c_Fun_Oinj__on(w,y,x,u) -> equal(hAPP(w,hAPP(c_Fun_Othe__inv__into(y,w,x,u),v)),v)**.
% 299.64/300.36 38576[4:Res:448.2,38471.0] class_Orderings_Olinorder(tc_bool) || -> c_lessequals(u,v_x,tc_bool)* hBOOL(u).
% 299.64/300.36 38471[4:SSi:38451.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,u,tc_bool)* -> hBOOL(u).
% 299.64/300.36 38560[4:Res:38472.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,t_a)*.
% 299.64/300.36 38472[4:SSi:38452.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u))*.
% 299.64/300.36 385[0:Inp] || c_Finite__Set_Ofinite(u,v) c_lessequals(hAPP(c_Set_Oimage(w,v,v),u),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(w,u,v,v) -> equal(hAPP(c_Set_Oimage(w,v,v),u),u).
% 299.64/300.36 38430[4:EqR:37922.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x))*.
% 299.64/300.36 37922[4:MRR:37868.1,6340.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)*+ -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.36 38180[0:MRR:38061.2,9320.0] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),u,tc_bool)* -> hBOOL(u).
% 299.64/300.36 493[0:Inp] || equal(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y)) c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y),v,w)* -> equal(x,y).
% 299.64/300.36 201[0:Inp] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,w,u,u),u)*.
% 299.64/300.36 13[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,y,tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.36 37920[0:SSi:37873.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* hBOOL(u) -> hBOOL(v).
% 299.64/300.36 37980[0:Res:37921.1,19641.0] || hBOOL(u) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,t_a)*.
% 299.64/300.36 37983[4:MRR:37976.0,6340.0] || equal(c_in(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))* -> .
% 299.64/300.36 37985[4:MRR:37966.1,37966.2,6340.0,826.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_in(t_a))** -> .
% 299.64/300.36 441[0:Inp] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))).
% 299.64/300.36 37984[4:MRR:37977.0,6340.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_in(tc_Com_Opname))** -> .
% 299.64/300.36 37921[0:SSi:37874.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v))*.
% 299.64/300.36 37799[0:Rew:351.0,37733.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u))*.
% 299.64/300.36 198[0:Inp] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Fun_Ocomp(c_Fun_Ocomp(x,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),v,y,w),u,w,y,v),x)**.
% 299.64/300.36 36804[0:SpR:3744.1,36588.0] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_Procs),v_x))*.
% 299.64/300.36 37607[0:SpL:10.0,36766.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_x))* -> .
% 299.64/300.36 36766[0:SpL:67.0,888.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_x))* -> .
% 299.64/300.36 205[0:Inp] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),hAPP(c_Set_Oimage(u,v,w),x)),x)**.
% 299.64/300.36 37410[0:SpR:10063.0,36687.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 37408[0:SpR:9987.0,36687.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 36687[0:SpR:353.0,36605.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 274[0:Inp] || equal(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(u,v),x))*+ -> hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(v),u),x))* equal(w,x).
% 299.64/300.36 471[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(hAPP(c_Set_Oimage(x,u,y),w),z,tc_fun(y,tc_bool))*+ -> hBOOL(hAPP(hAPP(c_in(y),hAPP(x,v)),z))*.
% 299.64/300.36 37060[7:SpL:10.0,36773.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_x)** -> .
% 299.64/300.36 36773[7:SpL:67.0,27287.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_x)** -> .
% 299.64/300.36 36768[0:SpL:67.0,3590.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.36 375[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),z,tc_fun(y,tc_bool))*+ -> c_lessequals(hAPP(x,v),z,tc_fun(y,tc_bool))*.
% 299.64/300.36 36965[0:MRR:36964.1,3591.0] || equal(c_COMBK(u,tc_bool,tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)))** -> hBOOL(u).
% 299.64/300.36 36683[0:SpR:8498.1,36605.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool))) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool))*.
% 299.64/300.36 66[0:Inp] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(x,w),v),tc_fun(w,tc_bool)))**.
% 299.64/300.36 36588[0:Res:9566.0,36406.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(v_x,t_a),w)),v_x))*.
% 299.64/300.36 36685[0:SpR:3744.1,36605.0] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_Procs,tc_Com_Opname,tc_bool))*.
% 299.64/300.36 36682[0:SpR:2097.1,36605.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool))*.
% 299.64/300.36 36605[0:SSi:36581.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(v_x,t_a),u),tc_Com_Opname,tc_bool))*.
% 299.64/300.36 36552[0:SpL:14216.0,36406.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* -> hBOOL(u).
% 299.64/300.36 36406[0:SSi:36381.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),u),v_x),v,tc_bool)* -> hBOOL(v).
% 299.64/300.36 372[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))**+ -> equal(hAPP(x,v),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))*.
% 299.64/300.36 36471[0:Res:36407.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(v_x,t_a),u),v_x)),v,t_a)*.
% 299.64/300.36 36407[0:SSi:36382.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(v_x,t_a),u),v_x)),v))*.
% 299.64/300.36 36264[0:SpR:414.0,35738.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Set_Oinsert(v_x,t_a),v),v_x)))*.
% 299.64/300.36 516[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),x)).
% 299.64/300.36 36017[0:Rew:15476.0,35998.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),v_x),tc_bool))*.
% 299.64/300.36 282[0:Inp] || c_Fun_Oinj__on(u,v,w,x)+ -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(u,w,x),v)))* c_Fun_Oinj__on(c_Fun_Ofun__upd(u,z,y,w,x),v,w,x)*.
% 299.64/300.36 35795[0:Rew:15476.0,35770.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ominus__class_Ominus(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(t_a,tc_bool)),v_x),tc_bool))*.
% 299.64/300.36 26119[0:SpR:338.0,423.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),w))*.
% 299.64/300.36 89[0:Inp] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,hAPP(c_COMBB(v,w,tc_fun(x,tc_bool),y),z),y,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(z,y,w),u),v,w,tc_fun(x,tc_bool)))*.
% 299.64/300.36 23772[0:SpR:23682.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,x,y),u))*.
% 299.64/300.36 29397[7:SpR:27278.1,10813.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,u),v_x),v))*.
% 299.64/300.36 35449[0:SpR:8385.1,35192.0] || equal(u,v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(v,tc_bool)),v_Procs))*.
% 299.64/300.36 35453[0:SpR:2089.0,35192.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(v,tc_bool)),v_Procs))*.
% 299.64/300.36 113[0:Inp] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))))**.
% 299.64/300.36 35466[0:SpR:10063.0,35192.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(tc_Com_Opname),t_a,tc_fun(u,tc_bool)),v_Procs))*.
% 299.64/300.36 35463[0:SpR:2095.0,35192.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs))*.
% 299.64/300.36 35464[0:SpR:9987.0,35192.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname),t_a,tc_fun(v,tc_bool)),v_Procs))*.
% 299.64/300.36 35192[0:SpR:410.0,675.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),c_in(tc_Com_Opname),u,tc_fun(w,tc_bool)),v_Procs))*.
% 299.64/300.36 410[0:Inp] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool))))*.
% 299.64/300.36 28910[0:SpR:351.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.36 28755[0:SpR:351.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.36 28356[0:SpR:3229.1,28335.0] || equal(u,v) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(v,v_x),tc_Com_Opname,w)))*.
% 299.64/300.36 28053[0:SpR:3229.1,28032.0] || equal(u,v) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),u,tc_Com_Opname,w)))*.
% 299.64/300.36 443[0:Inp] || c_Hoare__Mirabelle_Ohoare__derivs(u,v,w) c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*+ -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(w)),v),w)*.
% 299.64/300.36 27443[0:Res:1157.0,466.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x)),v_Procs))*.
% 299.64/300.36 27383[0:Res:1157.0,470.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x)),v_Procs))*.
% 299.64/300.36 27282[7:Res:27207.1,371.0] || equal(hAPP(c_Set_Oinsert(u,v),w),v_x)** -> hBOOL(hAPP(w,v_x)) equal(u,v_x).
% 299.64/300.36 34428[0:Rew:23682.0,34242.0] || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x),v_x)**.
% 299.64/300.36 55[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oinsert(v,u),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)))**.
% 299.64/300.36 34427[0:Rew:23840.0,33947.0] || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v_x)**.
% 299.64/300.36 24914[0:Res:648.0,467.0] || -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x))),hAPP(u,v_x))**.
% 299.64/300.36 24759[0:MRR:24758.0,15145.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.36 24636[0:SpR:414.0,24020.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v,v_x),v_x).
% 299.64/300.36 247[0:Inp] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,v,tc_fun(u,tc_bool)) -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) c_lessequals(c_Finite__Set_Olinorder__class_OMax(w,u),c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.64/300.36 23965[0:SpR:23912.0,3339.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> equal(c_Fun_Ofun__upd(u,v_x,v_x,v,w),u)**.
% 299.64/300.36 23881[0:SpR:23840.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),u))*.
% 299.64/300.36 23864[0:SpR:23840.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Obot__class_Obot(tc_bool),u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))**.
% 299.64/300.36 33787[7:Obv:33746.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* equal(u,v_x) -> .
% 299.64/300.36 248[0:Inp] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,v,tc_fun(u,tc_bool)) -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),c_Finite__Set_Olinorder__class_OMin(w,u),u)*.
% 299.64/300.36 31886[7:SpL:3229.1,31868.0] || equal(u,v)* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool))**+ equal(u,v_x)* -> .
% 299.64/300.36 28859[0:SpR:28334.0,10813.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)))*.
% 299.64/300.36 28704[0:SpR:28031.0,10813.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)))*.
% 299.64/300.36 27846[7:SpR:351.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBK(u,v,w),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)).
% 299.64/300.36 61[0:Inp] || c_Finite__Set_Ofinite(u,v) -> equal(c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,v),u),v))**.
% 299.64/300.36 27247[7:SpR:88.1,27207.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_x)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.36 23882[0:SpR:23840.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_bool)*.
% 299.64/300.36 453[0:Inp] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))*+ c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x)),w))* c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.64/300.36 23789[0:SpR:23682.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w),w,tc_bool)*.
% 299.64/300.36 32668[0:Res:31533.0,279.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.36 32447[7:SpL:135.0,27917.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* equal(u,v_x) -> .
% 299.64/300.36 32232[0:SpR:328.1,31669.0] || c_lessequals(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),v,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(v,v_x)).
% 299.64/300.36 94[0:Inp] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(y,hAPP(c_Set_Oimage(u,w,x),v),x,z)*+ -> c_Fun_Oinj__on(c_Fun_Ocomp(y,u,x,z,w),v,w,z)*.
% 299.64/300.36 32691[0:SpR:524.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,v),v_x)))*.
% 299.64/300.36 32724[0:SpR:9924.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.36 475[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(x,v),y),hAPP(c_Set_Oimage(x,u,y),w)),hAPP(c_Set_Oimage(x,u,y),w))**.
% 299.64/300.36 32703[0:SpR:10463.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),c_Orderings_Obot__class_Obot(tc_bool))))*.
% 299.64/300.36 32702[0:SpR:9911.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.36 32710[0:SpR:351.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,x),u)))*.
% 299.64/300.36 35[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(v,x,tc_fun(w,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(v,c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),u)**.
% 299.64/300.36 32728[0:SpR:23912.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x)))*.
% 299.64/300.36 32669[0:Res:31533.0,527.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x))))*.
% 299.64/300.36 31533[0:Res:648.0,473.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x))),v_Procs))*.
% 299.64/300.36 28361[0:SpR:525.1,28335.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_x,tc_Com_Opname,v)))*.
% 299.64/300.36 476[0:Inp] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,v)))*+ hBOOL(hAPP(hAPP(c_in(v),y),x))* -> hBOOL(hAPP(u,y))*.
% 299.64/300.36 28058[0:SpR:525.1,28032.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v)))*.
% 299.64/300.36 27917[7:SpL:2267.1,27887.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)**+ -> .
% 299.64/300.36 27892[7:MRR:27891.1,826.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 27354[7:MRR:22897.3,27297.0] class_Lattices_Obounded__lattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) equal(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(u))* -> .
% 299.64/300.36 477[0:Inp] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,v)))*+ hBOOL(hAPP(hAPP(c_in(v),y),w))* -> hBOOL(hAPP(u,y))*.
% 299.64/300.36 23753[0:SpR:23682.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),u)*.
% 299.64/300.36 31669[0:SpR:338.0,25828.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.36 31323[0:Res:31315.0,18625.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u),hAPP(v_Procs,u),tc_bool)*.
% 299.64/300.36 340[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v,tc_fun(w,tc_bool))*.
% 299.64/300.36 31836[7:SpL:23682.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x)** -> .
% 299.64/300.36 31899[7:SpL:414.0,31868.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Fun_Ofun__upd(v,v_x,u,w,x),v_x)** -> .
% 299.64/300.36 31819[7:SpL:351.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_COMBK(u,v,w),v_x)** -> .
% 299.64/300.36 151[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),v),x)) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))))*.
% 299.64/300.36 31837[7:SpL:23912.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x)** -> .
% 299.64/300.36 31909[7:SpL:351.0,31868.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(c_COMBK(u,v,w),v_x)** -> .
% 299.64/300.36 383[0:Inp] || -> equal(u,v) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(w,u,x,y,z),v,x1,y,z),c_Fun_Ofun__upd(c_Fun_Ofun__upd(w,v,x1,y,z),u,x,y,z))*.
% 299.64/300.36 31868[7:SSi:31867.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_x) -> .
% 299.64/300.36 31778[7:Rew:15476.0,31773.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(u,v_x) -> .
% 299.64/300.36 27896[7:MRR:27895.2,826.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 389[0:Inp] || equal(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y))*+ c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(x,y).
% 299.64/300.36 26028[0:SpR:338.0,1020.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)),v_x))*.
% 299.64/300.36 25828[0:SpR:339.0,1042.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)),v_x))*.
% 299.64/300.36 24939[0:SpR:23902.1,341.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v_x,tc_fun(u,tc_bool))*.
% 299.64/300.36 473[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))*+ -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v)),y))*.
% 299.64/300.36 24254[0:SpL:3229.1,24026.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.36 24086[0:Res:24071.1,48.1] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),u,tc_bool)*.
% 299.64/300.36 24034[0:SpL:23912.0,3698.2] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))* equal(c_Com_Ocom_OBODY,u) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.36 449[0:Inp] || hBOOL(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,u,w,x)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,u,w,x)))* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),u),t_a).
% 299.64/300.36 23964[0:SpR:23912.0,3316.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.36 23961[0:SpR:23912.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.36 23954[0:SpR:23912.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),t_a,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x))*.
% 299.64/300.36 31315[0:Rew:31262.0,5068.0] || -> c_lessequals(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.36 356[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))*+ -> equal(hAPP(c_Set_Oimage(c_COMBK(x,y,u),u,y),w),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.64/300.36 23936[0:SpR:23912.0,651.0] || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.64/300.36 23934[0:SpR:23912.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_Procs),u,v),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.36 28926[0:SpR:23912.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.36 28771[0:SpR:23912.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.36 535[0:Inp] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))*.
% 299.64/300.36 28312[0:SpR:23912.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u)),v_Procs))*.
% 299.64/300.36 28009[0:SpR:23912.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u)),v_Procs))*.
% 299.64/300.36 536[0:Inp] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))*.
% 299.64/300.36 27043[0:Res:23946.1,279.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),v_x),v_x)**.
% 299.64/300.36 28368[0:SpR:414.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ofun__upd(u,v_x,v,w,x),v,tc_Com_Opname,y)))*.
% 299.64/300.36 534[0:Inp] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))**.
% 299.64/300.36 28065[0:SpR:414.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_Fun_Ofun__upd(v,v_x,u,w,x),tc_Com_Opname,y)))*.
% 299.64/300.36 29388[7:SpR:27278.1,267.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_in(u),v),v_x))*.
% 299.64/300.36 27283[7:Res:27207.1,8513.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x)** -> equal(v_x,u).
% 299.64/300.36 27278[7:Res:27207.1,279.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(v,u),v_x),v_x)**.
% 299.64/300.36 537[0:Inp] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))**.
% 299.64/300.36 27232[7:SpR:302.1,27207.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.36 28334[0:Res:27441.0,279.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.36 28031[0:Res:27381.0,279.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.36 28359[0:SpR:524.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v_x,tc_Com_Opname,v)))*.
% 299.64/300.36 28390[0:SpR:9924.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,u)))*.
% 299.64/300.36 28371[0:SpR:10463.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v)))*.
% 299.64/300.36 28370[0:SpR:9911.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v)))*.
% 299.64/300.36 28378[0:SpR:351.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x)))*.
% 299.64/300.36 118[0:Inp] || -> equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,w,x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,z,x1,y),w,hAPP(u,x),y,x1))*.
% 299.64/300.36 28394[0:SpR:23912.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u)))*.
% 299.64/300.36 28335[0:Res:27441.0,527.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v)))*.
% 299.64/300.36 27441[0:Res:648.0,466.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.36 28056[0:SpR:524.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,v)))*.
% 299.64/300.36 31[0:Inp] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Fun_Ocomp(z,x1,x2,x,y))*+ -> equal(hAPP(u,hAPP(v,x3)),hAPP(z,hAPP(x1,x3)))*.
% 299.64/300.36 28086[0:SpR:9924.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname,u)))*.
% 299.64/300.36 28068[0:SpR:10463.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v)))*.
% 299.64/300.36 28067[0:SpR:9911.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v)))*.
% 299.64/300.36 28074[0:SpR:351.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x)))*.
% 299.64/300.36 465[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),hAPP(c_Set_Oimage(x,u,z),w))**.
% 299.64/300.36 28090[0:SpR:23912.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u)))*.
% 299.64/300.36 28032[0:Res:27381.0,527.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v)))*.
% 299.64/300.36 27381[0:Res:648.0,470.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.36 27890[7:MRR:27889.1,826.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 468[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,w,x,u,y)),v))* equal(hAPP(c_Set_Oimage(w,u,y),v),hAPP(c_Set_Oimage(x,u,y),v)).
% 299.64/300.36 27887[7:MRR:27886.1,826.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.36 27219[7:SpR:15476.0,27207.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.36 27810[7:SpL:6.0,27359.0] || equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),v_x)** -> .
% 299.64/300.36 27359[7:MRR:27272.1,826.0] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),v_x)** -> .
% 299.64/300.36 71[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,x,u,y),hAPP(x,v)),v)**.
% 299.64/300.36 27293[7:Res:27207.1,3863.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)** -> hBOOL(hAPP(u,v_x)).
% 299.64/300.36 27217[7:SpR:365.1,27207.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x)** -> hBOOL(c_Orderings_Obot__class_Obot(u)).
% 299.64/300.36 27216[7:SpR:397.1,27207.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.36 27222[7:SpR:3229.1,27207.1] || equal(u,v)*+ equal(v_x,u)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.36 373[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,x,u,y),hAPP(x,v)),v)**.
% 299.64/300.36 27358[7:MRR:27244.1,826.0] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),v_x)** -> .
% 299.64/300.36 27286[7:Res:27207.1,1811.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_x)** equal(v_Procs,u) -> .
% 299.64/300.36 27234[7:SpR:414.0,27207.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),v_x)** -> hBOOL(v).
% 299.64/300.36 466[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))*+ -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(y,w,v,x,u)),y))*.
% 299.64/300.36 27279[7:Res:27207.1,527.0] || equal(hAPP(c_in(u),v),v_x)** -> hBOOL(hAPP(v_x,v)).
% 299.64/300.36 27243[7:SpR:351.0,27207.1] || equal(c_COMBK(u,v,w),v_x)** -> hBOOL(u).
% 299.64/300.36 27287[7:Res:27207.1,888.0] || equal(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_x)** -> .
% 299.64/300.36 27285[7:Res:27207.1,836.0] || equal(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_x)** -> .
% 299.64/300.36 470[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))*+ -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__XimageE__1__1(y,v,w,x,u)),y))*.
% 299.64/300.36 27297[7:MRR:27237.1,826.0] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v_x)** -> .
% 299.64/300.36 27207[7:SpR:3229.1,27205.0] || equal(v_x,u) -> hBOOL(hAPP(u,v_x))*.
% 299.64/300.36 27205[7:Spt:26462.2] || -> hBOOL(hAPP(v_x,v_x))*.
% 299.64/300.36 450[0:Inp] || -> hBOOL(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,v,w,x)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(u,v,w,x)))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),w),v),t_a).
% 299.64/300.36 25031[0:SpR:10463.0,23902.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.36 25030[0:SpR:9911.0,23902.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.36 24627[0:SpR:524.0,24020.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.36 280[0:Inp] || hBOOL(hAPP(hAPP(u,v),w))* hBOOL(hAPP(hAPP(c_in(x),v),y))*+ -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,u,x,tc_fun(z,tc_bool)),w))*.
% 299.64/300.36 23952[0:SpR:23912.0,11030.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(t_a)) -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.36 23946[0:SpR:23912.0,3284.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),v_x))*.
% 299.64/300.36 26317[0:SSi:26315.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool),v_x)**.
% 299.64/300.36 175[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),hAPP(c_Set_Oinsert(y,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))* -> equal(hAPP(w,v),y).
% 299.64/300.36 25051[0:SpR:23682.0,23902.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.36 24656[0:SpR:9924.0,24020.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x),v_x).
% 299.64/300.36 23951[0:SpR:23912.0,10090.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.36 23941[2:SpR:23912.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.36 424[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(x,w,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool))*.
% 299.64/300.36 23817[0:SpL:23682.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_Procs)** -> .
% 299.64/300.36 23979[0:SpR:23912.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),u,u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))**.
% 299.64/300.36 24121[0:SSi:24087.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool))+ c_lessequals(v,u,tc_bool)* -> c_lessequals(v,w,tc_bool)*.
% 299.64/300.36 56[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)))**.
% 299.64/300.36 23997[0:SpR:23912.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),u),u,tc_bool)*.
% 299.64/300.36 25037[0:SpR:351.0,23902.1] || equal(c_COMBK(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> equal(hAPP(u,c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.36 24123[0:SSi:24099.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Obot__class_Obot(tc_bool))**+ -> c_lessequals(v,w,tc_bool)*.
% 299.64/300.36 244[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_Finite__Set_Ocard(w,u),c_HOL_Ozero__class_Ozero(tc_nat)) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(v,u),w),u),c_Suc(c_Finite__Set_Ocard(w,u)))**.
% 299.64/300.36 24122[0:SSi:24098.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Obot__class_Obot(tc_bool))**+ -> c_lessequals(u,w,tc_bool)*.
% 299.64/300.36 84[0:Inp] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),tc_fun(w,tc_bool))*.
% 299.64/300.36 24941[0:SpR:23902.1,309.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v_x,u)*.
% 299.64/300.36 24940[0:SpR:23902.1,306.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v_x,u)*.
% 299.64/300.36 85[0:Inp] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),x,tc_fun(v,tc_bool)).
% 299.64/300.36 26326[6:Spt:24737.0,24737.2] || equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(u,v_x).
% 299.64/300.36 23960[0:SpR:23912.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),u)*.
% 299.64/300.36 338[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))*.
% 299.64/300.36 24944[0:SpR:23902.1,9566.0] || equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> c_lessequals(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x,tc_bool)*.
% 299.64/300.36 23819[0:SpL:23682.0,3506.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Com_Ocom_OBODY)**+ equal(c_Com_Ocom_OSemi(u,v),v_x)** -> .
% 299.64/300.36 24639[0:SpR:10463.0,24020.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_x),v_x)**.
% 299.64/300.36 339[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))**.
% 299.64/300.36 24638[0:SpR:9911.0,24020.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x),v_x)**.
% 299.64/300.36 25052[0:SpR:23912.0,23902.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.36 273[0:Inp] || equal(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w))* -> equal(v,w).
% 299.64/300.36 24659[0:SpR:23682.0,24020.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.36 24025[0:SpL:23912.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_Procs)** -> .
% 299.64/300.36 25662[0:SSi:25661.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(v,u).
% 299.64/300.36 25618[0:Res:24071.1,24120.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool))*+ equal(v,c_Orderings_Obot__class_Obot(tc_bool))* -> equal(u,v)*.
% 299.64/300.36 455[0:Inp] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))*+ c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.64/300.36 24120[0:SSi:24089.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) c_lessequals(v,u,tc_bool)* -> equal(v,u).
% 299.64/300.36 24645[0:SpR:351.0,24020.1] || equal(c_COMBK(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(u,v_x),v_x).
% 299.64/300.36 24544[0:SpR:24020.1,9566.0] || equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> c_lessequals(hAPP(v_x,v_x),v_x,tc_bool)*.
% 299.64/300.36 24027[0:SpL:23912.0,3506.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Com_Ocom_OBODY)**+ equal(c_Com_Ocom_OSemi(u,v),v_x)** -> .
% 299.64/300.36 252[0:Inp] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),x),t_a) c_Natural_Oevaln(w,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(v,x,w,u),u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,x,w,u))*.
% 299.64/300.36 23902[0:SpR:3229.1,23840.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.36 23735[0:SpR:23682.0,3229.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u)*+ -> equal(hAPP(u,v_x),v_x)**.
% 299.64/300.36 23730[0:SpR:23682.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs),v_x))*.
% 299.64/300.36 24660[0:SpR:23912.0,24020.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.36 467[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))*+ -> equal(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v)),v)**.
% 299.64/300.36 23736[0:SpR:23682.0,3283.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.36 24395[0:MRR:24375.0,24375.2,1088.0,13431.0] || c_Fun_Oinj__on(c_COMBK(u,v,w),x,w,v)* -> c_Finite__Set_Ofinite(x,w).
% 299.64/300.36 24070[0:Res:23914.1,12717.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.36 614[0:Rew:240.2,226.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u))**.
% 299.64/300.36 24020[0:SpR:3229.1,23912.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(hAPP(u,v_x),v_x),v_x)**.
% 299.64/300.36 23942[0:SpR:23912.0,3229.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u)*+ -> equal(hAPP(u,v_x),v_x)**.
% 299.64/300.36 23937[0:SpR:23912.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_Procs),v_x))*.
% 299.64/300.36 208[0:Inp] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),v),u)) c_lessequals(u,x,tc_fun(w,tc_bool)).
% 299.64/300.36 23923[0:Rew:23840.0,23905.0] || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v_x)**.
% 299.64/300.36 23916[0:Rew:23840.0,23904.0] || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x)**.
% 299.64/300.36 23848[0:Rew:23682.0,23751.0] || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x)**.
% 299.64/300.36 23847[0:Rew:23682.0,23748.0] || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x,tc_Com_Opname,u),v_x)**.
% 299.64/300.36 393[0:Inp] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(c_Set_Oimage(c_COMBK(w,x,v),v,x),u),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.64/300.36 23943[0:SpR:23912.0,3283.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.36 23818[0:SpL:23682.0,3483.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.36 24026[0:SpL:23912.0,3483.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.36 542[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w))**.
% 299.64/300.36 24071[0:Res:23914.1,10428.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) -> c_lessequals(u,v,tc_bool)*.
% 299.64/300.36 23852[4:MRR:23851.0,6340.0] || -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname))*.
% 299.64/300.36 23850[4:MRR:23849.0,6340.0] || -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname))*.
% 299.64/300.36 75[0:Inp] || c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u) equal(c_Finite__Set_Ocard(v,u),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u))* -> equal(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))).
% 299.64/300.36 23912[0:SSi:23878.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),u),u)**.
% 299.64/300.36 23840[0:SSi:23768.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Obot__class_Obot(tc_bool)),u)**.
% 299.64/300.36 23682[0:SpR:414.0,23591.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u),u)**.
% 299.64/300.36 523[0:Inp] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)))**.
% 299.64/300.36 23443[0:SpL:135.0,23416.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)**+ equal(c_Set_Oinsert(u,v),c_in(tc_Com_Opname))** -> .
% 299.64/300.36 23416[0:SpL:2267.1,23316.0] || equal(u,v_Procs) equal(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v),c_in(tc_Com_Opname))** -> .
% 299.64/300.36 23316[0:Res:423.0,3489.1] || equal(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),u),c_in(tc_Com_Opname))** -> .
% 299.64/300.36 460[0:Inp] || class_Lattices_Olattice(t_b) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))**.
% 299.64/300.36 3489[0:SpL:3229.1,657.0] || equal(c_in(tc_Com_Opname),u) hBOOL(hAPP(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.36 22741[0:SpR:3294.1,342.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) -> c_lessequals(v_x,c_Orderings_Obot__class_Obot(tc_bool),tc_fun(u,tc_bool))*.
% 299.64/300.36 22737[0:SpR:3294.1,310.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> c_lessequals(v_x,c_Orderings_Obot__class_Obot(tc_bool),u)*.
% 299.64/300.36 23[0:Inp] || -> equal(c_Fun_Ocomp(u,c_Fun_Ocomp(v,w,x,y,z),y,x1,z),c_Fun_Ocomp(c_Fun_Ocomp(u,v,y,x1,x),w,x,x1,z))*.
% 299.64/300.36 22736[0:SpR:3294.1,305.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> c_lessequals(v_x,c_Orderings_Obot__class_Obot(tc_bool),u)*.
% 299.64/300.36 22902[0:MRR:22901.1,10475.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_in(t_a))** -> .
% 299.64/300.36 131[0:Inp] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),z)))*.
% 299.64/300.36 3294[0:SpR:3229.1,2935.0] || equal(c_in(t_a),u) -> equal(hAPP(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.36 19863[0:SpL:104.0,17939.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))** -> .
% 299.64/300.36 21234[0:SpR:351.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBK(u,v,w),t_a,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u))*.
% 299.64/300.36 21173[0:SpR:351.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBK(u,v,w),x,y),hAPP(c_in(tc_Com_Opname),v_x)),u))*.
% 299.64/300.36 158[0:Inp] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),z)))*.
% 299.64/300.36 21126[0:SpR:8385.1,20881.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),u),hAPP(v,v_x)))*.
% 299.64/300.36 22333[0:Rew:525.1,22332.1] class_Lattices_Oupper__semilattice(u) || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),v_x)**.
% 299.64/300.36 22318[0:Rew:301.1,21974.1] class_Lattices_Obounded__lattice(u) || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),v_x)**.
% 299.64/300.36 22317[0:Rew:300.1,22148.1] class_Lattices_Obounded__lattice(u) || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_Com_Opname,v),v_x)**.
% 299.64/300.36 97[0:Inp] || c_Fun_Oinj__on(u,v,w,x) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),hAPP(c_Set_Oimage(u,w,x),v)),v)**.
% 299.64/300.36 21704[0:Rew:525.1,21703.1] class_Lattices_Oupper__semilattice(u) || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x)**.
% 299.64/300.36 21689[0:Rew:301.1,21348.1] class_Lattices_Obounded__lattice(u) || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x)**.
% 299.64/300.36 21688[0:Rew:300.1,21521.1] class_Lattices_Obounded__lattice(u) || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v_x,tc_Com_Opname,v),v_x)**.
% 299.64/300.36 21893[0:Res:648.0,464.0] || -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v)),hAPP(u,v_x))**.
% 299.64/300.36 464[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))*+ -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(y,v,w,x,u)),v)**.
% 299.64/300.36 21131[0:SpR:2089.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),hAPP(u,v_x)))*.
% 299.64/300.36 21035[0:SpR:659.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),hAPP(c_Set_Oinsert(v_Procs,u),w)),v_Procs))*.
% 299.64/300.36 21143[0:SpR:10063.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(u,v_x)))*.
% 299.64/300.36 21267[0:Res:648.0,469.0] || -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v)),hAPP(u,v_x))**.
% 299.64/300.36 469[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))*+ -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(y,w,v,x,u)),v)**.
% 299.64/300.36 21141[0:SpR:9987.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(u,v_x)))*.
% 299.64/300.36 21152[0:SpR:659.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.36 21130[0:SpR:2093.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(u,v_Procs)))*.
% 299.64/300.36 20881[0:SpR:317.0,423.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(u,x)))*.
% 299.64/300.36 317[0:Inp] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oinsert(hAPP(u,x),w),hAPP(c_Set_Oimage(u,v,w),y)))*.
% 299.64/300.36 19748[0:SpR:104.0,649.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.64/300.36 16387[2:SpR:9935.1,4250.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY)**+ -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.36 16237[0:SpL:524.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v_Procs)** -> .
% 299.64/300.36 13069[0:SpR:10463.0,10090.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.36 129[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(x,y,w),u),hAPP(c_Set_Ovimage(x,y,w),v),tc_fun(y,tc_bool))*.
% 299.64/300.36 13068[0:SpR:9911.0,10090.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.36 11393[0:SpL:11177.1,3483.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.36 9223[0:Res:9071.0,2629.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.36 313[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(x,w,y),u),hAPP(c_Set_Oimage(x,w,y),v),tc_fun(y,tc_bool))*.
% 299.64/300.36 20720[0:Res:9209.2,522.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) equal(v_G,v_Procs) -> c_Hoare__Mirabelle_Otriple__valid(v_na,v_x,t_a)*.
% 299.64/300.36 9209[0:Res:8376.2,591.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) equal(v_G,v_Procs) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),v_x,t_a)*.
% 299.64/300.36 10705[0:SpR:414.0,9566.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Fun_Ofun__upd(x,y,u,z,x1)),y),tc_bool)*.
% 299.64/300.36 18625[0:SpR:329.1,9568.0] || c_lessequals(u,v,tc_fun(w,tc_bool))*+ -> c_lessequals(hAPP(u,x),hAPP(v,x),tc_bool)*.
% 299.64/300.37 99[0:Inp] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(u,x)),x)**.
% 299.64/300.37 20382[0:AED:24.0,20345.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v)* -> .
% 299.64/300.37 20379[0:AED:24.0,20332.1] || c_Fun_Oinj__on(c_COMBK(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y)* -> .
% 299.64/300.37 20381[0:AED:24.0,20323.1] || c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> .
% 299.64/300.37 20380[0:AED:24.0,20324.1] || c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> .
% 299.64/300.37 438[0:Inp] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(u,x)),x)**.
% 299.64/300.37 16816[0:SpR:3229.1,16814.1] class_Finite__Set_Ofinite_Ofinite(u) || equal(c_Set_Oimage(v,u,w),x)*+ -> c_Finite__Set_Ofinite(hAPP(x,v_x),w)*.
% 299.64/300.37 20186[0:SpR:135.0,20152.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.37 20152[0:Res:19747.0,109.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool))*.
% 299.64/300.37 19747[0:SpR:104.0,341.0] || -> c_lessequals(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.37 246[0:Inp] || c_Finite__Set_Ofinite(u,v) -> hBOOL(hAPP(hAPP(c_in(v),w),u)) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,v),u),v),c_Suc(c_Finite__Set_Ocard(u,v)))**.
% 299.64/300.37 19695[0:SpL:302.1,19641.0] class_Lattices_Obounded__lattice(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.37 19735[0:Res:7283.0,19641.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oimage(c_Option_Othe(u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),x,t_a)*.
% 299.64/300.37 19937[0:SpR:3229.1,19744.0] || equal(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v)*+ -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(v,v_x),v_x,t_a)*.
% 299.64/300.37 19743[0:MRR:19710.1,820.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,t_a)*.
% 299.64/300.37 215[0:Inp] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),x),w)*+ -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.64/300.37 19749[0:SpR:104.0,1042.0] || -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.37 20040[0:Obv:20039.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),u,v),w,t_a)*.
% 299.64/300.37 19742[0:MRR:19717.0,820.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y,t_a)*.
% 299.64/300.37 19741[0:MRR:19713.0,820.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,t_a)*.
% 299.64/300.37 19739[0:MRR:19711.1,9408.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,t_a)*.
% 299.64/300.37 19740[0:MRR:19712.0,820.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,t_a)*.
% 299.64/300.37 19702[0:SpL:351.0,19641.0] || hBOOL(u) -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBK(u,v,w),x,t_a)*.
% 299.64/300.37 19744[0:Obv:19723.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v),v,t_a)*.
% 299.64/300.37 104[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))**.
% 299.64/300.37 19738[0:MRR:19707.0,820.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,t_a)*.
% 299.64/300.37 19737[0:MRR:19697.0,820.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,t_a)*.
% 299.64/300.37 19736[0:Obv:19734.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,u,t_a)*.
% 299.64/300.37 19641[0:Obv:19640.1] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v)))* -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a).
% 299.64/300.37 496[0:Inp] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))*+ -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,v)),v))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.64/300.37 10500[0:Res:526.1,454.0] || hBOOL(hAPP(u,v)) -> c_Hoare__Mirabelle_Ohoare__valids(u,w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(u,w),v,t_a)*.
% 299.64/300.37 19436[0:SpR:8385.1,9067.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(c_Set_Oinsert(v,tc_Com_Opname),u)))*.
% 299.64/300.37 19441[0:SpR:2089.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))))*.
% 299.64/300.37 36[0:Inp] class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ominus__class_Ominus(x,y,u))* c_lessequals(w,v,u) -> c_lessequals(y,x,u).
% 299.64/300.37 19452[0:SpR:10063.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))))*.
% 299.64/300.37 19440[0:SpR:2093.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oinsert(v,u),hAPP(c_in(tc_Com_Opname),v_x))))*.
% 299.64/300.37 19451[0:SpR:9987.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))))*.
% 299.64/300.37 9067[0:Res:376.0,214.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(v,u),x))))*.
% 299.64/300.37 193[0:Inp] || c_Finite__Set_Ofinite(u,v) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(w,v,x),u),x),c_Finite__Set_Ocard(u,v))** -> c_Fun_Oinj__on(w,u,v,x).
% 299.64/300.37 15188[0:Res:15185.0,123.0] || c_Natural_Oevalc(u,v,w) -> c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSKIP)),u),v,w)*.
% 299.64/300.37 13472[0:SSi:13454.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))*+ -> c_lessequals(hAPP(u,w),hAPP(x,w),tc_bool)*.
% 299.64/300.37 13430[0:SSi:13412.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))*+ -> c_lessequals(hAPP(w,x),hAPP(u,x),tc_bool)*.
% 299.64/300.37 12719[0:Res:12533.1,12532.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_bool),tc_bool)*+ -> c_lessequals(c_HOL_Ominus__class_Ominus(u,x,tc_bool),v,tc_bool)*.
% 299.64/300.37 304[0:Inp] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(x,w,u) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),w,u)*.
% 299.64/300.37 12627[0:SSi:12614.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool),v,tc_bool)*.
% 299.64/300.37 19185[0:Res:10196.1,12626.0] || equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**+ -> c_lessequals(x,u,tc_bool)*.
% 299.64/300.37 12626[0:SSi:12613.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,w,tc_bool),x,tc_bool),tc_bool)* -> c_lessequals(u,v,tc_bool).
% 299.64/300.37 10931[0:SpR:2098.1,10813.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),v),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v)))*.
% 299.64/300.37 196[0:Inp] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),x)),x)**.
% 299.64/300.37 10697[0:SpR:524.0,9566.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u)),u),tc_bool)*.
% 299.64/300.37 9569[0:SSi:9497.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),v),tc_bool)*.
% 299.64/300.37 18843[0:Res:13387.1,18768.0] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))**+ -> c_lessequals(v_Procs,hAPP(v,v_Procs),tc_bool)*.
% 299.64/300.37 18842[0:Res:13385.1,18768.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))*+ -> c_lessequals(v_Procs,hAPP(u,v_Procs),tc_bool)*.
% 299.64/300.37 463[0:Inp] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x) -> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u)),v,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,w,v,x),x)*.
% 299.64/300.37 18768[0:SpR:329.1,18644.0] || c_lessequals(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool))* -> c_lessequals(v_Procs,hAPP(u,v_Procs),tc_bool).
% 299.64/300.37 18763[0:SpR:538.0,18644.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.37 18644[0:SpR:659.0,9568.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),v),v_Procs),tc_bool)*.
% 299.64/300.37 9568[0:SSi:9496.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v),tc_bool)*.
% 299.64/300.37 153[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x)) -> hBOOL(hAPP(hAPP(c_in(y),w),hAPP(c_Set_Ovimage(v,y,u),x)))*.
% 299.64/300.37 18529[0:Res:9246.0,11894.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**+ -> hBOOL(hAPP(u,w))*.
% 299.64/300.37 9246[0:SpR:135.0,8369.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))))* hBOOL(hAPP(w,v)).
% 299.64/300.37 18475[0:Res:3282.1,8513.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_Procs)** -> equal(v_x,u).
% 299.64/300.37 8513[0:Res:526.1,355.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w))* -> equal(w,u).
% 299.64/300.37 156[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y)))* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,v)),y)).
% 299.64/300.37 18432[0:SpR:6.0,18304.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),t_a)*.
% 299.64/300.37 18304[0:MRR:18276.1,826.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)),t_a)*.
% 299.64/300.37 18322[0:SpL:6.0,18303.0] || equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),v_Procs)** -> .
% 299.64/300.37 545[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,v)),hAPP(c_Set_Oimage(y,u,x),w)))*.
% 299.64/300.37 18303[0:MRR:18236.1,826.0] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),v_Procs)** -> .
% 299.64/300.37 15172[0:Res:11611.0,10429.0] || -> equal(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 13532[0:SpR:351.0,11030.1] || equal(c_COMBK(u,v,w),c_in(t_a))**+ -> hBOOL(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.64/300.37 17953[0:Res:9071.0,11894.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> .
% 299.64/300.37 362[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.64/300.37 17941[0:Res:652.1,11894.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool))* equal(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))) -> .
% 299.64/300.37 17939[0:Res:649.0,11894.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))** -> .
% 299.64/300.37 17938[0:Res:650.0,11894.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))** -> .
% 299.64/300.37 17943[0:Res:648.0,11894.1] || equal(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> .
% 299.64/300.37 263[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* -> hBOOL(hAPP(hAPP(c_in(u),v),x)) equal(v,w).
% 299.64/300.37 11894[0:MRR:11893.2,264.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_in(v),w),u))* -> .
% 299.64/300.37 11179[0:SSi:11146.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,tc_bool),u)**.
% 299.64/300.37 17912[0:MRR:17911.0,15141.1] || equal(c_in(u),c_Set_Ovimage(c_COMBK(v,w,x),x,w))* -> .
% 299.64/300.37 188[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))**.
% 299.64/300.37 10930[0:SpR:3586.1,10813.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,u),v_x),v))*.
% 299.64/300.37 10540[0:SpR:10463.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,c_Orderings_Obot__class_Obot(tc_bool),w,x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))**.
% 299.64/300.37 9961[0:SpR:9911.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Orderings_Otop__class_Otop(tc_bool),w,x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.37 17631[0:Res:12593.0,17530.1] || equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),u).
% 299.64/300.37 255[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))*+ c_lessequals(w,x,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),x))*.
% 299.64/300.37 17630[0:Res:12463.0,17530.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),u).
% 299.64/300.37 17530[0:Res:10196.1,16481.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) c_lessequals(u,v,tc_bool)* -> equal(c_Orderings_Otop__class_Otop(tc_bool),v).
% 299.64/300.37 16481[0:SSi:16412.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)*+ c_lessequals(u,v,tc_bool)* -> equal(c_Orderings_Otop__class_Otop(tc_bool),v).
% 299.64/300.37 17466[0:Obv:17441.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* equal(u,v_Procs) -> .
% 299.64/300.37 171[0:Inp] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) -> hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMin(v,u)),v))* equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.64/300.37 16327[0:SpL:3229.1,16286.0] || equal(u,v)* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool))**+ equal(u,v_Procs)* -> .
% 299.64/300.37 15938[2:SpR:351.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBK(u,v,w),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(u,tc_bool)).
% 299.64/300.37 15798[0:SpR:351.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBK(u,v,w),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)).
% 299.64/300.37 14526[0:Res:11610.0,10429.0] || -> equal(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),u)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 172[0:Inp] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) -> hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMax(v,u)),v))* equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.64/300.37 14405[2:SpR:12944.0,4250.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.37 13272[0:SpL:9493.1,3266.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool))**+ equal(u,v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.37 13073[0:SpR:351.0,10090.1] || equal(c_COMBK(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))**+ -> equal(hAPP(u,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 510[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))*.
% 299.64/300.37 17118[2:SpR:17045.0,4250.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.37 17173[0:MRR:17148.1,826.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)),t_a)*.
% 299.64/300.37 17172[0:MRR:17108.1,826.0] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),v_Procs)** -> .
% 299.64/300.37 17045[0:Res:11606.0,10429.0] || -> equal(hAPP(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 511[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w)))*.
% 299.64/300.37 10531[0:SpR:10463.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,u),u)*.
% 299.64/300.37 17001[0:SSi:16999.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 9952[0:SpR:9911.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,u),u)*.
% 299.64/300.37 600[0:Rew:538.0,159.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_HOL_Ominus__class_Ominus(w,v,tc_fun(u,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v))**.
% 299.64/300.37 16870[0:SpL:135.0,15896.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* equal(u,v_Procs) -> .
% 299.64/300.37 15896[0:SpL:2267.1,15825.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)**+ -> .
% 299.64/300.37 95[0:Inp] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),z,y,x)*+ -> c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(v,y,w),z),w,x)*.
% 299.64/300.37 15830[0:MRR:15829.1,826.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 16814[0:Res:16776.0,9877.1] class_Finite__Set_Ofinite_Ofinite(u) || -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,u,w),x),w)*.
% 299.64/300.37 16776[0:Res:429.0,390.0] || -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(u,v,w,x),hAPP(c_Set_Oimage(v,w,x),u),x,w)*.
% 299.64/300.37 390[0:Inp] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool))*+ -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(y,v,w,x),u,x,w)*.
% 299.64/300.37 16768[0:Res:1012.1,12979.0] || hBOOL(hAPP(v_G,v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v_na,hAPP(c_in(tc_Com_Opname),v_x))))* -> c_Hoare__Mirabelle_Otriple__valid(v_na,v_Procs,t_a).
% 299.64/300.37 12979[0:Res:678.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_in(tc_Com_Opname),v_x)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_Procs,t_a).
% 299.64/300.37 10612[0:AED:24.0,10604.2] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)))** -> .
% 299.64/300.37 16753[0:MRR:16744.1,13431.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) -> c_Fun_Oinj__on(w,u,v,v)*.
% 299.64/300.37 202[0:Inp] || c_Finite__Set_Ofinite(u,v) c_lessequals(u,hAPP(c_Set_Oimage(w,v,v),u),tc_fun(v,tc_bool))* -> c_Fun_Oinj__on(w,u,v,v).
% 299.64/300.37 9936[0:SSi:9897.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 16480[0:SSi:16479.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)* -> .
% 299.64/300.37 361[0:Inp] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(y,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,u),u)*.
% 299.64/300.37 9935[0:SSi:9894.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 16339[0:SpL:414.0,16286.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Fun_Ofun__upd(v,v_x,u,w,x),v_Procs)** -> .
% 299.64/300.37 194[0:Inp] || c_Finite__Set_Ofinite(u,v) c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,v)*+ -> c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(w,x,v),u),x)*.
% 299.64/300.37 16254[0:SpL:351.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_COMBK(u,v,w),v_Procs)** -> .
% 299.64/300.37 16347[0:SpL:351.0,16286.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(c_COMBK(u,v,w),v_Procs)** -> .
% 299.64/300.37 16286[0:SSi:16285.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_Procs) -> .
% 299.64/300.37 513[0:Inp] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),z),x1))* -> equal(x,x1).
% 299.64/300.37 16217[0:Rew:15476.0,16212.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(u,v_Procs) -> .
% 299.64/300.37 15834[0:MRR:15833.2,826.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 15262[0:SpR:10063.0,3317.1] || equal(c_in(t_a),u) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.37 13608[2:SpR:11473.0,4250.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.37 514[0:Inp] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),z),x1))* -> equal(w,z).
% 299.64/300.37 13018[0:SpR:10090.1,342.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,c_Orderings_Otop__class_Otop(tc_bool),tc_fun(u,tc_bool))*.
% 299.64/300.37 15966[2:Rew:3014.0,15945.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.37 15965[2:Rew:2990.0,15933.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.37 515[0:Inp] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),z),x1))* -> equal(v,y).
% 299.64/300.37 15964[2:Rew:3014.0,15932.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.37 15483[2:Rew:15475.0,15418.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.37 15828[0:MRR:15827.1,826.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 15825[0:MRR:15824.1,826.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 277[0:Inp] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),x))*+ -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,x,u,w)))*.
% 299.64/300.37 15482[0:Rew:15475.0,15410.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.37 15476[0:Rew:15475.0,11769.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))**.
% 299.64/300.37 15569[0:SpR:414.0,15475.0] || -> equal(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_bool))**.
% 299.64/300.37 278[0:Inp] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),x))*+ -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,y,u,w)))*.
% 299.64/300.37 10204[0:Res:10196.1,50.1] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(u,c_HOL_Ozero__class_Ozero(tc_bool),tc_bool)*.
% 299.64/300.37 15367[0:MRR:15360.0,379.0] || -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),w,tc_fun(v,tc_bool)),v)*.
% 299.64/300.37 62[0:Inp] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),w).
% 299.64/300.37 10042[0:SpL:9924.0,3506.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Com_Ocom_OBODY)**+ equal(c_Com_Ocom_OSemi(u,v),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.37 63[0:Inp] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),w) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(x,w),v),tc_fun(w,tc_bool)),w)*.
% 299.64/300.37 15276[0:SpL:10063.0,418.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** -> .
% 299.64/300.37 15261[0:SpR:10063.0,267.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.37 10063[0:MRR:10062.0,826.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.64/300.37 9371[0:SpL:599.0,347.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)*+ -> c_Fun_Oinj__on(u,x,v,w)*.
% 299.64/300.37 446[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(x,w),u),hAPP(c_Set_Oinsert(x,w),v),tc_fun(w,tc_bool))*.
% 299.64/300.37 15189[0:Res:15185.0,401.0] || c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSKIP)),u,v)* -> equal(v,u).
% 299.64/300.37 15185[0:Res:18.0,12959.0] || -> c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSKIP)),u,u)*.
% 299.64/300.37 12959[0:Res:11108.1,12956.0] || c_Natural_Oevaln(u,v,w,x)*+ -> c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,u)),v,x)*.
% 299.64/300.37 11611[0:SpR:351.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),z),u,tc_bool)*.
% 299.64/300.37 181[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),w),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))**.
% 299.64/300.37 15023[0:Obv:15010.1] class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),u)*.
% 299.64/300.37 11008[0:Res:10986.1,146.1] class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v,u)*.
% 299.64/300.37 14899[0:Obv:14882.1] class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.37 11007[0:Res:10986.1,144.1] class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u)*.
% 299.64/300.37 128[0:Inp] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)))*.
% 299.64/300.37 13402[0:Res:13385.1,437.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))*+ c_Finite__Set_Ofinite(u,v)* -> c_Finite__Set_Ofinite(w,v)*.
% 299.64/300.37 12537[0:SSi:12519.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(u,v,tc_bool),tc_bool)* -> equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),u).
% 299.64/300.37 11610[0:SpR:456.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Option_Ooption_OSome(x,u)),x,tc_bool)*.
% 299.64/300.37 169[0:Inp] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w))*+ c_Finite__Set_Ofinite(w,u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(w,u),u)*.
% 299.64/300.37 12944[0:Res:10713.0,9857.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 12581[0:Res:448.2,12532.0] class_Orderings_Olinorder(tc_bool) || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool)* c_lessequals(w,u,tc_bool).
% 299.64/300.37 12524[0:Res:12463.0,10214.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),u).
% 299.64/300.37 10215[0:SSi:10201.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u)+ c_lessequals(u,v,tc_bool)* -> c_lessequals(w,v,tc_bool)*.
% 299.64/300.37 170[0:Inp] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w))*+ c_Finite__Set_Ofinite(w,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(w,u),v,u)*.
% 299.64/300.37 11695[0:Res:10712.0,9857.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),w)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 14240[2:SpR:14216.0,4250.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.37 14216[0:Res:10707.0,9857.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 176[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),hAPP(c_Set_Oinsert(hAPP(w,v),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.64/300.37 9284[0:SpR:3229.1,9269.0] || equal(u,v)*+ -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))* hBOOL(hAPP(u,v_x))*.
% 299.64/300.37 13016[0:SpR:10090.1,310.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,c_Orderings_Otop__class_Otop(tc_bool),u)*.
% 299.64/300.37 13015[0:SpR:10090.1,305.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,c_Orderings_Otop__class_Otop(tc_bool),u)*.
% 299.64/300.37 543[0:Inp] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))**.
% 299.64/300.37 13945[0:SpL:414.0,13885.0] || hBOOL(c_HOL_Ominus__class_Ominus(u,v,tc_bool))* -> hBOOL(u).
% 299.64/300.37 544[0:Inp] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))**.
% 299.64/300.37 11499[0:Res:10746.0,9857.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 11473[0:Res:10745.0,9857.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 11204[2:SpR:11176.1,4250.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY)** -> c_Com_OWT(u).
% 299.64/300.37 13553[0:SpR:336.0,11030.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))*.
% 299.64/300.37 147[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool))))* -> .
% 299.64/300.37 11030[0:SpR:9987.0,3317.1] || equal(c_in(t_a),u) -> hBOOL(hAPP(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.37 10921[0:SpR:3744.1,10813.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),v_Procs),v_x))*.
% 299.64/300.37 10552[0:SpL:10463.0,3506.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Com_Ocom_OBODY)**+ equal(c_Com_Ocom_OSemi(v,w),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.37 218[0:Inp] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> equal(u,w).
% 299.64/300.37 13431[0:Res:13387.1,11087.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))*+ -> c_Finite__Set_Ofinite(u,v)*.
% 299.64/300.37 13387[0:MRR:13386.1,420.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) -> c_lessequals(u,w,tc_fun(v,tc_bool))*.
% 299.64/300.37 13385[0:MRR:13384.1,366.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> c_lessequals(w,u,tc_fun(v,tc_bool))*.
% 299.64/300.37 109[0:Inp] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> c_lessequals(w,u,tc_fun(v,tc_bool)).
% 299.64/300.37 9973[0:SpL:9911.0,3506.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Com_Ocom_OBODY)**+ equal(c_Com_Ocom_OSemi(v,w),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.37 13238[0:SpR:9493.1,267.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u))*.
% 299.64/300.37 9493[0:MRR:9492.1,826.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),u),u)**.
% 299.64/300.37 108[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.37 10090[0:SpR:3229.1,9925.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 9994[0:SpR:9924.0,3229.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u)*+ -> equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 9991[0:SpR:9924.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname,u),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 501[0:Inp] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))*+ c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.64/300.37 10611[0:Rew:9925.0,10591.1] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || equal(c_Orderings_Otop__class_Otop(tc_bool),c_HOL_Ozero__class_Ozero(tc_bool)) -> equal(c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ozero__class_Ozero(tc_bool))**.
% 299.64/300.37 9995[0:SpR:9924.0,3283.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_Procs)).
% 299.64/300.37 12960[0:Res:12957.0,123.0] || c_Natural_Oevalc(u,v,w) -> c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSKIP),u),v,w)*.
% 299.64/300.37 12961[0:Res:12957.0,401.0] || c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSKIP),u,v)* -> equal(v,u).
% 299.64/300.37 96[0:Inp] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(v,u,w,x),hAPP(c_Set_Oimage(u,w,x),v),x,w)*.
% 299.64/300.37 12957[0:Res:18.0,12956.0] || -> c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSKIP),u,u)*.
% 299.64/300.37 12956[0:Res:11108.1,250.0] || c_Natural_Oevaln(u,v,w,x)*+ -> c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,u),v,x)*.
% 299.64/300.37 11108[0:Res:18.0,121.0] || c_Natural_Oevaln(u,v,w,x) -> c_Natural_Oevaln(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,u),v,w,x)*.
% 299.64/300.37 10713[0:SpR:351.0,9566.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_COMBK(u,x,y)),z),tc_bool)*.
% 299.64/300.37 384[0:Inp] || equal(hAPP(u,v),hAPP(u,w))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y)*+ -> equal(v,w).
% 299.64/300.37 12621[0:Res:12593.0,12532.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,tc_bool),u,tc_bool)*.
% 299.64/300.37 12717[0:Res:12533.1,10429.0] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)*+ -> equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 430[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool))*+ c_lessequals(v,x,tc_fun(w,tc_bool))* -> c_lessequals(u,x,tc_fun(w,tc_bool))*.
% 299.64/300.37 12687[0:MRR:12686.0,820.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),v))*.
% 299.64/300.37 12533[0:SSi:12518.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,w,tc_bool),v,tc_bool)*.
% 299.64/300.37 12591[0:Res:10196.1,12532.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**+ -> c_lessequals(w,u,tc_bool)*.
% 299.64/300.37 519[0:Inp] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x))* -> hBOOL(hAPP(v,x)) hBOOL(hAPP(w,x)).
% 299.64/300.37 12593[0:Res:12463.0,12532.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),u,tc_bool)*.
% 299.64/300.37 12532[0:SSi:12517.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_bool),tc_bool)* -> c_lessequals(u,v,tc_bool).
% 299.64/300.37 148[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(u),v),w)).
% 299.64/300.37 12463[0:SpR:414.0,12239.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_bool),u,tc_bool)*.
% 299.64/300.37 324[0:Inp] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool))* -> c_lessequals(w,x,tc_fun(u,tc_bool)).
% 299.64/300.37 12130[0:SpR:414.0,11763.0] || -> equal(c_HOL_Ominus__class_Ominus(u,u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 11985[0:SpR:414.0,11761.0] || -> equal(c_HOL_Ominus__class_Ominus(u,c_Orderings_Obot__class_Obot(tc_bool),tc_bool),u)**.
% 299.64/300.37 325[0:Inp] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool))* -> c_lessequals(v,x,tc_fun(u,tc_bool)).
% 299.64/300.37 11918[0:SpR:414.0,11767.0] || -> equal(c_HOL_Ominus__class_Ominus(u,c_Orderings_Otop__class_Otop(tc_bool),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 11855[0:Obv:11854.2] class_Int_Onumber__ring(tc_bool) class_Ring__and__Field_Oidom(tc_bool) || -> .
% 299.64/300.37 150[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))))* -> .
% 299.64/300.37 11850[0:Obv:11849.1] class_OrderedGroup_Ogroup__add(tc_bool) || -> .
% 299.64/300.37 11846[0:MRR:11832.1,11827.1] class_OrderedGroup_Oab__group__add(tc_bool) || -> .
% 299.64/300.37 11796[0:SpR:414.0,11765.0] || -> equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_bool),u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 130[0:Inp] class_HOL_Ominus(u) || -> equal(hAPP(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_x),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))**.
% 299.64/300.37 10712[0:SpR:456.0,9566.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),c_Option_Ooption_OSome(u,x)),tc_bool)*.
% 299.64/300.37 11580[0:SpR:659.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.37 9567[0:SSi:9503.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),hAPP(u,x),tc_bool)*.
% 299.64/300.37 11561[0:MRR:11560.2,10196.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u)*+ equal(u,v)* -> c_lessequals(w,v,tc_bool)*.
% 299.64/300.37 229[0:Inp] || -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSKIP),w),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.64/300.37 11087[0:MRR:11061.0,379.0] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> c_Finite__Set_Ofinite(u,v).
% 299.64/300.37 10746[0:SSi:10744.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),u),tc_bool)*.
% 299.64/300.37 10745[0:SSi:10743.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),x),tc_bool)*.
% 299.64/300.37 344[0:Inp] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.64/300.37 11177[0:SSi:11141.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u),u)**.
% 299.64/300.37 11284[0:SSi:11283.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(u,c_Orderings_Obot__class_Obot(tc_bool))* -> .
% 299.64/300.37 345[0:Inp] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.64/300.37 11176[0:SSi:11138.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),u)**.
% 299.64/300.37 11170[0:Res:10196.1,10214.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u)*+ equal(c_Orderings_Otop__class_Otop(tc_bool),v)* -> equal(v,u)*.
% 299.64/300.37 10214[0:SSi:10202.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) c_lessequals(u,v,tc_bool)* -> equal(u,v).
% 299.64/300.37 10522[0:SpR:10463.0,3229.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v)*+ -> equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 121[0:Inp] || c_Natural_Oevaln(u,v,w,x)*+ c_Natural_Oevaln(y,x,w,z)* -> c_Natural_Oevaln(c_Com_Ocom_OSemi(u,y),v,w,z)*.
% 299.64/300.37 9943[0:SpR:9911.0,3229.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v)*+ -> equal(hAPP(v,v_x),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 10519[0:SpR:10463.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),v_Procs),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.37 357[0:Inp] || c_Finite__Set_Ofinite(u,v) c_lessequals(w,hAPP(c_Set_Oimage(x,v,y),u),tc_fun(y,tc_bool))* -> c_Finite__Set_Ofinite(w,y).
% 299.64/300.37 11029[0:SpR:9987.0,267.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.37 9987[0:MRR:9986.0,826.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.37 10986[0:MRR:10985.1,3591.0] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(v,v,u)*.
% 299.64/300.37 213[0:Inp] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_COMBK(x,u,w),w,u),x)**.
% 299.64/300.37 9940[0:SpR:9911.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 10523[0:SpR:10463.0,3283.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_in(tc_Com_Opname))**+ -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_Procs))*.
% 299.64/300.37 10813[0:SpR:353.0,423.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),w))*.
% 299.64/300.37 353[0:Inp] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(u,v),x)))*.
% 299.64/300.37 9944[0:SpR:9911.0,3283.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname))**+ -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_Procs))*.
% 299.64/300.37 10041[0:SpL:9924.0,3483.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 9877[0:Res:204.1,447.0] class_Finite__Set_Ofinite_Ofinite(u) || c_Fun_Oinj__on(v,w,x,u)* -> c_Finite__Set_Ofinite(w,x).
% 299.64/300.37 10684[0:SpR:659.0,9566.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.37 254[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(x,u),w)))*.
% 299.64/300.37 9566[0:SSi:9498.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(c_Set_Oinsert(w,x),u),v),tc_bool)*.
% 299.64/300.37 10609[0:AED:24.0,10603.3] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u))** -> .
% 299.64/300.37 9928[0:SSi:9900.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),u,v),tc_Com_Opname,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 10551[0:SpL:10463.0,3483.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 505[0:Inp] || c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u)),v,w,x)* -> c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,c_Suc(w),x).
% 299.64/300.37 9972[0:SpL:9911.0,3483.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 10428[0:SSi:10421.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)*+ -> c_lessequals(u,v,tc_bool)*.
% 299.64/300.37 10525[2:SpR:10463.0,4250.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.37 10484[0:MRR:10483.2,10475.0] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)* -> .
% 299.64/300.37 57[0:Inp] class_OrderedGroup_Olordered__ab__group__add(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ouminus__class_Ouminus(v,u)),c_HOL_Ozero__class_Ozero(u))** -> equal(v,c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.37 10477[0:MRR:9933.2,10475.0] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_HOL_Ozero__class_Ozero(tc_bool),tc_bool)* -> .
% 299.64/300.37 10463[0:Res:10316.0,10429.0] || -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 454[0:Inp] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))*+ -> c_Hoare__Mirabelle_Ohoare__valids(v,w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v,w),u,t_a)*.
% 299.64/300.37 10475[0:AED:24.0,10465.1] || equal(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.37 10429[0:SSi:10423.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)* -> equal(u,c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.37 10384[0:SpR:414.0,10351.0] || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),u,tc_bool)*.
% 299.64/300.37 590[0:Inp] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(v_Q,v_x)),t_a)* -> .
% 299.64/300.37 9997[2:SpR:9924.0,4250.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.37 395[0:Inp] || -> equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v,w,x,y),v,z,x,y),c_Fun_Ofun__upd(u,v,z,x,y))**.
% 299.64/300.37 9856[0:SSi:9850.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)*+ -> c_lessequals(v,u,tc_bool)*.
% 299.64/300.37 10196[0:MRR:10195.1,9810.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> c_lessequals(v,u,tc_bool)*.
% 299.64/300.37 9946[2:SpR:9911.0,4250.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.37 431[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool))*+ c_Fun_Oinj__on(x,v,w,y)* -> c_Fun_Oinj__on(x,u,w,y)*.
% 299.64/300.37 9925[0:SSi:9895.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 9924[0:SSi:9892.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 9911[0:Res:9747.0,9857.0] || -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 9857[0:SSi:9851.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* -> equal(c_Orderings_Otop__class_Otop(tc_bool),u).
% 299.64/300.37 447[0:Inp] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w)* c_Fun_Oinj__on(u,x,v,w) -> c_Finite__Set_Ofinite(x,v).
% 299.64/300.37 9810[0:SpR:414.0,9716.0] || -> c_lessequals(u,c_Orderings_Otop__class_Otop(tc_bool),tc_bool)*.
% 299.64/300.37 98[0:Inp] || c_Fun_Oinj__on(u,v,w,x) -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,w,x),v),x),c_Finite__Set_Ocard(v,w))**.
% 299.64/300.37 9595[0:SpR:524.0,9563.0] || -> c_lessequals(u,u,tc_bool)*.
% 299.64/300.37 251[0:Inp] class_HOL_Oord(u) || c_lessequals(v,w,tc_fun(x,u))*+ -> c_lessequals(hAPP(v,y),hAPP(w,y),u)*.
% 299.64/300.37 9268[0:Res:9258.0,279.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),u),u).
% 299.64/300.37 9409[0:SSi:9390.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)*+ -> hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool))* hBOOL(u)*.
% 299.64/300.37 9408[0:MRR:9407.1,826.0] || equal(u,c_Orderings_Otop__class_Otop(tc_bool))*+ -> hBOOL(u)*.
% 299.64/300.37 346[0:Inp] || c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v,y)* -> c_Fun_Oinj__on(u,x,v,y).
% 299.64/300.37 9320[0:Rew:351.0,9300.1] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))* hBOOL(u).
% 299.64/300.37 347[0:Inp] || c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v,y)* -> c_Fun_Oinj__on(u,w,v,y).
% 299.64/300.37 9258[0:SSi:9251.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u))* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)).
% 299.64/300.37 8369[0:Res:149.1,527.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),v))*.
% 299.64/300.37 9225[0:Res:9071.0,527.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),u))*.
% 299.64/300.37 616[0:MRR:238.0,474.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)*+ -> equal(c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(hAPP(u,x),u,w,v),x)**.
% 299.64/300.37 9071[0:Res:651.0,214.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,tc_fun(u,tc_bool))))*.
% 299.64/300.37 8625[0:SpL:8498.1,3266.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))*+ equal(u,w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.37 8376[0:SpR:3229.1,8366.1] || equal(c_in(tc_Com_Opname),u) equal(v,v_Procs) -> hBOOL(hAPP(hAPP(u,v_x),v))*.
% 299.64/300.37 8494[0:Res:8375.1,1815.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)))** equal(u,v_Procs) -> .
% 299.64/300.37 214[0:Inp] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),u),x)).
% 299.64/300.37 9001[4:MRR:8937.2,6340.0] || equal(v_Procs,v_x) equal(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> .
% 299.64/300.37 9000[4:MRR:8935.2,6340.0] || equal(v_Procs,v_x) equal(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> .
% 299.64/300.37 8999[4:MRR:8954.2,6340.0] || equal(v_Procs,v_x) equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> .
% 299.64/300.37 335[0:Inp] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(w,v) -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v)*.
% 299.64/300.37 117[0:Inp] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)))**.
% 299.64/300.37 8498[0:Res:8375.1,279.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(hAPP(c_Set_Oinsert(w,v),u),u)**.
% 299.64/300.37 8517[0:AED:24.0,8514.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> .
% 299.64/300.37 319[0:Inp] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> equal(x,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.64/300.37 8500[0:Res:8375.1,591.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G)**+ -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),u,t_a)*.
% 299.64/300.37 8495[0:Res:8375.1,656.0] || equal(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)))** -> .
% 299.64/300.37 8499[0:Res:8375.1,527.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))*+ -> hBOOL(hAPP(u,w))*.
% 299.64/300.37 8493[0:Res:8375.1,657.0] || equal(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)))** -> .
% 299.64/300.37 355[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> equal(v,w).
% 299.64/300.37 8375[0:MRR:8374.2,262.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> hBOOL(hAPP(hAPP(c_in(v),w),u))*.
% 299.64/300.37 8385[0:Res:8366.1,279.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),u)**.
% 299.64/300.37 8366[0:Res:149.1,1815.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),u))*.
% 299.64/300.37 149[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))))*.
% 299.64/300.37 76[0:Inp] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v)* -> c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v).
% 299.64/300.37 426[0:Inp] class_Orderings_Oorder(u) || c_lessequals(v,w,u)*+ c_lessequals(x,v,u)* -> c_lessequals(x,w,u)*.
% 299.64/300.37 5888[0:SpR:584.0,310.1] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),v),u)*.
% 299.64/300.37 5887[0:SpR:584.0,305.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),v),u)*.
% 299.64/300.37 5110[0:SpR:351.0,3339.1] || equal(u,c_COMBK(v,w,x))*+ -> equal(c_Fun_Ofun__upd(u,v_x,v,y,z),u)**.
% 299.64/300.37 427[0:Inp] class_Orderings_Opreorder(u) || c_lessequals(v,w,u)*+ c_lessequals(w,x,u)* -> c_lessequals(v,x,u)*.
% 299.64/300.37 7600[0:Res:7539.0,437.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),v)* -> c_Finite__Set_Ofinite(x,v).
% 299.64/300.37 7309[0:SpR:584.0,7253.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oimage(u,v,w),u,x,y,z),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.37 5727[0:Res:5724.1,401.0] || c_Natural_Oevalc(u,v,w)* c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,u),v,x)*+ -> equal(x,w)*.
% 299.64/300.37 7284[0:SpR:351.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBK(u,v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),u))*.
% 299.64/300.37 295[0:Inp] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,u)* -> c_lessequals(v,x,u).
% 299.64/300.37 5877[0:SpR:584.0,499.0] || -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Com_Ocom_OBODY,v,w,x),y),z),u)*.
% 299.64/300.37 4834[0:Obv:4830.1] class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),u),v,u)*.
% 299.64/300.37 4801[0:Obv:4794.1] class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),u),u)*.
% 299.64/300.37 4275[2:SpR:9.0,4250.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(u,hAPP(v,v_x))).
% 299.64/300.37 296[0:Inp] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,u)* -> c_lessequals(w,x,u).
% 299.64/300.37 3952[0:SpL:414.0,3506.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Com_Ocom_OBODY)**+ equal(c_Com_Ocom_OSemi(y,z),v)* -> .
% 299.64/300.37 3582[0:SpR:9.0,3282.1] || equal(c_Fun_Ocomp(u,v,w,x,y),v_Procs)** -> hBOOL(hAPP(u,hAPP(v,v_x))).
% 299.64/300.37 4654[0:SpL:351.0,3698.2] || equal(u,c_COMBK(v,w,x))* equal(c_Com_Ocom_OBODY,u) equal(v,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 293[0:Inp] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),u)*.
% 299.64/300.37 4518[0:SpR:351.0,3316.1] || equal(c_in(u),c_COMBK(v,w,x))*+ -> hBOOL(hAPP(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.37 4439[0:Res:3282.1,33.0] || equal(hAPP(c_Set_Ovimage(u,v,w),x),v_Procs)** -> hBOOL(hAPP(x,hAPP(u,v_x))).
% 299.64/300.37 3508[0:SpL:3229.1,377.0] || equal(c_Set_Oinsert(u,v),w)*+ c_Finite__Set_Ofinite(hAPP(w,v_x),v)* -> c_Finite__Set_Ofinite(v_x,v).
% 299.64/300.37 7576[0:Res:7542.0,437.1] || c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),v)* -> c_Finite__Set_Ofinite(v_x,v).
% 299.64/300.37 294[0:Inp] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w),u)*.
% 299.64/300.37 7599[0:Res:7539.0,682.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(c_in(tc_Com_Opname),v_x))),v_Procs))*.
% 299.64/300.37 7598[0:Res:7539.0,1051.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.37 7539[0:Res:376.0,363.0] || -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),u)),tc_fun(w,tc_bool))*.
% 299.64/300.37 7542[0:Res:651.0,363.0] || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.37 363[0:Inp] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* -> c_lessequals(w,x,tc_fun(v,tc_bool)).
% 299.64/300.37 3346[0:SpR:3229.1,267.0] || equal(c_Set_Oinsert(u,v),w) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(w,v_x)))*.
% 299.64/300.37 3307[0:SpR:3229.1,3229.1] || equal(u,v)*+ equal(u,w)* -> equal(hAPP(v,v_x),hAPP(w,v_x))*.
% 299.64/300.37 3274[0:SpR:3229.1,378.1] || equal(c_Set_Oinsert(u,v),w)*+ c_Finite__Set_Ofinite(v_x,v) -> c_Finite__Set_Ofinite(hAPP(w,v_x),v)*.
% 299.64/300.37 7460[0:Res:364.1,1051.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),u),v_x))*.
% 299.64/300.37 364[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(c_Set_Oinsert(x,w),v),tc_fun(w,tc_bool))*.
% 299.64/300.37 7082[0:SpR:78.0,7.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,u,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.64/300.37 4469[0:SpL:351.0,3493.1] || equal(c_COMBK(u,v,w),c_in(tc_Com_Opname))**+ equal(u,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> .
% 299.64/300.37 4421[0:SpR:351.0,3284.1] || equal(c_COMBK(u,v,w),c_in(tc_Com_Opname))**+ -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),u))*.
% 299.64/300.37 402[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool))*+ c_lessequals(v,u,tc_fun(w,tc_bool))* -> equal(u,v).
% 299.64/300.37 4382[0:Res:3282.1,371.0] || equal(hAPP(c_Set_Oinsert(u,v),w),v_Procs)** -> hBOOL(hAPP(w,v_x)) equal(u,v_x).
% 299.64/300.37 3742[0:SpR:586.0,3283.1] || equal(c_COMBB(u,v,w,x),c_in(tc_Com_Opname))**+ -> hBOOL(hAPP(u,hAPP(v_x,v_Procs)))*.
% 299.64/300.37 3741[0:SpR:585.0,3283.1] || equal(c_COMBC(u,v,w,x),c_in(tc_Com_Opname))**+ -> hBOOL(hAPP(hAPP(u,v_Procs),v_x))*.
% 299.64/300.37 7361[0:Obv:7360.2] class_Int_Onumber__ring(tc_fun(u,tc_bool)) class_Ring__and__Field_Oidom(tc_fun(u,tc_bool)) || -> .
% 299.64/300.37 125[0:Inp] class_Int_Onumber__ring(u) class_Ring__and__Field_Oidom(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u))** -> equal(v,w).
% 299.64/300.37 7283[0:SpR:456.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Option_Othe(u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),x))*.
% 299.64/300.37 7253[0:Res:474.0,527.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(u,x)))*.
% 299.64/300.37 474[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(v,x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.37 3317[0:SpR:3229.1,267.0] || equal(c_in(u),v) -> hBOOL(hAPP(hAPP(v,v_x),hAPP(c_Set_Oinsert(v_x,u),w)))*.
% 299.64/300.37 3305[0:SpR:3229.1,1158.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v_Procs),hAPP(v,v_x)))*.
% 299.64/300.37 6935[0:Res:212.1,3499.1] || hBOOL(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))*+ equal(c_in(u),c_Set_Oinsert(v,w))* -> .
% 299.64/300.37 6757[0:SpR:369.0,3291.1] || equal(c_Set_Oinsert(u,v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),v_Procs))*.
% 299.64/300.37 6546[0:SSi:6535.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool))*+ equal(u,v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.37 4273[2:SpR:88.1,4250.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.37 3724[0:SpR:3229.1,3283.1] || equal(u,v)* equal(c_in(tc_Com_Opname),u)*+ -> hBOOL(hAPP(hAPP(v,v_x),v_Procs))*.
% 299.64/300.37 311[0:Inp] class_Lattices_Obounded__lattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_Orderings_Obot__class_Obot(u))** -> equal(v,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.37 3580[0:SpR:88.1,3282.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_Procs)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.37 6933[0:Res:423.0,3499.1] || equal(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),c_in(u))** -> .
% 299.64/300.37 6973[0:AED:24.0,6972.2] class_Lattices_Obounded__lattice(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u))** -> .
% 299.64/300.37 6939[4:MRR:6927.1,6340.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(u))** -> .
% 299.64/300.37 312[0:Inp] class_Lattices_Obounded__lattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_Orderings_Obot__class_Obot(u))** -> equal(w,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.37 3499[0:SpL:3229.1,262.0] || equal(c_in(u),v) hBOOL(hAPP(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.37 3484[0:SpL:3229.1,541.0] || equal(c_Com_Ocom_OBODY,u) equal(hAPP(u,v_x),hAPP(c_Com_Ocom_OBODY,v))* -> equal(v_x,v).
% 299.64/300.37 3331[0:SpR:3229.1,525.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)*+ -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.37 3324[0:SpR:3229.1,525.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v)*+ -> equal(hAPP(hAPP(v,v_x),v_x),v_x)**.
% 299.64/300.37 328[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),u),v)**.
% 299.64/300.37 3291[0:SpR:3229.1,1119.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(u,v_x)),v_Procs))*.
% 299.64/300.37 3945[0:SpL:524.0,3506.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Com_Ocom_OBODY)**+ equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.37 329[0:Inp] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v),v)**.
% 299.64/300.37 3702[0:SpL:300.1,3483.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 3695[0:SpL:365.1,3483.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(u),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 3693[0:SpL:397.1,3483.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 3691[0:SpL:2097.1,3483.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_Com_Ocom_OBODY)**+ equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 327[0:Inp] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),w)** -> c_lessequals(v,w,tc_fun(u,tc_bool)).
% 299.64/300.37 3303[0:SpR:3229.1,1042.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),v)*+ -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.37 3302[0:SpR:3229.1,1020.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u),v)*+ -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.37 3285[0:SpR:3229.1,658.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.37 6480[5:Spt:4269.2] || -> c_Com_OWT(v_x)*.
% 299.64/300.37 538[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v))*.
% 299.64/300.37 3727[0:SpR:525.1,3283.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.37 6344[4:MRR:939.0,6340.0] || -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_Com_Opname))*.
% 299.64/300.37 6343[4:MRR:931.0,6340.0] || -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_Com_Opname))*.
% 299.64/300.37 6342[4:MRR:938.1,6340.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_Com_Opname))*.
% 299.64/300.37 178[0:Inp] || c_Finite__Set_Ofinite(u,v) equal(c_Finite__Set_Ocard(u,v),c_HOL_Ozero__class_Ozero(tc_nat))**+ -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))*.
% 299.64/300.37 6341[4:MRR:930.1,6340.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_Com_Opname))*.
% 299.64/300.37 6340[4:Spt:3578.2] || -> hBOOL(v_x)*.
% 299.64/300.37 70[0:Inp] || c_lessequals(u,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.64/300.37 6024[0:SpR:456.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),c_Option_Othe(w),x,y,z),c_Option_Ooption_OSome(u,w)))*.
% 299.64/300.37 6243[0:MRR:6242.1,429.0] class_OrderedGroup_Oordered__ab__group__add(tc_fun(u,tc_bool)) || -> .
% 299.64/300.37 6139[0:Obv:6131.1] class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.37 4787[0:Res:434.1,144.1] class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u)*.
% 299.64/300.37 5875[0:SpR:584.0,423.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(u,v),w),u,x,y,z),v))*.
% 299.64/300.37 584[0:Inp] || -> equal(hAPP(c_COMBS(u,v,w,x,y),z),hAPP(hAPP(u,z),hAPP(v,z)))*.
% 299.64/300.37 5810[0:Obv:5802.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.37 4785[0:Res:816.1,144.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u)*.
% 299.64/300.37 5724[0:Res:17.0,123.0] || c_Natural_Oevalc(u,v,w) -> c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,u),v,w)*.
% 299.64/300.37 123[0:Inp] || c_Natural_Oevalc(u,v,w)*+ c_Natural_Oevalc(x,w,y)* -> c_Natural_Oevalc(c_Com_Ocom_OSemi(u,x),v,y)*.
% 299.64/300.37 5602[0:Obv:5592.1] class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),u)*.
% 299.64/300.37 4695[0:Res:434.1,146.1] class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v,u)*.
% 299.64/300.37 5375[0:Obv:5366.1] class_Orderings_Oorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),u)*.
% 299.64/300.37 114[0:Inp] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(v,y,tc_fun(w,tc_bool)),w,x)*.
% 299.64/300.37 5390[0:MRR:5389.2,4786.2] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v)**.
% 299.64/300.37 5280[0:Obv:5271.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),u)*.
% 299.64/300.37 4693[0:Res:816.1,146.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v,u)*.
% 299.64/300.37 348[0:Inp] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x)* -> equal(c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,w,v,x)),w).
% 299.64/300.37 3340[0:SpR:3229.1,414.0] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),y)*+ -> equal(hAPP(y,v_x),v)*.
% 299.64/300.37 3339[0:SpR:3229.1,415.0] || equal(u,v) -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(v,v_x),w,x),u)**.
% 299.64/300.37 83[0:Inp] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),x)),x,tc_fun(w,tc_bool))*.
% 299.64/300.37 4805[0:SpR:74.1,4790.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.37 4722[0:SpR:73.1,4703.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.37 4714[0:Rew:73.1,4699.3] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.37 405[0:Inp] class_Orderings_Oorder(u) || c_lessequals(v,w,u)*+ c_lessequals(w,v,u)* -> equal(w,v).
% 299.64/300.37 4151[0:SpL:351.0,3929.0] || hBOOL(u) equal(c_COMBK(u,v,w),x)*+ -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.37 4964[0:Res:3282.1,3863.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_Procs)** -> hBOOL(hAPP(u,v_x)).
% 299.64/300.37 3863[0:Res:124.0,436.1] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x))* -> hBOOL(hAPP(u,x)).
% 299.64/300.37 3732[0:SpR:414.0,3283.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v,v_Procs)).
% 299.64/300.37 112[0:Inp] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u),u)* -> c_lessequals(w,v,u).
% 299.64/300.37 51[0:Inp] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(v,w,u).
% 299.64/300.37 3272[0:SpR:3229.1,376.0] || equal(c_Set_Oinsert(u,v),w)*+ -> c_lessequals(v_x,hAPP(w,v_x),tc_fun(v,tc_bool))*.
% 299.64/300.37 4557[0:SpR:3586.1,267.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_in(u),v),v_x))*.
% 299.64/300.37 4790[0:Res:367.1,144.1] class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),u)*.
% 299.64/300.37 144[0:Inp] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,u),u)*+ -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.37 4703[0:Res:421.1,146.1] class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),v,u)*.
% 299.64/300.37 146[0:Inp] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*+ -> c_lessequals(c_HOL_Ouminus__class_Ouminus(w,u),v,u)*.
% 299.64/300.37 4437[0:Res:3283.1,33.0] || equal(c_Set_Ovimage(u,v,w),c_in(tc_Com_Opname))**+ -> hBOOL(hAPP(v_x,hAPP(u,v_Procs)))*.
% 299.64/300.37 4266[2:SpR:302.1,4250.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.37 3698[0:SpL:3229.1,3483.1] || equal(u,v)* equal(c_Com_Ocom_OBODY,u)* equal(hAPP(v,v_x),c_Com_Ocom_OSKIP)**+ -> .
% 299.64/300.37 111[0:Inp] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(w,u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.37 3586[0:Res:3282.1,279.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(v,u),v_x),v_x)**.
% 299.64/300.37 3575[0:SpR:302.1,3282.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.37 3316[0:SpR:3229.1,264.0] || equal(c_in(u),v) -> hBOOL(hAPP(hAPP(v,v_x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.37 52[0:Inp] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,w,u) -> c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.37 4483[3:Spt:4380.0,4380.2] || equal(c_Set_Oinsert(u,v),c_in(tc_Com_Opname))** -> equal(u,v_Procs).
% 299.64/300.37 3497[0:SpL:3229.1,888.0] || equal(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v)*+ hBOOL(hAPP(v,v_x))* -> .
% 299.64/300.37 3330[0:SpR:3229.1,524.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)*+ -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.37 33[0:Inp] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y))* -> hBOOL(hAPP(x,hAPP(u,y))).
% 299.64/300.37 3320[0:SpR:3229.1,524.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)*+ -> equal(hAPP(hAPP(v,v_x),v_x),v_x)**.
% 299.64/300.37 3284[0:SpR:3229.1,678.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),hAPP(u,v_x)))*.
% 299.64/300.37 34[0:Inp] || hBOOL(hAPP(u,hAPP(v,w))) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,x,y),u),w))*.
% 299.64/300.37 3701[0:SpL:525.1,3483.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 371[0:Inp] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),x))* -> hBOOL(hAPP(w,x)) equal(u,x).
% 299.64/300.37 4255[2:SpR:365.1,4250.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(u)).
% 299.64/300.37 4253[2:SpR:397.1,4250.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.37 4258[2:SpR:3229.1,4250.1] || equal(u,v)*+ equal(c_Com_Ocom_OBODY,u)* -> c_Com_OWT(hAPP(v,v_x))*.
% 299.64/300.37 103[0:Inp] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,u,tc_fun(v,tc_bool)),v)* -> c_Finite__Set_Ofinite(w,v).
% 299.64/300.37 4268[2:SpR:414.0,4250.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Com_Ocom_OBODY)** -> c_Com_OWT(v).
% 299.64/300.37 297[0:Inp] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),w)**.
% 299.64/300.37 4272[2:SpR:351.0,4250.1] || equal(c_COMBK(u,v,w),c_Com_Ocom_OBODY)** -> c_Com_OWT(u).
% 299.64/300.37 4250[2:Spt:3264.0,3264.1] || equal(c_Com_Ocom_OBODY,u) -> c_Com_OWT(hAPP(u,v_x))*.
% 299.64/300.37 3726[0:SpR:524.0,3283.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.37 299[0:Inp] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v),w)**.
% 299.64/300.37 3956[0:SpL:351.0,3506.1] || equal(c_COMBK(u,v,w),c_Com_Ocom_OBODY)**+ equal(c_Com_Ocom_OSemi(x,y),u)* -> .
% 299.64/300.37 3706[0:SpL:414.0,3483.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Com_Ocom_OBODY)** equal(v,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 3929[0:SpL:2097.1,3266.0] || hBOOL(hAPP(u,v_x))*+ equal(u,v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.37 298[0:Inp] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),w)** -> c_lessequals(v,w,u).
% 299.64/300.37 3567[0:SpR:365.1,3282.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_Procs)** -> hBOOL(c_Orderings_Obot__class_Obot(u)).
% 299.64/300.37 3565[0:SpR:397.1,3282.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_Procs)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.37 3744[0:Res:3283.1,279.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(hAPP(c_Set_Oinsert(v_x,u),v_Procs),v_Procs)**.
% 299.64/300.37 42[0:Inp] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.37 3495[0:SpL:3229.1,836.0] || equal(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),u)*+ hBOOL(hAPP(u,v_x))* -> .
% 299.64/300.37 3700[0:SpL:524.0,3483.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 54[0:Inp] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u).
% 299.64/300.37 3353[0:SpR:3229.1,351.0] || equal(c_COMBK(u,v,w),x)*+ -> equal(hAPP(x,v_x),u)*.
% 299.64/300.37 3344[0:SpR:3229.1,423.0] || equal(c_Set_Oinsert(u,v),w)*+ -> hBOOL(hAPP(hAPP(w,v_x),u))*.
% 299.64/300.37 41[0:Inp] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.37 3735[0:SpR:351.0,3283.1] || equal(c_COMBK(u,v,w),c_in(tc_Com_Opname))** -> hBOOL(hAPP(u,v_Procs)).
% 299.64/300.37 3570[0:SpR:3229.1,3282.1] || equal(u,v)*+ equal(v_Procs,u)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.37 3506[0:SpL:3229.1,166.0] || equal(c_Com_Ocom_OBODY,u) equal(c_Com_Ocom_OSemi(v,w),hAPP(u,v_x))* -> .
% 299.64/300.37 3266[0:SpR:3229.1,423.0] || equal(hAPP(c_Set_Oinsert(v_x,u),v),w)*+ -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.37 53[0:Inp] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.37 3300[0:SpR:3229.1,839.0] || equal(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),v)*+ -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.37 436[0:Inp] || hBOOL(hAPP(u,v))* c_lessequals(u,w,tc_fun(x,tc_bool))*+ -> hBOOL(hAPP(w,v))*.
% 299.64/300.37 3577[0:SpR:414.0,3282.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),v_Procs)** -> hBOOL(v).
% 299.64/300.37 3709[0:SpL:351.0,3483.1] || equal(c_COMBK(u,v,w),c_Com_Ocom_OBODY)** equal(u,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 3587[0:Res:3282.1,527.0] || equal(hAPP(c_in(u),v),v_Procs)** -> hBOOL(hAPP(v_x,v)).
% 299.64/300.37 539[0:Inp] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v))*.
% 299.64/300.37 3283[0:SpR:3229.1,589.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(u,v_x),v_Procs))*.
% 299.64/300.37 3483[0:SpL:3229.1,167.0] || equal(c_Com_Ocom_OBODY,u) equal(hAPP(u,v_x),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.37 3579[0:SpR:351.0,3282.1] || equal(c_COMBK(u,v,w),v_Procs)** -> hBOOL(u).
% 299.64/300.37 540[0:Inp] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v))*.
% 299.64/300.37 3590[0:Res:3282.1,888.0] || equal(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 3591[0:Res:3282.1,392.0] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v_Procs)** -> .
% 299.64/300.37 3282[0:SpR:3229.1,660.0] || equal(v_Procs,u) -> hBOOL(hAPP(u,v_x))*.
% 299.64/300.37 3229[0:Rew:2807.0,3140.1] || equal(u,v) -> equal(hAPP(u,v_x),hAPP(v,v_x))*.
% 299.64/300.37 517[0:Inp] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v))*.
% 299.64/300.37 2771[0:SSi:2770.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.37 518[0:Inp] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),v))*.
% 299.64/300.37 502[0:Inp] || c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u)),v,w)* -> c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,u),v,w).
% 299.64/300.37 503[0:Inp] || c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,u),v,w) -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u)),v,w)*.
% 299.64/300.37 416[0:Inp] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.64/300.37 3014[0:SpR:2990.0,2807.0] || -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 2990[0:SSi:2982.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 2935[0:Rew:2934.0,492.0] || -> equal(hAPP(hAPP(c_in(t_a),v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 2807[0:SpR:414.0,2767.0] || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(u,tc_bool),tc_bool),u)**.
% 299.64/300.37 25[0:Inp] class_HOL_Ouminus(u) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))**.
% 299.64/300.37 2693[0:SpL:2267.1,2674.0] || equal(u,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v))*+ equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 1987[0:SSi:1985.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))*+ equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 336[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.37 1588[0:SSi:1584.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_in(tc_Com_Opname),v_x),u,v),tc_Com_Opname,tc_fun(w,tc_bool)),v_Procs))*.
% 299.64/300.37 2675[0:Res:1157.0,2629.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(c_COMBK(v_x,u,v),tc_Com_Opname,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 2674[0:Res:267.0,2629.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 337[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.37 1815[0:SSi:1796.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.37 445[0:Inp] || -> equal(u,v) equal(hAPP(c_Fun_Ofun__upd(w,v,x,y,z),u),hAPP(w,u))**.
% 299.64/300.37 360[0:Inp] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),x),w,y)* -> c_Fun_Oinj__on(u,x,w,y).
% 299.64/300.37 586[0:Inp] || -> equal(hAPP(hAPP(c_COMBB(u,v,w,x),y),z),hAPP(u,hAPP(y,z)))**.
% 299.64/300.37 585[0:Inp] || -> equal(hAPP(hAPP(c_COMBC(u,v,w,x),y),z),hAPP(hAPP(u,z),y))**.
% 299.64/300.37 369[0:Inp] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),w)),hAPP(c_Set_Oinsert(u,v),w))**.
% 299.64/300.37 46[0:Inp] class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.37 50[0:Inp] class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.37 45[0:Inp] class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.37 2463[0:Res:49.2,1048.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(tc_Com_Opname,tc_bool)) || c_lessequals(v_Procs,c_HOL_Ozero__class_Ozero(tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* -> .
% 299.64/300.37 49[0:Inp] class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.37 44[0:Inp] class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u).
% 299.64/300.37 48[0:Inp] class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u).
% 299.64/300.37 2267[0:SpL:135.0,2063.0] || equal(u,v) -> equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)))*.
% 299.64/300.37 2063[0:SpL:135.0,16.0] || equal(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)))*+ -> equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),v)*.
% 299.64/300.37 1157[0:SpR:351.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_COMBK(v,w,x),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.37 2089[0:Res:658.0,279.0] || -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs))**.
% 299.64/300.37 43[0:Inp] class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)*.
% 299.64/300.37 2214[0:SpL:2098.1,418.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)))*+ -> c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)*.
% 299.64/300.37 2098[0:Res:168.0,279.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) equal(hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),v),v)**.
% 299.64/300.37 2092[0:Res:652.1,279.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool))* -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),u).
% 299.64/300.37 2095[0:Res:264.0,279.0] || -> equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.64/300.37 47[0:Inp] class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)*.
% 299.64/300.37 2093[0:Res:678.0,279.0] || -> equal(hAPP(c_Set_Oinsert(v_Procs,u),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_in(tc_Com_Opname),v_x))**.
% 299.64/300.37 2127[0:SpL:2097.1,418.0] || hBOOL(hAPP(u,v))* equal(u,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))*+ -> .
% 299.64/300.37 2097[0:Res:526.1,279.0] || hBOOL(hAPP(u,v)) -> equal(hAPP(c_Set_Oinsert(v,w),u),u)**.
% 299.64/300.37 279[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(c_Set_Oinsert(v,u),w),w).
% 299.64/300.37 1145[0:SpR:351.0,651.0] || -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.37 16[0:Inp] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)))* -> equal(u,w).
% 299.64/300.37 1430[0:Res:651.0,437.1] || c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),v)* -> c_Finite__Set_Ofinite(hAPP(u,v_x),v).
% 299.64/300.37 1162[0:SpR:525.1,1158.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.37 65[0:Inp] class_Orderings_Olinorder(u) || -> equal(c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),u),v)**.
% 299.64/300.37 1944[0:Res:341.0,1937.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 1943[0:Res:342.0,1937.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 1977[0:SSi:1972.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(v_Procs,u) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 68[0:Inp] class_Orderings_Olinorder(u) || -> equal(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),u),v)**.
% 299.64/300.37 1945[0:Res:376.0,1937.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 1941[0:Res:429.0,1937.1] || equal(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 1937[0:SpL:135.0,1812.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool))* -> .
% 299.64/300.37 1812[0:SSi:1798.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,v_Procs) c_lessequals(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* -> .
% 299.64/300.37 10[0:Inp] || -> equal(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)))**.
% 299.64/300.37 1071[0:Res:448.2,1051.0] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) || -> c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(u,v_x)).
% 299.64/300.37 771[0:SpR:351.0,415.0] || -> equal(c_Fun_Ofun__upd(c_COMBK(u,v,w),x,u,y,z),c_COMBK(u,v,w))**.
% 299.64/300.37 9[0:Inp] || -> equal(hAPP(c_Fun_Ocomp(u,v,w,x,y),z),hAPP(u,hAPP(v,z)))**.
% 299.64/300.37 1857[0:SpL:135.0,1811.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** hBOOL(hAPP(u,v_x)) -> .
% 299.64/300.37 203[0:Inp] || equal(c_Fun_Ofun__upd(u,v,w,x,y),u)** -> equal(hAPP(u,v),w).
% 299.64/300.37 1811[0:SSi:1784.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(v_Procs,u) hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_x))* -> .
% 299.64/300.37 1840[0:EmS:1802.0,573.0] || equal(u,v)* -> equal(v,u).
% 299.64/300.37 419[0:Inp] || c_Hoare__Mirabelle_Ohoare__derivs(u,v,w)*+ c_Hoare__Mirabelle_Ohoare__derivs(x,u,w)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,v,w)*.
% 299.64/300.37 1628[0:Obv:1620.0] class_Lattices_Oboolean__algebra(u) || equal(v,w) -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u))*.
% 299.64/300.37 1605[0:Obv:1599.0] class_OrderedGroup_Ogroup__add(u) || equal(v,w) -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u))*.
% 299.64/300.37 1395[0:Obv:1378.0] class_Lattices_Oboolean__algebra(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u))*+ -> equal(c_HOL_Ouminus__class_Ouminus(v,u),w)*.
% 299.64/300.37 442[0:Inp] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),x),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,x,w).
% 299.64/300.37 1367[0:Obv:1352.0] class_OrderedGroup_Ogroup__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u))*+ -> equal(c_HOL_Ouminus__class_Ouminus(v,u),w)*.
% 299.64/300.37 1586[0:SSi:1583.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_Procs,u,v),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.37 989[0:SpR:351.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v,w,x),tc_Com_Opname,u),u)*.
% 299.64/300.37 1561[0:Rew:1.1,1560.1] class_OrderedGroup_Oab__group__add(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 141[0:Inp] class_OrderedGroup_Oab__group__add(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,u),u),c_HOL_Ominus__class_Ominus(w,v,u))**.
% 299.64/300.37 1421[0:Obv:1416.0] class_Lattices_Oboolean__algebra(u) || equal(v,c_Orderings_Obot__class_Obot(u)) -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.37 1409[0:Obv:1404.0] class_Lattices_Oboolean__algebra(u) || equal(v,c_Orderings_Otop__class_Otop(u)) -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u))**.
% 299.64/300.37 437[0:Inp] || c_Finite__Set_Ofinite(u,v) c_lessequals(w,u,tc_fun(v,tc_bool))* -> c_Finite__Set_Ofinite(w,v).
% 299.64/300.37 1394[0:Obv:1374.0] class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u))** -> equal(c_Orderings_Otop__class_Otop(u),v).
% 299.64/300.37 1393[0:Obv:1373.0] class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u))** -> equal(c_Orderings_Obot__class_Obot(u),v).
% 299.64/300.37 14[0:Inp] class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u))* -> equal(v,w).
% 299.64/300.37 1343[0:Obv:1342.1] class_OrderedGroup_Ogroup__add(tc_fun(u,tc_bool)) || -> .
% 299.64/300.37 15[0:Inp] class_OrderedGroup_Ogroup__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u))* -> equal(v,w).
% 299.64/300.37 126[0:Inp] class_OrderedGroup_Ogroup__add(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u))** -> equal(v,w).
% 299.64/300.37 1259[0:Obv:1255.0] class_OrderedGroup_Ogroup__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 1301[0:Obv:1300.1] class_OrderedGroup_Oab__group__add(tc_fun(u,tc_bool)) || -> .
% 299.64/300.37 127[0:Inp] class_OrderedGroup_Oab__group__add(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u))** -> equal(v,w).
% 299.64/300.37 1166[0:SpR:414.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v_x,v,w,x),tc_Com_Opname,y),v_Procs),v))*.
% 299.64/300.37 332[0:Inp] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)* -> c_Finite__Set_Ofinite(w,u).
% 299.64/300.37 1273[0:SSi:1266.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u)*+ -> c_Finite__Set_Ofinite(v,u)*.
% 299.64/300.37 333[0:Inp] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)* -> c_Finite__Set_Ofinite(v,u).
% 299.64/300.37 116[0:Inp] class_OrderedGroup_Ogroup__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u))** -> equal(c_HOL_Ozero__class_Ozero(u),v).
% 299.64/300.37 1196[0:Obv:1187.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.37 1195[0:Obv:1186.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Obot__class_Obot(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.37 1177[0:SpR:88.1,309.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.37 1176[0:SpR:88.1,306.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.37 87[0:Inp] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ouminus__class_Ouminus(v,u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.37 88[0:Inp] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),v),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.37 1106[0:SpR:302.1,1103.1] class_Lattices_Obounded__lattice(u) || -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),t_a)* hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.37 499[0:Inp] || -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),u)*.
% 299.64/300.37 1161[0:SpR:524.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.37 1167[0:SpR:351.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBK(u,v,w),tc_Com_Opname,x),v_Procs),u))*.
% 299.64/300.37 1158[0:Res:648.0,527.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),hAPP(u,v_x)))*.
% 299.64/300.37 648[0:Res:589.0,545.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,v_x)),hAPP(c_Set_Oimage(v,tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.37 38[0:Inp] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.64/300.37 651[0:Res:589.0,362.0] || -> c_lessequals(hAPP(u,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.37 105[0:Inp] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.64/300.37 1119[0:Res:376.0,682.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.37 682[0:Res:589.0,436.1] || c_lessequals(hAPP(c_in(tc_Com_Opname),v_x),u,tc_fun(v,tc_bool))* -> hBOOL(hAPP(u,v_Procs)).
% 299.64/300.37 1114[0:Res:1104.1,522.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_G,t_a) c_Hoare__Mirabelle_Otriple__valid(v_na,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_G),t_a)*.
% 299.64/300.37 1104[0:Res:168.0,591.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_G,t_a) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_G),t_a)*.
% 299.64/300.37 321[0:Inp] || -> equal(hAPP(c_Set_Oimage(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.64/300.37 1108[0:SpR:351.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_COMBK(v,w,x),t_a)* hBOOL(v).
% 299.64/300.37 1110[0:Res:1103.1,392.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),t_a)*.
% 299.64/300.37 1103[0:Res:168.0,527.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) hBOOL(hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v)))*.
% 299.64/300.37 168[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v)),v))* c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a).
% 299.64/300.37 653[0:Res:589.0,188.0] || -> equal(hAPP(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),v_Procs),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.37 676[0:Res:589.0,518.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.37 675[0:Res:589.0,517.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),v),v_Procs))*.
% 299.64/300.37 1088[0:MRR:1086.1,290.0] || -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v)*.
% 299.64/300.37 610[0:MRR:609.0,262.0] || -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat)))**.
% 299.64/300.37 1049[0:Res:652.1,656.0] || c_lessequals(v_Procs,c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* -> .
% 299.64/300.37 1051[0:Res:652.1,527.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(u,v_x)).
% 299.64/300.37 1048[0:Res:652.1,657.0] || c_lessequals(v_Procs,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* -> .
% 299.64/300.37 1050[0:Res:652.1,262.0] || c_lessequals(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* -> .
% 299.64/300.37 80[0:Inp] || -> equal(c_HOL_Ominus__class_Ominus(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.64/300.37 652[0:Res:589.0,255.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),u))*.
% 299.64/300.37 1042[0:Res:649.0,527.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),v_x))*.
% 299.64/300.37 649[0:Res:589.0,511.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs)))*.
% 299.64/300.37 1020[0:Res:650.0,527.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u),v_x))*.
% 299.64/300.37 11[0:Inp] || -> equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))**.
% 299.64/300.37 650[0:Res:589.0,510.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u)))*.
% 299.64/300.37 1014[0:Res:1013.1,720.0] || hBOOL(hAPP(v_G,v_n(v_na)))* -> .
% 299.64/300.37 1013[0:Res:1012.1,522.0] || hBOOL(hAPP(v_G,u)) -> c_Hoare__Mirabelle_Otriple__valid(v_na,u,t_a)*.
% 299.64/300.37 1012[0:Res:526.1,591.0] || hBOOL(hAPP(v_G,u)) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),u,t_a)*.
% 299.64/300.37 591[0:Inp] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_G))* -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),u,t_a).
% 299.64/300.37 401[0:Inp] || c_Natural_Oevalc(u,v,w)*+ c_Natural_Oevalc(u,v,x)* -> equal(x,w)*.
% 299.64/300.37 212[0:Inp] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),u),v))*.
% 299.64/300.37 134[0:Inp] class_OrderedGroup_Oordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),v)** -> equal(v,c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.37 227[0:Inp] || c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(u,v),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),t_a)* -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a).
% 299.64/300.37 5[0:Inp] class_Int_Onumber__ring(u) class_Ring__and__Field_Oidom(u) || -> equal(c_HOL_Ominus__class_Ominus(v,v,u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 683[0:Res:589.0,361.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(v,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,u),u)*.
% 299.64/300.37 341[0:Inp] || -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),tc_fun(v,tc_bool))*.
% 299.64/300.37 342[0:Inp] || -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),tc_fun(v,tc_bool))*.
% 299.64/300.37 943[0:SpR:302.1,309.1] class_Lattices_Obounded__lattice(u) class_Lattices_Olattice(u) || -> c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.37 303[0:Inp] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.37 942[0:SpR:302.1,306.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.37 302[0:Inp] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.37 687[0:Res:589.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.37 686[0:Res:589.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,v,u,tc_Com_Opname)))*.
% 299.64/300.37 330[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v)**.
% 299.64/300.37 331[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v),v)**.
% 299.64/300.37 79[0:Inp] || -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))**.
% 299.64/300.37 81[0:Inp] || -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.37 888[0:Res:526.1,656.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_x))* -> .
% 299.64/300.37 656[0:Res:589.0,147.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.37 655[0:Res:589.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.37 654[0:Res:589.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname),v_x,tc_Com_Opname)*.
% 299.64/300.37 288[0:Inp] || c_Natural_Oevaln(u,v,w,x) -> c_Natural_Oevaln(u,v,c_Suc(w),x)*.
% 299.64/300.37 770[0:SpR:456.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Option_Othe(u),c_Option_Ooption_OSome(v,u),v,w,x),c_Option_Othe(u))**.
% 299.64/300.37 318[0:Inp] || c_Finite__Set_Ofinite(u,v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(w,v,x),u),x)*.
% 299.64/300.37 115[0:Inp] || c_Finite__Set_Ofinite(u,v) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),v)*.
% 299.64/300.37 867[0:SpR:301.1,306.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.37 305[0:Inp] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u)*.
% 299.64/300.37 868[0:Obv:865.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,v,u)*.
% 299.64/300.37 306[0:Inp] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v),u)*.
% 299.64/300.37 858[0:SpR:300.1,310.1] class_Lattices_Obounded__lattice(u) class_Lattices_Olattice(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.37 309[0:Inp] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v),u)*.
% 299.64/300.37 310[0:Inp] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u)*.
% 299.64/300.37 132[0:Inp] class_OrderedGroup_Ogroup__add(u) || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ozero__class_Ozero(u),v,u),c_HOL_Ouminus__class_Ouminus(v,u))**.
% 299.64/300.37 839[0:Res:658.0,527.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),v_x))*.
% 299.64/300.37 527[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(w,v)).
% 299.64/300.37 836[0:Res:526.1,657.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_x))* -> .
% 299.64/300.37 526[0:Inp] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),v),u))*.
% 299.64/300.37 301[0:Inp] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(u)),v)**.
% 299.64/300.37 826[0:SSi:825.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(c_Orderings_Obot__class_Obot(tc_bool))* -> .
% 299.64/300.37 300[0:Inp] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v),v)**.
% 299.64/300.37 365[0:Inp] class_Orderings_Obot(u) || -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x),c_Orderings_Obot__class_Obot(u))**.
% 299.64/300.37 768[0:SpR:659.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,tc_Com_Opname),v_Procs,v_Procs,u,v),c_Set_Oinsert(v_x,tc_Com_Opname))**.
% 299.64/300.37 657[0:Res:589.0,150.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.37 820[0:SSi:818.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(c_Orderings_Otop__class_Otop(tc_bool))*.
% 299.64/300.37 397[0:Inp] class_Orderings_Otop(u) || -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.37 816[0:Fac:448.1,448.2] class_Orderings_Olinorder(u) || -> c_lessequals(v,v,u)*.
% 299.64/300.37 448[0:Inp] class_Orderings_Olinorder(u) || -> c_lessequals(v,w,u)* c_lessequals(w,v,u)*.
% 299.64/300.37 106[0:Inp] || equal(c_Com_Ocom_OSemi(u,v),c_Com_Ocom_OSemi(w,x))* -> equal(u,w).
% 299.64/300.37 107[0:Inp] || equal(c_Com_Ocom_OSemi(u,v),c_Com_Ocom_OSemi(w,x))* -> equal(v,x).
% 299.64/300.37 22[0:Inp] || -> equal(c_Finite__Set_Ofold(u,v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),w,x),v)**.
% 299.64/300.37 382[0:Inp] || equal(c_Option_Ooption_OSome(u,v),c_Option_Ooption_OSome(w,v))* -> equal(u,w).
% 299.64/300.37 377[0:Inp] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v)* -> c_Finite__Set_Ofinite(w,v).
% 299.64/300.37 378[0:Inp] || c_Finite__Set_Ofinite(u,v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(w,v),u),v)*.
% 299.64/300.37 267[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(v,u),w)))*.
% 299.64/300.37 124[0:Inp] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),u,tc_fun(w,tc_bool))*.
% 299.64/300.37 525[0:Inp] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v),v)**.
% 299.64/300.37 418[0:Inp] || equal(hAPP(c_Set_Oinsert(u,v),w),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> .
% 299.64/300.37 541[0:Inp] || equal(hAPP(c_Com_Ocom_OBODY,u),hAPP(c_Com_Ocom_OBODY,v))* -> equal(u,v).
% 299.64/300.37 135[0:Inp] || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),u)**.
% 299.64/300.37 7[0:Inp] || -> equal(c_HOL_Ominus__class_Ominus(u,u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.64/300.37 6[0:Inp] || -> equal(c_HOL_Ominus__class_Ominus(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),u)**.
% 299.64/300.37 710[0:Res:589.0,666.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(u,tc_bool)),v_Procs))*.
% 299.64/300.37 658[0:Res:589.0,254.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs)))*.
% 299.64/300.37 262[0:Inp] || hBOOL(hAPP(hAPP(c_in(u),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.37 414[0:Inp] || -> equal(hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v),w)**.
% 299.64/300.37 250[0:Inp] || c_Natural_Oevaln(u,v,w,x)* -> c_Natural_Oevalc(u,v,x).
% 299.64/300.37 415[0:Inp] || -> equal(c_Fun_Ofun__upd(u,v,hAPP(u,v),w,x),u)**.
% 299.64/300.37 522[0:Inp] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v,w)* -> c_Hoare__Mirabelle_Otriple__valid(u,v,w).
% 299.64/300.37 376[0:Inp] || -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),u),tc_fun(w,tc_bool))*.
% 299.64/300.37 137[0:Inp] class_Lattices_Oboolean__algebra(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v)**.
% 299.64/300.37 140[0:Inp] class_OrderedGroup_Ogroup__add(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v)**.
% 299.64/300.37 4[0:Inp] class_OrderedGroup_Ogroup__add(u) || -> equal(c_HOL_Ominus__class_Ominus(v,v,u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 1[0:Inp] class_OrderedGroup_Oab__group__add(u) || -> equal(c_HOL_Ominus__class_Ominus(v,v,u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 3[0:Inp] class_OrderedGroup_Ogroup__add(u) || -> equal(c_HOL_Ominus__class_Ominus(v,c_HOL_Ozero__class_Ozero(u),u),v)**.
% 299.64/300.37 28[0:Inp] c_Com_OWT(u) c_Com_OWT(v) || -> c_Com_OWT(c_Com_Ocom_OSemi(u,v))*.
% 299.64/300.37 553[0:Inp] class_Finite__Set_Ofinite_Ofinite(u) class_Finite__Set_Ofinite_Ofinite(v) || -> class_Finite__Set_Ofinite_Ofinite(tc_fun(u,v))*.
% 299.64/300.37 524[0:Inp] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v),v)**.
% 299.64/300.37 27[0:Inp] class_OrderedGroup_Ogroup__add(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 26[0:Inp] class_OrderedGroup_Oordered__ab__group__add(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 73[0:Inp] class_Lattices_Oboolean__algebra(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),c_Orderings_Obot__class_Obot(u))**.
% 299.64/300.37 74[0:Inp] class_Lattices_Oboolean__algebra(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.37 264[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.37 451[0:Inp] || -> c_Com_OWT(hAPP(c_Com_Ocom_OBODY,u))* equal(hAPP(c_Com_Obody,u),c_Option_Ooption_ONone(tc_Com_Ocom)).
% 299.64/300.37 678[0:Res:589.0,526.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_in(tc_Com_Opname),v_x)))*.
% 299.64/300.37 133[0:Inp] || c_Natural_Oevaln(c_Com_Ocom_OSKIP,u,v,w)* -> equal(w,u).
% 299.64/300.37 521[0:Inp] || equal(c_Suc(u),c_Suc(v))* -> equal(u,v).
% 299.64/300.37 59[0:Inp] || -> c_Finite__Set_Ofinite(u,v) equal(c_Finite__Set_Ocard(u,v),c_HOL_Ozero__class_Ozero(tc_nat))**.
% 299.64/300.37 420[0:Inp] || -> c_lessequals(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.37 366[0:Inp] || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))*.
% 299.64/300.37 60[0:Inp] || -> equal(c_Finite__Set_Ocard(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),u),c_HOL_Ozero__class_Ozero(tc_nat))**.
% 299.64/300.37 351[0:Inp] || -> equal(hAPP(c_COMBK(u,v,w),x),u)**.
% 299.64/300.37 588[0:Inp] || c_fequal(u,v,w)* -> equal(u,v).
% 299.64/300.37 423[0:Inp] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),u))*.
% 299.64/300.37 219[0:Inp] || -> c_Fun_Oinj__on(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v,w)*.
% 299.64/300.37 142[0:Inp] || c_Natural_Oevalc(c_Com_Ocom_OSKIP,u,v)* -> equal(v,u).
% 299.64/300.37 421[0:Inp] class_Orderings_Otop(u) || -> c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.37 367[0:Inp] class_Orderings_Obot(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.37 456[0:Inp] || -> equal(hAPP(c_Option_Othe(u),c_Option_Ooption_OSome(v,u)),v)**.
% 299.64/300.37 166[0:Inp] || equal(c_Com_Ocom_OSemi(u,v),hAPP(c_Com_Ocom_OBODY,w))* -> .
% 299.64/300.37 391[0:Inp] || -> c_Hoare__Mirabelle_Ohoare__derivs(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),v)*.
% 299.64/300.37 433[0:Inp] class_Orderings_Oorder(u) || -> c_lessequals(v,v,u)*.
% 299.64/300.37 434[0:Inp] class_Orderings_Opreorder(u) || -> c_lessequals(v,v,u)*.
% 299.64/300.37 19[0:Inp] || c_Com_OWT(c_Com_Ocom_OSemi(u,v))* -> c_Com_OWT(v).
% 299.64/300.37 20[0:Inp] || c_Com_OWT(c_Com_Ocom_OSemi(u,v))* -> c_Com_OWT(u).
% 299.64/300.37 381[0:Inp] || equal(c_Option_Ooption_OSome(u,v),c_Option_Ooption_ONone(v))** -> .
% 299.64/300.37 550[0:Inp] class_Lattices_Olattice(u) || -> class_Lattices_Oupper__semilattice(tc_fun(v,u))*.
% 299.64/300.37 555[0:Inp] class_Lattices_Olattice(u) || -> class_Lattices_Olattice(tc_fun(v,u))*.
% 299.64/300.37 549[0:Inp] class_Complete__Lattice_Ocomplete__lattice(u) || -> class_Complete__Lattice_Ocomplete__lattice(tc_fun(v,u))*.
% 299.64/300.37 551[0:Inp] class_Lattices_Obounded__lattice(u) || -> class_Lattices_Obounded__lattice(tc_fun(v,u))*.
% 299.64/300.37 552[0:Inp] class_Lattices_Oboolean__algebra(u) || -> class_Lattices_Oboolean__algebra(tc_fun(v,u))*.
% 299.64/300.37 556[0:Inp] class_Orderings_Oorder(u) || -> class_Orderings_Oorder(tc_fun(v,u))*.
% 299.64/300.37 554[0:Inp] class_Orderings_Opreorder(u) || -> class_Orderings_Opreorder(tc_fun(v,u))*.
% 299.64/300.37 558[0:Inp] class_Orderings_Obot(u) || -> class_Orderings_Obot(tc_fun(v,u))*.
% 299.64/300.37 557[0:Inp] class_Orderings_Otop(u) || -> class_Orderings_Otop(tc_fun(v,u))*.
% 299.64/300.37 560[0:Inp] class_HOL_Ominus(u) || -> class_HOL_Ominus(tc_fun(v,u))*.
% 299.64/300.37 561[0:Inp] class_HOL_Oord(u) || -> class_HOL_Oord(tc_fun(v,u))*.
% 299.64/300.37 559[0:Inp] class_HOL_Ouminus(u) || -> class_HOL_Ouminus(tc_fun(v,u))*.
% 299.64/300.37 659[0:Res:589.0,279.0] || -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.37 589[0:Inp] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v_Procs))*.
% 299.64/300.37 204[0:Inp] class_Finite__Set_Ofinite_Ofinite(u) || -> c_Finite__Set_Ofinite(v,u)*.
% 299.64/300.37 429[0:Inp] || -> c_lessequals(u,u,tc_fun(v,tc_bool))*.
% 299.64/300.37 39[0:Inp] || equal(c_Com_Ocom_OSemi(u,v),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.37 583[0:Inp] class_Finite__Set_Ofinite_Ofinite(u) || -> class_Finite__Set_Ofinite_Ofinite(tc_Option_Ooption(u))*.
% 299.64/300.37 379[0:Inp] || -> c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),u)*.
% 299.64/300.37 290[0:Inp] || equal(c_Suc(u),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.37 167[0:Inp] || equal(hAPP(c_Com_Ocom_OBODY,u),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.37 720[0:MRR:717.0,589.0] || c_Hoare__Mirabelle_Otriple__valid(v_na,v_n(v_na),t_a)* -> .
% 299.64/300.37 29[0:Inp] || -> c_Finite__Set_Ofinite(c_List_Oset(u,v),v)*.
% 299.64/300.37 18[0:Inp] || -> c_Natural_Oevaln(c_Com_Ocom_OSKIP,u,v,u)*.
% 299.64/300.37 509[0:Inp] || equal(c_Suc(u),u)** -> .
% 299.64/300.37 587[0:Inp] || -> c_fequal(u,u,v)*.
% 299.64/300.37 17[0:Inp] || -> c_Natural_Oevalc(c_Com_Ocom_OSKIP,u,u)*.
% 299.64/300.37 660[0:Res:589.0,527.0] || -> hBOOL(hAPP(v_Procs,v_x))*.
% 299.64/300.37 562[0:Inp] || -> class_Lattices_Oupper__semilattice(tc_nat)*.
% 299.64/300.37 571[0:Inp] || -> class_Lattices_Oupper__semilattice(tc_bool)*.
% 299.64/300.37 565[0:Inp] || -> class_Lattices_Olattice(tc_nat)*.
% 299.64/300.37 576[0:Inp] || -> class_Lattices_Olattice(tc_bool)*.
% 299.64/300.37 564[0:Inp] || -> class_Orderings_Olinorder(tc_nat)*.
% 299.64/300.37 122[0:Inp] || -> c_Com_OWT(c_Com_Ocom_OSKIP)*.
% 299.64/300.37 570[0:Inp] || -> class_Complete__Lattice_Ocomplete__lattice(tc_bool)*.
% 299.64/300.37 572[0:Inp] || -> class_Lattices_Obounded__lattice(tc_bool)*.
% 299.64/300.37 573[0:Inp] || -> class_Lattices_Oboolean__algebra(tc_bool)*.
% 299.64/300.37 566[0:Inp] || -> class_Orderings_Oorder(tc_nat)*.
% 299.64/300.37 574[0:Inp] || -> class_Finite__Set_Ofinite_Ofinite(tc_bool)*.
% 299.64/300.37 577[0:Inp] || -> class_Orderings_Oorder(tc_bool)*.
% 299.64/300.37 563[0:Inp] || -> class_Orderings_Opreorder(tc_nat)*.
% 299.64/300.37 567[0:Inp] || -> class_Orderings_Obot(tc_nat)*.
% 299.64/300.37 575[0:Inp] || -> class_Orderings_Opreorder(tc_bool)*.
% 299.64/300.37 579[0:Inp] || -> class_Orderings_Obot(tc_bool)*.
% 299.64/300.37 568[0:Inp] || -> class_HOL_Ominus(tc_nat)*.
% 299.64/300.37 569[0:Inp] || -> class_HOL_Oord(tc_nat)*.
% 299.64/300.37 578[0:Inp] || -> class_Orderings_Otop(tc_bool)*.
% 299.64/300.37 581[0:Inp] || -> class_HOL_Ominus(tc_bool)*.
% 299.64/300.37 582[0:Inp] || -> class_HOL_Oord(tc_bool)*.
% 299.64/300.37 580[0:Inp] || -> class_HOL_Ouminus(tc_bool)*.
% 299.64/300.37 722[1:Spt:595.0,595.2] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs)) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(v_Q,u)),t_a)*.93895[7:SpL:10.0,87829.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(u,tc_bool))))* -> .
% 299.64/300.37 94115[7:SpL:2267.1,94102.0] || equal(u,v_x) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x)** -> .
% 299.64/300.37 94125[7:SpL:2267.1,94103.0] || equal(u,v_x) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_Procs)** -> .
% 299.64/300.37 71723[7:SpL:71455.1,36406.0] || equal(u,v_x) c_lessequals(hAPP(u,v_x),v,tc_bool)* -> hBOOL(v).
% 299.64/300.37 72667[7:Res:10712.0,71881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(hAPP(v_x,v_x),w)))*.
% 299.64/300.37 72668[7:Res:10713.0,71881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(hAPP(v_x,v_x),w,x)),y))*.
% 299.64/300.37 77174[7:SpL:351.0,74788.1] || equal(c_COMBK(u,v,w),v_x)** equal(u,x)* -> hBOOL(x)*.
% 299.64/300.37 77933[7:Res:71878.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x),hAPP(v_x,v_x)))*.
% 299.64/300.37 78165[7:Res:77996.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(v_x,u),u)*.
% 299.64/300.37 78166[7:Res:77996.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_x,u),v_x,u)*.
% 299.64/300.37 78183[7:Res:77996.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,v_x,u,w)))*.
% 299.64/300.37 78184[7:Res:77996.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,v,u,w)))*.
% 299.64/300.37 78294[7:SpR:78167.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_x,v),tc_Com_Opname,u),u)*.
% 299.64/300.37 78671[4:SSi:78641.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(v_x,u)* hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool))* -> .
% 299.64/300.37 78691[4:Res:78665.1,527.0] || equal(hAPP(hAPP(c_in(u),v),w),v_x)** -> hBOOL(hAPP(w,v)).
% 299.64/300.37 78776[4:Res:78665.1,70856.2] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x)** equal(v,u)* hBOOL(v)* -> .
% 299.64/300.37 82176[7:SpR:78597.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,t_a,v),c_Set_Oinsert(v_x,w)),hAPP(u,v_x)))*.
% 299.64/300.37 82197[7:SpL:78597.0,44750.0] || c_lessequals(c_Set_Oinsert(v_x,u),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(v,v_x)).
% 299.64/300.37 84188[7:SpL:351.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) equal(c_COMBK(u,v,w),v_x)** -> .
% 299.64/300.37 85626[4:SpR:3229.1,85425.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(v,hAPP(hAPP(u,v_x),v),tc_bool)*.
% 299.64/300.37 86399[0:SpL:86109.1,36406.0] || equal(u,v_Procs) c_lessequals(hAPP(u,v_x),v,tc_bool)* -> hBOOL(v).
% 299.64/300.37 86733[4:SpL:351.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) equal(c_COMBK(u,v,w),v_Procs)** -> .
% 299.64/300.37 88102[7:SpL:3229.1,88100.0] || equal(v_x,u) equal(c_HOL_Ominus__class_Ominus(v,hAPP(u,v_x),tc_bool),v_x)** -> .
% 299.64/300.37 88251[7:SpR:3229.1,88170.0] || equal(v_x,u) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,hAPP(u,v_x),tc_bool),tc_bool))*.
% 299.64/300.37 88287[7:SSi:88267.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(v_x,v_x),tc_bool),v)* -> hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool))*.
% 299.64/300.37 88640[7:SpL:351.0,88086.1] || equal(c_COMBK(u,v,w),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(x,u,tc_bool))* -> .
% 299.64/300.37 92170[7:SpR:3229.1,92050.0] || equal(c_in(u),v)* -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(v,v_x),tc_Com_Opname,tc_bool))*.
% 299.64/300.37 94095[7:SpL:2267.1,93922.0] || equal(u,v_x) hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x))* -> .
% 299.64/300.37 94099[7:SpL:3229.1,93922.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(u,tc_bool)),v)* hBOOL(hAPP(v,v_x))* -> .
% 299.64/300.37 70592[7:SpL:3744.1,70491.0] || equal(c_in(tc_Com_Opname),c_in(t_a)) equal(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 70621[0:SpL:3744.1,70492.0] || equal(c_in(tc_Com_Opname),c_in(t_a)) equal(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 70738[0:Res:36017.0,70400.1] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),v_x))* -> .
% 299.64/300.37 70846[4:MRR:62486.3,70845.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool))* equal(v,u)* c_lessequals(v_x,v,tc_bool)* -> .
% 299.64/300.37 70847[4:MRR:62506.2,70845.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),v_x),u)* -> .
% 299.64/300.37 70848[4:MRR:62507.2,70845.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v),u)* -> .
% 299.64/300.37 71396[7:SpL:414.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)) equal(c_Fun_Ofun__upd(v,v_x,u,w,x),v_x)** -> .
% 299.64/300.37 71680[7:SpR:71455.1,36687.0] || equal(u,v_x) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(v,t_a),u),tc_Com_Opname,tc_bool))*.
% 299.64/300.37 72391[7:MRR:70428.0,72294.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname),v_x),tc_bool))* -> .
% 299.64/300.37 72392[7:MRR:70427.0,72294.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,hAPP(c_in(t_a),v_x),tc_Com_Opname),v_x),tc_bool))* -> .
% 299.64/300.37 72559[7:SSi:72548.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(v_x,v_x))))*.
% 299.64/300.37 72606[7:SSi:72578.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v_x,v_x)),v)))*.
% 299.64/300.37 72679[7:SSi:72637.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(v_x,v_x),u,tc_bool) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u))*.
% 299.64/300.37 72680[7:SSi:72640.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(v_x,v_x),u,tc_bool) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v))*.
% 299.64/300.37 72681[7:SSi:72659.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v))* -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_bool)).
% 299.64/300.37 72732[7:Res:71860.1,6935.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_in(u),c_Set_Oinsert(v,w))* -> .
% 299.64/300.37 72818[0:MRR:72738.3,868.1] class_OrderedGroup_Oab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || -> equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 73310[7:SpR:71835.1,2093.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),v_x),v_x)**.
% 299.64/300.37 73514[7:SpR:71835.1,524.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.37 73584[7:SpR:71835.1,414.0] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Set_Oinsert(v_x,t_a))** -> equal(v_x,v).
% 299.64/300.37 73794[7:SpR:71835.1,9924.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Set_Oinsert(v_x,t_a))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.37 74410[7:MRR:74021.2,6340.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,t_a))** equal(v_Procs,u) -> .
% 299.64/300.37 74411[7:MRR:74022.1,6340.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> .
% 299.64/300.37 74414[7:MRR:73696.1,52007.0] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> .
% 299.64/300.37 74424[7:Obv:74094.2] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> .
% 299.64/300.37 74855[7:SpR:414.0,72297.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_in(t_a))** -> hBOOL(hAPP(v,v_x)).
% 299.64/300.37 74881[7:SpR:9924.0,72297.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x)).
% 299.64/300.37 74941[7:Res:72297.1,33.0] || equal(c_Set_Ovimage(u,v,w),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(u,v_x)))*.
% 299.64/300.37 75157[7:Res:23729.0,71908.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_fun(u,tc_bool)),v_x))*.
% 299.64/300.37 77223[4:SpR:801.1,38616.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x)),v_x))*.
% 299.64/300.37 77500[7:Res:27219.1,72390.0] || equal(c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 77501[7:Res:15482.1,72390.0] || equal(c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 77628[7:SpR:71835.1,77503.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(t_a)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,v_x,tc_Com_Opname),v_x))*.
% 299.64/300.37 77630[7:SpR:3229.1,77503.0] || equal(c_in(t_a),u) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(u,v_x),tc_Com_Opname),v_x))*.
% 299.64/300.37 77634[7:SpR:3229.1,77503.0] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname),u)* -> hBOOL(hAPP(u,v_x))*.
% 299.64/300.37 77877[0:SpL:23912.0,5892.0] || hBOOL(u) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,x,y),u))*.
% 299.64/300.37 77995[0:Rew:538.0,77940.0,584.0,77940.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_x),v_Procs)))*.
% 299.64/300.37 78002[7:MRR:45444.0,77996.0] || equal(c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(tc_Com_Opname),v_x),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 78005[7:Rew:584.0,77953.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)))*.
% 299.64/300.37 78007[4:Rew:584.0,77973.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(u,v_x)))*.
% 299.64/300.37 78164[7:Res:77996.0,255.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),v_x),u))*.
% 299.64/300.37 78177[7:Res:77996.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,v_x)),v_x))* c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.37 78246[7:SpR:78167.0,651.0] || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_x,u),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.37 78252[7:SpR:78167.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_x,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.37 78256[7:SpR:78167.0,3284.1] || equal(c_Set_Oinsert(v_x,u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),v_x))*.
% 299.64/300.37 78267[7:SpR:78167.0,10090.1] || equal(c_Set_Oinsert(v_x,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 78268[7:SpR:78167.0,11030.1] || equal(c_Set_Oinsert(v_x,u),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.37 78270[7:SpR:78167.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.37 78271[7:SpR:78167.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,u),v_x,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.37 78273[7:SpR:78167.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,u),v_x,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.37 78274[7:SpR:78167.0,21267.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,u),v_x,tc_Com_Opname,v)),v_x)**.
% 299.64/300.37 78277[7:SpR:78167.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,u),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.37 78279[7:SpR:78167.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,u),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.37 78280[7:SpR:78167.0,21893.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,u),tc_Com_Opname,v)),v_x)**.
% 299.64/300.37 78295[7:SpR:78167.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,v),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.37 78298[7:SpR:78167.0,3316.1] || equal(c_in(u),c_Set_Oinsert(v_x,v))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.37 78299[7:SpR:78167.0,3339.1] || equal(u,c_Set_Oinsert(v_x,v))* -> equal(c_Fun_Ofun__upd(u,v_x,v_x,w,x),u)**.
% 299.64/300.37 78349[7:SpR:78167.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x))*.
% 299.64/300.37 78411[7:SpL:78167.0,3698.2] || equal(u,c_Set_Oinsert(v_x,v))* equal(c_Com_Ocom_OBODY,u) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 78497[4:SpR:3229.1,77988.0] || equal(c_in(u),v)* -> hBOOL(hAPP(hAPP(v,v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))*.
% 299.64/300.37 78541[4:MRR:15783.2,78524.0] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 78557[7:MRR:27830.2,78524.0] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 78587[7:MRR:65949.2,78524.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 78588[4:MRR:65950.2,78524.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 78591[7:MRR:73353.1,78524.0] || equal(c_HOL_Ominus__class_Ominus(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> .
% 299.64/300.37 78658[7:Res:27219.1,78632.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** equal(hAPP(u,v_x),v_x) -> .
% 299.64/300.37 78659[4:Res:15482.1,78632.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** equal(hAPP(u,v_x),v_x) -> .
% 299.64/300.37 78661[4:Res:35795.0,78632.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(t_a,tc_bool)),v_x),v_x)** -> .
% 299.64/300.37 78667[7:MRR:71795.1,78665.1] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(v_x,t_a),u),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oinsert(v_x,t_a),u,t_a)*.
% 299.64/300.37 78676[4:Res:78665.1,656.0] || equal(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool))),v_x)** -> .
% 299.64/300.37 78729[4:Res:78665.1,1811.1] || equal(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_x),v_x)** equal(v_Procs,u) -> .
% 299.64/300.37 78730[4:Res:78665.1,37607.0] || equal(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_x),v_x)** -> .
% 299.64/300.37 78733[4:Res:78665.1,3929.0] || equal(hAPP(u,v_x),v_x)** equal(u,v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.37 78770[4:Res:78665.1,70405.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(v_Procs,v_x),tc_bool),v_x)** equal(c_in(tc_Com_Opname),c_in(t_a)) -> .
% 299.64/300.37 78772[7:Res:78665.1,72390.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname),v_x),tc_bool),v_x)** -> .
% 299.64/300.37 78778[4:Res:78665.1,47829.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w))*.
% 299.64/300.37 78779[4:Res:78665.1,47109.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u))*.
% 299.64/300.37 78782[4:Res:78665.1,38142.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),v_x)** c_lessequals(u,w,tc_bool)* -> hBOOL(w).
% 299.64/300.37 78898[4:SpL:3229.1,78728.0] || equal(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),u)* equal(hAPP(u,v_x),v_x)** -> .
% 299.64/300.37 78908[7:SpL:2267.1,78595.0] || equal(u,c_Set_Oinsert(v_x,v))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 78918[7:SpL:2267.1,78596.0] || equal(u,c_Set_Oinsert(v_x,v))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 79089[7:SpR:3229.1,78199.0] || equal(c_in(u),v)* -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(v,v_x)))*.
% 299.64/300.37 79091[7:SpR:3229.1,78199.0] || equal(c_in(u),v)* -> hBOOL(hAPP(hAPP(v,v_x),hAPP(c_in(w),v_x)))*.
% 299.64/300.37 79118[7:SpL:3229.1,79106.0] || equal(c_in(u),v)* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(v,v_x),v_x),tc_bool))* -> .
% 299.64/300.37 79120[7:SpL:3229.1,79106.0] || equal(hAPP(c_in(u),v_x),v)* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))* -> .
% 299.64/300.37 79140[7:SSi:79125.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_in(u),v_x),v_x),v)* hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool))* -> .
% 299.64/300.37 79281[7:SpL:3229.1,79139.0] || equal(c_in(u),v)* equal(hAPP(hAPP(v,v_x),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.37 79283[7:SpL:3229.1,79139.0] || equal(hAPP(c_in(u),v_x),v)* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.37 79329[4:SSi:79294.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool))*.
% 299.64/300.37 79340[7:SpL:3229.1,79105.0] || equal(c_in(u),v)* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.37 82222[7:SpL:78597.0,21018.0] || equal(hAPP(c_Set_Oimage(u,t_a,v),c_Set_Oinsert(v_x,w)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> .
% 299.64/300.37 82594[7:SpR:3229.1,82186.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,w)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.37 83216[7:SpR:524.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v,w),v_x),v_x))*.
% 299.64/300.37 83227[7:SpR:414.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v_x,v,w,x),y,z),v_x),v))*.
% 299.64/300.37 83253[7:SpR:9924.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,v),v_x),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 83295[7:Rew:584.0,83294.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,v),w,x),v_x)))*.
% 299.64/300.37 84947[7:Res:83237.0,3499.1] || equal(c_Set_Oimage(c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w),x,y),c_in(u))** -> .
% 299.64/300.37 84964[0:SpR:8498.1,84957.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(w),u),u))*.
% 299.64/300.37 85148[0:SpL:8498.1,85001.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* equal(u,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.37 85324[7:SpL:78167.0,26240.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.37 85433[4:SpR:78507.0,35192.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs))*.
% 299.64/300.37 85434[4:SpR:78507.0,42583.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(v,tc_bool)),w))*.
% 299.64/300.37 85435[4:SpR:78507.0,43177.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(v,tc_bool)),w,t_a)*.
% 299.64/300.37 85478[4:SpR:78507.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(u,v_x)))*.
% 299.64/300.37 85479[4:SpR:78507.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(v,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))))*.
% 299.64/300.37 85622[4:SSi:85601.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v_x,tc_bool) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v),tc_bool)*.
% 299.64/300.37 85623[4:SSi:85602.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),v,tc_bool)* -> c_lessequals(v_x,v,tc_bool).
% 299.64/300.37 85720[4:SSi:85676.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v),tc_bool)*.
% 299.64/300.37 85721[4:SSi:85677.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),v,tc_bool)* -> c_lessequals(u,v,tc_bool).
% 299.64/300.37 86044[0:SpL:414.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)) equal(c_Fun_Ofun__upd(v,v_x,u,w,x),v_Procs)** -> .
% 299.64/300.37 86343[0:SpR:86109.1,36687.0] || equal(u,v_Procs) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(v,t_a),u),tc_Com_Opname,tc_bool))*.
% 299.64/300.37 86529[0:Obv:86153.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,v),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.37 86591[0:Res:19823.1,1811.1] || hBOOL(hAPP(u,v_x)) equal(c_HOL_Ominus__class_Ominus(v,u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 87246[7:Res:78665.1,87157.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v)),v_x),tc_bool),v_x)** -> .
% 299.64/300.37 87247[7:Res:27219.1,87157.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v)),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 87248[7:Res:15482.1,87157.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v)),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 87309[7:SpR:351.0,71492.1] || equal(c_COMBK(u,v,w),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x))*.
% 299.64/300.37 87457[7:SpR:351.0,71493.1] || equal(c_COMBK(u,v,w),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x,t_a)*.
% 299.64/300.37 87587[7:SpR:351.0,71679.1] || equal(c_COMBK(u,v,w),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u))*.
% 299.64/300.37 87882[7:Res:87822.0,70856.2] || equal(u,hAPP(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(t_a,tc_bool)),v_x))* hBOOL(u)* -> .
% 299.64/300.37 88335[7:SpL:3229.1,88286.0] || equal(v_x,u) equal(c_HOL_Ominus__class_Ominus(v,hAPP(u,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.37 88659[7:SpL:23682.0,88086.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(u,v_x,tc_bool))* -> .
% 299.64/300.37 88764[7:Res:78665.1,88660.1] || equal(c_HOL_Ominus__class_Ominus(u,v_x,tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x)** -> .
% 299.64/300.37 89059[0:Res:78099.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_in(v),w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))*.
% 299.64/300.37 89430[7:SpR:78590.1,36588.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x))*.
% 299.64/300.37 89851[4:SpR:26183.0,37987.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(c_Set_Oinsert(v,u),v_x))*.
% 299.64/300.37 90220[4:SpR:78660.1,36588.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x))*.
% 299.64/300.37 90279[4:SpL:78660.1,78769.0] || equal(hAPP(u,v_x),v_x) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v_x)** -> .
% 299.64/300.37 90585[4:Rew:9.0,90516.0] || equal(hAPP(u,hAPP(v,v_x)),v_x) -> hBOOL(hAPP(u,hAPP(v,v_x)))*.
% 299.64/300.37 90587[4:Rew:585.0,90517.0] || equal(hAPP(hAPP(u,v_x),v),v_x) -> hBOOL(hAPP(hAPP(u,v_x),v))*.
% 299.64/300.37 91007[4:Rew:397.1,90906.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(u),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool))* -> .
% 299.64/300.37 91008[4:Rew:365.1,90907.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool))* -> .
% 299.64/300.37 91010[4:Rew:302.1,90926.1] class_Lattices_Obounded__lattice(u) || equal(c_Orderings_Otop__class_Otop(u),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool))* -> .
% 299.64/300.37 91016[4:Rew:88.1,90943.1] class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Otop__class_Otop(u),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool))* -> .
% 299.64/300.37 91288[0:MRR:91287.1,379.0] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,v,u),c_Orderings_Obot__class_Obot(u))**.
% 299.64/300.37 91927[4:SpR:79073.0,42357.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(w,tc_bool)),v_x))*.
% 299.64/300.37 91957[0:SpR:79073.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(u,v_Procs)))*.
% 299.64/300.37 91958[0:SpR:79073.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oinsert(v,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.37 91966[0:SpR:79073.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_Procs))*.
% 299.64/300.37 91973[0:SpR:79073.0,21035.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_Procs))*.
% 299.64/300.37 91989[0:SpL:79073.0,35720.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(v,v_Procs)).
% 299.64/300.37 92049[7:SpR:79101.0,36608.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(hAPP(c_in(u),v_x),v_x),v,w),tc_Com_Opname,tc_bool))*.
% 299.64/300.37 92063[7:SpR:79101.0,35192.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_in(u),v_x),c_in(tc_Com_Opname),v,tc_fun(w,tc_bool)),v_Procs))*.
% 299.64/300.37 92064[7:SpR:79101.0,42583.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_in(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(w,tc_bool)),x))*.
% 299.64/300.37 92065[7:SpR:79101.0,43177.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_in(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(w,tc_bool)),x,t_a)*.
% 299.64/300.37 92107[7:SpR:79101.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_in(x),v_x)),hAPP(u,v_x)))*.
% 299.64/300.37 92108[7:SpR:79101.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(v,u),hAPP(c_in(w),v_x))))*.
% 299.64/300.37 92118[7:SpR:79101.0,36599.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_in(v),v_x)),w),v_x))*.
% 299.64/300.37 92120[7:SpR:79101.0,36600.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_in(w),v_x)),v_x))*.
% 299.64/300.37 92136[7:SpL:79101.0,44750.0] || c_lessequals(hAPP(c_in(u),v_x),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(v,v_x)).
% 299.64/300.37 92482[7:Res:448.2,92132.0] class_Orderings_Olinorder(tc_bool) || -> c_lessequals(u,hAPP(hAPP(c_in(v),v_x),v_x),tc_bool)* hBOOL(u).
% 299.64/300.37 92546[7:SSi:92489.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(hAPP(hAPP(c_in(u),v_x),v_x),v)* -> hBOOL(v)*.
% 299.64/300.37 92633[7:SpR:351.0,82151.1] || equal(c_COMBK(u,v,w),c_in(t_a))** -> hBOOL(hAPP(u,c_Set_Oinsert(v_x,x)))*.
% 299.64/300.37 92653[7:SpR:23912.0,82151.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(t_a)) -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,u)))*.
% 299.64/300.37 93293[4:SpR:351.0,85556.1] || equal(c_COMBK(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(u,x),tc_bool)*.
% 299.64/300.37 93313[4:SpR:23912.0,85556.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(v_x,u),tc_bool)*.
% 299.64/300.37 93346[4:SpR:87.1,85556.1] class_Lattices_Oboolean__algebra(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.37 93380[4:SpR:303.1,85556.1] class_Lattices_Obounded__lattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.37 93481[0:SpR:351.0,86147.1] || equal(c_COMBK(u,v,w),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x))*.
% 299.64/300.37 93632[0:SpR:351.0,86148.1] || equal(c_COMBK(u,v,w),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x,t_a)*.
% 299.64/300.37 93776[0:SpR:351.0,86342.1] || equal(c_COMBK(u,v,w),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u))*.
% 299.64/300.37 93914[7:Res:78665.1,87829.0] || equal(hAPP(hAPP(c_in(u),v_x),c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool))),v_x)** -> .
% 299.64/300.37 93927[7:SpL:3229.1,93904.0] || equal(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),w)* hBOOL(hAPP(w,v_x))* -> .
% 299.64/300.37 94219[7:SpL:2267.1,94101.0] || equal(u,v_x) equal(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x),v_x)** -> .
% 299.64/300.37 94223[7:SpL:3229.1,94101.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(u,tc_bool)),v)* equal(hAPP(v,v_x),v_x)** -> .
% 299.64/300.37 94244[7:SpL:2267.1,94233.0] || equal(u,v_x) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> .
% 299.64/300.37 65947[0:SpR:65404.1,1158.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.37 65953[0:SpR:65404.1,3229.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)* -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.37 65964[4:SpR:65404.1,37987.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.37 65971[0:SpR:65404.1,28335.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_x,tc_Com_Opname,v)))*.
% 299.64/300.37 65977[0:SpR:65404.1,28032.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v)))*.
% 299.64/300.37 65988[4:SpR:65404.1,38042.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.37 66170[0:SpR:3229.1,65404.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v)* -> equal(hAPP(hAPP(v,v_x),v_x),v_x)**.
% 299.64/300.37 66186[0:SpL:65404.1,58055.0] class_Lattices_Olattice(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> .
% 299.64/300.37 66290[0:Rew:65404.1,66289.1] class_Lattices_Olattice(u) || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),v_x)**.
% 299.64/300.37 66294[0:Rew:65404.1,66293.1] class_Lattices_Olattice(u) || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x)**.
% 299.64/300.37 68449[0:Obv:68387.3] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Ogroup__add(u) class_Lattices_Obounded__lattice(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u))** -> .
% 299.64/300.37 70392[0:Res:1157.0,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(c_COMBK(v_x,u,v),tc_Com_Opname,t_a),v_Procs),v_x),tc_bool))* -> .
% 299.64/300.37 70398[0:Res:9071.0,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,tc_fun(t_a,tc_bool)),v_x),tc_bool))* -> .
% 299.64/300.37 70403[0:Res:9067.0,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),v_x),tc_bool))* -> .
% 299.64/300.37 70417[0:Res:23961.0,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,t_a),v_Procs),v_x),tc_bool))* -> .
% 299.64/300.37 70474[0:SpL:3229.1,70390.0] || equal(hAPP(c_Set_Oinsert(v_x,t_a),u),v)* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))* -> .
% 299.64/300.37 70505[0:SSi:70482.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),u),v_x),v)* hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool))* -> .
% 299.64/300.37 70511[0:SpL:353.0,70504.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.37 70527[0:SpL:3229.1,70504.0] || equal(hAPP(c_Set_Oinsert(v_x,t_a),u),v)* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.37 70849[0:MRR:62505.2,70845.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),v),v_x),u)* -> .
% 299.64/300.37 71328[0:Res:7538.0,85.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),u),tc_fun(w,tc_bool))*.
% 299.64/300.37 71378[7:SpL:3229.1,71221.0] || equal(u,v)* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))* equal(u,v_x)* -> .
% 299.64/300.37 71469[7:SSi:71444.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(u,v_x),v)* hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool))* equal(u,v_x) -> .
% 299.64/300.37 71494[7:SpR:71455.1,36608.0] || equal(u,v_x) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(u,v_x),v,w),tc_Com_Opname,tc_bool))*.
% 299.64/300.37 71592[7:SpR:71455.1,35192.0] || equal(u,v_x) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_in(tc_Com_Opname),t_a,tc_fun(v,tc_bool)),v_Procs))*.
% 299.64/300.37 71593[7:SpR:71455.1,42583.0] || equal(u,v_x) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w))*.
% 299.64/300.37 71594[7:SpR:71455.1,43177.0] || equal(u,v_x) -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w,t_a)*.
% 299.64/300.37 71611[7:SpR:71455.1,3317.1] || equal(u,v_x) equal(c_in(t_a),v) -> hBOOL(hAPP(hAPP(v,v_x),u))*.
% 299.64/300.37 71661[7:SpR:71455.1,20881.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,t_a,w),u),hAPP(v,v_x)))*.
% 299.64/300.37 71671[7:SpR:71455.1,9067.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(c_Set_Oinsert(v,t_a),u)))*.
% 299.64/300.37 71681[7:SpR:71455.1,36599.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x))*.
% 299.64/300.37 71683[7:SpR:71455.1,36600.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x))*.
% 299.64/300.37 71722[7:SpL:71455.1,33513.1] || equal(u,v_x) c_Finite__Set_Ofinite(u,t_a) equal(c_Finite__Set_Ocard(u,t_a),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.37 71726[7:SpL:71455.1,44750.0] || equal(u,v_x) c_lessequals(u,v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(v,v_x)).
% 299.64/300.37 72669[7:Res:10705.0,71881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,hAPP(v_x,v_x),y,z)),x))*.
% 299.64/300.37 72869[0:Res:367.1,4486.2] class_Orderings_Obot(u) class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.37 72879[0:Res:421.1,4486.2] class_Orderings_Otop(u) class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.37 73130[0:Res:367.1,4487.2] class_Orderings_Obot(u) class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.37 73140[0:Res:421.1,4487.2] class_Orderings_Otop(u) class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.37 73266[7:SpR:71835.1,23979.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_Fun_Ofun__upd(v_x,v_x,v_x,u,v),v_x)**.
% 299.64/300.37 73327[7:SpR:71835.1,71608.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(t_a)) equal(u,v_x) -> hBOOL(hAPP(v_x,u))*.
% 299.64/300.37 73335[7:SpR:71835.1,72313.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(t_a)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(u,t_a),v_x)))*.
% 299.64/300.37 73364[7:SpR:71835.1,3229.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(u,v)* -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.37 73365[7:SpR:71835.1,3283.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(v_x,v_Procs))*.
% 299.64/300.37 73377[7:SpR:71835.1,37987.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.37 73401[7:SpR:71835.1,38042.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.37 73534[7:SpR:71835.1,65404.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* -> equal(hAPP(v_x,v_x),v_x)**.
% 299.64/300.37 73535[7:SpR:71835.1,525.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* -> equal(hAPP(v_x,v_x),v_x)**.
% 299.64/300.37 73709[7:SpR:71835.1,16814.1] class_Finite__Set_Ofinite_Ofinite(u) || equal(c_Set_Oimage(v,u,w),c_Set_Oinsert(v_x,t_a))** -> c_Finite__Set_Ofinite(v_x,w).
% 299.64/300.37 74420[7:MRR:74024.1,6340.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> .
% 299.64/300.37 74425[7:MRR:74244.1,6340.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(u,v_x)).
% 299.64/300.37 74435[7:MRR:73914.1,52007.0] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> .
% 299.64/300.37 74442[7:Obv:74242.1] || equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(v_x,hAPP(u,v_x)))*.
% 299.64/300.37 74604[7:SpR:71835.1,71906.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(hAPP(v_x,v),v_x))*.
% 299.64/300.37 74606[7:SpR:3229.1,71906.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* -> hBOOL(hAPP(hAPP(hAPP(v,v_x),w),v_x))*.
% 299.64/300.37 74632[7:SpR:338.0,71906.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w)),v_x))*.
% 299.64/300.37 74653[7:SpR:3229.1,71906.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.37 74679[7:SpR:3229.1,71907.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)* -> hBOOL(hAPP(hAPP(w,v_x),v_x))*.
% 299.64/300.37 74702[7:SpR:339.0,71907.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),v_x))*.
% 299.64/300.37 74709[7:SpR:3229.1,71907.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.37 74777[7:Res:9268.0,72021.1] || equal(hAPP(v_x,v_x),hAPP(u,v_x)) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),u),u)**.
% 299.64/300.37 74784[7:SSi:74758.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(hAPP(v_x,v_x),u)* hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool))* -> .
% 299.64/300.37 74837[7:SpR:3229.1,72297.1] || equal(u,v)* equal(c_in(t_a),u)* -> hBOOL(hAPP(hAPP(v,v_x),v_x))*.
% 299.64/300.37 74926[7:SpR:585.0,72297.1] || equal(c_COMBC(u,v,w,x),c_in(t_a))** -> hBOOL(hAPP(hAPP(u,v_x),v_x))*.
% 299.64/300.37 74927[7:SpR:586.0,72297.1] || equal(c_COMBB(u,v,w,x),c_in(t_a))** -> hBOOL(hAPP(u,hAPP(v_x,v_x)))*.
% 299.64/300.37 74970[7:SpL:3229.1,74770.0] || equal(v_x,u) equal(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(v,tc_bool))* hBOOL(v) -> .
% 299.64/300.37 74998[7:SSi:74981.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(hAPP(v_x,v_x),c_HOL_Ouminus__class_Ouminus(v,tc_bool))* hBOOL(u)* -> .
% 299.64/300.37 75135[0:Obv:75073.2] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(v,w) -> c_lessequals(v,w,tc_fun(u,tc_bool))*.
% 299.64/300.37 75143[7:SpL:3229.1,74783.1] || equal(v_x,u) equal(v,c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(u,v_x),v)* -> .
% 299.64/300.37 75152[7:Res:364.1,71908.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,v),u),v_x))*.
% 299.64/300.37 75162[7:Res:7538.0,71908.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),v_x)),v_x))*.
% 299.64/300.37 75174[7:Res:448.2,71908.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,v_x,tc_fun(u,tc_bool))* hBOOL(hAPP(v,v_x)).
% 299.64/300.37 75236[7:SpR:71835.1,72312.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,t_a,v),v_x),v_x))*.
% 299.64/300.37 75304[7:SpR:71835.1,72312.0] || equal(c_Set_Oimage(u,t_a,v),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(v_x,hAPP(u,v_x)))*.
% 299.64/300.37 77164[7:SpL:414.0,74788.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),v_x)** equal(v,y)* -> hBOOL(y)*.
% 299.64/300.37 77429[0:MRR:77409.2,9320.1] class_Orderings_Olinorder(tc_bool) class_OrderedGroup_Olordered__ab__group__add(tc_bool) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),u,tc_bool)* hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)).
% 299.64/300.37 77918[4:Res:38611.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oinsert(v,w),x,y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))*.
% 299.64/300.37 77919[4:Res:38615.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oinsert(v,w),x,y,z),c_COMBK(v_x,x1,x2)))*.
% 299.64/300.37 77997[7:MRR:2678.0,77996.0] || equal(c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,hAPP(c_in(tc_Com_Opname),v_x),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 77998[7:MRR:2677.0,77996.0] || equal(c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,hAPP(c_in(tc_Com_Opname),v_x),tc_Com_Opname),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 78008[0:Rew:584.0,77916.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_COMBK(v_Procs,v,w),tc_Com_Opname,x),v_Procs)))*.
% 299.64/300.37 78009[0:Rew:584.0,77950.1] || equal(hAPP(u,v_x),v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(u,v_x)))*.
% 299.64/300.37 78014[7:Rew:584.0,77964.1] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(u,v_x)))*.
% 299.64/300.37 78032[0:MRR:77881.0,820.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oinsert(v,w),x,y,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))))*.
% 299.64/300.37 78071[7:MRR:78070.1,6340.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v_x))*.
% 299.64/300.37 78259[7:SpR:78167.0,3285.1] || equal(c_Set_Oinsert(v_x,u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.37 78260[7:SpR:78167.0,3291.1] || equal(c_Set_Oinsert(v_x,u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),v_Procs))*.
% 299.64/300.37 78261[7:SpR:78167.0,39023.1] || equal(c_Set_Oinsert(v_x,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),x))*.
% 299.64/300.37 78262[7:SpR:78167.0,39064.1] || equal(c_Set_Oinsert(v_x,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),v_x),x,t_a)*.
% 299.64/300.37 78266[7:SpR:78167.0,8376.2] || equal(c_Set_Oinsert(v_x,u),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.37 78269[7:SpR:78167.0,15262.1] || equal(c_Set_Oinsert(v_x,u),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.37 78275[7:SpR:78167.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.37 78276[7:SpR:78167.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.37 78283[7:SpR:78167.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,u),tc_Com_Opname,v),v_x)),v_Procs))*.
% 299.64/300.37 78285[7:SpR:78167.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,u),tc_Com_Opname,v),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.37 78287[7:SpR:78167.0,24914.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,u),tc_Com_Opname,v),v_x)),v_x)**.
% 299.64/300.37 78290[7:SpR:78167.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 78300[7:SpR:78167.0,3305.1] || equal(u,c_Set_Oinsert(v_x,v))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.37 78301[7:SpR:78167.0,3317.1] || equal(c_in(u),c_Set_Oinsert(v_x,v))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,u),w)))*.
% 299.64/300.37 78302[7:SpR:78167.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,v),tc_Com_Opname,w),u),v_x))*.
% 299.64/300.37 78303[7:SpR:78167.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,v),tc_Com_Opname,w)))*.
% 299.64/300.37 78304[7:SpR:78167.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,v),v_x,tc_Com_Opname,w)))*.
% 299.64/300.37 78305[7:SpR:78167.0,28053.1] || equal(u,c_Set_Oinsert(v_x,v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,w)))*.
% 299.64/300.37 78306[7:SpR:78167.0,28356.1] || equal(u,c_Set_Oinsert(v_x,v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,w)))*.
% 299.64/300.37 78307[7:SpR:78167.0,3346.1] || equal(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,w))* -> hBOOL(hAPP(hAPP(c_in(v),u),v_x))*.
% 299.64/300.37 78318[7:SpR:78167.0,9568.0] || -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,v)),w),v_x),tc_bool)*.
% 299.64/300.37 78319[7:SpR:78167.0,9569.0] || -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,w)),v_x),tc_bool)*.
% 299.64/300.37 78354[7:SpR:78167.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),v_x))*.
% 299.64/300.37 78392[7:SpL:78167.0,55992.1] || equal(c_Set_Oinsert(v_x,u),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v) -> .
% 299.64/300.37 78398[7:SpL:78167.0,3484.1] || equal(c_Set_Oinsert(v_x,u),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,v),v_x)** -> equal(v_x,v).
% 299.64/300.37 78405[7:SpL:78167.0,24254.1] || equal(c_Set_Oinsert(v_x,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 78410[7:SpL:78167.0,58170.1] || equal(u,c_Set_Oinsert(v_x,v))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),u)* -> .
% 299.64/300.37 78417[7:SpL:78167.0,55910.1] || equal(c_COMBK(u,v,w),c_Set_Oinsert(v_x,x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) -> .
% 299.64/300.37 78481[7:MRR:78419.0,6340.0] || -> hBOOL(hAPP(c_Set_Oinsert(v_x,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v_x,u),w)))*.
% 299.64/300.37 78482[7:MRR:78420.0,6340.0] || -> hBOOL(hAPP(c_Set_Oinsert(v_x,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Set_Oinsert(v_x,u),v)))*.
% 299.64/300.37 78518[4:Res:77988.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.37 78542[4:MRR:15767.2,78524.0] || hBOOL(hAPP(v_x,u)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(u,v),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 78543[4:MRR:15784.2,78524.0] class_Lattices_Obounded__lattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 78551[4:MRR:23733.0,78524.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)))**.
% 299.64/300.37 78553[4:MRR:24503.2,78524.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 78555[4:MRR:26918.2,78524.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 78558[7:MRR:27813.2,78524.0] || hBOOL(hAPP(v_x,u)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(u,v),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 78559[7:MRR:27831.2,78524.0] class_Lattices_Obounded__lattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 78560[7:MRR:27865.2,78524.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 78571[7:MRR:29832.2,78524.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 78594[7:MRR:73354.1,78524.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> .
% 299.64/300.37 78662[4:Res:36017.0,78632.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),v_x),v_x)** -> .
% 299.64/300.37 78695[4:Res:78665.1,591.0] || equal(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_G),v_x)** -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),u,t_a).
% 299.64/300.37 78732[4:Res:78665.1,36766.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_x),v_x)** -> .
% 299.64/300.37 78742[4:Res:78665.1,38144.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs),v_x)** -> hBOOL(v_Procs).
% 299.64/300.37 78749[4:Res:78665.1,16768.0] || equal(hAPP(v_G,v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v_na,hAPP(c_in(tc_Com_Opname),v_x))),v_x)** -> c_Hoare__Mirabelle_Otriple__valid(v_na,v_Procs,t_a).
% 299.64/300.37 78752[4:Res:78665.1,3863.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),v_x)** -> hBOOL(hAPP(u,x)).
% 299.64/300.37 78783[4:Res:78665.1,38140.0] || equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,tc_bool),v_x)** -> hBOOL(u).
% 299.64/300.37 79082[0:Res:78077.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_Procs,t_a).
% 299.64/300.37 79112[7:Res:78199.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_in(v),v_x)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.37 80319[0:Rew:23682.0,79927.0] || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,u,w),v)**.
% 299.64/300.37 80320[0:Rew:23840.0,79419.0] || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,w),v)**.
% 299.64/300.37 80534[4:SpL:3229.1,78731.0] || equal(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v)* equal(hAPP(v,v_x),v_x)** -> .
% 299.64/300.37 81514[0:Rew:23682.0,81121.0] || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,w),v)**.
% 299.64/300.37 81515[0:Rew:23840.0,80612.0] || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,w),v)**.
% 299.64/300.37 81694[7:SpL:3229.1,79134.0] || equal(c_in(u),v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(v,v_x),v_x),tc_bool),v_x)** -> .
% 299.64/300.37 81696[7:SpL:3229.1,79134.0] || equal(hAPP(c_in(u),v_x),v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),v_x)** -> .
% 299.64/300.37 81710[7:SSi:81701.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_in(u),v_x),v_x),v)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),v_x)** -> .
% 299.64/300.37 81711[7:SpL:3229.1,79135.0] || equal(c_in(u),v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 81720[7:SpL:2267.1,79135.0] || equal(u,hAPP(c_in(v),v_x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 81722[7:SpL:3229.1,79136.0] || equal(c_in(u),v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 81731[7:SpL:2267.1,79136.0] || equal(u,hAPP(c_in(v),v_x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 81733[7:SpR:3229.1,78247.0] || equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),tc_Com_Opname,v),v_Procs),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.37 82159[7:SpR:78597.0,15630.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Set_Oinsert(v_x,v),w,u,t_a)))*.
% 299.64/300.37 82182[7:SpR:78597.0,15858.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Set_Oinsert(v_x,w),u,t_a)))*.
% 299.64/300.37 82193[7:SpL:78597.0,33513.1] || c_Finite__Set_Ofinite(c_Set_Oinsert(v_x,u),t_a) equal(c_Finite__Set_Ocard(c_Set_Oinsert(v_x,u),t_a),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.37 82822[7:SpR:3229.1,77991.0] || equal(c_Set_Oinsert(u,v),w)* -> hBOOL(hAPP(hAPP(c_in(x),v_x),hAPP(w,v_x)))*.
% 299.64/300.37 82830[7:SpR:3229.1,77991.0] || equal(c_in(u),v)* -> hBOOL(hAPP(hAPP(v,v_x),hAPP(c_Set_Oinsert(w,x),v_x)))*.
% 299.64/300.37 82841[7:Res:77991.0,279.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(c_Set_Oinsert(v,w),v_x)),hAPP(c_Set_Oinsert(v,w),v_x))**.
% 299.64/300.37 82865[7:SpL:3229.1,82846.0] || equal(c_Set_Oinsert(u,v),w)* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(w,v_x),v_x),tc_bool))* -> .
% 299.64/300.37 82873[7:SpL:3229.1,82846.0] || equal(hAPP(c_Set_Oinsert(u,v),v_x),w)* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool))* -> .
% 299.64/300.37 82895[7:SSi:82878.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),v_x),w)* hBOOL(c_HOL_Ouminus__class_Ouminus(w,tc_bool))* -> .
% 299.64/300.37 82901[7:SpL:3229.1,82894.0] || equal(c_Set_Oinsert(u,v),w)* equal(hAPP(hAPP(w,v_x),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.37 82909[7:SpL:3229.1,82894.0] || equal(hAPP(c_Set_Oinsert(u,v),v_x),w)* equal(hAPP(w,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.37 82940[7:SpL:3229.1,78156.0] || equal(c_in(u),v)* equal(hAPP(v,v_x),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.37 82943[7:SpR:3229.1,78322.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(v,tc_bool)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.37 83176[7:SpL:56980.1,78393.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),c_Set_Oinsert(v_x,w))* -> .
% 299.64/300.37 83178[7:SSi:83171.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(v_x,u) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v,w),c_Set_Oinsert(v_x,x))* -> .
% 299.64/300.37 83184[7:SpL:3229.1,82845.0] || equal(c_Set_Oinsert(u,v),w)* equal(hAPP(w,v_x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> .
% 299.64/300.37 83210[7:SpR:3229.1,78357.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,w,x),v_x),hAPP(v,v_x)))*.
% 299.64/300.37 83217[7:SpR:65404.1,78357.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v,w),v_x),v_x))*.
% 299.64/300.37 83218[7:SpR:525.1,78357.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v,w),v_x),v_x))*.
% 299.64/300.37 83276[7:SpR:3229.1,78357.0] || equal(c_Set_Oimage(u,v,w),x)* -> hBOOL(hAPP(hAPP(x,v_x),hAPP(u,v_x)))*.
% 299.64/300.37 83286[7:SpR:3229.1,83273.0] || equal(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),x)* -> hBOOL(hAPP(hAPP(x,v_x),v_x))*.
% 299.64/300.37 83288[7:SpR:3229.1,83273.0] || equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),v_x),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.37 84178[7:SpL:414.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) equal(c_Fun_Ofun__upd(v,v_x,u,w,x),v_x)** -> .
% 299.64/300.37 84635[7:Rew:584.0,84634.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,w),v_x)))*.
% 299.64/300.37 84775[7:Res:78317.0,40433.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,w)),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(x)*.
% 299.64/300.37 84784[7:MRR:84765.1,6340.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,w)),v_x),x,tc_bool)* -> hBOOL(x).
% 299.64/300.37 84785[7:MRR:84767.0,6340.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,w)),v_x)),x))*.
% 299.64/300.37 84786[7:MRR:84768.0,6340.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,x)),v_x)))*.
% 299.64/300.37 84948[7:Res:83237.0,3489.1] || equal(c_Set_Oimage(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),u,v),w,x),c_in(tc_Com_Opname))** -> .
% 299.64/300.37 84953[7:Rew:584.0,84952.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_COMBK(v_x,v,w),x,y),v_x)))*.
% 299.64/300.37 84997[0:Res:84957.0,279.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,w),u)),hAPP(c_Set_Oinsert(u,w),u))**.
% 299.64/300.37 85517[4:SpL:78507.0,2693.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 85518[4:SpL:78507.0,10885.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 85540[4:SpL:78507.0,21018.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.37 85868[4:SpL:3229.1,85505.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 86027[0:SpL:3229.1,86011.0] || equal(u,v)* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))* equal(u,v_Procs)* -> .
% 299.64/300.37 86124[0:SSi:86097.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(u,v_x),v)* hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool))* equal(u,v_Procs) -> .
% 299.64/300.37 86149[0:SpR:86109.1,36608.0] || equal(u,v_Procs) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(u,v_x),v,w),tc_Com_Opname,tc_bool))*.
% 299.64/300.37 86245[0:SpR:86109.1,35192.0] || equal(u,v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_in(tc_Com_Opname),t_a,tc_fun(v,tc_bool)),v_Procs))*.
% 299.64/300.37 86246[4:SpR:86109.1,42583.0] || equal(u,v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w))*.
% 299.64/300.37 86247[4:SpR:86109.1,43177.0] || equal(u,v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w,t_a)*.
% 299.64/300.37 86264[0:SpR:86109.1,3317.1] || equal(u,v_Procs) equal(c_in(t_a),v) -> hBOOL(hAPP(hAPP(v,v_x),u))*.
% 299.64/300.37 86319[0:SpR:86109.1,20881.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,t_a,w),u),hAPP(v,v_x)))*.
% 299.64/300.37 86332[0:SpR:86109.1,9067.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(c_Set_Oinsert(v,t_a),u)))*.
% 299.64/300.37 86344[0:SpR:86109.1,36599.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x))*.
% 299.64/300.37 86346[0:SpR:86109.1,36600.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x))*.
% 299.64/300.37 86398[0:SpL:86109.1,33513.1] || equal(u,v_Procs) c_Finite__Set_Ofinite(u,t_a) equal(c_Finite__Set_Ocard(u,t_a),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.37 86403[0:SpL:86109.1,44750.0] || equal(u,v_Procs) c_lessequals(u,v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(v,v_x)).
% 299.64/300.37 86723[4:SpL:414.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) equal(c_Fun_Ofun__upd(v,v_x,u,w,x),v_Procs)** -> .
% 299.64/300.37 87862[7:SpR:3229.1,87822.0] || equal(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(t_a,tc_bool)),v)* -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))*.
% 299.64/300.37 87892[7:SSi:87868.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(t_a,tc_bool)),v_x),v)* -> hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool))*.
% 299.64/300.37 88076[7:SpL:57008.1,87988.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(v_x,v_x))** hBOOL(hAPP(u,v_x)) -> .
% 299.64/300.37 88366[7:SpL:3229.1,88276.0] || equal(v_x,u) equal(c_HOL_Ominus__class_Ominus(v,hAPP(u,v_x),tc_bool),hAPP(u,v_x))** -> .
% 299.64/300.37 88382[7:SpL:3229.1,88098.0] || equal(v_x,u) equal(v,c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* hBOOL(v)* -> .
% 299.64/300.37 88395[7:SSi:88386.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(v_x,v_x),u)* equal(v,c_HOL_Ouminus__class_Ouminus(u,tc_bool))* hBOOL(v)* -> .
% 299.64/300.37 88597[7:SpL:2267.1,88524.0] || equal(u,v_x) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> .
% 299.64/300.37 88619[7:SpL:524.0,88086.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,v_x,tc_bool))* -> .
% 299.64/300.37 88630[7:SpL:414.0,88086.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(y,v,tc_bool))* -> .
% 299.64/300.37 88726[7:SpL:55036.1,88278.0] || equal(u,c_HOL_Ouminus__class_Ouminus(hAPP(v_x,v_x),tc_bool))* equal(v,u)* hBOOL(v)* -> .
% 299.64/300.37 90017[4:SpR:78660.1,36407.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),v))*.
% 299.64/300.37 90018[4:SpR:78660.1,36471.0] || equal(hAPP(u,v_x),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),v,t_a)*.
% 299.64/300.37 90217[4:SpR:78660.1,36264.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(u,v_x)))*.
% 299.64/300.37 90277[4:SpL:78660.1,36406.0] || equal(hAPP(u,v_x),v_x) c_lessequals(hAPP(u,v_x),v,tc_bool)* -> hBOOL(v).
% 299.64/300.37 91025[4:Rew:336.0,90947.0,538.0,90947.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool))* -> .
% 299.64/300.37 91294[0:Rew:91288.1,91082.2] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v),v)**.
% 299.64/300.37 91295[0:Rew:91288.1,91083.2] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v),v)**.
% 299.64/300.37 91310[0:Rew:91289.1,91207.1,91288.1,91207.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),v_x)**.
% 299.64/300.37 91311[0:Rew:91289.1,91205.1,91288.1,91205.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x)**.
% 299.64/300.37 91781[4:SpR:834.1,38616.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x)),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.37 92006[0:SpL:79073.0,21018.0] || equal(hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.37 92143[7:SpL:79101.0,2693.0] || equal(u,hAPP(c_in(v),v_x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 92144[7:SpL:79101.0,10885.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_in(v),v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 92165[7:SpL:79101.0,21018.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_in(x),v_x)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.37 92243[7:SpL:3229.1,92131.0] || equal(c_in(u),v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 92254[7:SpR:3229.1,92094.0] || equal(c_in(u),v)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(v,v_x)),v_x))*.
% 299.64/300.37 92267[7:SpR:3229.1,92094.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_in(w),v_x)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.37 92302[7:SpR:584.0,92047.0] || -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),hAPP(hAPP(c_in(y),v_x),v_x)))*.
% 299.64/300.37 92625[7:SpR:9911.0,82151.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Set_Oinsert(v_x,v)))*.
% 299.64/300.37 92626[7:SpR:10463.0,82151.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Set_Oinsert(v_x,v)))*.
% 299.64/300.37 92652[7:SpR:23682.0,82151.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(t_a)) -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,u)))*.
% 299.64/300.37 92695[7:Res:82151.1,11894.1] || equal(c_in(t_a),c_in(u)) equal(c_Set_Oinsert(v_x,v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))* -> .
% 299.64/300.37 93127[7:SpR:104.0,82187.0] || -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_Set_Oinsert(v_x,v),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v_x))*.
% 299.64/300.37 93285[4:SpR:9911.0,85556.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(c_Orderings_Otop__class_Otop(tc_bool),v),tc_bool)*.
% 299.64/300.37 93286[4:SpR:10463.0,85556.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(c_Orderings_Obot__class_Obot(tc_bool),v),tc_bool)*.
% 299.64/300.37 93312[4:SpR:23682.0,85556.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(v_x,u),tc_bool)*.
% 299.64/300.37 93381[4:SpR:336.0,85556.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool)*.
% 299.64/300.37 94357[7:SpL:3229.1,93931.0] || equal(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),w)* equal(hAPP(w,v_x),v_x)** -> .
% 299.64/300.37 94387[7:SpL:2267.1,94371.0] || equal(u,v_x) c_lessequals(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* -> .
% 299.64/300.37 983[0:SpR:524.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),tc_Com_Opname,u),u)*.
% 299.64/300.37 988[0:SpR:414.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Fun_Ofun__upd(w,v_x,v,x,y),tc_Com_Opname,u),u)*.
% 299.64/300.37 1109[0:Res:1103.1,527.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a) hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(v),w)),w))*.
% 299.64/300.37 1159[0:SpR:397.1,1158.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,v),v_Procs),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.37 1160[0:SpR:365.1,1158.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,v),v_Procs),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.37 1163[0:SpR:300.1,1158.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.37 1587[0:SSi:1585.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,tc_fun(x,tc_bool)),x)* -> c_Finite__Set_Ofinite(u,x).
% 299.64/300.37 2010[0:SSi:2001.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,v)* equal(v_Procs,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 2113[0:SpR:2097.1,1158.0] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.37 3175[0:SpR:351.0,2771.1] || equal(u,c_COMBK(v,w,x))* -> equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.37 3270[0:SpR:3229.1,1167.0] || equal(hAPP(c_Set_Oimage(c_COMBK(v_x,u,v),tc_Com_Opname,w),v_Procs),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.37 3273[0:SpR:3229.1,2097.1] || equal(c_Set_Oinsert(u,v),w)* hBOOL(hAPP(v_x,u))* -> equal(hAPP(w,v_x),v_x)**.
% 299.64/300.37 3276[0:SpR:3229.1,318.1] || equal(c_Set_Oimage(u,v,w),x)* c_Finite__Set_Ofinite(v_x,v) -> c_Finite__Set_Ofinite(hAPP(x,v_x),w)*.
% 299.64/300.37 3292[0:SpR:3229.1,2093.0] || equal(c_in(tc_Com_Opname),u) -> equal(hAPP(c_Set_Oinsert(v_Procs,v),hAPP(u,v_x)),hAPP(u,v_x))**.
% 299.64/300.37 3295[0:SpR:3229.1,397.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v)* -> equal(hAPP(v,v_x),c_Orderings_Otop__class_Otop(u))*.
% 299.64/300.37 3297[0:SpR:3229.1,365.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v)* -> equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(u))*.
% 299.64/300.37 3319[0:SpR:3229.1,526.1] || equal(c_in(u),v)* hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(hAPP(v,v_x),w))*.
% 299.64/300.37 3325[0:SpR:3229.1,301.1] class_Lattices_Obounded__lattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v) -> equal(hAPP(hAPP(v,v_x),c_Orderings_Obot__class_Obot(u)),v_x)**.
% 299.64/300.37 3326[0:SpR:3229.1,305.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v) -> c_lessequals(v_x,hAPP(hAPP(v,v_x),w),u)*.
% 299.64/300.37 3327[0:SpR:3229.1,310.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v) -> c_lessequals(v_x,hAPP(hAPP(v,v_x),w),u)*.
% 299.64/300.37 3332[0:SpR:3229.1,300.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v)* -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.37 3333[0:SpR:3229.1,306.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)* -> c_lessequals(v_x,hAPP(w,v_x),u)*.
% 299.64/300.37 3334[0:SpR:3229.1,309.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)* -> c_lessequals(v_x,hAPP(w,v_x),u)*.
% 299.64/300.37 3347[0:SpR:3229.1,305.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w) -> c_lessequals(v,hAPP(w,v_x),u)*.
% 299.64/300.37 3348[0:SpR:3229.1,310.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w) -> c_lessequals(v,hAPP(w,v_x),u)*.
% 299.64/300.37 3350[0:SpR:3229.1,306.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v) -> c_lessequals(w,hAPP(hAPP(v,v_x),w),u)*.
% 299.64/300.37 3351[0:SpR:3229.1,309.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v) -> c_lessequals(w,hAPP(hAPP(v,v_x),w),u)*.
% 299.64/300.37 3355[0:SpR:3229.1,526.1] || equal(hAPP(c_in(u),v),w)* hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.37 3501[0:SpL:3229.1,527.0] || equal(c_in(u),v)* hBOOL(hAPP(hAPP(v,v_x),w))* -> hBOOL(hAPP(w,v_x)).
% 299.64/300.37 3512[0:SpL:3229.1,527.0] || equal(hAPP(c_in(u),v),w)* hBOOL(hAPP(w,v_x))* -> hBOOL(hAPP(v_x,v)).
% 299.64/300.37 3564[0:SpR:445.1,3282.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),v_Procs)** -> equal(v_x,v) hBOOL(hAPP(u,v_x)).
% 299.64/300.37 3583[0:SpR:585.0,3282.1] || equal(hAPP(c_COMBC(u,v,w,x),y),v_Procs)** -> hBOOL(hAPP(hAPP(u,v_x),y)).
% 299.64/300.37 3584[0:SpR:586.0,3282.1] || equal(hAPP(c_COMBB(u,v,w,x),y),v_Procs)** -> hBOOL(hAPP(u,hAPP(y,v_x))).
% 299.64/300.37 3704[0:SpL:302.1,3483.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 3717[0:SpR:2097.1,3283.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs))*.
% 299.64/300.37 3719[0:SpR:397.1,3283.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_Procs))*.
% 299.64/300.37 3721[0:SpR:365.1,3283.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(u),v_Procs))*.
% 299.64/300.37 3728[0:SpR:300.1,3283.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.37 3943[0:SpL:3229.1,3506.1] || equal(u,v)* equal(c_Com_Ocom_OBODY,u)* equal(c_Com_Ocom_OSemi(w,x),hAPP(v,v_x))* -> .
% 299.64/300.37 3946[0:SpL:525.1,3506.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.37 4147[0:SpL:414.0,3929.0] || hBOOL(u) equal(c_Fun_Ofun__upd(v,v_x,u,w,x),y)* -> hBOOL(hAPP(y,v_x))*.
% 299.64/300.37 4252[2:SpR:445.1,4250.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Com_Ocom_OBODY)** -> equal(v_x,v) c_Com_OWT(hAPP(u,v_x)).
% 299.64/300.37 4276[2:SpR:585.0,4250.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(hAPP(u,v_x),y)).
% 299.64/300.37 4277[2:SpR:586.0,4250.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(u,hAPP(y,v_x))).
% 299.64/300.37 4318[0:SpR:297.2,3283.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v_Procs,u)* equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) -> hBOOL(v_Procs).
% 299.64/300.37 4701[0:Res:943.2,146.1] class_Lattices_Obounded__lattice(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),v,u)*.
% 299.64/300.37 4702[0:Res:942.2,146.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),v,u)*.
% 299.64/300.37 4788[0:Res:867.2,144.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),u)*.
% 299.64/300.37 4789[0:Res:858.2,144.1] class_Lattices_Obounded__lattice(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),u)*.
% 299.64/300.37 5856[0:MRR:5848.3,5375.2] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 6055[0:Rew:584.0,6008.1] || equal(u,v) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(hAPP(v,v_x),w),v_x),hAPP(u,v_x)))*.
% 299.64/300.37 6185[0:MRR:6177.3,5602.2] class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 6326[0:SpR:351.0,3279.1] || equal(c_COMBK(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(u,v_Procs),v_x))*.
% 299.64/300.37 6507[0:SpR:351.0,3285.1] || equal(c_COMBK(u,v,w),c_in(tc_Com_Opname))** -> hBOOL(hAPP(u,hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)))*.
% 299.64/300.37 6745[0:SpR:351.0,3291.1] || equal(c_COMBK(u,v,w),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),u),v_Procs))*.
% 299.64/300.37 6875[0:SpL:351.0,3484.1] || equal(c_COMBK(u,v,w),c_Com_Ocom_OBODY)** equal(u,hAPP(c_Com_Ocom_OBODY,x))* -> equal(v_x,x).
% 299.64/300.37 6911[0:SpL:351.0,3499.1] || equal(c_in(u),c_COMBK(v,w,x))* hBOOL(hAPP(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.37 7132[0:SpR:351.0,3305.1] || equal(u,c_COMBK(v,w,x))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,y),v_Procs),v))*.
% 299.64/300.37 7175[0:SpR:351.0,3317.1] || equal(c_in(u),c_COMBK(v,w,x))* -> hBOOL(hAPP(v,hAPP(c_Set_Oinsert(v_x,u),y)))*.
% 299.64/300.37 7299[0:SpR:2935.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_in(t_a),v_x),u,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.37 7312[0:SpR:584.0,7283.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oimage(c_Option_Othe(u),v,w),x,y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.37 7337[0:SpL:351.0,3507.1] || equal(c_Set_Oinsert(u,v),c_COMBK(w,x,y))* equal(w,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.37 7508[0:SpR:351.0,3346.1] || equal(c_Set_Oinsert(u,v),c_COMBK(w,x,y))* -> hBOOL(hAPP(hAPP(c_in(v),u),w))*.
% 299.64/300.37 7595[0:Res:7539.0,6546.0] || equal(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.37 8433[0:SpR:8385.1,415.0] || equal(u,v_Procs) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,tc_Com_Opname),u,u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname))**.
% 299.64/300.37 8854[0:SpR:8415.2,423.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Set_Oinsert(u,v))* -> hBOOL(hAPP(v_x,u))*.
% 299.64/300.37 8875[0:SpR:8415.2,351.0] || equal(v_Procs,v_x) equal(c_COMBK(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(v_x,u).
% 299.64/300.37 9166[0:SpR:351.0,8376.2] || equal(c_COMBK(u,v,w),c_in(tc_Com_Opname))** equal(x,v_Procs) -> hBOOL(hAPP(u,x))*.
% 299.64/300.37 9507[0:Res:868.1,251.1] class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(w,x),v)*.
% 299.64/300.37 9509[0:Res:816.1,251.1] class_Orderings_Olinorder(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(w,x),v)*.
% 299.64/300.37 9570[0:SSi:9499.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(c_Set_Oinsert(y,x),u)),v),tc_bool)*.
% 299.64/300.37 9571[0:SSi:9504.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(hAPP(hAPP(u,v_x),v),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(w,tc_bool)),v),tc_bool)*.
% 299.64/300.37 9572[0:SSi:9505.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(hAPP(v_x,u),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,tc_fun(w,tc_bool)),u),tc_bool)*.
% 299.64/300.37 9939[0:SpR:9911.0,651.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.37 9953[0:SpR:9911.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.37 9956[0:SpR:9911.0,3316.1] || equal(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.37 9957[0:SpR:9911.0,3339.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* -> equal(c_Fun_Ofun__upd(u,v_x,c_Orderings_Otop__class_Otop(tc_bool),w,x),u)**.
% 299.64/300.37 9965[0:SpR:9911.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 9976[0:SpL:9911.0,3698.2] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* equal(c_Com_Ocom_OBODY,u) equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 10003[0:SpR:9924.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname,u),u)*.
% 299.64/300.37 10072[0:SpR:9925.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))**.
% 299.64/300.37 10080[0:SpR:9925.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 10518[0:SpR:10463.0,651.0] || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.37 10532[0:SpR:10463.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.37 10535[0:SpR:10463.0,3316.1] || equal(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.37 10536[0:SpR:10463.0,3339.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> equal(c_Fun_Ofun__upd(u,v_x,c_Orderings_Obot__class_Obot(tc_bool),w,x),u)**.
% 299.64/300.37 10544[0:SpR:10463.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.37 10555[0:SpL:10463.0,3698.2] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* equal(c_Com_Ocom_OBODY,u) equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 10671[0:SpR:3229.1,9566.0] || equal(c_Set_Oinsert(u,v),w)* -> c_lessequals(hAPP(v_x,x),hAPP(hAPP(w,v_x),x),tc_bool)*.
% 299.64/300.37 10677[0:SpR:3229.1,9566.0] || equal(hAPP(c_Set_Oinsert(u,v),w),x)* -> c_lessequals(hAPP(w,v_x),hAPP(x,v_x),tc_bool)*.
% 299.64/300.37 10682[0:SpR:8385.1,9566.0] || equal(u,v_Procs) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,tc_Com_Opname)),u),tc_bool)*.
% 299.64/300.37 10694[0:SpR:3229.1,9566.0] || equal(u,v) -> c_lessequals(hAPP(v,v_x),hAPP(hAPP(c_Set_Oinsert(w,x),u),v_x),tc_bool)*.
% 299.64/300.37 10698[0:SpR:525.1,9566.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),v),tc_bool)*.
% 299.64/300.37 10888[0:SpL:353.0,3266.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(v_x,v),w)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.37 10925[0:SpR:353.0,10813.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(x,v),y))),x))*.
% 299.64/300.37 10928[0:SpR:3229.1,10813.0] || equal(c_Set_Oinsert(u,v),w) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,v),hAPP(w,v_x)),u))*.
% 299.64/300.37 11003[0:Res:10986.1,251.1] class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(w,x),v)*.
% 299.64/300.37 11183[0:SSi:11144.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),u),u)**.
% 299.64/300.37 11184[0:SSi:11150.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool),hAPP(u,v_x))**.
% 299.64/300.37 11264[0:SpL:11176.1,3483.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY)** equal(u,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 11459[0:SpR:8385.1,10745.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_Procs) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool)*.
% 299.64/300.37 11460[0:SpR:2098.1,10745.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),t_a)* c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),tc_bool)*.
% 299.64/300.37 11464[0:SpR:584.0,10745.0] || -> c_lessequals(u,hAPP(c_COMBS(c_Set_Oinsert(v,w),x,y,z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),tc_bool)*.
% 299.64/300.37 11485[0:SpR:8385.1,10746.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_Procs) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool)*.
% 299.64/300.37 11486[0:SpR:2098.1,10746.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),t_a)* c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),tc_bool)*.
% 299.64/300.37 11595[0:SpR:524.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,tc_fun(x,tc_bool)),v),v,tc_bool)*.
% 299.64/300.37 11603[0:SpR:414.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Fun_Ofun__upd(u,v,w,x,y),z,tc_fun(x1,tc_bool)),v),w,tc_bool)*.
% 299.64/300.37 12721[0:Rew:12524.1,12718.2] || c_lessequals(u,v,tc_bool)* equal(c_HOL_Ominus__class_Ominus(u,w,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(u,v).
% 299.64/300.37 12744[0:SpR:2267.1,12687.1] || equal(u,v)* -> hBOOL(hAPP(v,w))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(x,tc_bool)),w))*.
% 299.64/300.37 12748[0:SpR:3229.1,12687.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w)* -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(w,v_x))*.
% 299.64/300.37 12916[0:Res:12621.0,12532.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,tc_bool),y,tc_bool),u,tc_bool)*.
% 299.64/300.37 12935[0:SpR:584.0,10713.0] || -> c_lessequals(u,hAPP(c_COMBS(c_Set_Oinsert(v,w),x,y,z,x1),c_COMBK(u,x2,x3)),tc_bool)*.
% 299.64/300.37 13099[0:SpL:10090.1,333.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_bool),u) -> c_Finite__Set_Ofinite(v_x,u).
% 299.64/300.37 14266[0:SpR:14216.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 14283[0:SpL:14216.0,3483.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 14953[0:MRR:14944.3,5375.2] class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 15187[0:Res:11108.1,12959.0] || c_Natural_Oevaln(u,v,w,x)* -> c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,u))),v,x)*.
% 299.64/300.37 15381[0:SpR:3229.1,15367.0] || equal(c_Set_Oinsert(u,v),w)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(w,v_x),v_x,tc_fun(v,tc_bool)),v)*.
% 299.64/300.37 15392[0:Res:15367.0,62.0] || -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),x,tc_fun(v,tc_bool)),v)*.
% 299.64/300.37 15626[0:Res:678.0,278.1] || hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_in(tc_Com_Opname),v_x),v,u,w)))*.
% 299.64/300.37 15647[0:Res:11029.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,u,t_a)))*.
% 299.64/300.37 15836[0:MRR:15835.1,826.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 15854[0:Res:678.0,277.1] || hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_in(tc_Com_Opname),v_x),u,w)))*.
% 299.64/300.37 15875[0:Res:11029.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,t_a)))*.
% 299.64/300.37 16157[0:SpR:351.0,15262.1] || equal(c_COMBK(u,v,w),c_in(t_a))** -> hBOOL(hAPP(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.37 16246[0:SpL:414.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Fun_Ofun__upd(v,v_x,u,w,x),v_Procs)** -> .
% 299.64/300.37 16321[0:SpL:397.1,16286.0] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_Procs)** -> .
% 299.64/300.37 16322[0:SpL:365.1,16286.0] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_Procs)** -> .
% 299.64/300.37 16780[0:Res:13387.1,390.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(w,x,y,v),u,v,y)*.
% 299.64/300.37 17295[0:SpL:351.0,13272.0] || equal(u,c_Orderings_Otop__class_Otop(tc_bool)) equal(c_COMBK(u,v,w),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.37 17446[0:SpL:351.0,16327.1] || equal(u,c_COMBK(v,w,x))* equal(v,c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_Procs) -> .
% 299.64/300.37 17467[0:Obv:17447.1] || equal(u,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)))* equal(u,v_Procs) -> .
% 299.64/300.37 18246[2:SpR:15172.0,4250.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.37 18679[0:SpR:456.0,9568.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Option_Othe(w)),x),c_Option_Ooption_OSome(u,w)),tc_bool)*.
% 299.64/300.37 18681[0:SpR:351.0,9568.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_COMBK(u,w,x)),y),z),tc_bool)*.
% 299.64/300.37 18741[0:SSi:18730.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),w),x),tc_bool)*.
% 299.64/300.37 18742[0:SSi:18731.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),u),tc_bool)*.
% 299.64/300.37 18839[0:Res:7539.0,18768.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),c_Set_Oinsert(v_x,tc_Com_Opname))),v_Procs),tc_bool)*.
% 299.64/300.37 18990[0:SpR:456.0,9569.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Option_Othe(x)),c_Option_Ooption_OSome(u,x)),tc_bool)*.
% 299.64/300.37 18992[0:SpR:351.0,9569.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_COMBK(u,x,y)),z),tc_bool)*.
% 299.64/300.37 19052[0:SSi:19041.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),x),tc_bool)*.
% 299.64/300.37 19053[0:SSi:19042.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),u),tc_bool)*.
% 299.64/300.37 19434[0:SpR:2097.1,9067.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Oinsert(x,w),u)))*.
% 299.64/300.37 19623[0:Res:19436.1,2629.1] || equal(u,v_Procs) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,tc_Com_Opname),u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 19750[0:SpR:104.0,676.0] || -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(c_in(tc_Com_Opname),v_x),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),v_Procs))*.
% 299.64/300.37 20207[0:Res:20152.0,437.1] || c_Finite__Set_Ofinite(u,v) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),v)*.
% 299.64/300.37 20260[0:Res:20186.0,437.1] || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,u,tc_fun(v,tc_bool)),v)*.
% 299.64/300.37 20394[0:AED:24.0,20351.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y)* -> .
% 299.64/300.37 20705[0:Res:10705.0,9857.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,c_Orderings_Otop__class_Otop(tc_bool),y,z)),x),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 21074[0:SpR:456.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Option_Othe(u),v,w),hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(x,u),v),y)),x))*.
% 299.64/300.37 21076[0:SpR:351.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBK(u,v,w),x,y),hAPP(c_Set_Oinsert(z,x),x1)),u))*.
% 299.64/300.37 21124[0:SpR:2097.1,20881.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,x,y),u),hAPP(w,v)))*.
% 299.64/300.37 21166[0:SpR:9911.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 21167[0:SpR:10463.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.37 21227[0:SpR:9911.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 21228[0:SpR:10463.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.37 21692[0:Rew:331.0,21526.0] || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_x,tc_Com_Opname,v),v_x)**.
% 299.64/300.37 21693[0:Rew:330.0,21339.0] || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,v),v_x)**.
% 299.64/300.37 21782[0:SpR:351.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBK(u,v,w),t_a,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u))*.
% 299.64/300.37 21804[0:SpR:2097.1,21035.0] || hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,w),u),v_Procs))*.
% 299.64/300.37 22321[0:Rew:331.0,22153.0] || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_Com_Opname,v),v_x)**.
% 299.64/300.37 22322[0:Rew:330.0,21965.0] || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),tc_Com_Opname,v),v_x)**.
% 299.64/300.37 22483[0:SpR:351.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBK(v,w,x),tc_Com_Opname,y),u),v))*.
% 299.64/300.37 22583[0:SpR:158.0,16814.1] class_Finite__Set_Ofinite_Ofinite(u) || -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,u,w),z)),x)*.
% 299.64/300.37 22625[0:SpR:158.0,16814.1] class_Finite__Set_Ofinite_Ofinite(u) || -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,u,x,y),y,x),z),x)*.
% 299.64/300.37 22869[0:SpL:3294.1,333.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a))** c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_bool),u) -> c_Finite__Set_Ofinite(v_x,u).
% 299.64/300.37 23758[0:SpR:23682.0,3339.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) -> equal(c_Fun_Ofun__upd(u,v_x,v_x,v,w),u)**.
% 299.64/300.37 23771[0:SpR:23682.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)))**.
% 299.64/300.37 23788[0:SpR:23682.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),w))*.
% 299.64/300.37 23966[0:SpR:23912.0,3305.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.37 23967[0:SpR:23912.0,3317.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,u),v)))*.
% 299.64/300.37 23968[0:SpR:23912.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),u),v_x))*.
% 299.64/300.37 23969[0:SpR:23912.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),u),v_x))*.
% 299.64/300.37 24001[0:SpR:23912.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_Set_Oinsert(u,v),x)),u))*.
% 299.64/300.37 24051[0:Rew:23884.1,23999.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(c_Orderings_Obot__class_Obot(tc_bool),u).
% 299.64/300.37 24416[0:SpR:3229.1,23916.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x),tc_Com_Opname,v),v_x)**.
% 299.64/300.37 24423[0:SpR:3229.1,23923.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,v),v_x)**.
% 299.64/300.37 24486[0:SpR:3229.1,23937.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(u,v_x),tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.37 24489[0:SpR:3229.1,23937.0] || equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_Procs),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.37 24494[0:SpL:3229.1,23942.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),v)* -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.37 24578[0:SpR:24020.1,9568.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(hAPP(v,v_x),v_x,tc_bool).
% 299.64/300.37 24609[0:SpR:24020.1,585.0] || equal(c_COMBC(u,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(u,v_x),v_x),v_x)**.
% 299.64/300.37 24610[0:SpR:24020.1,586.0] || equal(c_COMBB(u,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(u,hAPP(v_x,v_x)),v_x)**.
% 299.64/300.37 24611[0:SpR:24020.1,5877.0] || equal(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Com_Ocom_OBODY,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),v_x,u).
% 299.64/300.37 24624[0:SpR:3229.1,24020.1] || equal(u,v)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)* -> equal(hAPP(hAPP(v,v_x),v_x),v_x)**.
% 299.64/300.37 25028[0:SpR:414.0,23902.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.37 25090[0:SpL:23902.1,332.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** c_Finite__Set_Ofinite(v_x,u) -> c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_bool),u).
% 299.64/300.37 25630[0:Res:12533.1,24120.1] || c_lessequals(u,v,tc_bool)* equal(v,c_Orderings_Obot__class_Obot(tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(u,w,tc_bool),v)*.
% 299.64/300.37 26319[0:SSi:26309.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(u,tc_bool)),u)* -> c_Finite__Set_Ofinite(v_x,u).
% 299.64/300.37 27215[7:SpR:445.1,27207.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),v_x)** -> equal(v_x,v) hBOOL(hAPP(u,v_x)).
% 299.64/300.37 27266[7:SpR:585.0,27207.1] || equal(hAPP(c_COMBC(u,v,w,x),y),v_x)** -> hBOOL(hAPP(hAPP(u,v_x),y)).
% 299.64/300.37 27267[7:SpR:586.0,27207.1] || equal(hAPP(c_COMBB(u,v,w,x),y),v_x)** -> hBOOL(hAPP(u,hAPP(y,v_x))).
% 299.64/300.37 27302[7:MRR:8537.2,27297.0] || equal(u,c_Set_Oimage(v,w,x))* equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> .
% 299.64/300.37 27484[7:SpL:2267.1,27286.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_x)** equal(v_Procs,v)* -> .
% 299.64/300.37 27505[7:SpL:2267.1,27481.1] || equal(u,v)* equal(v,v_x)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 27898[7:MRR:27897.1,826.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 28041[0:SpR:2097.1,28032.0] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(u,v),tc_Com_Opname,w)))*.
% 299.64/300.37 28047[0:SpR:397.1,28032.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,v)))*.
% 299.64/300.37 28048[0:SpR:365.1,28032.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,v)))*.
% 299.64/300.37 28093[0:SpR:24020.1,28032.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(u,v_x),tc_Com_Opname,v)))*.
% 299.64/300.37 28344[0:SpR:2097.1,28335.0] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),v_x,tc_Com_Opname,w)))*.
% 299.64/300.37 28350[0:SpR:397.1,28335.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v)))*.
% 299.64/300.37 28351[0:SpR:365.1,28335.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Orderings_Obot__class_Obot(u),tc_Com_Opname,v)))*.
% 299.64/300.37 28397[0:SpR:24020.1,28335.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(u,v_x),v_x,tc_Com_Opname,v)))*.
% 299.64/300.37 31091[0:SpR:28771.0,10813.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)))*.
% 299.64/300.37 31177[0:SpR:28926.0,10813.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)))*.
% 299.64/300.37 31327[0:Res:31315.0,436.1] || hBOOL(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u))* -> hBOOL(hAPP(v_Procs,u)).
% 299.64/300.37 31477[0:SpL:351.0,24254.1] || equal(c_COMBK(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(u,c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 31535[0:Res:1157.0,473.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,x),u)),v_Procs))*.
% 299.64/300.37 31809[7:SpL:414.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Fun_Ofun__upd(v,v_x,u,w,x),v_x)** -> .
% 299.64/300.37 31880[7:SpL:397.1,31868.0] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x)** -> .
% 299.64/300.37 31881[7:SpL:365.1,31868.0] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x)** -> .
% 299.64/300.37 32687[0:SpR:3229.1,32669.0] || equal(u,v) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,w),hAPP(v,v_x))))*.
% 299.64/300.37 32693[0:SpR:525.1,32669.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x)))*.
% 299.64/300.37 33103[0:Res:7539.0,32232.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))),v_x))*.
% 299.64/300.37 33233[0:SpR:32668.0,10813.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))))*.
% 299.64/300.37 33285[0:SpR:351.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,x),u),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.37 33571[0:SpR:351.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y)))*.
% 299.64/300.37 33662[0:SpR:351.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y)))*.
% 299.64/300.37 33753[7:SpL:351.0,31886.1] || equal(u,c_COMBK(v,w,x))* equal(v,c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_x) -> .
% 299.64/300.37 33788[7:Obv:33754.1] || equal(u,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)))* equal(u,v_x) -> .
% 299.64/300.37 33848[0:SpR:23965.1,28368.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,v)))*.
% 299.64/300.37 33849[0:SpR:23965.1,28065.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,v)))*.
% 299.64/300.37 33865[0:SpL:23965.1,3732.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))* equal(u,c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.37 33866[0:SpL:23965.1,3340.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))* equal(u,v)* -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.37 34432[0:Rew:300.1,34209.1] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.37 34436[0:Rew:301.1,33989.1] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x)),v_x)**.
% 299.64/300.37 34478[0:Rew:525.1,34477.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x)),v_x)**.
% 299.64/300.37 34880[0:SpR:351.0,28053.1] || equal(u,c_COMBK(v,w,x))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,u,tc_Com_Opname,y)))*.
% 299.64/300.37 34959[0:SpR:351.0,28356.1] || equal(u,c_COMBK(v,w,x))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v,tc_Com_Opname,y)))*.
% 299.64/300.37 35447[0:SpR:2097.1,35192.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_in(tc_Com_Opname),v,tc_fun(w,tc_bool)),v_Procs))*.
% 299.64/300.37 36462[0:SpR:584.0,36407.0] || -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),hAPP(hAPP(c_Set_Oinsert(v_x,t_a),y),v_x)))*.
% 299.64/300.37 36485[0:SpR:9493.1,36471.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),v,t_a)*.
% 299.64/300.37 36767[0:SpL:67.0,1049.0] || c_lessequals(v_Procs,c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* -> .
% 299.64/300.37 36770[0:SpL:67.0,8495.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)))** -> .
% 299.64/300.37 36806[0:SpR:353.0,36588.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Set_Oinsert(v_x,t_a),x))),v_x))*.
% 299.64/300.37 36833[0:SpR:3229.1,36588.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(v_x,t_a),w)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.37 37084[7:SpL:2267.1,37060.0] || equal(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_x)** -> .
% 299.64/300.37 38125[0:Res:18644.0,37920.0] || hBOOL(v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),v),v_Procs))*.
% 299.64/300.37 38126[0:Res:18763.0,37920.0] || hBOOL(v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs))*.
% 299.64/300.37 38132[0:Res:10697.0,37920.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u)),u))*.
% 299.64/300.37 38135[0:Res:10705.0,37920.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Fun_Ofun__upd(x,y,u,z,x1)),y))*.
% 299.64/300.37 38143[0:Res:12627.1,37920.0] || c_lessequals(u,v,tc_bool)* hBOOL(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool))* -> hBOOL(v).
% 299.64/300.37 38145[0:Res:23789.0,37920.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w))* -> hBOOL(w).
% 299.64/300.37 38149[0:Res:23882.0,37920.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)))* -> hBOOL(u).
% 299.64/300.37 38680[4:SpR:2097.1,37987.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.37 38686[4:SpR:397.1,37987.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v))*.
% 299.64/300.37 38687[4:SpR:365.1,37987.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(u),v))*.
% 299.64/300.37 38700[4:SpR:300.1,37987.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.37 38737[4:SpR:24020.1,37987.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.37 38756[4:SpR:539.1,37987.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x))*.
% 299.64/300.37 38757[4:SpR:540.1,37987.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x))*.
% 299.64/300.37 38758[4:SpR:297.2,37987.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> hBOOL(v).
% 299.64/300.37 38869[4:SpR:2097.1,38042.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,w,t_a)*.
% 299.64/300.37 38875[4:SpR:397.1,38042.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Otop__class_Otop(u),v,t_a)*.
% 299.64/300.37 38876[4:SpR:365.1,38042.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(u),v,t_a)*.
% 299.64/300.37 38889[4:SpR:300.1,38042.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.37 38926[4:SpR:24020.1,38042.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.37 39954[4:SpR:3229.1,38473.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(v,v_x)))*.
% 299.64/300.37 40026[4:SpR:3229.1,38566.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(u,v_x),w)))*.
% 299.64/300.37 40302[4:SpL:3229.1,40016.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* c_lessequals(hAPP(v,v_x),w,tc_bool)* -> hBOOL(w).
% 299.64/300.37 40364[4:Res:10745.0,40016.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v_x))),x))*.
% 299.64/300.37 40365[4:Res:10746.0,40016.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v_x)))*.
% 299.64/300.37 40367[4:Res:10712.0,40016.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v_x),w)))*.
% 299.64/300.37 40368[4:Res:10713.0,40016.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v_x),x,y)),z))*.
% 299.64/300.37 40409[4:SpL:3229.1,40363.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(w)*.
% 299.64/300.37 40466[4:SpL:3229.1,40434.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(hAPP(u,v_x),v),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(w)*.
% 299.64/300.37 40508[4:SpL:3229.1,40105.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) c_lessequals(hAPP(hAPP(u,v_x),v),w,tc_bool)* -> hBOOL(w).
% 299.64/300.37 40583[4:Res:10745.0,40105.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w))),x))*.
% 299.64/300.37 40584[4:Res:10746.0,40105.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),x)))*.
% 299.64/300.37 40586[4:Res:10712.0,40105.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),x),w)))*.
% 299.64/300.37 40587[4:Res:10713.0,40105.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w),x,y)),z))*.
% 299.64/300.37 40659[4:Res:10745.0,40433.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(x)*.
% 299.64/300.37 40660[4:Res:10746.0,40433.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(x)*.
% 299.64/300.37 40662[4:Res:10712.0,40433.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(v_x,w)),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(x)*.
% 299.64/300.37 40663[4:Res:10713.0,40433.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(v_x,w,x)),y),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(z)*.
% 299.64/300.37 40793[4:Res:9567.0,40171.0] || c_lessequals(v_x,hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),tc_bool)* -> hBOOL(hAPP(u,x)).
% 299.64/300.37 40800[4:Res:10745.0,40171.0] || c_lessequals(v_x,u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),x))*.
% 299.64/300.37 40801[4:Res:10746.0,40171.0] || c_lessequals(v_x,u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),u))*.
% 299.64/300.37 40803[4:Res:10712.0,40171.0] || c_lessequals(v_x,u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),c_Option_Ooption_OSome(u,x)))*.
% 299.64/300.37 40804[4:Res:10713.0,40171.0] || c_lessequals(v_x,u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_COMBK(u,x,y)),z))*.
% 299.64/300.37 40810[4:Res:12621.0,40171.0] || c_lessequals(v_x,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,tc_bool),tc_bool)* -> hBOOL(u).
% 299.64/300.37 40814[4:Res:11580.0,40171.0] || c_lessequals(v_x,hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs),tc_bool)* -> hBOOL(v_Procs).
% 299.64/300.37 41071[4:Res:12621.0,40323.1] || equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(u).
% 299.64/300.37 41075[4:Res:11580.0,40323.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(v_Procs).
% 299.64/300.37 41466[4:SpR:414.0,38236.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,tc_bool)).
% 299.64/300.37 42185[4:SSi:42142.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(v_x,tc_bool),u),tc_bool,tc_bool))*.
% 299.64/300.37 42409[4:SpR:104.0,40372.0] || -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v_x))*.
% 299.64/300.37 42814[4:SpR:104.0,40591.0] || -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),w))*.
% 299.64/300.37 43215[4:SpR:104.0,42829.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),w,t_a)*.
% 299.64/300.37 43268[4:Res:1145.0,42356.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),tc_Com_Opname,tc_fun(x,tc_bool)),v_x))*.
% 299.64/300.37 43374[4:Res:1145.0,42582.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v),tc_Com_Opname,tc_fun(w,tc_bool)),x))*.
% 299.64/300.37 43610[4:Res:1145.0,43176.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v),tc_Com_Opname,tc_fun(w,tc_bool)),x,t_a)*.
% 299.64/300.37 44028[4:SpL:23965.1,38706.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))* equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.37 44039[4:SpL:23965.1,38895.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))* equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.37 44751[0:SpR:410.0,36599.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)),v_x))*.
% 299.64/300.37 44891[0:SpR:104.0,44824.0] || -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v_x))*.
% 299.64/300.37 44928[0:Res:1145.0,44833.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w),tc_Com_Opname,tc_fun(x,tc_bool)),v_x))*.
% 299.64/300.37 45193[0:SpR:584.0,36600.0] || -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),v,w,x),y),v_x))*.
% 299.64/300.37 46401[0:SpR:584.0,37989.1] || hBOOL(u) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x),y))*.
% 299.64/300.37 46632[4:SpL:9911.0,46565.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.37 46633[4:SpL:10463.0,46565.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.37 46681[0:Res:7539.0,44639.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),u)),v_x))*.
% 299.64/300.37 46693[0:Res:651.0,44639.0] || equal(hAPP(u,v_x),v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.37 46854[0:Res:7539.0,44750.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(v_x,t_a),x))),v_x))*.
% 299.64/300.37 46968[0:SpR:3229.1,46859.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,tc_fun(u,tc_bool)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.37 47110[0:Res:12593.0,38189.0] || hBOOL(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u))*.
% 299.64/300.37 47133[0:SSi:47057.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool)))*.
% 299.64/300.37 47478[4:Res:448.2,47318.0] class_Orderings_Olinorder(tc_bool) || -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool),tc_bool)* hBOOL(u).
% 299.64/300.37 47515[4:SSi:47494.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool),u,v),tc_Com_Opname,tc_bool))*.
% 299.64/300.37 47830[0:Res:12593.0,38190.0] || hBOOL(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x))*.
% 299.64/300.37 47857[0:SSi:47777.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool)),v))*.
% 299.64/300.37 48134[4:SpR:351.0,39023.1] || equal(c_COMBK(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),u),z))*.
% 299.64/300.37 48153[4:SpR:23912.0,39023.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),w))*.
% 299.64/300.37 48249[4:SpR:351.0,39064.1] || equal(c_COMBK(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(x,y),u),z,t_a)*.
% 299.64/300.37 48268[4:SpR:23912.0,39064.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),v_x),w,t_a)*.
% 299.64/300.37 48700[4:SpR:2097.1,42357.0] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,tc_fun(x,tc_bool)),v_x))*.
% 299.64/300.37 48716[4:SpR:2098.1,42357.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a)* hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Hoare__Mirabelle_Otriple(t_a),tc_fun(w,tc_bool)),v_x))*.
% 299.64/300.37 48863[4:SpR:2097.1,42583.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(w,tc_bool)),x))*.
% 299.64/300.37 49402[0:SpR:49342.1,10813.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.37 50092[4:SpR:2097.1,43177.0] || hBOOL(hAPP(u,v_x)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(w,tc_bool)),x,t_a)*.
% 299.64/300.37 51041[0:SSi:50963.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(hAPP(u,v_x)) -> hBOOL(v)*.
% 299.64/300.37 51346[0:SpR:351.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(u,hAPP(hAPP(c_Set_Oinsert(v,t_a),c_COMBK(u,w,x)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 51467[0:SpL:2097.1,33513.1] || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,w) equal(c_Finite__Set_Ocard(u,w),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.37 52013[4:MRR:23073.2,52007.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v_x,tc_fun(u,tc_bool))* -> .
% 299.64/300.37 52016[4:MRR:24987.2,52007.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(v_x,c_Orderings_Obot__class_Obot(tc_bool),tc_fun(u,tc_bool))* -> .
% 299.64/300.37 52017[4:MRR:25129.2,52007.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) c_Fun_Oinj__on(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> .
% 299.64/300.37 52030[4:SSi:52021.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> .
% 299.64/300.37 52031[4:SSi:52020.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> .
% 299.64/300.37 52140[0:SSi:52072.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool),v,tc_bool)* hBOOL(hAPP(u,v_x)) -> hBOOL(v).
% 299.64/300.37 53137[0:SpR:3229.1,53111.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(u,v_x),v_x,tc_Com_Opname,v),v_x,tc_bool)*.
% 299.64/300.37 53255[0:SpR:3229.1,53243.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(u,v_x),tc_Com_Opname,v),v_x,tc_bool)*.
% 299.64/300.37 53770[0:Res:7226.0,467.0] || -> equal(hAPP(c_Option_Othe(u),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(u),v,w),x)),x)**.
% 299.64/300.37 54264[0:SpL:8667.0,4964.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_Procs) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x))*.
% 299.64/300.37 54265[7:SpL:8667.0,27293.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x))*.
% 299.64/300.37 54369[0:SpR:2267.1,54251.0] || equal(u,v) -> equal(c_HOL_Ominus__class_Ominus(v,c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v)**.
% 299.64/300.37 54604[4:SpL:54406.0,41073.1] || c_lessequals(hAPP(u,v_x),v,tc_bool)* equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(v).
% 299.64/300.37 54994[4:SpL:54650.0,41073.1] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v,tc_bool)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(v).
% 299.64/300.37 55110[0:SSi:55027.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(w,u)* -> equal(c_HOL_Ominus__class_Ominus(w,c_HOL_Ouminus__class_Ouminus(v,tc_bool),tc_bool),w)**.
% 299.64/300.37 55369[0:Obv:55187.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> equal(c_Orderings_Otop__class_Otop(u),v).
% 299.64/300.37 55817[0:Rew:336.0,55772.0,538.0,55772.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.37 56060[0:Rew:2807.0,55881.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v)* equal(hAPP(u,v_x),hAPP(v,v_x))* -> .
% 299.64/300.37 56874[0:Obv:56796.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(u),v) -> c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)*.
% 299.64/300.37 57080[7:MRR:57047.2,826.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 57081[0:MRR:57048.2,826.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 57939[0:SpL:351.0,55910.1] || equal(c_COMBK(u,v,w),c_COMBK(x,y,z))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),x) -> .
% 299.64/300.37 57959[0:SpL:23912.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) -> .
% 299.64/300.37 58116[0:SpL:23912.0,55992.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_COMBK(u,v,w))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u) -> .
% 299.64/300.37 58145[0:Rew:3014.0,58112.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_COMBK(u,v,w))* equal(c_Orderings_Obot__class_Obot(tc_bool),u) -> .
% 299.64/300.37 58158[0:SpL:2097.1,58055.0] || hBOOL(hAPP(v_x,u))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v,w),c_Set_Oinsert(u,x))* -> .
% 299.64/300.37 58164[0:SpL:397.1,58055.0] class_Orderings_Otop(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v,w),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)))** -> .
% 299.64/300.37 58165[0:SpL:365.1,58055.0] class_Orderings_Obot(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool),v,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)))** -> .
% 299.64/300.37 58180[0:SpL:300.1,58055.0] class_Lattices_Obounded__lattice(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))* -> .
% 299.64/300.37 58221[0:SpL:24020.1,58055.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v,w),hAPP(u,v_x))* -> .
% 299.64/300.37 58249[0:Rew:56980.1,58216.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w))* -> .
% 299.64/300.37 58250[0:Rew:56980.1,58220.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* -> .
% 299.64/300.37 58252[0:Rew:2990.0,58199.0] || equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),u,v),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x,tc_fun(y,tc_bool)))* -> .
% 299.64/300.37 58253[0:Rew:3014.0,58223.0] || equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* -> .
% 299.64/300.37 58254[0:Rew:3014.0,58230.0] || equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),hAPP(c_Set_Oinsert(w,x),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),y,z)))* -> .
% 299.64/300.37 58331[0:SSi:58324.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(v_x,u) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))** -> .
% 299.64/300.37 58348[0:SpL:56980.1,58198.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),c_COMBK(u,x,y))* -> .
% 299.64/300.37 58349[0:SpL:57059.1,58198.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),v,w),c_COMBK(u,x,y))* -> .
% 299.64/300.37 58355[0:SSi:58339.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v,tc_bool),w,x),c_COMBK(u,y,z))* -> .
% 299.64/300.37 58452[0:SpL:524.0,58248.0] || equal(c_COMBK(v_x,u,v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.37 58463[0:SpL:414.0,58248.0] || equal(c_COMBK(u,v,w),c_HOL_Ouminus__class_Ouminus(c_Fun_Ofun__upd(x,v_x,u,y,z),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.37 58489[0:SpL:9924.0,58248.0] || equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),u,v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.37 58651[0:SpL:23965.1,58188.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v,w),u)* -> .
% 299.64/300.37 58725[0:SpL:456.0,15629.0] || hBOOL(u)* -> hBOOL(hAPP(c_Option_Othe(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Option_Othe(v),w)))*.
% 299.64/300.37 59233[0:SpL:456.0,15857.0] || hBOOL(u)* -> hBOOL(hAPP(c_Option_Othe(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Option_Othe(v),x)))*.
% 299.64/300.37 59733[0:SpL:8385.1,21018.0] || equal(u,v_Procs) equal(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.37 59754[0:SpL:10063.0,21018.0] || equal(hAPP(c_Set_Oimage(u,t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> .
% 299.64/300.37 59985[0:MRR:11125.3,59984.0] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),u,tc_bool)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> .
% 299.64/300.37 59986[0:MRR:25580.3,59984.0] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(u,c_HOL_Ozero__class_Ozero(tc_bool),tc_bool)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) -> .
% 299.64/300.37 60208[0:SpL:351.0,58170.1] || equal(u,c_COMBK(v,w,x))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v,tc_bool),y,z),u)* -> .
% 299.64/300.37 60257[0:Rew:3014.0,60224.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))* equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),u)* -> .
% 299.64/300.37 62251[0:Res:367.1,4246.1] class_Orderings_Obot(u) class_Lattices_Oupper__semilattice(u) || equal(v,c_Orderings_Obot__class_Obot(u)) -> c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.37 62268[0:Res:421.1,4246.1] class_Orderings_Otop(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(u),v) -> c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)*.
% 299.64/300.37 62586[0:Res:367.1,4340.1] class_Orderings_Obot(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> equal(v,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.37 62603[0:Res:421.1,4340.1] class_Orderings_Otop(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> equal(c_Orderings_Otop__class_Otop(u),v).
% 299.64/300.37 63745[0:SSi:63708.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(u,v)* equal(c_Orderings_Otop__class_Otop(tc_bool),u)* -> equal(c_Orderings_Otop__class_Otop(tc_bool),v)*.
% 299.64/300.37 63746[4:SSi:63722.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool),u)* -> hBOOL(u)*.
% 299.64/300.37 63765[4:SSi:63654.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v)* -> hBOOL(hAPP(v,w))*.
% 299.64/300.37 63766[4:SSi:63653.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v)* -> c_Hoare__Mirabelle_Ohoare__valids(v,w,t_a)*.
% 299.64/300.37 63767[0:SSi:63641.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(v,w)* c_Finite__Set_Ofinite(w,u)* -> c_Finite__Set_Ofinite(v,u)*.
% 299.64/300.37 63768[0:SSi:63640.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(hAPP(c_in(tc_Com_Opname),v_x),v)* -> hBOOL(hAPP(v,v_Procs))*.
% 299.64/300.37 63952[0:SpR:647.0,115.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),tc_Com_Opname) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname)*.
% 299.64/300.37 65877[0:Res:65647.1,251.1] class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(w,x),v)*.
% 299.64/300.37 65958[0:SpR:65404.1,24020.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.37 65983[0:SpR:65404.1,32669.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x)))*.
% 299.64/300.37 66022[0:SpR:65404.1,9566.0] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),v),tc_bool)*.
% 299.64/300.37 66189[0:SpL:65404.1,3506.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.37 66307[0:Rew:65404.1,66306.1] class_Lattices_Olattice(u) || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x)),v_x)**.
% 299.64/300.37 66330[0:SpR:3229.1,65575.1] || equal(u,v)* equal(hAPP(u,v_x),v_Procs)** -> hBOOL(hAPP(hAPP(v,v_x),v_x))*.
% 299.64/300.37 66454[0:Rew:15476.0,66327.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v_Procs) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v_x))*.
% 299.64/300.37 66461[0:Rew:9.0,66384.0] || equal(hAPP(u,hAPP(v,v_x)),v_Procs) -> hBOOL(hAPP(hAPP(u,hAPP(v,v_x)),v_x))*.
% 299.64/300.37 66465[0:Rew:585.0,66385.0] || equal(hAPP(hAPP(u,v_x),v),v_Procs) -> hBOOL(hAPP(hAPP(hAPP(u,v_x),v),v_x))*.
% 299.64/300.37 69779[0:MRR:69760.3,5375.2] class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 69832[0:Res:67118.3,51.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,w,u)*.
% 299.64/300.37 70078[7:Res:27207.1,11883.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x) hBOOL(hAPP(hAPP(c_in(v),v_x),u))* -> .
% 299.64/300.37 70079[0:Res:3282.1,11883.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_Procs) hBOOL(hAPP(hAPP(c_in(v),v_x),u))* -> .
% 299.64/300.37 70145[0:Res:68748.3,51.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,w,u)*.
% 299.64/300.37 70374[0:Res:1012.1,12983.0] || hBOOL(hAPP(v_G,v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v_na,hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v))))* -> c_Hoare__Mirabelle_Otriple__valid(v_na,u,t_a).
% 299.64/300.37 70418[0:Res:23754.0,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,t_a),v_Procs),v_x),tc_bool))* -> .
% 299.64/300.37 70419[0:Res:7226.0,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(c_Option_Othe(u),v,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x),tc_bool))* -> .
% 299.64/300.37 70594[7:SpL:353.0,70491.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 70616[7:SpL:2267.1,70491.0] || equal(u,hAPP(c_Set_Oinsert(v_x,t_a),v))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 70623[0:SpL:353.0,70492.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 70645[0:SpL:2267.1,70492.0] || equal(u,hAPP(c_Set_Oinsert(v_x,t_a),v))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 70659[0:SpL:3229.1,70400.1] || equal(u,v)* hBOOL(hAPP(u,v_x))* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))* -> .
% 299.64/300.37 70850[4:MRR:62502.2,70845.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool),u)* -> .
% 299.64/300.37 70977[0:Res:9268.0,70856.2] || equal(u,hAPP(v,v_x))* hBOOL(u)* -> equal(hAPP(c_Set_Oinsert(v_x,t_a),v),v)**.
% 299.64/300.37 70984[0:SSi:70958.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(w,u)* hBOOL(w)* hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool))* -> .
% 299.64/300.37 71012[0:SSi:70995.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(w,c_HOL_Ouminus__class_Ouminus(v,tc_bool))* hBOOL(w)* hBOOL(u)* -> .
% 299.64/300.37 71372[7:SpL:397.1,71221.0] class_Orderings_Otop(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool))* equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x) -> .
% 299.64/300.37 71373[7:SpL:365.1,71221.0] class_Orderings_Obot(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool))* equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x) -> .
% 299.64/300.37 71500[7:SpR:71455.1,10745.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool)*.
% 299.64/300.37 71513[7:SpR:71455.1,10746.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool)*.
% 299.64/300.37 71586[7:SpR:71455.1,415.0] || equal(u,v_x) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,t_a),u,u,v,w),c_Set_Oinsert(v_x,t_a))**.
% 299.64/300.37 71588[7:SpR:71455.1,9566.0] || equal(u,v_x) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,t_a)),u),tc_bool)*.
% 299.64/300.37 71807[7:SpL:71455.1,21018.0] || equal(u,v_x) equal(hAPP(c_Set_Oimage(v,t_a,w),u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.37 72484[7:Res:27207.1,12554.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)** -> hBOOL(hAPP(hAPP(c_in(w),v_x),u))*.
% 299.64/300.37 72485[0:Res:3282.1,12554.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(w),v_x),u))*.
% 299.64/300.37 72613[0:Res:1012.1,12988.1] || hBOOL(hAPP(v_G,v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v_na,u)))* hBOOL(hAPP(u,v))* -> c_Hoare__Mirabelle_Otriple__valid(v_na,v,t_a)*.
% 299.64/300.37 73086[7:Res:71608.1,19641.0] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_in(t_a),v_x),u),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_in(t_a),v_x),u,t_a)*.
% 299.64/300.37 73227[7:SpR:71835.1,318.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a))** c_Finite__Set_Ofinite(v_x,v) -> c_Finite__Set_Ofinite(v_x,w).
% 299.64/300.37 73267[7:SpR:71835.1,23864.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_Fun_Ofun__upd(v_x,c_Orderings_Obot__class_Obot(tc_bool),v_x,u,v),v_x)**.
% 299.64/300.37 73336[7:SpR:71835.1,397.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Set_Oinsert(v_x,t_a))** -> equal(c_Orderings_Otop__class_Otop(u),v_x).
% 299.64/300.37 73341[7:SpR:71835.1,365.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Set_Oinsert(v_x,t_a))** -> equal(c_Orderings_Obot__class_Obot(u),v_x).
% 299.64/300.37 73370[7:SpR:71835.1,24020.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(v_x,v_x),v_x)**.
% 299.64/300.37 73386[7:SpR:71835.1,21267.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,v)),v_x)**.
% 299.64/300.37 73392[7:SpR:71835.1,21893.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,v)),v_x)**.
% 299.64/300.37 73396[7:SpR:71835.1,32669.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),v_x)))*.
% 299.64/300.37 73429[7:SpR:71835.1,23916.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x,tc_Com_Opname,u),v_x)**.
% 299.64/300.37 73430[7:SpR:71835.1,23923.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v_x)**.
% 299.64/300.37 73431[7:SpR:71835.1,23937.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,tc_Com_Opname,u),v_Procs),v_x))*.
% 299.64/300.37 73439[7:SpR:71835.1,28090.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u)))*.
% 299.64/300.37 73442[7:SpR:71835.1,53243.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u),v_x,tc_bool)*.
% 299.64/300.37 73443[7:SpR:71835.1,28394.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u)))*.
% 299.64/300.37 73446[7:SpR:71835.1,53111.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u),v_x,tc_bool)*.
% 299.64/300.37 73459[7:SpR:71835.1,38566.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(v_x,v)))*.
% 299.64/300.37 73513[7:SpR:71835.1,526.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u))* hBOOL(hAPP(v,v_x))* -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.37 73536[7:SpR:71835.1,301.1] class_Lattices_Obounded__lattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(u)),v_x)**.
% 299.64/300.37 73537[7:SpR:71835.1,305.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,hAPP(v_x,v),u)*.
% 299.64/300.37 73538[7:SpR:71835.1,310.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,hAPP(v_x,v),u)*.
% 299.64/300.37 73578[7:SpR:71835.1,9566.0] || equal(hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(hAPP(w,v_x),v_x,tc_bool)*.
% 299.64/300.37 73581[7:SpR:71835.1,9566.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x),tc_bool)*.
% 299.64/300.37 73632[7:SpR:71835.1,305.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(v,v_x,u).
% 299.64/300.37 73633[7:SpR:71835.1,310.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(v,v_x,u).
% 299.64/300.37 73643[7:SpR:71835.1,306.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v,hAPP(v_x,v),u)*.
% 299.64/300.37 73644[7:SpR:71835.1,309.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v,hAPP(v_x,v),u)*.
% 299.64/300.37 73680[7:SpR:71835.1,10813.0] || equal(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(u,v)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,v),v_x),u))*.
% 299.64/300.37 74036[7:SpL:71835.1,3506.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_Com_Ocom_OBODY,u) equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.37 74080[7:SpL:71835.1,23942.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(v_x,u) -> equal(hAPP(u,v_x),v_x)**.
% 299.64/300.37 74095[7:SpL:71835.1,40434.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(v_x,u),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(v)*.
% 299.64/300.37 74096[7:SpL:71835.1,40105.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(hAPP(v_x,u),v,tc_bool)* -> hBOOL(v).
% 299.64/300.37 74124[7:SpL:71835.1,527.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u))* hBOOL(hAPP(v_x,v))* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.37 74443[7:MRR:74260.1,6340.0] || equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(c_Set_Oinsert(v,u),v_x),v_x)**.
% 299.64/300.37 74444[7:MRR:74312.1,6340.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Set_Oinsert(v_x,t_a))** -> equal(v_x,u).
% 299.64/300.37 74445[7:MRR:74328.1,6340.0] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> hBOOL(u).
% 299.64/300.37 74452[7:Obv:74064.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> .
% 299.64/300.37 74776[7:Res:15482.1,72021.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** equal(hAPP(v_x,v_x),hAPP(u,v_x)) -> .
% 299.64/300.37 74778[7:Res:35795.0,72021.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(t_a,tc_bool)),v_x),hAPP(v_x,v_x))** -> .
% 299.64/300.37 74830[7:SpR:397.1,72297.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_x))*.
% 299.64/300.37 74831[7:SpR:365.1,72297.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(u),v_x))*.
% 299.64/300.37 75685[7:SpR:71883.1,72312.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,t_a,u),v_x),v_x))*.
% 299.64/300.37 75734[7:SpL:71883.1,58055.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u,v),v_x)** -> .
% 299.64/300.37 76216[7:SpL:2267.1,71453.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** equal(v,v_x)* -> .
% 299.64/300.37 76243[7:SpL:2267.1,71454.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** equal(v,v_x)* -> .
% 299.64/300.37 76449[7:SpL:2267.1,76240.1] || equal(u,v)* equal(v,v_Procs)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 76732[7:SpR:3229.1,75159.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.37 76746[7:SpR:369.0,71682.1] || equal(hAPP(c_Set_Oinsert(u,v),w),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),v_x))*.
% 299.64/300.37 76786[7:SpR:3229.1,71682.1] || equal(hAPP(c_Set_Oinsert(u,v),w),x)* equal(w,v_x) -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.37 77108[7:SpL:3229.1,72516.0] || equal(c_Set_Oinsert(u,v),w)* equal(hAPP(w,v_x),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.37 77119[7:SpR:3229.1,72588.0] || equal(v_x,u) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),hAPP(u,v_x)))*.
% 299.64/300.37 77145[7:SpL:3229.1,74788.1] || equal(u,v)* equal(v_x,u)* equal(hAPP(v,v_x),w)* -> hBOOL(w)*.
% 299.64/300.37 77264[7:SpR:3229.1,75151.0] || equal(c_Set_Oinsert(u,v),w)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,v),hAPP(w,v_x)),v_x))*.
% 299.64/300.37 77283[7:SpR:3229.1,75151.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.37 77292[7:SpR:71835.1,75266.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),t_a,x),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(v_x,u)).
% 299.64/300.37 77480[7:MRR:77479.2,52007.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Fun_Oinj__on(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v)* -> .
% 299.64/300.37 77834[0:SpL:524.0,5892.0] || hBOOL(u) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,y,z),u))*.
% 299.64/300.37 77903[0:Res:526.1,5892.0] || hBOOL(hAPP(u,u))* -> hBOOL(hAPP(c_COMBS(c_in(v),c_in(w),x,y,z),u))*.
% 299.64/300.37 77912[4:Res:38631.1,5892.0] || c_lessequals(v_x,u,tc_bool) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,x,y),u))*.
% 299.64/300.37 77930[4:Res:38473.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v_x)))*.
% 299.64/300.37 77931[4:Res:38566.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),y)))*.
% 299.64/300.37 78176[7:Res:77996.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) c_Hoare__Mirabelle_Otriple__valid(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.64/300.37 78205[7:MRR:78186.1,6340.0] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname))*.
% 299.64/300.37 78281[7:SpR:78167.0,3294.1] || equal(c_Set_Oinsert(v_x,u),c_in(t_a))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 78394[7:SpL:78167.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_x,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 78522[4:Res:77988.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,w)))*.
% 299.64/300.37 78523[4:Res:77988.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,u,w)))*.
% 299.64/300.37 78529[4:MRR:9458.1,78524.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))**.
% 299.64/300.37 78530[4:MRR:9444.1,78524.0] || hBOOL(hAPP(v_x,u)) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(u,v)),c_Set_Oinsert(u,v))**.
% 299.64/300.37 78544[4:MRR:15789.1,78524.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 78561[7:MRR:27836.1,78524.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 78575[4:MRR:34684.1,78524.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 78576[7:MRR:34683.1,78524.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 78580[4:MRR:52635.2,78524.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 78582[7:MRR:52868.2,78524.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 78589[4:MRR:65951.1,78524.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))**.
% 299.64/300.37 78604[7:Res:27207.1,5986.0] || equal(c_COMBS(c_in(u),v,w,x,y),v_x)** -> hBOOL(hAPP(hAPP(v,v_x),v_x)).
% 299.64/300.37 78605[0:Res:3282.1,5986.0] || equal(c_COMBS(c_in(u),v,w,x,y),v_Procs)** -> hBOOL(hAPP(hAPP(v,v_x),v_x)).
% 299.64/300.37 78690[4:Res:78665.1,279.0] || equal(hAPP(hAPP(c_in(u),v),w),v_x)** -> equal(hAPP(c_Set_Oinsert(v,u),w),w).
% 299.64/300.37 78713[4:Res:78665.1,11894.1] || equal(hAPP(hAPP(c_in(u),v),w),v_x)** equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) -> .
% 299.64/300.37 78715[4:Res:78665.1,8513.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w),v_x)** -> equal(w,u).
% 299.64/300.37 78717[4:Res:78665.1,3499.1] || equal(hAPP(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x)** equal(c_in(v),u) -> .
% 299.64/300.37 78719[4:Res:78665.1,70070.1] || equal(hAPP(hAPP(c_in(t_a),v_x),u),v_x)** hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)) -> .
% 299.64/300.37 78750[4:Res:78665.1,53381.0] || equal(hAPP(v_G,v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v_na,c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)))),v_x)** -> c_Hoare__Mirabelle_Otriple__valid(v_na,u,t_a)*.
% 299.64/300.37 78760[4:Res:78665.1,6935.0] || equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_x)** equal(c_in(u),c_Set_Oinsert(v,w))* -> .
% 299.64/300.37 78762[4:Res:78665.1,38148.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),u),v_x)** -> hBOOL(u).
% 299.64/300.37 78763[4:Res:78665.1,38146.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Option_Ooption_OSome(x,u)),v_x)** -> hBOOL(x).
% 299.64/300.37 78764[4:Res:78665.1,38147.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),z),v_x)** -> hBOOL(u).
% 299.64/300.37 79086[0:Res:78077.0,277.1] || hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,x)))*.
% 299.64/300.37 79087[0:Res:78077.0,278.1] || hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,u,x)))*.
% 299.64/300.37 79113[7:Res:78199.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_in(u),v_x),v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_in(u),v_x),v),v_x,t_a)*.
% 299.64/300.37 79116[7:Res:78199.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_in(w),v_x),u,x)))*.
% 299.64/300.37 79117[7:Res:78199.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_in(v),v_x),w,u,x)))*.
% 299.64/300.37 82126[7:SpR:78597.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(v_x,u),c_Set_Oinsert(v_x,u),v,w),c_Set_Oinsert(v_x,t_a))**.
% 299.64/300.37 82128[7:SpR:78597.0,9566.0] || -> c_lessequals(c_Set_Oinsert(v_x,u),hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,t_a)),c_Set_Oinsert(v_x,u)),tc_bool)*.
% 299.64/300.37 82163[7:SpR:78597.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Set_Oinsert(v_x,w)))*.
% 299.64/300.37 82211[7:SpL:78597.0,214.0] || c_lessequals(c_Set_Oinsert(v_x,u),v,tc_fun(t_a,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.64/300.37 82661[0:Res:367.1,7671.1] class_Orderings_Obot(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(v,w,u)*.
% 299.64/300.37 82852[7:Res:77991.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oinsert(v,w),v_x)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.37 83198[7:SpR:2097.1,78357.0] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),v_x),v_x))*.
% 299.64/300.37 83205[7:SpR:397.1,78357.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,w),v_x),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.37 83206[7:SpR:365.1,78357.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,w),v_x),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.37 83219[7:SpR:300.1,78357.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w),v_x),v_x))*.
% 299.64/300.37 83260[7:SpR:24020.1,78357.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),v_x),v_x))*.
% 299.64/300.37 83510[7:SpL:3229.1,78423.0] || equal(c_Set_Oinsert(u,tc_Com_Opname),v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 83524[7:SpL:2267.1,78423.0] || equal(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 84098[4:SpL:353.0,78769.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),v_x),tc_bool),v_x)** -> .
% 299.64/300.37 84116[4:SpL:3229.1,78769.0] || equal(hAPP(c_Set_Oinsert(v_x,t_a),u),v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),v_x)** -> .
% 299.64/300.37 84144[4:SSi:84124.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),u),v_x),v)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),v_x)** -> .
% 299.64/300.37 84145[7:SpR:3229.1,78284.0] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,u),tc_Com_Opname,v),w)* -> hBOOL(hAPP(v_Procs,hAPP(w,v_x)))*.
% 299.64/300.37 84161[7:SpL:3229.1,78767.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),v_x)** equal(u,v_x)* -> .
% 299.64/300.37 84248[7:SSi:84231.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(u,v_x),v)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),v_x)** equal(u,v_x) -> .
% 299.64/300.37 84279[7:SSi:84262.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),v_x)** equal(hAPP(v_x,v_x),u)* -> .
% 299.64/300.37 84283[0:SpL:768.0,10287.0] || equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,tc_Com_Opname),v_Procs,u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(u,v_Procs).
% 299.64/300.37 84284[0:SpL:770.0,10287.0] || equal(c_Fun_Ofun__upd(c_Option_Othe(u),c_Option_Ooption_OSome(v,u),w,x,y),c_Option_Othe(u))** -> equal(w,v).
% 299.64/300.37 84323[7:SpL:3229.1,82887.0] || equal(c_Set_Oinsert(u,v),w)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(w,v_x),v_x),tc_bool),v_x)** -> .
% 299.64/300.37 84331[7:SpL:3229.1,82887.0] || equal(hAPP(c_Set_Oinsert(u,v),v_x),w)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool),v_x)** -> .
% 299.64/300.37 84346[7:SSi:84336.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),v_x),w)* equal(c_HOL_Ouminus__class_Ouminus(w,tc_bool),v_x)** -> .
% 299.64/300.37 84352[7:SpL:3229.1,82888.0] || equal(c_Set_Oinsert(u,v),w)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 84367[7:SpL:2267.1,82888.0] || equal(u,hAPP(c_Set_Oinsert(v,w),v_x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 84375[7:SpL:3229.1,82889.0] || equal(c_Set_Oinsert(u,v),w)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 84390[7:SpL:2267.1,82889.0] || equal(u,hAPP(c_Set_Oinsert(v,w),v_x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 84425[4:SpR:3229.1,82965.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v,v_x)),w))*.
% 299.64/300.37 84514[4:SpR:3229.1,82966.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(u,v_x),v)),w))*.
% 299.64/300.37 84626[7:SpR:3229.1,83257.0] || equal(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v),w)* -> hBOOL(hAPP(hAPP(w,v_x),v_x))*.
% 299.64/300.37 84628[7:SpR:3229.1,83257.0] || equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v),v_x),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.37 84636[7:SpL:3229.1,84274.1] || equal(v_x,u) equal(v,v_x) equal(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(v,tc_bool))* -> .
% 299.64/300.37 84663[7:SSi:84646.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(u,v_x)* equal(hAPP(v_x,v_x),c_HOL_Ouminus__class_Ouminus(v,tc_bool))* -> .
% 299.64/300.37 84671[4:SpR:3229.1,84492.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v,v_x)),w,t_a)*.
% 299.64/300.37 84700[4:SpR:3229.1,84598.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(u,v_x),v)),w,t_a)*.
% 299.64/300.37 84757[7:SpR:3229.1,78317.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,w)),x)* -> c_lessequals(v_x,hAPP(x,v_x),tc_bool)*.
% 299.64/300.37 84773[7:Res:78317.0,10214.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,w)),v_x),v_x)**.
% 299.64/300.37 84823[7:SpL:78315.0,10287.0] || equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,u),v_x,v,w,x),c_Set_Oinsert(v_x,u))** -> equal(v,v_x).
% 299.64/300.37 84895[4:SpL:302.1,78744.0] class_Lattices_Obounded__lattice(u) || equal(c_Orderings_Otop__class_Otop(u),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.37 84939[7:SpR:3229.1,83237.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),x,y),z)* -> hBOOL(hAPP(hAPP(z,v_x),u))*.
% 299.64/300.37 84941[7:SpR:3229.1,83237.0] || equal(hAPP(c_Set_Oimage(c_COMBK(v_x,u,v),w,x),v_x),y)* -> hBOOL(hAPP(y,v_x))*.
% 299.64/300.37 84954[0:SpR:3229.1,77906.0] || equal(c_COMBS(c_in(u),c_Set_Oinsert(v_x,v),w,x,y),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.64/300.37 85008[0:Res:84957.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oinsert(v,w),v)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v,t_a).
% 299.64/300.37 85115[0:Rew:610.0,85040.1] || c_Fun_Oinj__on(c_COMBK(u,v,tc_Com_Opname),v_Procs,tc_Com_Opname,v)* -> equal(c_Finite__Set_Ocard(v_Procs,tc_Com_Opname),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 299.64/300.37 85320[7:SpL:78597.0,26240.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),c_Set_Oinsert(v_x,v)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** -> .
% 299.64/300.37 85502[4:SpR:3229.1,78507.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(c_Set_Oinsert(v_x,v),hAPP(u,v_x)),hAPP(u,v_x))**.
% 299.64/300.37 85750[7:SpR:78597.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),c_Set_Oinsert(v_x,v))))*.
% 299.64/300.37 85858[0:Con:85838.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oinsert(v,w),x),u,w)))*.
% 299.64/300.37 85863[0:Con:85829.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,w),x),u,w)))* -> hBOOL(hAPP(u,v)).
% 299.64/300.37 86022[0:SpL:397.1,86011.0] class_Orderings_Otop(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool))* equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_Procs) -> .
% 299.64/300.37 86023[0:SpL:365.1,86011.0] class_Orderings_Obot(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool))* equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_Procs) -> .
% 299.64/300.37 86239[0:SpR:86109.1,415.0] || equal(u,v_Procs) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,t_a),u,u,v,w),c_Set_Oinsert(v_x,t_a))**.
% 299.64/300.37 86241[0:SpR:86109.1,9566.0] || equal(u,v_Procs) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,t_a)),u),tc_bool)*.
% 299.64/300.37 86493[0:SpL:86109.1,21018.0] || equal(u,v_Procs) equal(hAPP(c_Set_Oimage(v,t_a,w),u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.37 86543[7:MRR:86542.1,6340.0] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname))*.
% 299.64/300.37 86583[0:SpR:15476.0,19823.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ominus__class_Ominus(v,u,tc_fun(t_a,tc_bool)),v_x),tc_bool))*.
% 299.64/300.37 86681[0:Res:86261.1,19641.0] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_in(t_a),v_x),u),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_in(t_a),v_x),u,t_a)*.
% 299.64/300.37 86706[4:SpL:3229.1,86106.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),v_x)** equal(u,v_Procs)* -> .
% 299.64/300.37 86793[4:SSi:86776.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(u,v_x),v)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),v_x)** equal(u,v_Procs) -> .
% 299.64/300.37 86820[0:SpL:2267.1,86108.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** equal(v,v_Procs)* -> .
% 299.64/300.37 86851[0:SpR:369.0,86345.1] || equal(hAPP(c_Set_Oinsert(u,v),w),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),v_x))*.
% 299.64/300.37 86891[0:SpR:3229.1,86345.1] || equal(hAPP(c_Set_Oinsert(u,v),w),x)* equal(w,v_Procs) -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.37 87181[7:Rew:584.0,87180.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,w),v_x)))*.
% 299.64/300.37 87299[7:SpR:414.0,71492.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),y))*.
% 299.64/300.37 87447[7:SpR:414.0,71493.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),y,t_a)*.
% 299.64/300.37 87577[7:SpR:414.0,71679.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v))*.
% 299.64/300.37 87699[7:SpR:584.0,72664.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v_x,v_x))))*.
% 299.64/300.37 88224[7:SpR:57008.1,87889.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(v_x,v_x)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.37 88475[7:SpL:3229.1,87890.0] || equal(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(t_a,tc_bool)),v)* equal(hAPP(v,v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.37 88485[7:SpL:3229.1,88114.0] || equal(v_x,u) equal(v,c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* equal(v,v_x) -> .
% 299.64/300.37 88498[7:SSi:88489.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(v_x,v_x),u)* equal(v,c_HOL_Ouminus__class_Ouminus(u,tc_bool))* equal(v,v_x) -> .
% 299.64/300.37 88500[7:SpL:3229.1,88263.0] || equal(v_x,u) equal(v,c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool))*.
% 299.64/300.37 88516[7:SSi:88504.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(v_x,v_x),u)* equal(v,c_HOL_Ouminus__class_Ouminus(u,tc_bool))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool))*.
% 299.64/300.37 88553[0:Res:124.0,8306.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)),u,tc_fun(w,tc_bool))*.
% 299.64/300.37 88613[7:SpL:3229.1,88086.1] || equal(u,v)* equal(v_x,u)* hBOOL(c_HOL_Ominus__class_Ominus(w,hAPP(v,v_x),tc_bool))* -> .
% 299.64/300.37 88620[7:SpL:65404.1,88086.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,v_x,tc_bool))* -> .
% 299.64/300.37 88621[7:SpL:525.1,88086.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,v_x,tc_bool))* -> .
% 299.64/300.37 88714[7:SpL:3229.1,88278.0] || equal(v_x,u) equal(v,c_HOL_Ominus__class_Ominus(w,hAPP(u,v_x),tc_bool))* hBOOL(v)* -> .
% 299.64/300.37 88762[7:SpL:55036.1,88660.1] || equal(u,c_HOL_Ouminus__class_Ouminus(v_x,tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x)** hBOOL(u)* -> .
% 299.64/300.37 89048[0:Res:78099.0,279.0] || -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.64/300.37 89428[7:SpR:78590.1,36687.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(v,t_a),u),tc_Com_Opname,tc_bool))*.
% 299.64/300.37 90218[4:SpR:78660.1,36687.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(v,t_a),u),tc_Com_Opname,tc_bool))*.
% 299.64/300.37 91296[0:Rew:91288.1,91203.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(v,v_x),c_Orderings_Obot__class_Obot(u)),v_x)**.
% 299.64/300.37 91297[0:Rew:91288.1,91112.2] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(v,w,u)*.
% 299.64/300.37 91312[0:Rew:91288.1,91216.3,91288.1,91216.2] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(v,c_Orderings_Obot__class_Obot(u)) -> c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.37 91313[0:Rew:91289.1,91204.1,91288.1,91204.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x)),v_x)**.
% 299.64/300.37 91316[0:Rew:91288.1,91084.3,91288.1,91084.2] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> equal(v,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.37 91417[0:Res:91291.2,144.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),u)*.
% 299.64/300.37 91488[0:Res:91292.2,144.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),u)*.
% 299.64/300.37 91749[0:Rew:66819.3,91675.4] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_HOL_Ozero__class_Ozero(u),v)*.
% 299.64/300.37 91750[0:Rew:66821.3,91674.4] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_HOL_Ozero__class_Ozero(u),v)*.
% 299.64/300.37 91751[0:Rew:67585.3,91672.4] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_HOL_Ozero__class_Ozero(u),v)*.
% 299.64/300.37 91752[0:Rew:67583.3,91671.4] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_HOL_Ozero__class_Ozero(u),v)*.
% 299.64/300.37 92128[7:SpR:3229.1,79101.0] || equal(c_in(u),v)* -> equal(hAPP(c_Set_Oinsert(v_x,w),hAPP(v,v_x)),hAPP(v,v_x))**.
% 299.64/300.37 92274[7:SpR:3229.1,92047.0] || equal(c_in(u),v)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(v,v_x),v_x)),w))*.
% 299.64/300.37 92276[7:SpR:3229.1,92047.0] || equal(hAPP(c_in(u),v_x),v)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v,v_x)),w))*.
% 299.64/300.37 92318[7:Res:92047.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x),hAPP(hAPP(c_in(y),v_x),v_x)))*.
% 299.64/300.37 92326[7:SpR:3229.1,92048.0] || equal(c_in(u),v)* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(v,v_x),v_x)),w,t_a)*.
% 299.64/300.37 92328[7:SpR:3229.1,92048.0] || equal(hAPP(c_in(u),v_x),v)* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v,v_x)),w,t_a)*.
% 299.64/300.37 92432[7:SpR:3229.1,92116.0] || equal(c_in(u),v)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(v,v_x),v_x)))*.
% 299.64/300.37 92434[7:SpR:3229.1,92116.0] || equal(hAPP(c_in(u),v_x),v)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(v,v_x)))*.
% 299.64/300.37 92470[7:SpL:3229.1,92132.0] || equal(c_in(u),v)* c_lessequals(hAPP(hAPP(v,v_x),v_x),w,tc_bool)* -> hBOOL(w).
% 299.64/300.37 92472[7:SpL:3229.1,92132.0] || equal(hAPP(c_in(u),v_x),v)* c_lessequals(hAPP(v,v_x),w,tc_bool)* -> hBOOL(w).
% 299.64/300.37 92529[7:Res:10745.0,92132.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_in(w),v_x),v_x))),x))*.
% 299.64/300.37 92530[7:Res:10746.0,92132.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),hAPP(hAPP(c_in(x),v_x),v_x)))*.
% 299.64/300.37 92532[7:Res:10712.0,92132.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(hAPP(hAPP(c_in(x),v_x),v_x),w)))*.
% 299.64/300.37 92533[7:Res:10713.0,92132.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(hAPP(hAPP(c_in(w),v_x),v_x),x,y)),z))*.
% 299.64/300.37 92612[7:SpR:524.0,82151.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,v)))*.
% 299.64/300.37 92623[7:SpR:414.0,82151.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_in(t_a))** -> hBOOL(hAPP(v,c_Set_Oinsert(v_x,y)))*.
% 299.64/300.37 92649[7:SpR:9924.0,82151.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(t_a)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Set_Oinsert(v_x,u)))*.
% 299.64/300.37 92697[7:Res:82151.1,33.0] || equal(c_Set_Ovimage(u,v,w),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(u,c_Set_Oinsert(v_x,x))))*.
% 299.64/300.37 92747[7:SpR:584.0,82185.0] || -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),c_Set_Oinsert(v_x,z)),v_x))*.
% 299.64/300.37 92784[7:Rew:538.0,92767.0,584.0,92767.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),c_Set_Oinsert(v_x,w))))*.
% 299.64/300.37 93272[4:SpR:524.0,85556.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v_x,v),tc_bool)*.
% 299.64/300.37 93283[4:SpR:414.0,85556.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v,y),tc_bool)*.
% 299.64/300.37 93309[4:SpR:9924.0,85556.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(c_Orderings_Otop__class_Otop(tc_bool),u),tc_bool)*.
% 299.64/300.37 93363[4:SpR:26183.0,85556.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(c_Set_Oinsert(v,u),v_x),tc_bool)*.
% 299.64/300.37 93471[0:SpR:414.0,86147.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),y))*.
% 299.64/300.37 93547[0:SpR:584.0,86147.1] || equal(u,v_Procs) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),hAPP(u,v_x)))*.
% 299.64/300.37 93622[0:SpR:414.0,86148.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),y,t_a)*.
% 299.64/300.37 93766[0:SpR:414.0,86342.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v))*.
% 299.64/300.37 94321[4:Res:14491.3,38471.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v_x))* c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.64/300.37 984[0:SpR:525.1,683.1] class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v)*.
% 299.64/300.37 1139[0:SpR:524.0,651.0] || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.37 1144[0:SpR:414.0,651.0] || -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Fun_Ofun__upd(v,v_x,u,w,x),tc_Com_Opname,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.64/300.37 1151[0:SpR:524.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.37 1156[0:SpR:414.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v_x,v,x,y),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.37 1164[0:SpR:302.1,1158.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),v_Procs),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.37 1165[0:SpR:331.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.37 1402[0:SpL:26.1,1393.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 1414[0:SpL:26.1,1394.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u))** -> equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.37 1569[0:SpR:1561.1,88.1] class_OrderedGroup_Oab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),c_HOL_Ozero__class_Ozero(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.37 1572[0:SpR:1561.1,1421.2] class_OrderedGroup_Oab__group__add(u) class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u))** -> equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.37 1573[0:SpR:1561.1,1409.2] class_OrderedGroup_Oab__group__add(u) class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 1577[0:SpL:1561.1,14.1] class_OrderedGroup_Oab__group__add(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u))** -> equal(c_HOL_Ozero__class_Ozero(u),v).
% 299.64/300.37 1614[0:SpL:1561.1,1395.1] class_OrderedGroup_Oab__group__add(u) class_Lattices_Oboolean__algebra(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 1616[0:SpL:26.1,1395.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.37 1860[0:SSi:1854.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,v)* equal(v_Procs,v)* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_x))* -> .
% 299.64/300.37 1887[0:SSi:1881.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** hBOOL(hAPP(v,v_x))* -> .
% 299.64/300.37 1969[0:SSi:1962.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_Procs,u,v),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 2116[0:SpR:2097.1,415.0] || hBOOL(hAPP(u,v)) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v,w),u,u,x,y),c_Set_Oinsert(v,w))**.
% 299.64/300.37 2268[0:SpL:81.0,2063.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.64/300.37 2269[0:SpL:79.0,2063.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) -> equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.64/300.37 2661[0:SpR:337.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),t_a)* hBOOL(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))).
% 299.64/300.37 2854[0:SpR:2807.0,47.2] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_bool),tc_bool)* -> c_lessequals(u,c_HOL_Ouminus__class_Ouminus(u,tc_bool),tc_bool)*.
% 299.64/300.37 2856[0:SpR:2807.0,49.2] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_HOL_Ozero__class_Ozero(tc_bool),tc_bool)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_bool),u,tc_bool)*.
% 299.64/300.37 2885[0:SpL:2807.0,48.1] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(u,c_HOL_Ouminus__class_Ouminus(u,tc_bool),tc_bool)* -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_bool),tc_bool)*.
% 299.64/300.37 2887[0:SpL:2807.0,50.1] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_bool),u,tc_bool)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_HOL_Ozero__class_Ozero(tc_bool),tc_bool)*.
% 299.64/300.37 3267[0:SpR:3229.1,341.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)* -> c_lessequals(v_x,hAPP(w,v_x),tc_fun(u,tc_bool))*.
% 299.64/300.37 3275[0:SpR:3229.1,212.1] || equal(c_Set_Oinsert(u,v),w)* hBOOL(hAPP(v_x,x)) -> hBOOL(hAPP(hAPP(w,v_x),x))*.
% 299.64/300.37 3277[0:SpR:3229.1,342.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v) -> c_lessequals(v_x,hAPP(hAPP(v,v_x),w),tc_fun(u,tc_bool))*.
% 299.64/300.37 3308[0:SpR:3229.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(v,w) -> c_lessequals(hAPP(w,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,u),u)*.
% 299.64/300.37 3314[0:SpR:3229.1,1586.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_Procs,u,v),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.37 3321[0:SpR:3229.1,330.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v) -> equal(hAPP(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_x)**.
% 299.64/300.37 3328[0:SpR:3229.1,303.1] class_Lattices_Obounded__lattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v) -> equal(hAPP(hAPP(v,v_x),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.37 3335[0:SpR:3229.1,302.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v)* -> equal(hAPP(v,v_x),c_Orderings_Otop__class_Otop(u))*.
% 299.64/300.37 3336[0:SpR:3229.1,331.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v)* -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.37 3338[0:SpR:3229.1,212.1] || equal(hAPP(c_Set_Oinsert(u,v),w),x)* hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.37 3345[0:SpR:3229.1,369.0] || equal(c_Set_Oinsert(u,v),w) -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(w,v_x)),hAPP(w,v_x))**.
% 299.64/300.37 3349[0:SpR:3229.1,342.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w) -> c_lessequals(v,hAPP(w,v_x),tc_fun(u,tc_bool))*.
% 299.64/300.37 3352[0:SpR:3229.1,341.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v) -> c_lessequals(w,hAPP(hAPP(v,v_x),w),tc_fun(u,tc_bool))*.
% 299.64/300.37 3490[0:SpL:3229.1,656.0] || equal(c_in(tc_Com_Opname),u) hBOOL(hAPP(hAPP(u,v_x),c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.37 3496[0:SpL:3229.1,1811.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v)* equal(v_Procs,u) hBOOL(hAPP(v,v_x))* -> .
% 299.64/300.37 3569[0:SpR:25.1,3282.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))*.
% 299.64/300.37 3581[0:SpR:337.0,3282.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_Procs)** -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))).
% 299.64/300.37 3605[0:SpR:540.1,3282.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))*.
% 299.64/300.37 3707[0:SpL:2098.1,3483.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a).
% 299.64/300.37 3710[0:SpL:88.1,3483.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 3712[0:SpL:9.0,3483.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Com_Ocom_OBODY)** equal(hAPP(u,hAPP(v,v_x)),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 3730[0:SpR:302.1,3283.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_Procs)).
% 299.64/300.37 3731[0:SpR:331.0,3283.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.37 3753[0:SpR:539.1,3282.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))*.
% 299.64/300.37 3936[0:SpL:2097.1,3506.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(w,x),v_x)** -> .
% 299.64/300.37 3938[0:SpL:397.1,3506.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),c_Orderings_Otop__class_Otop(u))* -> .
% 299.64/300.37 3940[0:SpL:365.1,3506.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),c_Orderings_Obot__class_Obot(u))* -> .
% 299.64/300.37 3947[0:SpL:300.1,3506.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.37 4024[0:SpL:3229.1,3700.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* equal(hAPP(v,v_x),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 4138[0:SpL:3229.1,3929.0] || equal(u,v)* hBOOL(hAPP(v,v_x))* equal(u,w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.37 4191[0:SpR:299.2,3282.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs)** -> hBOOL(v).
% 299.64/300.37 4257[2:SpR:25.1,4250.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))*.
% 299.64/300.37 4263[2:SpR:299.2,4250.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Com_Ocom_OBODY)** -> c_Com_OWT(v).
% 299.64/300.37 4264[2:SpR:539.1,4250.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Com_Ocom_OBODY) -> c_Com_OWT(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))*.
% 299.64/300.37 4265[2:SpR:540.1,4250.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Com_Ocom_OBODY) -> c_Com_OWT(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))*.
% 299.64/300.37 4274[2:SpR:337.0,4250.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))).
% 299.64/300.37 4408[0:SpR:524.0,3284.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),v_x))*.
% 299.64/300.37 4416[0:SpR:414.0,3284.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(y),v_Procs),v))*.
% 299.64/300.37 4464[0:SpL:414.0,3493.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_in(tc_Com_Opname))** equal(v,c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))* -> .
% 299.64/300.37 4505[0:SpR:524.0,3316.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.37 4513[0:SpR:414.0,3316.1] || equal(c_in(u),c_Fun_Ofun__upd(v,v_x,w,x,y))* -> hBOOL(hAPP(w,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.37 4530[0:Res:3316.1,2629.1] || equal(c_in(u),c_in(tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 4534[0:Res:3316.1,33.0] || equal(c_in(u),c_Set_Ovimage(v,w,x))* -> hBOOL(hAPP(v_x,hAPP(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))))*.
% 299.64/300.37 4560[0:SpL:3586.1,3483.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 4641[0:SpL:524.0,3698.2] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x))* equal(c_Com_Ocom_OBODY,u) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 4649[0:SpL:414.0,3698.2] || equal(u,c_Fun_Ofun__upd(v,v_x,w,x,y))* equal(c_Com_Ocom_OBODY,u) equal(w,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 5097[0:SpR:524.0,3339.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x))* -> equal(c_Fun_Ofun__upd(u,v_x,v_x,w,x),u)**.
% 299.64/300.37 5105[0:SpR:414.0,3339.1] || equal(u,c_Fun_Ofun__upd(v,v_x,w,x,y))* -> equal(c_Fun_Ofun__upd(u,v_x,w,z,x1),u)**.
% 299.64/300.37 5184[0:Rew:140.1,5141.4] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w) -> c_lessequals(v,w,u)*.
% 299.64/300.37 5285[0:Rew:140.1,5241.4] class_OrderedGroup_Ogroup__add(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w) -> c_lessequals(v,w,u)*.
% 299.64/300.37 5286[0:Rew:137.1,5240.4] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w) -> c_lessequals(v,w,u)*.
% 299.64/300.37 5380[0:Rew:140.1,5336.4] class_OrderedGroup_Ogroup__add(u) class_Orderings_Oorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w) -> c_lessequals(v,w,u)*.
% 299.64/300.37 5381[0:Rew:137.1,5335.4] class_Lattices_Oboolean__algebra(u) class_Orderings_Oorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w) -> c_lessequals(v,w,u)*.
% 299.64/300.37 5608[0:Rew:140.1,5561.4] class_OrderedGroup_Ogroup__add(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w) -> c_lessequals(v,w,u)*.
% 299.64/300.37 5609[0:Rew:137.1,5560.4] class_Lattices_Oboolean__algebra(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w) -> c_lessequals(v,w,u)*.
% 299.64/300.37 5857[0:SpR:584.0,3282.1] || equal(c_COMBS(u,v,w,x,y),v_Procs)** -> hBOOL(hAPP(hAPP(u,v_x),hAPP(v,v_x)))*.
% 299.64/300.37 5863[2:SpR:584.0,4250.1] || equal(c_COMBS(u,v,w,x,y),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(hAPP(u,v_x),hAPP(v,v_x)))*.
% 299.64/300.37 5884[0:SpR:584.0,675.0] || -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.37 6045[0:SpR:3229.1,5875.0] || equal(c_COMBS(c_Set_Oinsert(hAPP(u,v_x),v),u,w,x,y),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.64/300.37 6652[0:SpR:329.1,3283.1] || c_lessequals(v_x,v_Procs,tc_fun(u,tc_bool))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(v_Procs).
% 299.64/300.37 6940[4:MRR:6922.3,6340.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),v_x,u)* equal(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(u)) -> .
% 299.64/300.37 7199[0:SpR:659.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))))*.
% 299.64/300.37 7259[0:SpR:2093.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_in(tc_Com_Opname),v_x)))*.
% 299.64/300.37 7270[0:SpR:524.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v))*.
% 299.64/300.37 7278[0:SpR:414.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),w))*.
% 299.64/300.37 7303[0:SpR:2095.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.37 7310[0:SpR:3229.1,7283.0] || equal(hAPP(c_Set_Oimage(c_Option_Othe(u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.37 7575[0:Res:7542.0,436.1] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,tc_fun(w,tc_bool)),u))*.
% 299.64/300.37 7594[0:Res:7539.0,436.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(c_Set_Oinsert(y,x),u)),v))*.
% 299.64/300.37 7813[0:Res:683.1,296.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,u),u)*.
% 299.64/300.37 7829[0:SSi:7789.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.64/300.37 7890[0:Obv:7881.1] class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),u),u),v,u)*.
% 299.64/300.37 7966[0:Obv:7956.1] class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),u),u),u)*.
% 299.64/300.37 8058[0:Res:683.1,295.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,u),u)*.
% 299.64/300.37 8074[0:SSi:8034.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.37 8434[0:SpR:8385.1,5875.0] || equal(u,v_Procs) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname),w,x,y),u))*.
% 299.64/300.37 8511[0:Res:652.1,355.0] || c_lessequals(v_Procs,hAPP(c_Set_Oinsert(u,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),tc_fun(tc_Com_Opname,tc_bool))* -> equal(v_x,u).
% 299.64/300.37 8616[0:SpL:8498.1,3483.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 9006[4:MRR:8992.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(v_x,v)).
% 299.64/300.37 9054[0:SpL:2093.0,214.0] || c_lessequals(hAPP(c_in(tc_Com_Opname),v_x),u,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),u)).
% 299.64/300.37 9062[0:SpL:2095.0,214.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),w),v))*.
% 299.64/300.37 9197[0:SpR:303.1,8376.2] class_Lattices_Obounded__lattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) equal(c_Orderings_Otop__class_Otop(u),v_Procs) -> hBOOL(c_Orderings_Otop__class_Otop(u))*.
% 299.64/300.37 9207[0:Res:8376.2,279.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(v,v_Procs) -> equal(hAPP(c_Set_Oinsert(v_x,u),v),v)**.
% 299.64/300.37 9260[0:SpR:3229.1,9258.0] || equal(c_in(t_a),u) -> hBOOL(hAPP(hAPP(u,v_x),v))* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool)).
% 299.64/300.37 9454[0:SpR:3229.1,9268.0] || equal(u,v)* -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),u),u)**.
% 299.64/300.37 9470[0:SpR:351.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_COMBK(u,v,w)),c_COMBK(u,v,w))**.
% 299.64/300.37 9491[0:SSi:9486.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(v,v_x))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),v),v)**.
% 299.64/300.37 9573[0:SSi:9501.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(hAPP(u,v),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,w,x),tc_Com_Opname,tc_fun(y,tc_bool)),v),tc_bool)*.
% 299.64/300.37 9860[0:SpR:8415.2,9747.0] || equal(v_Procs,v_x) equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(v,v_x,tc_bool)*.
% 299.64/300.37 9945[0:SpR:9911.0,3279.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))* -> hBOOL(hAPP(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_Procs),v_x))*.
% 299.64/300.37 9948[0:SpR:9911.0,3285.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.37 9949[0:SpR:9911.0,3291.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_bool)),v_Procs))*.
% 299.64/300.37 9950[0:SpR:9911.0,8415.2] || equal(v_Procs,v_x) equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.37 9951[0:SpR:9911.0,8376.2] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v))*.
% 299.64/300.37 9958[0:SpR:9911.0,3305.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 9959[0:SpR:9911.0,3317.1] || equal(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(v_x,u),w)))*.
% 299.64/300.37 9960[0:SpR:9911.0,3346.1] || equal(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(v),u),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 9975[0:SpL:9911.0,3484.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,v),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(v_x,v).
% 299.64/300.37 9978[0:SpL:9911.0,3499.1] || equal(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.37 9979[0:SpL:9911.0,3507.1] || equal(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))* equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.37 9990[0:SpR:9924.0,651.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.64/300.37 9998[0:SpR:9924.0,3284.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 10004[0:SpR:9924.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.37 10007[0:SpR:9924.0,3316.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.37 10008[0:SpR:9924.0,3339.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))) -> equal(c_Fun_Ofun__upd(u,v_x,c_Orderings_Otop__class_Otop(tc_bool),v,w),u)**.
% 299.64/300.37 10019[0:SpR:9924.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,c_Orderings_Otop__class_Otop(tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.64/300.37 10043[0:SpL:9924.0,3493.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(tc_Com_Opname))** equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.37 10045[0:SpL:9924.0,3698.2] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))* equal(c_Com_Ocom_OBODY,u) equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 10504[0:Res:3283.1,454.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) -> c_Hoare__Mirabelle_Ohoare__valids(v_Procs,u,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v_Procs,u),v_x,t_a)*.
% 299.64/300.37 10524[0:SpR:10463.0,3279.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_Procs),v_x))*.
% 299.64/300.37 10527[0:SpR:10463.0,3285.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.37 10528[0:SpR:10463.0,3291.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_bool)),v_Procs))*.
% 299.64/300.37 10530[0:SpR:10463.0,8376.2] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v))*.
% 299.64/300.37 10537[0:SpR:10463.0,3305.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v_Procs),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.37 10538[0:SpR:10463.0,3317.1] || equal(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Set_Oinsert(v_x,u),w)))*.
% 299.64/300.37 10539[0:SpR:10463.0,3346.1] || equal(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(v),u),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.37 10554[0:SpL:10463.0,3484.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,v),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(v_x,v).
% 299.64/300.37 10557[0:SpL:10463.0,3499.1] || equal(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.37 10558[0:SpL:10463.0,3507.1] || equal(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.37 10679[0:SpR:584.0,9566.0] || -> c_lessequals(hAPP(u,hAPP(v,u)),hAPP(c_COMBS(c_Set_Oinsert(w,x),v,y,z,x1),u),tc_bool)*.
% 299.64/300.37 10680[0:SpR:2097.1,9566.0] || hBOOL(hAPP(u,v)) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(w,x),c_Set_Oinsert(v,y)),u),tc_bool)*.
% 299.64/300.37 10690[0:SpR:397.1,9566.0] class_Orderings_Otop(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(t_a,u))),v_x),tc_bool)*.
% 299.64/300.37 10691[0:SpR:365.1,9566.0] class_Orderings_Obot(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(u),hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,u))),v_x),tc_bool)*.
% 299.64/300.37 10699[0:SpR:300.1,9566.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u))),v),tc_bool)*.
% 299.64/300.37 10724[0:SpR:301.1,9566.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),c_Orderings_Obot__class_Obot(u)),tc_bool)*.
% 299.64/300.37 10747[0:SSi:10741.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),w),x),y,tc_bool)* -> c_lessequals(hAPP(w,x),y,tc_bool).
% 299.64/300.37 10748[0:SSi:10740.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(v,w),tc_bool) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(x,y),v),w),tc_bool)*.
% 299.64/300.37 10786[0:SSi:10780.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),w,tc_bool)* -> c_lessequals(v_Procs,w,tc_bool).
% 299.64/300.37 10787[0:SSi:10779.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v_Procs,tc_bool) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.37 10790[0:Res:114.1,9877.1] class_Finite__Set_Ofinite_Ofinite(u) || c_Fun_Oinj__on(v,w,x,u)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,y,tc_fun(x,tc_bool)),x)*.
% 299.64/300.37 11036[0:SpR:9987.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.37 11046[0:SpL:9987.0,214.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(t_a,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.64/300.37 11198[0:SpR:11176.1,1158.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),v_Procs),u))*.
% 299.64/300.37 11201[0:SpR:11176.1,3229.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* -> equal(u,hAPP(v,v_x))*.
% 299.64/300.37 11202[0:SpR:11176.1,3283.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(u,v_Procs)).
% 299.64/300.37 11261[0:SpR:3229.1,11176.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(hAPP(hAPP(u,v_x),v),v_x)**.
% 299.64/300.37 11326[0:SpR:11177.1,1158.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.37 11329[0:SpR:11177.1,3229.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.37 11330[0:SpR:11177.1,3283.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.37 11390[0:SpR:3229.1,11177.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_Orderings_Otop__class_Otop(tc_bool),v) -> equal(hAPP(hAPP(u,v_x),v),v)**.
% 299.64/300.37 11455[0:SpR:3229.1,10745.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(u,v_x)),x),tc_bool)*.
% 299.64/300.37 11457[0:SpR:2097.1,10745.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v))* -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),tc_bool)*.
% 299.64/300.37 11462[0:SpR:3229.1,10745.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x)* -> c_lessequals(w,hAPP(x,v_x),tc_bool)*.
% 299.64/300.37 11471[0:Res:10745.0,10214.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),x),u)**.
% 299.64/300.37 11481[0:SpR:3229.1,10746.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(v,hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(u,v_x)),v),tc_bool)*.
% 299.64/300.37 11483[0:SpR:2097.1,10746.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v))* -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),tc_bool)*.
% 299.64/300.37 11488[0:SpR:3229.1,10746.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x)* -> c_lessequals(v_x,hAPP(x,v_x),tc_bool)*.
% 299.64/300.37 11497[0:Res:10746.0,10214.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),u),u)**.
% 299.64/300.37 11578[0:SpR:8385.1,9567.0] || equal(u,v_Procs) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),v,tc_fun(w,tc_bool)),u),u,tc_bool)*.
% 299.64/300.37 11592[0:SpR:3229.1,9567.0] || equal(u,v) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,w,tc_fun(x,tc_bool)),v_x),hAPP(v,v_x),tc_bool)*.
% 299.64/300.37 11596[0:SpR:525.1,9567.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(x,tc_bool)),v),v,tc_bool)*.
% 299.64/300.37 11653[0:SpR:3229.1,9567.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)* -> c_lessequals(hAPP(x,v_x),hAPP(u,v_x),tc_bool)*.
% 299.64/300.37 11693[0:Res:10712.0,10214.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),c_Option_Ooption_OSome(u,x)),u)**.
% 299.64/300.37 12722[0:SSi:12710.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(v,w,tc_bool)* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,x,tc_bool),w,tc_bool)*.
% 299.64/300.37 12723[0:SSi:12709.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(w,c_HOL_Ominus__class_Ominus(u,x,tc_bool),tc_bool)* -> c_lessequals(w,v,tc_bool)*.
% 299.64/300.37 12933[0:SpR:3229.1,10713.0] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(w,x,y)),z)* -> c_lessequals(w,hAPP(z,v_x),tc_bool)*.
% 299.64/300.37 12942[0:Res:10713.0,10214.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(hAPP(c_Set_Oinsert(v,w),c_COMBK(u,x,y)),z),u)**.
% 299.64/300.37 12971[0:Res:12960.1,401.0] || c_Natural_Oevalc(u,v,w)* c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSKIP),u),v,x)* -> equal(x,w)*.
% 299.64/300.37 13045[0:SpR:10090.1,5877.0] || equal(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Com_Ocom_OBODY,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Otop__class_Otop(tc_bool),u).
% 299.64/300.37 13058[0:SpR:524.0,10090.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.37 13066[0:SpR:414.0,10090.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.37 13080[0:SpR:9924.0,10090.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.37 13305[0:Res:13238.1,355.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(v_x,u).
% 299.64/300.37 13393[0:Res:13385.1,402.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) c_lessequals(u,w,tc_fun(v,tc_bool))* -> equal(w,u).
% 299.64/300.37 13410[0:Res:13385.1,109.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> c_lessequals(u,w,tc_fun(v,tc_bool))*.
% 299.64/300.37 13435[0:Res:13387.1,402.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) c_lessequals(w,u,tc_fun(v,tc_bool))* -> equal(u,w).
% 299.64/300.37 13452[0:Res:13387.1,109.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) -> c_lessequals(w,u,tc_fun(v,tc_bool))*.
% 299.64/300.37 13517[0:SpR:524.0,11030.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.37 13525[0:SpR:414.0,11030.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_in(t_a))** -> hBOOL(hAPP(v,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))))*.
% 299.64/300.37 13539[0:SpR:9924.0,11030.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(t_a)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.37 13556[0:Res:11030.1,2629.1] || equal(c_in(tc_Com_Opname),c_in(t_a)) equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 13560[0:Res:11030.1,33.0] || equal(c_Set_Ovimage(u,v,w),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.37 13633[0:SpR:11473.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 13650[0:SpL:11473.0,3483.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 14234[0:SpR:14216.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_Com_Opname,x),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 14237[0:SpR:14216.0,3229.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)* -> equal(hAPP(x,v_x),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 14238[0:SpR:14216.0,3283.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_Procs)).
% 299.64/300.37 14352[0:Res:8366.1,170.1] class_Orderings_Olinorder(tc_Com_Opname) || equal(u,v_Procs) c_Finite__Set_Ofinite(u,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(u,tc_Com_Opname),v_x,tc_Com_Opname)*.
% 299.64/300.37 14431[0:SpR:12944.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x1,x2)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 14447[0:SpL:12944.0,3483.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 14479[0:Res:8366.1,169.1] class_Orderings_Olinorder(tc_Com_Opname) || equal(u,v_Procs) c_Finite__Set_Ofinite(u,tc_Com_Opname) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(u,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.37 14528[0:Res:11610.0,12532.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Option_Ooption_OSome(c_HOL_Ominus__class_Ominus(x,y,tc_bool),u)),x,tc_bool)*.
% 299.64/300.37 14562[0:Rew:12629.1,14557.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),tc_bool)* -> equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),u).
% 299.64/300.37 14563[0:Rew:14562.1,12629.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),tc_bool)* -> equal(c_HOL_Ominus__class_Ominus(u,w,tc_bool),u).
% 299.64/300.37 14904[0:Rew:140.1,14834.4] class_OrderedGroup_Ogroup__add(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w) -> c_lessequals(w,v,u)*.
% 299.64/300.37 14905[0:Rew:137.1,14833.4] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w) -> c_lessequals(w,v,u)*.
% 299.64/300.37 15174[0:Res:11611.0,12532.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,x),y,tc_fun(z,tc_bool)),x1),u,tc_bool)*.
% 299.64/300.37 15478[0:Rew:15475.0,13315.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(hAPP(c_in(t_a),v_x),u))* -> .
% 299.64/300.37 15488[0:Rew:15475.0,15412.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),tc_Com_Opname,v),v_Procs),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)))*.
% 299.64/300.37 15489[0:Rew:15475.0,15415.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(v,v_x))*.
% 299.64/300.37 15490[0:Rew:15475.0,15416.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v_Procs))*.
% 299.64/300.37 15523[0:Rew:2807.0,15522.1] || equal(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)))* -> equal(hAPP(v,v_x),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.37 15621[0:Res:658.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),w,u,tc_Com_Opname)))*.
% 299.64/300.37 15624[0:Res:8366.1,278.1] || equal(u,v_Procs) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,w,v,tc_Com_Opname)))*.
% 299.64/300.37 15648[0:Res:15261.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v,u,t_a)))*.
% 299.64/300.37 15790[0:SpR:414.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Fun_Ofun__upd(u,v_x,v,w,x),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool)).
% 299.64/300.37 15849[0:Res:658.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),u,tc_Com_Opname)))*.
% 299.64/300.37 15852[0:Res:8366.1,277.1] || equal(u,v_Procs) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,u,v,tc_Com_Opname)))*.
% 299.64/300.37 15876[0:Res:15261.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,t_a)))*.
% 299.64/300.37 15921[2:SpR:524.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.37 15930[2:SpR:414.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Fun_Ofun__upd(u,v_x,v,w,x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v,tc_bool)).
% 299.64/300.37 16042[0:SSi:16038.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(hAPP(v_x,v),hAPP(c_Orderings_Otop__class_Otop(tc_bool),v),tc_bool)*.
% 299.64/300.37 16151[0:SpR:9911.0,15262.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.37 16152[0:SpR:10463.0,15262.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.37 16234[0:SpL:3229.1,16217.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(u,v_Procs)* -> .
% 299.64/300.37 16239[0:SpL:525.1,16217.0] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_Procs)** -> .
% 299.64/300.37 16284[0:SSi:16276.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(v,v_x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(v,v_Procs) -> .
% 299.64/300.37 16324[0:SpL:15476.0,16286.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs) -> .
% 299.64/300.37 16337[0:SpL:302.1,16286.0] class_Lattices_Obounded__lattice(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> .
% 299.64/300.37 16490[0:MRR:16489.2,826.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 16727[0:MRR:16726.2,826.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.37 16852[0:Res:16753.1,95.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) -> c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(x,v,y),u),y,v)*.
% 299.64/300.37 17004[0:SSi:16992.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),v)* -> c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_bool),v).
% 299.64/300.37 17023[0:SSi:17017.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),v)* -> c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_bool),v).
% 299.64/300.37 17162[0:SpL:17045.0,3483.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 17633[0:Res:12533.1,17530.1] || c_lessequals(u,v,tc_bool)* equal(c_HOL_Ominus__class_Ominus(u,w,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v).
% 299.64/300.37 17832[0:Res:10930.1,3499.1] || equal(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_Procs)** equal(c_in(v),c_Set_Oinsert(w,u))* -> .
% 299.64/300.37 17960[0:Res:3317.1,11894.1] || equal(c_in(u),c_in(v)) equal(hAPP(c_Set_Oinsert(v_x,u),w),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.37 17961[0:Res:3285.1,11894.1] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))* -> .
% 299.64/300.37 17962[0:Res:15262.1,11894.1] || equal(c_in(t_a),c_in(u)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))* -> .
% 299.64/300.37 18311[0:Obv:18300.1] || equal(u,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)))* equal(u,v_Procs) -> .
% 299.64/300.37 18452[0:Res:3284.1,156.0] || equal(c_Set_Ovimage(u,v,w),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_Procs)),v_x))*.
% 299.64/300.37 18672[0:SpR:9911.0,9568.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w),x),tc_bool)*.
% 299.64/300.37 18841[0:Res:1145.0,18768.0] || -> c_lessequals(v_Procs,hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),tc_Com_Opname,tc_fun(w,tc_bool)),v_Procs),tc_bool)*.
% 299.64/300.37 18983[0:SpR:9911.0,9569.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x),tc_bool)*.
% 299.64/300.37 19080[0:Res:10697.0,9857.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 19174[0:Res:448.2,12626.0] class_Orderings_Olinorder(tc_bool) || -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,tc_bool)* c_lessequals(x,u,tc_bool).
% 299.64/300.37 19385[0:Res:448.2,12719.0] class_Orderings_Olinorder(tc_bool) || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool)* c_lessequals(c_HOL_Ominus__class_Ominus(w,x,tc_bool),u,tc_bool)*.
% 299.64/300.37 19439[0:SpR:3744.1,9067.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(v,u),v_Procs)))*.
% 299.64/300.37 19721[0:Res:526.1,19641.0] || hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_in(u),v),w),v))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_in(u),v),w,t_a).
% 299.64/300.37 19746[0:MRR:19709.1,9408.1] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Otop__class_Otop(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,t_a)*.
% 299.64/300.37 19818[0:SpR:104.0,18763.0] || -> c_lessequals(v_Procs,hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_Set_Oinsert(v_x,tc_Com_Opname),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),v_Procs),tc_bool)*.
% 299.64/300.37 19824[0:SpR:104.0,9569.0] || -> c_lessequals(hAPP(u,v),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),v),tc_bool)*.
% 299.64/300.37 19862[0:SpL:104.0,3303.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.37 20057[0:SpR:2267.1,19749.0] || equal(u,c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.37 20219[0:SSi:20209.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),x),hAPP(v,x),tc_bool)*.
% 299.64/300.37 20268[0:SSi:20261.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),x),tc_bool)*.
% 299.64/300.37 20383[0:AED:24.0,20349.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> .
% 299.64/300.37 20398[0:AED:24.0,20374.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,z)* -> .
% 299.64/300.37 20399[0:AED:24.0,20352.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> .
% 299.64/300.37 20401[0:AED:24.0,20333.1] || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y)* -> .
% 299.64/300.37 20853[0:SpR:317.0,16814.1] class_Finite__Set_Ofinite_Ofinite(u) || -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(hAPP(v,w),x),hAPP(c_Set_Oimage(v,u,x),y)),x)*.
% 299.64/300.37 21067[0:SpR:9911.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w),hAPP(c_Set_Oinsert(x,v),y)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 21068[0:SpR:10463.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w),hAPP(c_Set_Oinsert(x,v),y)),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.37 21129[0:SpR:3744.1,20881.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,u,w),v_Procs),hAPP(v,v_x)))*.
% 299.64/300.37 21155[0:SpR:524.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_Procs),v,w),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.37 21164[0:SpR:414.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v_Procs,v,w,x),y,z),hAPP(c_in(tc_Com_Opname),v_x)),v))*.
% 299.64/300.37 21182[0:SpR:9924.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,v),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 21216[0:SpR:524.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.37 21225[0:SpR:414.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v_x,v,w,x),t_a,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),v))*.
% 299.64/300.37 21243[0:SpR:9924.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),t_a,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 21284[0:SpR:21267.0,451.0] || -> c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_x)) equal(hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,v_x),tc_Com_Opname,u)),c_Option_Ooption_ONone(tc_Com_Ocom))**.
% 299.64/300.37 21370[0:SpR:21267.0,415.0] || -> equal(c_Fun_Ofun__upd(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),hAPP(u,v_x),w,x),u)**.
% 299.64/300.37 21775[0:SpR:9911.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 21776[0:SpR:10463.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.37 21910[0:SpR:21893.0,451.0] || -> c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_x)) equal(hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Ocom_OBODY,v_x),c_Com_Ocom_OBODY,tc_Com_Opname,u)),c_Option_Ooption_ONone(tc_Com_Ocom))**.
% 299.64/300.37 21996[0:SpR:21893.0,415.0] || -> equal(c_Fun_Ofun__upd(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),hAPP(u,v_x),w,x),u)**.
% 299.64/300.37 22476[0:SpR:9911.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w),u),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.37 22477[0:SpR:10463.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w),u),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.37 22642[0:SpL:158.0,17943.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,tc_Com_Opname,v),v_Procs)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.37 22723[0:SpR:3294.1,306.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),u)*.
% 299.64/300.37 22724[0:SpR:3294.1,309.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),u)*.
% 299.64/300.37 22727[0:SpR:3294.1,9566.0] || equal(c_Set_Oinsert(u,v),c_in(t_a))** -> c_lessequals(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)*.
% 299.64/300.37 22768[0:SpR:3294.1,9568.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a))** -> c_lessequals(hAPP(v_x,v),hAPP(c_Orderings_Obot__class_Obot(tc_bool),v),tc_bool)*.
% 299.64/300.37 22787[0:SpR:3294.1,5877.0] || equal(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Com_Ocom_OBODY,v,w,x),c_in(t_a))** -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),c_Orderings_Obot__class_Obot(tc_bool),u).
% 299.64/300.37 22820[0:SpR:351.0,3294.1] || equal(c_COMBK(u,v,w),c_in(t_a))** -> equal(hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 23200[0:SpL:351.0,3487.1] || equal(c_COMBK(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 23277[0:SpL:351.0,3489.1] || equal(c_COMBK(u,v,w),c_in(tc_Com_Opname))** hBOOL(hAPP(u,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.37 23317[0:Res:8375.1,3489.1] || equal(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))* equal(c_in(tc_Com_Opname),c_in(u)) -> .
% 299.64/300.37 23319[0:Res:13238.1,3489.1] || equal(hAPP(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_in(tc_Com_Opname),c_in(t_a)) -> .
% 299.64/300.37 23613[0:Rew:23612.0,3247.1] || equal(u,v) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ominus__class_Ominus(v,u,tc_fun(t_a,tc_bool)),v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.37 23737[0:SpR:23682.0,3279.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.37 23740[0:SpR:23682.0,3285.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs)))*.
% 299.64/300.37 23741[0:SpR:23682.0,3291.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),v_Procs))*.
% 299.64/300.37 23743[0:SpR:23682.0,8376.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(u,v_Procs) -> hBOOL(hAPP(v_x,u))*.
% 299.64/300.37 23746[0:SpR:23682.0,15262.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(t_a)) -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.37 23749[0:SpR:23682.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),t_a,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.37 23750[0:SpR:23682.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.37 23759[0:SpR:23682.0,3305.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.37 23760[0:SpR:23682.0,3317.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,u),v)))*.
% 299.64/300.37 23761[0:SpR:23682.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),u),v_x))*.
% 299.64/300.37 23762[0:SpR:23682.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(v),u),v_x))*.
% 299.64/300.37 23793[0:SpR:23682.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v),hAPP(c_Set_Oinsert(w,u),x)),w))*.
% 299.64/300.37 23821[0:SpL:23682.0,3484.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,u),v_x)** -> equal(v_x,u).
% 299.64/300.37 23828[0:SpL:23682.0,3499.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) hBOOL(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.37 23886[0:SpR:23840.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),v),x)),u))*.
% 299.64/300.37 23959[0:SpR:23912.0,3294.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(t_a)) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 24017[0:SpR:23912.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x,y),v),hAPP(hAPP(u,v),v))**.
% 299.64/300.37 24018[0:SpR:23912.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x,y),u),hAPP(u,hAPP(v,u)))**.
% 299.64/300.37 24033[0:SpL:23912.0,3489.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.37 24511[0:SpR:24020.1,24020.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x)**.
% 299.64/300.37 24545[0:SpR:24020.1,415.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(c_Fun_Ofun__upd(hAPP(u,v_x),v_x,v_x,v,w),hAPP(u,v_x))**.
% 299.64/300.37 24612[0:SpR:2097.1,24020.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.37 24618[0:SpR:397.1,24020.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Orderings_Otop__class_Otop(u),v_x),v_x)**.
% 299.64/300.37 24619[0:SpR:365.1,24020.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Orderings_Obot__class_Obot(u),v_x),v_x)**.
% 299.64/300.37 24630[0:SpR:300.1,24020.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.37 24676[0:SpL:24020.1,3506.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.37 24750[0:Rew:9911.0,24651.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.37 24893[0:Res:114.1,24395.0] || c_Fun_Oinj__on(c_COMBK(u,v,w),x,w,v)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),w)*.
% 299.64/300.37 24934[0:SpR:3229.1,23730.0] || equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.37 24973[0:SpR:23902.1,9569.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x,tc_bool)*.
% 299.64/300.37 24975[0:SpR:23902.1,9568.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(hAPP(v,c_Orderings_Obot__class_Obot(tc_bool)),v_x,tc_bool)*.
% 299.64/300.37 24983[0:SpR:23902.1,9569.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v),hAPP(v_x,v),tc_bool)*.
% 299.64/300.37 25001[0:SpR:23902.1,585.0] || equal(c_COMBC(u,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(u,c_Orderings_Obot__class_Obot(tc_bool)),v_x),v_x)**.
% 299.64/300.37 25002[0:SpR:23902.1,586.0] || equal(c_COMBB(u,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(u,hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool))),v_x)**.
% 299.64/300.37 25016[0:SpR:3229.1,23902.1] || equal(u,v)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)* -> equal(hAPP(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.37 25021[0:SpR:525.1,23902.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.37 25632[0:Res:11580.0,24120.1] || equal(c_Orderings_Obot__class_Obot(tc_bool),v_Procs) -> equal(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs),v_Procs)**.
% 299.64/300.37 25671[0:Rew:25670.1,25619.1,25611.1,25619.1] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(x,w).
% 299.64/300.37 25741[0:SpL:3229.1,25662.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(hAPP(u,v_x),v),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(v,v_x).
% 299.64/300.37 25746[0:SpL:3229.1,25662.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(v_x,u).
% 299.64/300.37 26320[0:SSi:26304.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(hAPP(v_x,u),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(v,tc_bool)),u),tc_bool)*.
% 299.64/300.37 26583[0:SpL:584.0,24122.0] || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),y),c_Orderings_Obot__class_Obot(tc_bool))** -> c_lessequals(y,z,tc_bool)*.
% 299.64/300.37 27218[7:SpR:25.1,27207.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))*.
% 299.64/300.37 27229[7:SpR:299.2,27207.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)** -> hBOOL(v).
% 299.64/300.37 27230[7:SpR:539.1,27207.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))*.
% 299.64/300.37 27231[7:SpR:540.1,27207.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))*.
% 299.64/300.37 27249[7:SpR:337.0,27207.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x)** -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))).
% 299.64/300.37 27268[7:SpR:584.0,27207.1] || equal(c_COMBS(u,v,w,x,y),v_x)** -> hBOOL(hAPP(hAPP(u,v_x),hAPP(v,v_x)))*.
% 299.64/300.37 27837[7:SpR:414.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Fun_Ofun__upd(u,v_x,v,w,x),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool)).
% 299.64/300.37 27904[7:MRR:27903.2,826.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 27906[7:MRR:27905.2,826.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.37 27975[0:SpR:524.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.37 27984[0:SpR:414.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_Fun_Ofun__upd(v,v_x,u,w,x),tc_Com_Opname,y)),v_Procs))*.
% 299.64/300.37 28005[0:SpR:9924.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname,u)),v_Procs))*.
% 299.64/300.37 28050[0:SpR:15476.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),tc_Com_Opname,v)))*.
% 299.64/300.37 28063[0:SpR:302.1,28032.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v)))*.
% 299.64/300.37 28088[0:SpR:11177.1,28032.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v)))*.
% 299.64/300.37 28092[0:SpR:11176.1,28032.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v)))*.
% 299.64/300.37 28094[0:SpR:14216.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_Com_Opname,x)))*.
% 299.64/300.37 28277[0:SpR:524.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v_x,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.37 28286[0:SpR:414.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ofun__upd(u,v_x,v,w,x),v,tc_Com_Opname,y)),v_Procs))*.
% 299.64/300.37 28308[0:SpR:9924.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,u)),v_Procs))*.
% 299.64/300.37 28353[0:SpR:15476.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),tc_Com_Opname,v)))*.
% 299.64/300.37 28366[0:SpR:302.1,28335.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v)))*.
% 299.64/300.37 28392[0:SpR:11177.1,28335.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x,tc_Com_Opname,v)))*.
% 299.64/300.37 28396[0:SpR:11176.1,28335.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),u,tc_Com_Opname,v)))*.
% 299.64/300.37 28398[0:SpR:14216.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x)))*.
% 299.64/300.37 28736[0:SpR:524.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.37 28745[0:SpR:414.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_Fun_Ofun__upd(v,v_x,u,w,x),tc_Com_Opname,y),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.37 28767[0:SpR:9924.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname,u),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.37 28891[0:SpR:524.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v_x,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.37 28900[0:SpR:414.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ofun__upd(u,v_x,v,w,x),v,tc_Com_Opname,y),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.37 28922[0:SpR:9924.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,u),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.37 29420[7:SpL:27278.1,3483.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 31358[0:Res:23961.0,467.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x)),v_x)**.
% 299.64/300.37 31469[0:SpL:9911.0,24254.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 31470[0:SpL:10463.0,24254.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 31494[0:SpL:23682.0,24254.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 31679[0:Rew:26279.0,31662.0] || -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.37 31796[7:SpL:3229.1,31778.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(u,v_x)* -> .
% 299.64/300.37 31802[7:SpL:525.1,31778.0] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_x)** -> .
% 299.64/300.37 31866[7:SSi:31858.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(v,v_x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(v,v_x) -> .
% 299.64/300.37 31883[7:SpL:15476.0,31868.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x) -> .
% 299.64/300.37 31897[7:SpL:302.1,31868.0] class_Lattices_Obounded__lattice(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> .
% 299.64/300.37 32271[0:SSi:32261.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_fun(u,tc_bool)),u)* -> c_Finite__Set_Ofinite(v_x,u).
% 299.64/300.37 32621[0:SpR:9911.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool))),v_Procs))*.
% 299.64/300.37 32622[0:SpR:10463.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),c_Orderings_Obot__class_Obot(tc_bool))),v_Procs))*.
% 299.64/300.37 32675[0:SpR:2097.1,32669.0] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),v_x)))*.
% 299.64/300.37 32681[0:SpR:397.1,32669.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u))))*.
% 299.64/300.37 32682[0:SpR:365.1,32669.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,v),c_Orderings_Obot__class_Obot(u))))*.
% 299.64/300.37 32731[0:SpR:24020.1,32669.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(u,v_x),tc_Com_Opname,v),v_x)))*.
% 299.64/300.37 32750[0:SpR:3229.1,32728.0] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v)* -> hBOOL(hAPP(v_Procs,hAPP(v,v_x)))*.
% 299.64/300.37 32828[0:SpR:3229.1,32710.0] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBK(v_x,u,v),tc_Com_Opname,w),x)* -> hBOOL(hAPP(v_Procs,hAPP(x,v_x)))*.
% 299.64/300.37 33105[0:Res:1145.0,32232.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),v,w),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.37 33277[0:SpR:9911.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.37 33278[0:SpR:10463.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.37 33563[0:SpR:9911.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w)))*.
% 299.64/300.37 33564[0:SpR:10463.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w)))*.
% 299.64/300.37 33654[0:SpR:9911.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))*.
% 299.64/300.37 33655[0:SpR:10463.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w)))*.
% 299.64/300.37 33789[7:Obv:33784.1] || equal(u,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)))* equal(u,v_x) -> .
% 299.64/300.37 33857[0:SpR:23965.1,10705.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x),tc_bool)*.
% 299.64/300.37 33862[0:SpL:23965.1,3952.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))* equal(u,c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.37 33901[0:SpL:23965.1,24636.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))* equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.37 34451[0:Rew:331.0,34214.0] || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.37 34455[0:Rew:330.0,33977.0] || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),tc_Com_Opname,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x)),v_x)**.
% 299.64/300.37 34560[0:SpR:34427.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x))*.
% 299.64/300.37 34570[0:SpR:3229.1,34427.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,v),hAPP(u,v_x)),v_x)**.
% 299.64/300.37 34681[0:SpR:34428.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.37 34687[0:SpR:34428.0,3229.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v)* -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.37 34688[0:SpR:34428.0,3283.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.37 34702[0:SpR:34428.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x,tc_Com_Opname,v)))*.
% 299.64/300.37 34708[0:SpR:34428.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_Com_Opname,v)))*.
% 299.64/300.37 34872[0:SpR:9911.0,28053.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),u,tc_Com_Opname,w)))*.
% 299.64/300.37 34873[0:SpR:10463.0,28053.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),u,tc_Com_Opname,w)))*.
% 299.64/300.37 34897[0:SpR:23682.0,28053.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,v)))*.
% 299.64/300.37 34951[0:SpR:9911.0,28356.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))*.
% 299.64/300.37 34952[0:SpR:10463.0,28356.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w)))*.
% 299.64/300.37 34976[0:SpR:23682.0,28356.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,v)))*.
% 299.64/300.37 35452[0:SpR:3744.1,35192.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_in(tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs))*.
% 299.64/300.37 35594[7:Res:29397.1,3499.1] || equal(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x)** equal(c_in(v),c_Set_Oinsert(w,u))* -> .
% 299.64/300.37 35659[0:SpR:3744.1,26119.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs),v_x))*.
% 299.64/300.37 35718[0:SpR:104.0,26119.0] || -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v))*.
% 299.64/300.37 36347[0:SpR:353.0,36264.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Set_Oinsert(v_x,t_a),w)),v_x)))*.
% 299.64/300.37 36366[0:SpR:3229.1,36264.0] || equal(hAPP(c_Set_Oinsert(v_x,t_a),u),v)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(v,v_x)))*.
% 299.64/300.37 36414[0:SpR:353.0,36407.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),v_x)),w))*.
% 299.64/300.37 36433[0:SpR:3229.1,36407.0] || equal(hAPP(c_Set_Oinsert(v_x,t_a),u),v)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v,v_x)),w))*.
% 299.64/300.37 36488[0:SpR:353.0,36471.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),v_x)),w,t_a)*.
% 299.64/300.37 36507[0:SpR:3229.1,36471.0] || equal(hAPP(c_Set_Oinsert(v_x,t_a),u),v)* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v,v_x)),w,t_a)*.
% 299.64/300.37 36530[0:SpL:353.0,36406.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),v_x),w,tc_bool)* -> hBOOL(w).
% 299.64/300.37 36549[0:SpL:3229.1,36406.0] || equal(hAPP(c_Set_Oinsert(v_x,t_a),u),v)* c_lessequals(hAPP(v,v_x),w,tc_bool)* -> hBOOL(w).
% 299.64/300.37 36592[0:Res:10745.0,36406.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(v_x,t_a),w),v_x))),x))*.
% 299.64/300.37 36593[0:Res:10746.0,36406.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),hAPP(hAPP(c_Set_Oinsert(v_x,t_a),x),v_x)))*.
% 299.64/300.37 36595[0:Res:10712.0,36406.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),x),v_x),w)))*.
% 299.64/300.37 36596[0:Res:10713.0,36406.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),w),v_x),x,y)),z))*.
% 299.64/300.37 36765[0:SpL:67.0,656.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.37 37396[0:SpR:9493.1,36687.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(v,t_a),u),tc_Com_Opname,tc_bool))*.
% 299.64/300.37 37539[0:SpR:414.0,36690.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Set_Oinsert(v_x,t_a))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,tc_bool)).
% 299.64/300.37 37640[0:SpL:2267.1,37607.0] || equal(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_x))* -> .
% 299.64/300.37 37643[0:SpL:3229.1,37607.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v)* hBOOL(hAPP(v,v_x))* -> .
% 299.64/300.37 38689[4:SpR:15476.0,37987.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v))*.
% 299.64/300.37 38696[4:SpR:34428.0,37987.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.37 38704[4:SpR:302.1,37987.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v))*.
% 299.64/300.37 38705[4:SpR:331.0,37987.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.37 38732[4:SpR:11177.1,37987.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.37 38736[4:SpR:11176.1,37987.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(u,v))*.
% 299.64/300.37 38738[4:SpR:14216.0,37987.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),x))*.
% 299.64/300.37 38769[4:SpR:538.0,37987.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x))*.
% 299.64/300.37 38771[4:SpR:542.0,37987.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))*.
% 299.64/300.37 38775[4:SpR:329.1,37987.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(u).
% 299.64/300.37 38878[4:SpR:15476.0,38042.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v,t_a)*.
% 299.64/300.37 38885[4:SpR:34428.0,38042.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.37 38893[4:SpR:302.1,38042.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Otop__class_Otop(u),v,t_a)*.
% 299.64/300.37 38894[4:SpR:331.0,38042.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.37 38921[4:SpR:11177.1,38042.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.37 38925[4:SpR:11176.1,38042.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a)*.
% 299.64/300.37 38927[4:SpR:14216.0,38042.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Otop__class_Otop(tc_bool),x,t_a)*.
% 299.64/300.37 40023[4:SSi:40001.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v_x))))*.
% 299.64/300.37 40110[4:SSi:40086.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w))))*.
% 299.64/300.37 40148[4:SpR:584.0,38631.1] || c_lessequals(v_x,hAPP(u,v),tc_bool) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,w,x,y),v))*.
% 299.64/300.37 40166[4:Res:38631.1,19641.0] || c_lessequals(v_x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool)* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,t_a).
% 299.64/300.37 40174[4:SSi:40139.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,u,tc_bool) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u)))*.
% 299.64/300.37 40269[4:SSi:40233.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,u,tc_bool) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w)))*.
% 299.64/300.37 40389[4:SSi:40357.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u,tc_bool))*.
% 299.64/300.37 40390[4:SSi:40344.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),v,tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w))*.
% 299.64/300.37 40391[4:SSi:40341.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),v,tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v))*.
% 299.64/300.37 40392[4:SSi:40316.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),v_x)),w,tc_bool)* -> hBOOL(w).
% 299.64/300.37 40437[4:SSi:40423.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(w)*.
% 299.64/300.37 40506[4:SSi:40485.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v)),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(w)*.
% 299.64/300.37 40607[4:SSi:40576.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_bool))*.
% 299.64/300.37 40608[4:SSi:40563.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),v,tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w))*.
% 299.64/300.37 40609[4:SSi:40560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),v,tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v))*.
% 299.64/300.37 40610[4:SSi:40527.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v)),w,tc_bool)* -> hBOOL(w).
% 299.64/300.37 40685[4:SSi:40637.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,u,tc_bool) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(w)*.
% 299.64/300.37 40686[4:SSi:40634.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,u,tc_bool) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(w)*.
% 299.64/300.37 40816[4:Res:11610.0,40171.0] || c_lessequals(v_x,hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Option_Ooption_OSome(x,u)),tc_bool)* -> hBOOL(x).
% 299.64/300.37 40817[4:Res:11611.0,40171.0] || c_lessequals(v_x,hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),z),tc_bool)* -> hBOOL(u).
% 299.64/300.37 40818[4:Res:23997.0,40171.0] || c_lessequals(v_x,hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),u),tc_bool)* -> hBOOL(u).
% 299.64/300.37 40844[4:SSi:40749.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(v_x,u,tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w))*.
% 299.64/300.37 40845[4:SSi:40746.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(v_x,u,tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v))*.
% 299.64/300.37 41077[4:Res:11610.0,40323.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Option_Ooption_OSome(x,u)),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(x).
% 299.64/300.37 41078[4:Res:11611.0,40323.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),z),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(u).
% 299.64/300.37 41079[4:Res:23997.0,40323.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),u),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(u).
% 299.64/300.37 41452[4:SpR:3229.1,38236.1] || equal(u,v)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)* -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(v,v_x),tc_Com_Opname,tc_bool))*.
% 299.64/300.37 41756[4:SpR:3229.1,38613.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(v,v_x)),v_x))*.
% 299.64/300.37 41764[4:SpR:3229.1,38613.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.37 41773[4:SpR:3229.1,40094.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x),v,w,x),y))*.
% 299.64/300.37 41924[4:SpR:3229.1,41783.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x),v,w,x),y,t_a)*.
% 299.64/300.37 42036[4:SpR:3229.1,38616.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,v_x,v_x,x,y)),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.64/300.37 42358[4:SpR:584.0,40371.0] || -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z)),v_x))*.
% 299.64/300.37 42584[4:SpR:584.0,40590.0] || -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),z))*.
% 299.64/300.37 42596[4:SpR:584.0,40590.0] || -> hBOOL(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v,w,x,y),z))*.
% 299.64/300.37 42785[4:SpL:3229.1,42604.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(u,v_x)))* -> .
% 299.64/300.37 42823[4:SpR:584.0,40591.0] || -> hBOOL(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))*.
% 299.64/300.37 43179[4:SpR:584.0,42609.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),z,t_a)*.
% 299.64/300.37 43840[0:SpR:584.0,38130.1] || hBOOL(u) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(v,w),x,y,z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)))*.
% 299.64/300.37 44106[0:SpR:584.0,38134.1] || hBOOL(u) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(v,w),x,y,z,x1),c_COMBK(u,x2,x3)))*.
% 299.64/300.37 44479[0:Res:448.2,36528.1] class_Orderings_Olinorder(tc_bool) || equal(c_in(tc_Com_Opname),c_in(t_a)) -> c_lessequals(u,hAPP(v_Procs,v_x),tc_bool)* hBOOL(u).
% 299.64/300.37 44517[0:Res:9568.0,36528.1] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_Procs),v),v_x))*.
% 299.64/300.37 44518[0:Res:9569.0,36528.1] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs),v_x))*.
% 299.64/300.37 44525[0:SSi:44495.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(v_Procs,v_x),u,v),tc_Com_Opname,tc_bool))*.
% 299.64/300.37 44632[0:SpR:104.0,35656.1] || equal(u,v_Procs) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.37 44834[0:SpR:584.0,44716.0] || -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),v_x))*.
% 299.64/300.37 45188[0:SpR:104.0,36600.0] || -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v_x,t_a),v),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v_x))*.
% 299.64/300.37 46630[4:SpL:414.0,46565.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),v)* -> .
% 299.64/300.37 46655[4:SpL:9924.0,46565.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.37 46683[0:Res:1145.0,44639.0] || equal(u,v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.37 46699[0:Res:20186.0,44639.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.37 46706[0:Res:20152.0,44639.0] || equal(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> hBOOL(hAPP(v,v_x)).
% 299.64/300.37 46833[0:SpL:3744.1,44750.0] || equal(c_in(tc_Com_Opname),c_in(t_a)) c_lessequals(v_Procs,u,tc_fun(v,tc_bool))* -> hBOOL(hAPP(u,v_x)).
% 299.64/300.37 46856[0:Res:1145.0,44750.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_Set_Oinsert(v_x,t_a),u),v,w),tc_Com_Opname,tc_fun(x,tc_bool)),v_x))*.
% 299.64/300.37 47029[0:Res:448.2,38189.0] class_Orderings_Olinorder(tc_bool) || hBOOL(u) -> c_lessequals(v,u,tc_bool)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v))*.
% 299.64/300.37 47151[0:SSi:47053.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,w,x),tc_Com_Opname,tc_bool)))*.
% 299.64/300.37 47448[4:SpR:584.0,47319.0] || -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool)))*.
% 299.64/300.37 47693[4:Res:448.2,47549.0] class_Orderings_Olinorder(tc_bool) || -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool),tc_bool)* hBOOL(u).
% 299.64/300.37 47734[4:SSi:47709.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool),u,v),tc_Com_Opname,tc_bool))*.
% 299.64/300.37 47749[0:Res:448.2,38190.0] class_Orderings_Olinorder(tc_bool) || hBOOL(u) -> c_lessequals(v,u,tc_bool)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w))*.
% 299.64/300.37 47873[0:SSi:47773.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,tc_bool)),x))*.
% 299.64/300.37 48126[4:SpR:9911.0,39023.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_bool)),x))*.
% 299.64/300.37 48127[4:SpR:10463.0,39023.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_bool)),x))*.
% 299.64/300.37 48152[4:SpR:23682.0,39023.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),w))*.
% 299.64/300.37 48241[4:SpR:9911.0,39064.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_bool)),x,t_a)*.
% 299.64/300.37 48242[4:SpR:10463.0,39064.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_bool)),x,t_a)*.
% 299.64/300.37 48267[4:SpR:23682.0,39064.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),v_x),w,t_a)*.
% 299.64/300.37 48868[4:SpR:3744.1,42583.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(v,tc_bool)),w))*.
% 299.64/300.37 49847[0:Res:49657.0,95.0] || -> c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),x,z)*.
% 299.64/300.37 50097[4:SpR:3744.1,43177.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(v,tc_bool)),w,t_a)*.
% 299.64/300.37 50319[0:Res:448.2,46309.0] class_Orderings_Olinorder(tc_bool) || hBOOL(u) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u),tc_bool)* hBOOL(v).
% 299.64/300.37 50359[0:Res:9568.0,46309.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),u))*.
% 299.64/300.37 50360[0:Res:9569.0,46309.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),u))*.
% 299.64/300.37 50375[0:SSi:50335.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(u) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u),w,x),tc_Com_Opname,tc_bool))*.
% 299.64/300.37 50702[0:Res:448.2,46413.0] class_Orderings_Olinorder(tc_bool) || hBOOL(u) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),tc_bool)* hBOOL(v).
% 299.64/300.37 50742[0:Res:9568.0,46413.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),w),x))*.
% 299.64/300.37 50743[0:Res:9569.0,46413.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),x))*.
% 299.64/300.37 50757[0:SSi:50718.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(u) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,x),tc_Com_Opname,tc_bool))*.
% 299.64/300.37 51064[0:SSi:50959.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(u) -> hBOOL(x)*.
% 299.64/300.37 51365[0:SpR:23682.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.37 51463[0:SpR:23965.1,32700.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),v_x)))*.
% 299.64/300.37 51472[0:SpL:3744.1,33513.1] || equal(c_in(tc_Com_Opname),c_in(u)) c_Finite__Set_Ofinite(v_Procs,u) equal(c_Finite__Set_Ocard(v_Procs,u),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.37 51483[0:SpL:2098.1,33513.1] || c_Finite__Set_Ofinite(u,tc_Hoare__Mirabelle_Otriple(t_a)) equal(c_Finite__Set_Ocard(u,tc_Hoare__Mirabelle_Otriple(t_a)),c_HOL_Ozero__class_Ozero(tc_nat))** -> c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)*.
% 299.64/300.37 51852[4:Res:40792.1,3499.1] || c_lessequals(v_x,hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_bool)* equal(c_in(u),c_Set_Oinsert(v,w))* -> .
% 299.64/300.37 52044[0:Res:448.2,50366.0] class_Orderings_Olinorder(tc_bool) || c_lessequals(u,v,tc_bool)* hBOOL(w) -> c_lessequals(u,w,tc_bool)* hBOOL(v).
% 299.64/300.37 52154[0:SSi:52068.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,tc_bool),x,tc_bool)* hBOOL(u) -> hBOOL(x).
% 299.64/300.37 52252[0:SpL:3744.1,35720.0] || equal(c_in(tc_Com_Opname),c_in(u)) c_lessequals(v_Procs,v,tc_fun(u,tc_bool))* -> hBOOL(hAPP(v,v_x)).
% 299.64/300.37 52292[0:Res:1145.0,35720.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_Set_Oinsert(u,v),w),x,y),tc_Com_Opname,tc_fun(v,tc_bool)),u))*.
% 299.64/300.37 53112[0:SSi:53097.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,u,tc_bool) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v),u,tc_bool)*.
% 299.64/300.37 53113[0:SSi:53063.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v),tc_bool)* -> c_lessequals(u,v_x,tc_bool).
% 299.64/300.37 53149[0:Res:53111.0,17530.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.37 53244[0:SSi:53229.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,u,tc_bool) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),u,tc_bool)*.
% 299.64/300.37 53245[0:SSi:53195.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),tc_bool)* -> c_lessequals(u,v_x,tc_bool).
% 299.64/300.37 53267[0:Res:53243.0,17530.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.37 53440[0:SpR:33303.0,10813.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x)))*.
% 299.64/300.37 53753[0:Res:7226.0,2629.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(c_Option_Othe(u),v,tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 55491[0:SpR:3229.1,54593.1] || equal(u,v)* equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> c_lessequals(w,hAPP(v,v_x),tc_bool)*.
% 299.64/300.37 55606[0:Rew:9.0,55543.0] || equal(hAPP(u,hAPP(v,v_x)),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(w,hAPP(u,hAPP(v,v_x)),tc_bool)*.
% 299.64/300.37 55619[0:Rew:585.0,55544.0] || equal(hAPP(hAPP(u,v_x),v),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(w,hAPP(hAPP(u,v_x),v),tc_bool)*.
% 299.64/300.37 55714[0:SSi:55660.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(u,tc_bool),tc_bool)*.
% 299.64/300.37 55900[0:SpL:414.0,55174.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),y)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),hAPP(y,v_x))* -> .
% 299.64/300.37 55982[0:SpL:414.0,55174.1] || equal(u,c_Fun_Ofun__upd(v,v_x,w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),w)* -> .
% 299.64/300.37 56125[7:SpR:30368.2,27207.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.37 56126[0:SpR:30368.2,3282.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.37 56137[2:SpR:30368.2,4250.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.37 56321[0:SpR:30368.2,1103.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),t_a)* hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.37 56566[7:SpR:30928.2,27207.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.37 56567[0:SpR:30928.2,3282.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.37 56578[2:SpR:30928.2,4250.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.37 56763[0:SpR:30928.2,1103.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),t_a)* hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.37 57931[0:SpL:9911.0,55910.1] || equal(c_COMBK(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> .
% 299.64/300.37 57932[0:SpL:10463.0,55910.1] || equal(c_COMBK(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) -> .
% 299.64/300.37 57958[0:SpL:23682.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) -> .
% 299.64/300.37 58115[0:SpL:23682.0,55992.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_COMBK(u,v,w))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u) -> .
% 299.64/300.37 58149[0:Rew:2807.0,58065.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_COMBK(v,w,x))* equal(hAPP(u,v_x),v) -> .
% 299.64/300.37 58176[0:SpL:34428.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u,v),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,w))* -> .
% 299.64/300.37 58186[0:SpL:302.1,58055.0] class_Lattices_Obounded__lattice(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> .
% 299.64/300.37 58187[0:SpL:331.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))* -> .
% 299.64/300.37 58255[0:Rew:3014.0,58215.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w))* -> .
% 299.64/300.37 58256[0:Rew:3014.0,58219.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* -> .
% 299.64/300.37 58257[0:Rew:2990.0,58231.0] || equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),u,v),c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),y,tc_fun(z,tc_bool)))* -> .
% 299.64/300.37 58432[0:SSi:58428.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v_x) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)))** -> .
% 299.64/300.37 58445[0:SpL:3229.1,58248.0] || equal(u,v) equal(c_COMBK(hAPP(v,v_x),w,x),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.37 58454[0:SpL:525.1,58248.0] class_Lattices_Oupper__semilattice(u) || equal(c_COMBK(v_x,v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.37 58838[0:Res:264.0,15629.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w)))*.
% 299.64/300.37 58908[0:Res:36264.0,15629.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)))*.
% 299.64/300.37 59346[0:Res:264.0,15857.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x)))*.
% 299.64/300.37 59416[0:Res:36264.0,15857.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w)))*.
% 299.64/300.37 59731[0:SpL:2097.1,21018.0] || hBOOL(hAPP(u,v))* equal(hAPP(c_Set_Oimage(w,x,y),u),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))** -> .
% 299.64/300.37 59747[0:SpL:2098.1,21018.0] || equal(hAPP(c_Set_Oimage(u,tc_Hoare__Mirabelle_Otriple(t_a),v),w),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> c_Hoare__Mirabelle_Ohoare__valids(x,w,t_a)*.
% 299.64/300.37 60227[0:SpL:23682.0,58170.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v,w),u)* -> .
% 299.64/300.37 60261[0:Rew:2807.0,60177.1] || equal(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool))) equal(c_COMBK(hAPP(v,v_x),w,x),u)* -> .
% 299.64/300.37 61186[4:Obv:61143.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Obot__class_Obot(u),v_x)** equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> .
% 299.64/300.37 61707[0:SpL:2097.1,10885.0] || hBOOL(hAPP(u,v_x)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,tc_Com_Opname),u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 61934[0:SpL:351.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBK(u,v,w),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 61954[0:SpL:23912.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 61983[0:Rew:3014.0,61950.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.37 62157[0:Res:23754.0,2629.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.37 62384[0:SSi:62221.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(w,u) -> c_lessequals(w,u,tc_fun(v,tc_bool))*.
% 299.64/300.37 62385[0:SSi:62217.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) equal(u,w) -> c_lessequals(u,w,tc_fun(v,tc_bool))*.
% 299.64/300.37 63555[4:Res:62367.1,40171.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),u) c_lessequals(v_x,u,tc_bool) -> hBOOL(c_HOL_Ominus__class_Ominus(u,v,tc_bool))*.
% 299.64/300.37 63748[0:SSi:63730.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(hAPP(v_Procs,v_x),u)* equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(u)*.
% 299.64/300.38 63749[0:SSi:63729.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w)* hBOOL(v) -> hBOOL(w)*.
% 299.64/300.38 63750[0:SSi:63728.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w)* hBOOL(u) -> hBOOL(w)*.
% 299.64/300.38 63751[4:SSi:63723.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool),u)* -> hBOOL(u)*.
% 299.64/300.38 63752[0:SSi:63713.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(u,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,w,tc_bool),x,tc_bool))* -> c_lessequals(u,v,tc_bool)*.
% 299.64/300.38 63753[0:SSi:63710.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(u,c_HOL_Ominus__class_Ominus(v,w,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,x,tc_bool),v,tc_bool)*.
% 299.64/300.38 63754[0:SSi:63704.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(u,v)* hBOOL(u)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v))*.
% 299.64/300.38 63755[0:SSi:63703.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(u,v)* hBOOL(u)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w))*.
% 299.64/300.38 63756[0:SSi:63701.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Olinorder(tc_bool) || equal(u,v)* c_lessequals(v,w,tc_bool)* hBOOL(u)* -> hBOOL(w).
% 299.64/300.38 63771[0:SSi:63659.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(c_Set_Oinsert(v_x,tc_Com_Opname),v) -> c_lessequals(v_Procs,hAPP(v,v_Procs),tc_bool)*.
% 299.64/300.38 63772[0:SSi:63649.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(hAPP(c_Set_Oinsert(v,u),w),x)* -> hBOOL(hAPP(x,v))*.
% 299.64/300.38 63773[0:SSi:63621.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(v,w) -> c_lessequals(hAPP(v,x),hAPP(w,x),tc_bool)*.
% 299.64/300.38 63954[0:SpR:647.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v),tc_bool)*.
% 299.64/300.38 64146[4:Obv:64132.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(u),v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a))** -> .
% 299.64/300.38 64528[0:SpL:351.0,24257.1] || equal(c_COMBK(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(u,c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.38 65981[0:SpR:65404.1,23902.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.38 65992[0:SpR:65404.1,683.1] class_Lattices_Olattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v)*.
% 299.64/300.38 66020[0:SpR:65404.1,415.0] class_Lattices_Olattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v,v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.64/300.38 66046[0:SpR:65404.1,9567.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(x,tc_bool)),v),v,tc_bool)*.
% 299.64/300.38 66182[7:SpL:65404.1,31778.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_x)** -> .
% 299.64/300.38 66183[0:SpL:65404.1,16217.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_Procs)** -> .
% 299.64/300.38 66200[0:SpL:65404.1,58248.0] class_Lattices_Olattice(u) || equal(c_COMBK(v_x,v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.38 66679[0:Rew:140.1,66554.4] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w) -> c_lessequals(w,v,u)*.
% 299.64/300.38 66680[0:Rew:137.1,66553.4] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w) -> c_lessequals(w,v,u)*.
% 299.64/300.38 67659[0:SpR:67115.3,367.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.38 67946[0:SpR:67416.3,367.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.38 69133[0:SpR:67573.3,367.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Orderings_Obot(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.38 69425[0:SpR:68745.3,367.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.38 70063[0:SpL:135.0,11883.0] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))))* -> .
% 299.64/300.38 70407[0:Res:3317.1,70070.1] || equal(c_in(u),c_in(t_a)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(v_x,u),v),v_x),tc_bool))* -> .
% 299.64/300.38 70408[0:Res:3285.1,70070.1] || equal(c_in(tc_Com_Opname),c_in(t_a)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),v_x),tc_bool))* -> .
% 299.64/300.38 70851[4:MRR:62503.2,70845.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool),u)* -> .
% 299.64/300.38 70852[0:MRR:62508.3,70845.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),u)* hBOOL(v) -> .
% 299.64/300.38 70853[0:MRR:62509.3,70845.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),u)* hBOOL(w) -> .
% 299.64/300.38 70854[0:MRR:62510.3,70845.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(v_Procs,v_x),u)* equal(c_in(tc_Com_Opname),c_in(t_a)) -> .
% 299.64/300.38 70975[7:Res:27219.1,70856.2] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** equal(v,hAPP(u,v_x))* hBOOL(v)* -> .
% 299.64/300.38 70976[0:Res:15482.1,70856.2] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** equal(v,hAPP(u,v_x))* hBOOL(v)* -> .
% 299.64/300.38 70978[0:Res:35795.0,70856.2] || equal(u,hAPP(c_HOL_Ominus__class_Ominus(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_fun(t_a,tc_bool)),v_x))* hBOOL(u)* -> .
% 299.64/300.38 71194[0:SSi:71184.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(v_Procs,v_x)) equal(c_in(tc_Com_Opname),c_in(t_a)) hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))* -> .
% 299.64/300.38 71219[7:SpL:2267.1,70589.1] || equal(u,v)* hBOOL(hAPP(v,v_x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.38 71394[7:SpL:302.1,71221.0] class_Lattices_Obounded__lattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> .
% 299.64/300.38 71587[7:SpR:71455.1,5875.0] || equal(u,v_x) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,t_a),w,x,y),u))*.
% 299.64/300.38 71620[7:SpR:71455.1,9567.0] || equal(u,v_x) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,t_a),v,tc_fun(w,tc_bool)),u),u,tc_bool)*.
% 299.64/300.38 72499[0:SSi:72473.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),hAPP(v,v_x),tc_bool))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)).
% 299.64/300.38 72666[7:Res:10697.0,71881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(v_x,v_x))),hAPP(v_x,v_x)))*.
% 299.64/300.38 73049[7:Res:71608.1,169.1] class_Orderings_Olinorder(t_a) || equal(u,v_x) c_Finite__Set_Ofinite(u,t_a) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(u,t_a),t_a)*.
% 299.64/300.38 73050[7:Res:71608.1,170.1] class_Orderings_Olinorder(t_a) || equal(u,v_x) c_Finite__Set_Ofinite(u,t_a) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(u,t_a),v_x,t_a)*.
% 299.64/300.38 73092[7:Res:71608.1,277.1] || equal(u,v_x) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,u,v,t_a)))*.
% 299.64/300.38 73093[7:Res:71608.1,278.1] || equal(u,v_x) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,w,v,t_a)))*.
% 299.64/300.38 73236[7:SpR:71835.1,342.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> c_lessequals(v_x,hAPP(v_x,v),tc_fun(u,tc_bool))*.
% 299.64/300.38 73250[7:SpR:71835.1,11176.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(hAPP(v_x,u),v_x)**.
% 299.64/300.38 73254[7:SpR:71835.1,10745.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(u,v),v_x),w),tc_bool)*.
% 299.64/300.38 73329[7:SpR:71835.1,9258.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(t_a)) -> hBOOL(hAPP(v_x,u)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.38 73347[7:SpR:71835.1,15476.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v_x)**.
% 299.64/300.38 73394[7:SpR:71835.1,23902.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.38 73399[7:SpR:71835.1,24914.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),v_x)),v_x)**.
% 299.64/300.38 73405[7:SpR:71835.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Set_Oinsert(v_x,t_a),v) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,u),u)*.
% 299.64/300.38 73450[7:SpR:71835.1,32728.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_x,tc_Com_Opname,u),v_x)))*.
% 299.64/300.38 73453[7:SpR:71835.1,34427.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v_x),v_x)**.
% 299.64/300.38 73460[7:SpR:71835.1,40094.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x,u,v,w),x))*.
% 299.64/300.38 73461[7:SpR:71835.1,41783.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x,u,v,w),x,t_a)*.
% 299.64/300.38 73470[7:SpR:71835.1,23955.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(v_x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u)),v_x)**.
% 299.64/300.38 73471[7:SpR:71835.1,23958.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(v_x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u)),v_x)**.
% 299.64/300.38 73515[7:SpR:71835.1,330.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_x)**.
% 299.64/300.38 73544[7:SpR:71835.1,303.1] class_Lattices_Obounded__lattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.38 73554[7:SpR:71835.1,11177.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(v_x,u),u)**.
% 299.64/300.38 73573[7:SpR:71835.1,302.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Set_Oinsert(v_x,t_a))** -> equal(c_Orderings_Otop__class_Otop(u),v_x).
% 299.64/300.38 73641[7:SpR:71835.1,342.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(v,v_x,tc_fun(u,tc_bool)).
% 299.64/300.38 73652[7:SpR:71835.1,341.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> c_lessequals(v,hAPP(v_x,v),tc_fun(u,tc_bool))*.
% 299.64/300.38 73687[7:SpR:71835.1,10746.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),v_x),u),tc_bool)*.
% 299.64/300.38 73695[7:SpR:71835.1,9567.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(v_x,hAPP(u,v_x),tc_bool).
% 299.64/300.38 73698[7:SpR:71835.1,9567.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x),v_x,tc_bool)*.
% 299.64/300.38 73806[7:SpR:71835.1,11176.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Set_Oinsert(v_x,t_a))** equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(v_x,u).
% 299.64/300.38 73838[7:SpR:71835.1,14216.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Set_Oinsert(v_x,t_a))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.38 73862[7:SpR:71835.1,10745.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(w,v_x,tc_bool).
% 299.64/300.38 73889[7:SpR:71835.1,10713.0] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(w,x,y)),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(w,v_x,tc_bool).
% 299.64/300.38 73990[7:SpL:71835.1,25662.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(v_x,u),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(u,v_x).
% 299.64/300.38 74011[7:SpL:71835.1,656.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) hBOOL(hAPP(v_x,c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.38 74029[7:SpL:71835.1,31778.0] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(u,v_x) -> .
% 299.64/300.38 74030[7:SpL:71835.1,16217.0] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(u,v_Procs) -> .
% 299.64/300.38 74056[7:SpL:71835.1,3700.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 74075[7:SpL:71835.1,24027.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(c_Com_Ocom_OSemi(u,v),v_x)** -> .
% 299.64/300.38 74099[7:SpL:71835.1,42604.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x))* -> .
% 299.64/300.38 74446[7:MRR:74330.1,6340.0] || equal(hAPP(c_Set_Ovimage(u,v,w),x),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(x,hAPP(u,v_x))).
% 299.64/300.38 74447[7:MRR:74311.1,6340.0] || equal(hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(w,v_x)) equal(u,v_x).
% 299.64/300.38 74449[7:MRR:74175.1,6340.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,u,v)))*.
% 299.64/300.38 74450[7:MRR:74174.1,6340.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,w)))*.
% 299.64/300.38 74459[7:Rew:71835.1,73324.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,u,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v_x,u),v_Procs,t_a)*.
% 299.64/300.38 74460[7:Rew:71835.1,73323.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v_x,u),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,u,t_a)*.
% 299.64/300.38 74779[7:Res:36017.0,72021.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),v_x),hAPP(v_x,v_x))** -> .
% 299.64/300.38 74833[7:SpR:15476.0,72297.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_in(t_a)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v_x))*.
% 299.64/300.38 74853[7:SpR:302.1,72297.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_x)).
% 299.64/300.38 74887[7:SpR:11176.1,72297.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a))** -> hBOOL(hAPP(u,v_x)).
% 299.64/300.38 74889[7:SpR:14216.0,72297.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x)).
% 299.64/300.38 75566[0:SSi:75412.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),v_x),tc_bool)*.
% 299.64/300.38 75567[0:SSi:75410.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),v_x),tc_bool)*.
% 299.64/300.38 77138[7:SpL:397.1,74788.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x)** equal(c_Orderings_Otop__class_Otop(u),v)* -> hBOOL(v)*.
% 299.64/300.38 77139[7:SpL:365.1,74788.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x)** equal(c_Orderings_Obot__class_Obot(u),v)* -> hBOOL(v)*.
% 299.64/300.38 77481[7:SpL:71835.1,72390.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(t_a)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,v_x,tc_Com_Opname),v_x),tc_bool))* -> .
% 299.64/300.38 77483[7:SpL:3229.1,72390.0] || equal(c_in(t_a),u) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(u,v_x),tc_Com_Opname),v_x),tc_bool))* -> .
% 299.64/300.38 77487[7:SpL:3229.1,72390.0] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname),u)* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* -> .
% 299.64/300.38 77505[7:SSi:77494.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname),v_x))* hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))* -> .
% 299.64/300.38 77639[7:SpL:71835.1,77504.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(t_a)) equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,v_x,tc_Com_Opname),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.38 77641[7:SpL:3229.1,77504.0] || equal(c_in(t_a),u) equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(u,v_x),tc_Com_Opname),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.38 77645[7:SpL:3229.1,77504.0] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname),u)* equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.38 77835[0:SpL:65404.1,5892.0] class_Lattices_Olattice(u) || hBOOL(v) -> hBOOL(hAPP(c_COMBS(c_in(w),c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z),v))*.
% 299.64/300.38 77836[0:SpL:525.1,5892.0] class_Lattices_Oupper__semilattice(u) || hBOOL(v) -> hBOOL(hAPP(c_COMBS(c_in(w),c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z),v))*.
% 299.64/300.38 77929[0:Res:36264.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x),hAPP(hAPP(c_Set_Oinsert(v_x,t_a),y),v_x)))*.
% 299.64/300.38 77967[0:Res:212.1,5892.0] || hBOOL(hAPP(u,u))* -> hBOOL(hAPP(c_COMBS(c_in(v),c_Set_Oinsert(w,x),y,z,x1),u))*.
% 299.64/300.38 77979[0:Res:7283.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(c_Option_Othe(v),w,x),y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.38 78023[0:Rew:538.0,77915.0,584.0,77915.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_Procs),hAPP(c_in(tc_Com_Opname),v_x))))*.
% 299.64/300.38 78025[4:Rew:538.0,77943.0,584.0,77943.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w))))*.
% 299.64/300.38 78026[0:Rew:538.0,77945.0,584.0,77945.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.38 78029[0:Rew:584.0,77971.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(v,v_x,v_Procs,w,x),tc_Com_Opname,y),v_Procs)))*.
% 299.64/300.38 78047[0:MRR:77878.1,820.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,x,y),u))*.
% 299.64/300.38 78051[7:MRR:78050.1,6340.0] || equal(hAPP(u,v_x),c_Set_Oinsert(v_x,t_a)) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(u,v_x)))*.
% 299.64/300.38 78169[7:Res:77996.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,u,w,tc_fun(x,tc_bool)),v))*.
% 299.64/300.38 78325[7:SpR:78167.0,446.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,v),u),v_x,tc_fun(v,tc_bool))*.
% 299.64/300.38 78344[7:SpR:78167.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.38 78504[4:Res:77988.0,255.0] || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),v_x),u)).
% 299.64/300.38 78531[4:MRR:9457.0,78524.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x))**.
% 299.64/300.38 78532[4:MRR:9453.2,78524.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),u),u)**.
% 299.64/300.38 78545[4:MRR:15791.2,78524.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(t_a,tc_bool)),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a).
% 299.64/300.38 78546[4:MRR:15780.2,78524.0] || equal(hAPP(c_in(u),v),v_Procs) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v,u),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.38 78547[4:MRR:15768.2,78524.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v,u),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.38 78562[7:MRR:27838.2,78524.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(t_a,tc_bool)),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a).
% 299.64/300.38 78563[7:MRR:27827.2,78524.0] || equal(hAPP(c_in(u),v),v_Procs) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v,u),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.38 78564[7:MRR:27814.2,78524.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v,u),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.38 78568[7:MRR:29328.2,78524.0] || equal(hAPP(c_in(u),v),v_x) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v,u),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.38 78569[7:MRR:29327.2,78524.0] || equal(hAPP(c_in(u),v),v_x) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v,u),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.38 78656[4:SpL:2771.1,78632.1] || equal(u,v)* equal(hAPP(u,v_x),v_x)** hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))* -> .
% 299.64/300.38 78675[4:Res:78665.1,1815.1] || equal(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool))),v_x)** equal(u,v_Procs) -> .
% 299.64/300.38 78714[4:Res:78665.1,371.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),w),x),v_x)** -> hBOOL(hAPP(w,x)) equal(u,x).
% 299.64/300.38 78716[4:Res:78665.1,33.0] || equal(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y),v_x)** -> hBOOL(hAPP(x,hAPP(u,y))).
% 299.64/300.38 78718[4:Res:78665.1,3489.1] || equal(hAPP(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))),v_x)** equal(c_in(tc_Com_Opname),u) -> .
% 299.64/300.38 78734[4:Res:78665.1,15857.0] || equal(hAPP(u,v),v_x)** -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,x)))*.
% 299.64/300.38 78735[4:Res:78665.1,15629.0] || equal(hAPP(u,v),v_x)** -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,u,w)))*.
% 299.64/300.38 78759[4:Res:78665.1,24036.1] || equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_x)** equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> .
% 299.64/300.38 78761[4:Res:78665.1,23321.0] || equal(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))),v_x)** equal(c_Set_Oinsert(u,v),c_in(tc_Com_Opname))** -> .
% 299.64/300.38 78831[4:SpL:2771.1,78653.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),v_x)** hBOOL(hAPP(u,v_x))* -> .
% 299.64/300.38 79050[0:Rew:23682.0,78998.0] || hBOOL(u) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v))*.
% 299.64/300.38 79070[0:Res:78077.0,255.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),v)).
% 299.64/300.38 79098[7:Res:78199.0,255.0] || c_lessequals(hAPP(c_in(u),v_x),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),v_x),v)).
% 299.64/300.38 79270[0:Rew:23682.0,79218.0] || hBOOL(u) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(u,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w))*.
% 299.64/300.38 79830[0:SpR:659.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),v_Procs,u,v)),v_Procs)**.
% 299.64/300.38 79979[7:SpR:78167.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,u),v_x,v,w)),v_x)**.
% 299.64/300.38 80510[4:SSi:80502.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_Procs) -> .
% 299.64/300.38 80522[7:SSi:80514.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) -> .
% 299.64/300.38 81024[0:SpR:659.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_Procs,c_Set_Oinsert(v_x,tc_Com_Opname),u,v)),v_Procs)**.
% 299.64/300.38 81173[7:SpR:78167.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v_x,c_Set_Oinsert(v_x,u),v,w)),v_x)**.
% 299.64/300.38 82127[7:SpR:78597.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(c_Set_Oinsert(v_x,u),v),c_Set_Oinsert(v_x,t_a),w,x,y),c_Set_Oinsert(v_x,u)))*.
% 299.64/300.38 82164[7:SpR:78597.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,t_a),u,tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,w)),c_Set_Oinsert(v_x,w),tc_bool)*.
% 299.64/300.38 82567[7:Res:82148.0,169.1] class_Orderings_Olinorder(t_a) || c_Finite__Set_Ofinite(c_Set_Oinsert(v_x,u),t_a) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(v_x,u),t_a),t_a)*.
% 299.64/300.38 82568[7:Res:82148.0,170.1] class_Orderings_Olinorder(t_a) || c_Finite__Set_Ofinite(c_Set_Oinsert(v_x,u),t_a) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(v_x,u),t_a),v_x,t_a)*.
% 299.64/300.38 82856[7:Res:77991.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(w,x),v_x),u,y)))*.
% 299.64/300.38 82857[7:Res:77991.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,w),v_x),x,u,y)))*.
% 299.64/300.38 83208[7:SpR:15476.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v,w),v_x),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)))*.
% 299.64/300.38 83215[7:SpR:34428.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v,w),v_x),v_x))*.
% 299.64/300.38 83225[7:SpR:302.1,78357.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),v_x),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.38 83226[7:SpR:331.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,w),v_x),v_x))*.
% 299.64/300.38 83255[7:SpR:11177.1,78357.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),v_x),v_x))*.
% 299.64/300.38 83259[7:SpR:11176.1,78357.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),v_x),u))*.
% 299.64/300.38 83261[7:SpR:14216.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,y),v_x),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.38 84156[7:SpL:397.1,78767.0] class_Orderings_Otop(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v_x)** equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x) -> .
% 299.64/300.38 84157[7:SpL:365.1,78767.0] class_Orderings_Obot(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool),v_x) equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x)** -> .
% 299.64/300.38 84699[4:SSi:84687.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),v_x))),w,t_a)*.
% 299.64/300.38 84745[4:SSi:84718.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v))),w,t_a)*.
% 299.64/300.38 84787[7:SSi:84763.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,w)),v_x),x,tc_bool)* -> c_lessequals(v_x,x,tc_bool).
% 299.64/300.38 84788[7:SSi:84762.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v_x,tc_bool) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,x)),v_x),tc_bool)*.
% 299.64/300.38 84843[7:SpL:158.0,78444.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.38 85012[0:Res:84957.0,277.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oinsert(v,x),v),u,y)))*.
% 299.64/300.38 85013[0:Res:84957.0,278.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,w),v),x,u,y)))*.
% 299.64/300.38 85289[7:SpR:3229.1,75156.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(u,v_x),tc_Com_Opname,tc_fun(v,tc_bool)),v_x))*.
% 299.64/300.38 85291[7:SpR:3229.1,75156.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(u,tc_bool)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.38 85466[4:SpR:78507.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))*.
% 299.64/300.38 85504[4:SpL:78507.0,33513.1] || c_Finite__Set_Ofinite(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u) equal(c_Finite__Set_Ocard(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.38 85543[4:SpL:78507.0,26240.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.38 85733[0:SpR:2093.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_in(tc_Com_Opname),v_x))))*.
% 299.64/300.38 85745[0:SpR:9987.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))))*.
% 299.64/300.38 85755[4:SpR:78507.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))))*.
% 299.64/300.38 85879[4:SSi:85871.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))** equal(c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> .
% 299.64/300.38 85880[4:SpL:3229.1,78540.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.38 85889[4:SpL:2267.1,78540.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.38 85892[7:SpL:3229.1,78556.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.38 85901[7:SpL:2267.1,78556.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.38 85904[4:SpR:3229.1,85486.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(v,t_a),hAPP(u,v_x)),tc_Com_Opname,tc_bool))*.
% 299.64/300.38 85943[7:Res:27207.1,13582.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)** hBOOL(hAPP(hAPP(c_in(w),v_x),v))* -> .
% 299.64/300.38 85944[0:Res:3282.1,13582.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_Procs)** hBOOL(hAPP(hAPP(c_in(w),v_x),v))* -> .
% 299.64/300.38 85964[4:SpR:3229.1,85725.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(u,v_x),tc_Com_Opname,v),v_x),v_x,tc_bool)*.
% 299.64/300.38 85966[4:SpR:3229.1,85725.0] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v)* -> c_lessequals(hAPP(v,v_x),v_x,tc_bool)*.
% 299.64/300.38 86009[0:SpL:2267.1,70618.1] || equal(u,v)* hBOOL(hAPP(v,v_x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.38 86042[0:SpL:302.1,86011.0] class_Lattices_Obounded__lattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> .
% 299.64/300.38 86240[0:SpR:86109.1,5875.0] || equal(u,v_Procs) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,t_a),w,x,y),u))*.
% 299.64/300.38 86273[0:SpR:86109.1,15630.1] || equal(u,v_Procs) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,w,v,t_a)))*.
% 299.64/300.38 86278[0:SpR:86109.1,9567.0] || equal(u,v_Procs) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,t_a),v,tc_fun(w,tc_bool)),u),u,tc_bool)*.
% 299.64/300.38 86340[0:SpR:86109.1,15858.1] || equal(u,v_Procs) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,u,v,t_a)))*.
% 299.64/300.38 86611[0:MRR:86610.2,826.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** hBOOL(hAPP(v,x))* -> .
% 299.64/300.38 86643[0:Res:86261.1,169.1] class_Orderings_Olinorder(t_a) || equal(u,v_Procs) c_Finite__Set_Ofinite(u,t_a) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(u,t_a),t_a)*.
% 299.64/300.38 86644[0:Res:86261.1,170.1] class_Orderings_Olinorder(t_a) || equal(u,v_Procs) c_Finite__Set_Ofinite(u,t_a) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(u,t_a),v_x,t_a)*.
% 299.64/300.38 86701[4:SpL:397.1,86106.0] class_Orderings_Otop(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v_x)** equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_Procs) -> .
% 299.64/300.38 86702[4:SpL:365.1,86106.0] class_Orderings_Obot(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool),v_x) equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_Procs)** -> .
% 299.64/300.38 87119[0:SpL:3229.1,70737.0] || equal(c_HOL_Ominus__class_Ominus(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(t_a,tc_bool)),w)* hBOOL(hAPP(w,v_x))* -> .
% 299.64/300.38 87141[7:SpR:3229.1,82177.0] || equal(c_in(t_a),u) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oinsert(v,t_a),c_Set_Oinsert(v_x,w))))*.
% 299.64/300.38 87172[7:SpR:3229.1,83256.0] || equal(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v),w)* -> hBOOL(hAPP(hAPP(w,v_x),v_x))*.
% 299.64/300.38 87174[7:SpR:3229.1,83256.0] || equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v),v_x),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 87233[7:SpL:3229.1,87157.0] || equal(hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v)),w)* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool))* -> .
% 299.64/300.38 87257[7:SSi:87240.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(hAPP(c_Set_Oinsert(v,t_a),c_Set_Oinsert(v_x,w)),v_x))* hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))* -> .
% 299.64/300.38 87264[7:SpL:3229.1,87254.0] || equal(hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v)),w)* equal(hAPP(w,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.38 87282[7:SpR:3229.1,71492.1] || equal(u,v)* equal(u,v_x)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v,v_x)),w))*.
% 299.64/300.38 87390[7:Res:71492.1,5892.0] || equal(u,v_x) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,x,y),hAPP(u,v_x)))*.
% 299.64/300.38 87430[7:SpR:3229.1,71493.1] || equal(u,v)* equal(u,v_x)* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v,v_x)),w,t_a)*.
% 299.64/300.38 87560[7:SpR:3229.1,71679.1] || equal(u,v)* equal(u,v_x)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(v,v_x)))*.
% 299.64/300.38 87688[7:SpR:3229.1,72664.0] || equal(v_x,u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x))),x))*.
% 299.64/300.38 87710[7:Res:72664.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oinsert(v,w),x,y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v_x,v_x))))*.
% 299.64/300.38 87717[7:SpR:3229.1,72665.0] || equal(v_x,u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),hAPP(u,v_x)))*.
% 299.64/300.38 87819[7:SpR:2267.1,74701.0] || equal(u,c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(w,tc_bool)))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),v_x))*.
% 299.64/300.38 87823[7:SpR:3229.1,74701.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 88600[7:SpL:2097.1,88086.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(w,v_x,tc_bool))* -> .
% 299.64/300.38 88608[7:SpL:397.1,88086.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x) hBOOL(c_HOL_Ominus__class_Ominus(v,c_Orderings_Otop__class_Otop(u),tc_bool))* -> .
% 299.64/300.38 88609[7:SpL:365.1,88086.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x) hBOOL(c_HOL_Ominus__class_Ominus(v,c_Orderings_Obot__class_Obot(u),tc_bool))* -> .
% 299.64/300.38 88622[7:SpL:300.1,88086.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,v_x,tc_bool))* -> .
% 299.64/300.38 88663[7:SpL:24020.1,88086.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,v_x,tc_bool))* -> .
% 299.64/300.38 88730[0:Res:1012.1,12998.0] || hBOOL(hAPP(v_G,v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v_na,u))) -> c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a) c_Hoare__Mirabelle_Otriple__valid(v_na,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,u),t_a)*.
% 299.64/300.38 88743[7:SpL:3229.1,87880.0] || equal(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(t_a,tc_bool)),v)* equal(hAPP(v,v_x),hAPP(v_x,v_x))* -> .
% 299.64/300.38 88796[7:SSi:88781.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(hAPP(v_x,v_x),v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.38 88801[7:SpL:3229.1,88347.0] || equal(v_x,u) equal(v,c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* equal(v,c_Orderings_Otop__class_Otop(tc_bool)) -> .
% 299.64/300.38 88816[7:SSi:88808.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(v_x,v_x))* equal(v,c_HOL_Ouminus__class_Ouminus(u,tc_bool))* equal(v,c_Orderings_Otop__class_Otop(tc_bool)) -> .
% 299.64/300.38 89027[7:SpR:3229.1,75153.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_x,u,v),tc_Com_Opname,tc_fun(w,tc_bool)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.38 89077[7:SpR:3229.1,78350.0] || equal(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,u),v,tc_fun(w,tc_bool)),x)* -> c_lessequals(hAPP(x,v_x),v_x,tc_bool)*.
% 299.64/300.38 89113[7:SpL:2267.1,78407.0] || equal(u,c_Set_Oinsert(v_x,v))* equal(c_COMBK(v_x,w,x),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.38 89328[7:SpR:78590.1,35192.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_in(tc_Com_Opname),t_a,tc_fun(v,tc_bool)),v_Procs))*.
% 299.64/300.38 89329[7:SpR:78590.1,42583.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w))*.
% 299.64/300.38 89330[7:SpR:78590.1,43177.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w,t_a)*.
% 299.64/300.38 89347[7:SpR:78590.1,3317.1] || equal(c_Set_Oinsert(v_x,t_a),u) equal(c_in(t_a),v) -> hBOOL(hAPP(hAPP(v,v_x),u))*.
% 299.64/300.38 89404[7:SpR:78590.1,20881.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,t_a,w),u),hAPP(v,v_x)))*.
% 299.64/300.38 89417[7:SpR:78590.1,9067.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(c_Set_Oinsert(v,t_a),u)))*.
% 299.64/300.38 89429[7:SpR:78590.1,36599.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x))*.
% 299.64/300.38 89431[7:SpR:78590.1,36600.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x))*.
% 299.64/300.38 89485[7:SpL:78590.1,33513.1] || equal(c_Set_Oinsert(v_x,t_a),u) c_Finite__Set_Ofinite(u,t_a) equal(c_Finite__Set_Ocard(u,t_a),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.38 89490[7:SpL:78590.1,44750.0] || equal(c_Set_Oinsert(v_x,t_a),u) c_lessequals(u,v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(v,v_x)).
% 299.64/300.38 89491[7:SpL:78590.1,46860.0] || equal(c_Set_Oinsert(v_x,t_a),u) equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 90019[4:SpR:78660.1,36608.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(u,v_x),v,w),tc_Com_Opname,tc_bool))*.
% 299.64/300.38 90118[4:SpR:78660.1,35192.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_in(tc_Com_Opname),t_a,tc_fun(v,tc_bool)),v_Procs))*.
% 299.64/300.38 90119[4:SpR:78660.1,42583.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w))*.
% 299.64/300.38 90120[4:SpR:78660.1,43177.0] || equal(hAPP(u,v_x),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w,t_a)*.
% 299.64/300.38 90137[4:SpR:78660.1,3317.1] || equal(hAPP(u,v_x),v_x) equal(c_in(t_a),v) -> hBOOL(hAPP(hAPP(v,v_x),u))*.
% 299.64/300.38 90194[4:SpR:78660.1,20881.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,t_a,w),u),hAPP(v,v_x)))*.
% 299.64/300.38 90207[4:SpR:78660.1,9067.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(c_Set_Oinsert(v,t_a),u)))*.
% 299.64/300.38 90219[4:SpR:78660.1,36599.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x))*.
% 299.64/300.38 90221[4:SpR:78660.1,36600.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x))*.
% 299.64/300.38 90276[4:SpL:78660.1,33513.1] || equal(hAPP(u,v_x),v_x)** c_Finite__Set_Ofinite(u,t_a) equal(c_Finite__Set_Ocard(u,t_a),c_HOL_Ozero__class_Ozero(tc_nat)) -> .
% 299.64/300.38 90281[4:SpL:78660.1,44750.0] || equal(hAPP(u,v_x),v_x) c_lessequals(u,v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(v,v_x)).
% 299.64/300.38 90589[4:Rew:25.1,90460.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))*.
% 299.64/300.38 90744[4:Rew:66691.3,90743.3] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ozero__class_Ozero(u),v_x) -> hBOOL(c_HOL_Ozero__class_Ozero(u))*.
% 299.64/300.38 90746[4:Rew:66692.3,90745.3] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ozero__class_Ozero(u),v_x) -> hBOOL(c_HOL_Ozero__class_Ozero(u))*.
% 299.64/300.38 90748[4:Rew:67446.3,90747.3] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ozero__class_Ozero(u),v_x) -> hBOOL(c_HOL_Ozero__class_Ozero(u))*.
% 299.64/300.38 90750[4:Rew:67447.3,90749.3] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ozero__class_Ozero(u),v_x) -> hBOOL(c_HOL_Ozero__class_Ozero(u))*.
% 299.64/300.38 91014[4:Rew:9.0,90964.0] || equal(hAPP(u,hAPP(v,v_x)),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool))* -> .
% 299.64/300.38 91020[4:Rew:585.0,90965.0] || equal(hAPP(hAPP(u,v_x),v),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool))* -> .
% 299.64/300.38 91290[0:Rew:91288.1,91070.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),c_Orderings_Obot__class_Obot(u)),tc_bool)*.
% 299.64/300.38 91444[0:Obv:91384.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Olattice(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.38 91445[0:Obv:91380.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Olattice(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.38 91520[0:Obv:91454.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.38 91521[0:Obv:91452.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.38 91943[0:SpR:79073.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.64/300.38 91961[0:SpR:79073.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.38 91980[0:SpL:79073.0,33513.1] || c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v) equal(c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.38 92009[0:SpL:79073.0,26240.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.38 92096[7:SpR:79101.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_in(x),v_x)))*.
% 299.64/300.38 92111[7:SpR:79101.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_in(w),v_x))))*.
% 299.64/300.38 92130[7:SpL:79101.0,33513.1] || c_Finite__Set_Ofinite(hAPP(c_in(u),v_x),v) equal(c_Finite__Set_Ocard(hAPP(c_in(u),v_x),v),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.38 92168[7:SpL:79101.0,26240.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_in(w),v_x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.38 92324[7:SSi:92295.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_in(v),v_x),v_x)),w)))*.
% 299.64/300.38 92469[7:SSi:92458.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_in(w),v_x),v_x))))*.
% 299.64/300.38 92547[7:SSi:92522.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_in(w),v_x),u,tc_bool))*.
% 299.64/300.38 92548[7:SSi:92497.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_in(u),v_x),v_x),v,tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w))*.
% 299.64/300.38 92549[7:SSi:92494.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_in(u),v_x),v_x),v,tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v))*.
% 299.64/300.38 92550[7:SpR:3229.1,92117.0] || equal(c_in(u),v)* -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(w,t_a),hAPP(v,v_x)),tc_Com_Opname,tc_bool))*.
% 299.64/300.38 92561[7:SpR:3229.1,82133.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(v_x,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 92606[7:SpR:3229.1,82151.1] || equal(u,v)* equal(c_in(t_a),u)* -> hBOOL(hAPP(hAPP(v,v_x),c_Set_Oinsert(v_x,w)))*.
% 299.64/300.38 92613[7:SpR:65404.1,82151.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,v)))*.
% 299.64/300.38 92614[7:SpR:525.1,82151.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,v)))*.
% 299.64/300.38 92682[7:SpR:585.0,82151.1] || equal(c_COMBC(u,v,w,x),c_in(t_a))** -> hBOOL(hAPP(hAPP(u,c_Set_Oinsert(v_x,y)),v_x))*.
% 299.64/300.38 92683[7:SpR:586.0,82151.1] || equal(c_COMBB(u,v,w,x),c_in(t_a))** -> hBOOL(hAPP(u,hAPP(v_x,c_Set_Oinsert(v_x,y))))*.
% 299.64/300.38 92692[7:Res:82151.1,279.0] || equal(c_in(t_a),c_in(u)) -> equal(hAPP(c_Set_Oinsert(v_x,u),c_Set_Oinsert(v_x,v)),c_Set_Oinsert(v_x,v))**.
% 299.64/300.38 92740[7:SpR:338.0,82185.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,w)),x)),v_x))*.
% 299.64/300.38 92760[7:SpR:3229.1,82185.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,v)),w),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.38 93128[7:SpR:339.0,82187.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_x,x))),v_x))*.
% 299.64/300.38 93132[7:SpR:3229.1,82187.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,w)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.38 93167[7:SpR:3229.1,83229.0] || equal(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w),x)* -> hBOOL(hAPP(hAPP(x,v_x),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.38 93182[7:SpR:3229.1,83230.0] || equal(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w),x)* -> hBOOL(hAPP(hAPP(x,v_x),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.38 93266[4:SpR:3229.1,85556.1] || equal(u,v)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)* -> c_lessequals(v_x,hAPP(hAPP(v,v_x),w),tc_bool)*.
% 299.64/300.38 93273[4:SpR:65404.1,85556.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v_x,v),tc_bool)*.
% 299.64/300.38 93274[4:SpR:525.1,85556.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v_x,v),tc_bool)*.
% 299.64/300.38 93384[4:SpR:585.0,85556.1] || equal(c_COMBC(u,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(hAPP(u,y),v_x),tc_bool)*.
% 299.64/300.38 93385[4:SpR:586.0,85556.1] || equal(c_COMBB(u,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(u,hAPP(v_x,y)),tc_bool)*.
% 299.64/300.38 93454[0:SpR:3229.1,86147.1] || equal(u,v)* equal(u,v_Procs)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v,v_x)),w))*.
% 299.64/300.38 93563[0:Res:86147.1,5892.0] || equal(u,v_Procs) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,x,y),hAPP(u,v_x)))*.
% 299.64/300.38 93605[0:SpR:3229.1,86148.1] || equal(u,v)* equal(u,v_Procs)* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v,v_x)),w,t_a)*.
% 299.64/300.38 93749[0:SpR:3229.1,86342.1] || equal(u,v)* equal(u,v_Procs)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(v,v_x)))*.
% 299.64/300.38 93877[7:SpR:3229.1,87712.0] || equal(v_x,u) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x))),x,t_a)*.
% 299.64/300.38 93899[7:SpL:3229.1,87829.0] || equal(c_in(u),v) hBOOL(hAPP(hAPP(v,v_x),c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(u,tc_bool))))* -> .
% 299.64/300.38 773[0:SpR:414.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v,w,x,y),v,w,z,x1),c_Fun_Ofun__upd(u,v,w,x,y))**.
% 299.64/300.38 981[0:SpR:397.1,683.1] class_Orderings_Otop(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,v),v)*.
% 299.64/300.38 982[0:SpR:365.1,683.1] class_Orderings_Obot(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,v),v)*.
% 299.64/300.38 985[0:SpR:300.1,683.1] class_Lattices_Obounded__lattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_Com_Opname,v),v)*.
% 299.64/300.38 1125[0:Res:448.2,682.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,hAPP(c_in(tc_Com_Opname),v_x),tc_fun(u,tc_bool))* hBOOL(hAPP(v,v_Procs)).
% 299.64/300.38 1140[0:SpR:525.1,651.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.38 1152[0:SpR:525.1,648.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.38 1173[0:SpR:88.1,1158.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,v),v_Procs),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.38 1370[0:Obv:1360.0] class_OrderedGroup_Ogroup__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u))* equal(c_HOL_Ouminus__class_Ouminus(w,u),c_HOL_Ozero__class_Ozero(u))** -> equal(w,v)*.
% 299.64/300.38 1482[0:Obv:1473.0] class_Lattices_Oboolean__algebra(u) || equal(v,c_Orderings_Otop__class_Otop(u))* equal(c_HOL_Ouminus__class_Ouminus(w,u),c_Orderings_Obot__class_Obot(u))** -> equal(w,v)*.
% 299.64/300.38 1484[0:Obv:1471.0] class_Lattices_Oboolean__algebra(u) || equal(v,c_Orderings_Otop__class_Otop(u)) equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u))** -> equal(c_Orderings_Obot__class_Obot(u),v)*.
% 299.64/300.38 1487[0:Obv:1458.0] class_Lattices_Oboolean__algebra(u) || equal(v,c_Orderings_Otop__class_Otop(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.38 1488[0:Obv:1457.0] class_Lattices_Oboolean__algebra(u) || equal(v,c_Orderings_Otop__class_Otop(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.38 1523[0:Obv:1514.0] class_Lattices_Oboolean__algebra(u) || equal(v,c_Orderings_Obot__class_Obot(u))* equal(c_HOL_Ouminus__class_Ouminus(w,u),c_Orderings_Otop__class_Otop(u))** -> equal(w,v)*.
% 299.64/300.38 1524[0:Obv:1513.0] class_Lattices_Oboolean__algebra(u) || equal(v,c_Orderings_Obot__class_Obot(u))* equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u))** -> equal(c_Orderings_Otop__class_Otop(u),v).
% 299.64/300.38 1528[0:Obv:1501.0] class_Lattices_Oboolean__algebra(u) || equal(v,c_Orderings_Obot__class_Obot(u))* equal(v,c_Orderings_Otop__class_Otop(u)) -> equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.38 1529[0:Obv:1498.0] class_Lattices_Oboolean__algebra(u) || equal(v,c_Orderings_Obot__class_Obot(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.38 1530[0:Obv:1497.0] class_Lattices_Oboolean__algebra(u) || equal(v,c_Orderings_Obot__class_Obot(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.38 1713[0:Obv:1699.0] class_OrderedGroup_Ogroup__add(u) || equal(v,w)* equal(x,c_HOL_Ouminus__class_Ouminus(v,u))* -> equal(c_HOL_Ouminus__class_Ouminus(x,u),w)*.
% 299.64/300.38 1714[0:Obv:1697.0] class_OrderedGroup_Ogroup__add(u) || equal(v,w)* equal(c_HOL_Ouminus__class_Ouminus(x,u),c_HOL_Ouminus__class_Ouminus(v,u))* -> equal(x,w)*.
% 299.64/300.38 1716[0:Obv:1691.0] class_OrderedGroup_Ogroup__add(u) || equal(v,w)* equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u))** -> equal(c_HOL_Ozero__class_Ozero(u),w)*.
% 299.64/300.38 1721[0:Obv:1671.0] class_OrderedGroup_Ogroup__add(u) || equal(v,w)* equal(x,w)* -> equal(c_HOL_Ouminus__class_Ouminus(x,u),c_HOL_Ouminus__class_Ouminus(v,u))*.
% 299.64/300.38 1723[0:Obv:1665.0] class_OrderedGroup_Ogroup__add(u) || equal(v,w)* equal(w,c_HOL_Ozero__class_Ozero(u))* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.38 1816[0:Obv:1794.0] class_Lattices_Oboolean__algebra(u) || equal(v,w)* equal(x,c_HOL_Ouminus__class_Ouminus(v,u))* -> equal(c_HOL_Ouminus__class_Ouminus(x,u),w)*.
% 299.64/300.38 1817[0:Obv:1792.0] class_Lattices_Oboolean__algebra(u) || equal(v,w)* equal(c_HOL_Ouminus__class_Ouminus(x,u),c_HOL_Ouminus__class_Ouminus(v,u))* -> equal(x,w)*.
% 299.64/300.38 1818[0:Obv:1791.0] class_Lattices_Oboolean__algebra(u) || equal(v,w)* equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u))** -> equal(c_Orderings_Otop__class_Otop(u),w)*.
% 299.64/300.38 1819[0:Obv:1790.0] class_Lattices_Oboolean__algebra(u) || equal(v,w)* equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u))** -> equal(c_Orderings_Obot__class_Obot(u),w)*.
% 299.64/300.38 1826[0:Obv:1766.0] class_Lattices_Oboolean__algebra(u) || equal(v,w)* equal(x,w)* -> equal(c_HOL_Ouminus__class_Ouminus(x,u),c_HOL_Ouminus__class_Ouminus(v,u))*.
% 299.64/300.38 1827[0:Obv:1763.0] class_Lattices_Oboolean__algebra(u) || equal(v,w)* equal(w,c_Orderings_Otop__class_Otop(u))* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u))**.
% 299.64/300.38 1828[0:Obv:1762.0] class_Lattices_Oboolean__algebra(u) || equal(v,w)* equal(w,c_Orderings_Obot__class_Obot(u))* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.38 1830[0:Obv:1758.0] class_Lattices_Oboolean__algebra(u) || equal(v,w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_HOL_Ouminus__class_Ouminus(v,u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.38 1831[0:Obv:1757.0] class_Lattices_Oboolean__algebra(u) || equal(v,w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),w),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.38 1890[0:SpR:9.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname,z),v_Procs),hAPP(u,hAPP(v,v_x))))*.
% 299.64/300.38 2114[0:SpR:2097.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(v_x,v)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,u),u)*.
% 299.64/300.38 2137[0:SpR:2093.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_Procs,u),hAPP(c_in(tc_Com_Opname),v_x),hAPP(c_in(tc_Com_Opname),v_x),v,w),c_Set_Oinsert(v_Procs,u))**.
% 299.64/300.38 2166[0:SpR:2095.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,x),c_Set_Oinsert(u,v))**.
% 299.64/300.38 2184[0:Res:448.2,2092.0] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) || -> c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),u).
% 299.64/300.38 2202[0:SpR:2098.1,1158.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.38 3173[0:SpR:414.0,2771.1] || equal(u,c_Fun_Ofun__upd(v,v_x,w,x,y))* -> equal(c_HOL_Ouminus__class_Ouminus(w,tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.38 3268[0:SpR:3229.1,650.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(u,v_x)))*.
% 299.64/300.38 3278[0:SpR:3229.1,649.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(hAPP(u,v_x),v_Procs)))*.
% 299.64/300.38 3286[0:SpR:3229.1,650.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)))*.
% 299.64/300.38 3287[0:SpR:3229.1,649.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)))*.
% 299.64/300.38 3288[0:SpR:3229.1,652.1] || equal(c_in(tc_Com_Opname),u) c_lessequals(v_Procs,v,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(u,v_x),v))*.
% 299.64/300.38 3289[0:SpR:3229.1,675.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(u,v_x)),w),v_Procs))*.
% 299.64/300.38 3290[0:SpR:3229.1,676.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(u,v_x)),v_Procs))*.
% 299.64/300.38 3301[0:SpR:3229.1,1161.0] || equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,v),v_Procs),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 3304[0:SpR:3229.1,651.0] || equal(u,v) -> c_lessequals(hAPP(v,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.38 3309[0:SpR:3229.1,648.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(v,v_x)),hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v_Procs)))*.
% 299.64/300.38 3312[0:SpR:3229.1,1161.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(v,v_x),tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.38 3322[0:SpR:3229.1,676.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* -> hBOOL(hAPP(hAPP(hAPP(v,v_x),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.38 3329[0:SpR:3229.1,87.1] class_Lattices_Oboolean__algebra(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v) -> equal(hAPP(hAPP(v,v_x),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.38 3337[0:SpR:3229.1,675.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),v)* -> hBOOL(hAPP(hAPP(v,v_x),v_Procs))*.
% 299.64/300.38 3341[0:SpR:3229.1,499.0] || equal(c_Hoare__Mirabelle_Otriple_Otriple(u),v) -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(hAPP(v,v_x),hAPP(c_Com_Ocom_OBODY,w)),x),u)*.
% 299.64/300.38 3342[0:SpR:3229.1,2098.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),v)* -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(hAPP(v,v_x),v_x)**.
% 299.64/300.38 3343[0:SpR:3229.1,499.0] || equal(c_Com_Ocom_OBODY,u) -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(u,v_x)),x),v)*.
% 299.64/300.38 3357[0:SpR:3229.1,168.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x)),v)* -> hBOOL(hAPP(v,v_x))* c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a).
% 299.64/300.38 3358[0:SpR:3229.1,499.0] || equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x)* -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(x,v_x),u)*.
% 299.64/300.38 3361[0:SpR:3229.1,88.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v)* -> equal(hAPP(v,v_x),c_Orderings_Otop__class_Otop(u))*.
% 299.64/300.38 3365[0:SpR:3229.1,1166.0] || equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v_x,v_x,v,w),tc_Com_Opname,x),v_Procs),y)* -> hBOOL(hAPP(y,v_x))*.
% 299.64/300.38 3367[0:SpR:3229.1,9.0] || equal(c_Fun_Ocomp(u,v,w,x,y),z)* -> equal(hAPP(z,v_x),hAPP(u,hAPP(v,v_x)))*.
% 299.64/300.38 3482[0:SpL:3229.1,591.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u) hBOOL(hAPP(hAPP(u,v_x),v_G))* -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),v_x,t_a).
% 299.64/300.38 3492[0:SpL:3229.1,682.0] || equal(c_in(tc_Com_Opname),u) c_lessequals(hAPP(u,v_x),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(v,v_Procs)).
% 299.64/300.38 3502[0:SpL:3229.1,332.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v) c_Finite__Set_Ofinite(hAPP(hAPP(v,v_x),w),u)* -> c_Finite__Set_Ofinite(w,u).
% 299.64/300.38 3503[0:SpL:3229.1,333.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v) c_Finite__Set_Ofinite(hAPP(hAPP(v,v_x),w),u)* -> c_Finite__Set_Ofinite(v_x,u).
% 299.64/300.38 3509[0:SpL:3229.1,442.0] || equal(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(v)),w)* c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(w,v_x),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,v_x,v).
% 299.64/300.38 3514[0:SpL:3229.1,332.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)* c_Finite__Set_Ofinite(hAPP(w,v_x),u)* -> c_Finite__Set_Ofinite(v_x,u).
% 299.64/300.38 3515[0:SpL:3229.1,333.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)* c_Finite__Set_Ofinite(hAPP(w,v_x),u)* -> c_Finite__Set_Ofinite(v,u).
% 299.64/300.38 3692[0:SpL:445.1,3483.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Com_Ocom_OBODY)** equal(hAPP(u,v_x),c_Com_Ocom_OSKIP) -> equal(v_x,v).
% 299.64/300.38 3713[0:SpL:585.0,3483.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Com_Ocom_OBODY)** equal(hAPP(hAPP(u,v_x),y),c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 3714[0:SpL:586.0,3483.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Com_Ocom_OBODY)** equal(hAPP(u,hAPP(y,v_x)),c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 3733[0:SpR:2098.1,3283.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.38 3736[0:SpR:88.1,3283.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_Procs)).
% 299.64/300.38 3738[0:SpR:9.0,3283.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(u,hAPP(v,v_x)),v_Procs))*.
% 299.64/300.38 3861[0:Res:1145.0,436.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,w,x),tc_Com_Opname,tc_fun(y,tc_bool)),v))*.
% 299.64/300.38 3950[0:SpL:302.1,3506.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),c_Orderings_Otop__class_Otop(u))* -> .
% 299.64/300.38 3951[0:SpL:331.0,3506.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.38 4075[0:SpR:3744.1,415.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,u),v_Procs,v_Procs,v,w),c_Set_Oinsert(v_x,u))**.
% 299.64/300.38 4133[0:SpL:397.1,3929.0] class_Orderings_Otop(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.38 4135[0:SpL:365.1,3929.0] class_Orderings_Obot(u) || hBOOL(c_Orderings_Obot__class_Obot(u)) equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.38 4248[0:SpL:3229.1,3726.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* equal(hAPP(v,v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.38 4389[0:SpL:3229.1,3701.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v)* equal(hAPP(v,v_x),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 4406[0:SpR:3229.1,3284.1] || equal(u,v)* equal(c_in(tc_Com_Opname),u)* -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(v,v_x)))*.
% 299.64/300.38 4409[0:SpR:525.1,3284.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),v_x))*.
% 299.64/300.38 4445[0:SpL:3229.1,3330.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* equal(hAPP(v,v_x),w)* -> equal(hAPP(w,v_x),v_x)**.
% 299.64/300.38 4454[0:SpL:3229.1,3493.1] || equal(u,v)* equal(c_in(tc_Com_Opname),u)* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.38 4503[0:SpR:3229.1,3316.1] || equal(u,v)* equal(c_in(w),u)* -> hBOOL(hAPP(hAPP(v,v_x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.38 4506[0:SpR:525.1,3316.1] class_Lattices_Oupper__semilattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 4528[0:SpR:585.0,3316.1] || equal(c_in(u),c_COMBC(v,w,x,y))* -> hBOOL(hAPP(hAPP(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x))*.
% 299.64/300.38 4529[0:SpR:586.0,3316.1] || equal(c_in(u),c_COMBB(v,w,x,y))* -> hBOOL(hAPP(v,hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))))*.
% 299.64/300.38 4541[0:SpR:3586.1,1158.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.38 4543[0:SpR:3586.1,3229.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),w)* -> equal(hAPP(w,v_x),v_x)**.
% 299.64/300.38 4544[0:SpR:3586.1,3283.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.38 4638[0:SpL:3229.1,3698.2] || equal(u,v)* equal(w,u)* equal(c_Com_Ocom_OBODY,w)* equal(hAPP(v,v_x),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.38 4642[0:SpL:525.1,3698.2] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* equal(c_Com_Ocom_OBODY,v) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 4696[0:Res:448.2,146.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,u),u) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.38 4866[0:Res:448.2,51.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ominus__class_Ominus(v,w,u),u)* c_lessequals(v,w,u).
% 299.64/300.38 4937[0:Res:448.2,112.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u),u)* c_lessequals(v,w,u).
% 299.64/300.38 4962[0:SpL:3229.1,3863.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)* hBOOL(hAPP(x,v_x))* -> hBOOL(hAPP(u,v_x)).
% 299.64/300.38 5094[0:SpR:3229.1,3339.1] || equal(u,v)* equal(w,u)* -> equal(c_Fun_Ofun__upd(w,v_x,hAPP(v,v_x),x,y),w)**.
% 299.64/300.38 5098[0:SpR:525.1,3339.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> equal(c_Fun_Ofun__upd(v,v_x,v_x,w,x),v)**.
% 299.64/300.38 5283[0:Obv:5270.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),u),u)*.
% 299.64/300.38 5606[0:Obv:5591.1] class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),u),u)*.
% 299.64/300.38 5726[0:Res:5724.1,123.0] || c_Natural_Oevalc(u,v,w)* c_Natural_Oevalc(x,w,y)* -> c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,u),x),v,y)*.
% 299.64/300.38 5813[0:Obv:5803.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),u),v,u)*.
% 299.64/300.38 5885[0:SpR:584.0,212.1] || hBOOL(hAPP(u,hAPP(v,u)))* -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(w,x),v,y,z,x1),u))*.
% 299.64/300.38 5995[0:SpR:2097.1,5875.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,w),c_Set_Oinsert(v,x),y,z,x1),u))*.
% 299.64/300.38 6013[0:SpR:300.1,5875.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,y,z),v))*.
% 299.64/300.38 6142[0:Obv:6132.1] class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),u),v,u)*.
% 299.64/300.38 6313[0:SpR:524.0,3279.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x)).
% 299.64/300.38 6321[0:SpR:414.0,3279.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(v,v_Procs),v_x)).
% 299.64/300.38 6356[0:SpR:538.0,3282.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))*.
% 299.64/300.38 6363[2:SpR:538.0,4250.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Com_Ocom_OBODY) -> c_Com_OWT(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))*.
% 299.64/300.38 6494[0:SpR:524.0,3285.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.38 6502[0:SpR:414.0,3285.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v,hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)))*.
% 299.64/300.38 6524[0:Res:3285.1,33.0] || equal(c_Set_Ovimage(u,v,w),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(u,hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs))))*.
% 299.64/300.38 6732[0:SpR:524.0,3291.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),v_Procs))*.
% 299.64/300.38 6740[0:SpR:414.0,3291.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,z),v),v_Procs))*.
% 299.64/300.38 6768[0:SpR:328.1,3282.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_Procs)** -> hBOOL(u).
% 299.64/300.38 6775[2:SpR:328.1,4250.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Com_Ocom_OBODY)** -> c_Com_OWT(u).
% 299.64/300.38 6862[0:SpL:524.0,3484.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,v),v_x)** -> equal(v_x,v).
% 299.64/300.38 6870[0:SpL:414.0,3484.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Com_Ocom_OBODY)** equal(v,hAPP(c_Com_Ocom_OBODY,y))* -> equal(v_x,y).
% 299.64/300.38 6906[0:SpL:414.0,3499.1] || equal(c_in(u),c_Fun_Ofun__upd(v,v_x,w,x,y))* hBOOL(hAPP(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.38 6934[0:Res:34.1,3499.1] || hBOOL(hAPP(v_x,hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))* equal(c_in(v),c_Set_Ovimage(u,w,x))* -> .
% 299.64/300.38 6936[0:Res:518.1,3499.1] || hBOOL(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* -> .
% 299.64/300.38 6937[0:Res:517.1,3499.1] || hBOOL(hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u))* -> .
% 299.64/300.38 6941[4:MRR:6924.2,6340.0] || c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v_x,tc_fun(v,tc_bool))* equal(c_in(u),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) -> .
% 299.64/300.38 7119[0:SpR:524.0,3305.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.38 7127[0:SpR:414.0,3305.1] || equal(u,c_Fun_Ofun__upd(v,v_x,w,x,y))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,z),v_Procs),w))*.
% 299.64/300.38 7162[0:SpR:524.0,3317.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,u),w)))*.
% 299.64/300.38 7170[0:SpR:414.0,3317.1] || equal(c_in(u),c_Fun_Ofun__upd(v,v_x,w,x,y))* -> hBOOL(hAPP(w,hAPP(c_Set_Oinsert(v_x,u),z)))*.
% 299.64/300.38 7192[0:Res:3317.1,2629.1] || equal(c_in(u),c_in(tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v_x,u),v),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.38 7196[0:Res:3317.1,33.0] || equal(c_in(u),c_Set_Ovimage(v,w,x))* -> hBOOL(hAPP(v_x,hAPP(v,hAPP(c_Set_Oinsert(v_x,u),y))))*.
% 299.64/300.38 7260[0:SpR:2089.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.38 7267[0:SpR:3229.1,7253.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(v,v_x)))*.
% 299.64/300.38 7271[0:SpR:525.1,7253.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v))*.
% 299.64/300.38 7294[0:SpR:301.1,7253.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v))*.
% 299.64/300.38 7297[0:SpR:321.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(u,v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.64/300.38 7298[0:SpR:38.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))*.
% 299.64/300.38 7302[0:SpR:105.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 7332[0:SpL:414.0,3507.1] || equal(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,v_x,x,y,z))* equal(x,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.38 7461[0:Res:364.1,682.0] || c_lessequals(hAPP(c_in(tc_Com_Opname),v_x),u,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,v),u),v_Procs))*.
% 299.64/300.38 7495[0:SpR:524.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x))* -> hBOOL(hAPP(hAPP(c_in(v),u),v_x))*.
% 299.64/300.38 7503[0:SpR:414.0,3346.1] || equal(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,v_x,x,y,z))* -> hBOOL(hAPP(hAPP(c_in(v),u),x))*.
% 299.64/300.38 7584[0:SpR:3229.1,7539.0] || equal(c_Set_Oinsert(u,v),w)* -> c_lessequals(v_x,hAPP(c_Set_Oinsert(x,v),hAPP(w,v_x)),tc_fun(v,tc_bool))*.
% 299.64/300.38 7601[0:Res:7539.0,363.0] || -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oinsert(y,w),u))),tc_fun(w,tc_bool))*.
% 299.64/300.38 7673[0:SSi:7661.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u),v_x))*.
% 299.64/300.38 7736[0:SSi:7725.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_x))*.
% 299.64/300.38 7895[0:Rew:140.1,7844.4] class_OrderedGroup_Ogroup__add(u) class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) -> c_lessequals(w,v,u)*.
% 299.64/300.38 7896[0:Rew:137.1,7843.4] class_Lattices_Oboolean__algebra(u) class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) -> c_lessequals(w,v,u)*.
% 299.64/300.38 7970[0:Rew:140.1,7927.4] class_OrderedGroup_Ogroup__add(u) class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) -> c_lessequals(v,w,u)*.
% 299.64/300.38 7971[0:Rew:137.1,7926.4] class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) -> c_lessequals(v,w,u)*.
% 299.64/300.38 7995[0:SpR:584.0,5877.0] || -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_COMBS(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Com_Ocom_OBODY,v,w,x),y,z,x1,x2),x3),u)*.
% 299.64/300.38 8441[0:SpR:8385.1,7253.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),u))*.
% 299.64/300.38 8487[0:SpR:3229.1,8375.1] || equal(c_in(u),v)* equal(w,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))* -> hBOOL(hAPP(hAPP(v,v_x),w))*.
% 299.64/300.38 8489[0:SpR:3229.1,8375.1] || equal(hAPP(c_in(u),v),w)* equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 8570[0:SpR:8498.1,1158.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.38 8572[0:SpR:8498.1,3229.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),w)* -> equal(hAPP(w,v_x),v_x)**.
% 299.64/300.38 8573[0:SpR:8498.1,3283.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.38 8673[0:SpL:117.0,4964.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_Procs) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x))*.
% 299.64/300.38 8768[0:SpR:8415.2,2093.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),v_x),v_x)**.
% 299.64/300.38 8815[0:SpR:8415.2,524.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.38 8845[0:SpR:8415.2,414.0] || equal(v_Procs,v_x) equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(v_x,v).
% 299.64/300.38 9009[4:MRR:8936.3,6340.0] || equal(v_Procs,v_x) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(v_Procs,u) -> .
% 299.64/300.38 9051[0:SpL:8385.1,214.0] || equal(u,v_Procs) c_lessequals(u,v,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v))*.
% 299.64/300.38 9055[0:SpL:2089.0,214.0] || c_lessequals(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),v,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v)).
% 299.64/300.38 9153[0:SpR:524.0,8376.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.38 9161[0:SpR:414.0,8376.2] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_in(tc_Com_Opname))** equal(y,v_Procs) -> hBOOL(hAPP(v,y))*.
% 299.64/300.38 9188[0:SpR:87.1,8376.2] class_Lattices_Oboolean__algebra(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(v_x,u),v_Procs)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.38 9210[0:Res:8376.2,371.0] || equal(c_Set_Oinsert(u,v),c_in(tc_Com_Opname))** equal(w,v_Procs) -> hBOOL(hAPP(v_x,w))* equal(u,w)*.
% 299.64/300.38 9211[0:Res:8376.2,33.0] || equal(c_Set_Ovimage(u,v,w),c_in(tc_Com_Opname))** equal(x,v_Procs) -> hBOOL(hAPP(v_x,hAPP(u,x)))*.
% 299.64/300.38 9574[0:SSi:9506.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),x)),y),hAPP(x,y),tc_bool)*.
% 299.64/300.38 9969[0:SpR:9911.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,x,y),z),hAPP(hAPP(u,z),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.64/300.38 9970[0:SpR:9911.0,584.0] || -> equal(hAPP(c_COMBS(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w,x,y),z),hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(v,z)))**.
% 299.64/300.38 9996[0:SpR:9924.0,3279.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_Procs),v_x))*.
% 299.64/300.38 9999[0:SpR:9924.0,3285.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs)))*.
% 299.64/300.38 10000[0:SpR:9924.0,3291.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_bool)),v_Procs))*.
% 299.64/300.38 10001[0:SpR:9924.0,8415.2] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.38 10002[0:SpR:9924.0,8376.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(tc_Com_Opname))** equal(u,v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),u))*.
% 299.64/300.38 10009[0:SpR:9924.0,3305.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.38 10010[0:SpR:9924.0,3317.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(v_x,u),v)))*.
% 299.64/300.38 10011[0:SpR:9924.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(v),u),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.38 10044[0:SpL:9924.0,3484.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,u),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(v_x,u).
% 299.64/300.38 10047[0:SpL:9924.0,3499.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))) hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.38 10048[0:SpL:9924.0,3507.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))* equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.38 10420[0:Res:1012.1,590.0] || hBOOL(hAPP(v_G,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(v_Q,v_x))))* -> .
% 299.64/300.38 10508[0:Res:4557.1,454.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v_x,v),u,t_a)*.
% 299.64/300.38 10548[0:SpR:10463.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,x,y),z),hAPP(hAPP(u,z),c_Orderings_Obot__class_Obot(tc_bool)))**.
% 299.64/300.38 10549[0:SpR:10463.0,584.0] || -> equal(hAPP(c_COMBS(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w,x,y),z),hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(v,z)))**.
% 299.64/300.38 10685[0:SpR:3744.1,9566.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,u)),v_Procs),tc_bool)*.
% 299.64/300.38 10687[0:SpR:2093.0,9566.0] || -> c_lessequals(hAPP(c_in(tc_Com_Opname),v_x),hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_Procs,w)),hAPP(c_in(tc_Com_Opname),v_x)),tc_bool)*.
% 299.64/300.38 10703[0:SpR:302.1,9566.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),x),tc_bool)*.
% 299.64/300.38 10704[0:SpR:331.0,9566.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),u),tc_bool)*.
% 299.64/300.38 10726[0:SpR:330.0,9566.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_bool)*.
% 299.64/300.38 10730[0:SpR:303.1,9566.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x)),c_Orderings_Otop__class_Otop(u)),tc_bool)*.
% 299.64/300.38 10733[0:SpR:2095.0,9566.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(x,u)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_bool)*.
% 299.64/300.38 11023[0:SpR:9987.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w),c_Set_Oinsert(v_x,t_a))**.
% 299.64/300.38 11025[0:SpR:9987.0,9566.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,t_a)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_bool)*.
% 299.64/300.38 11166[0:Res:9566.0,10214.1] || equal(hAPP(u,v),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(hAPP(c_Set_Oinsert(w,x),u),v),hAPP(u,v))**.
% 299.64/300.38 11265[0:SpL:11176.1,3506.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),u)* -> .
% 299.64/300.38 11394[0:SpL:11177.1,3506.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.38 11475[0:SSi:11470.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u))),y),tc_bool)*.
% 299.64/300.38 11476[0:SSi:11469.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x))),y),tc_bool)*.
% 299.64/300.38 11477[0:SSi:11466.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),y,tc_bool)* -> c_lessequals(w,y,tc_bool).
% 299.64/300.38 11478[0:SSi:11465.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v)),y),tc_bool)*.
% 299.64/300.38 11501[0:SSi:11496.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),u)),tc_bool)*.
% 299.64/300.38 11502[0:SSi:11495.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),y)),tc_bool)*.
% 299.64/300.38 11503[0:SSi:11492.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),y,tc_bool)* -> c_lessequals(x,y,tc_bool).
% 299.64/300.38 11504[0:SSi:11491.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y)),v),tc_bool)*.
% 299.64/300.38 11559[0:SSi:11541.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(u,v)* c_lessequals(v,w,tc_bool)* -> c_lessequals(u,w,tc_bool)*.
% 299.64/300.38 11576[0:SpR:2097.1,9567.0] || hBOOL(hAPP(u,v)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v,w),x,tc_fun(y,tc_bool)),u),u,tc_bool)*.
% 299.64/300.38 11588[0:SpR:397.1,9567.0] class_Orderings_Otop(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,tc_fun(w,tc_bool)),v_x),c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.38 11589[0:SpR:365.1,9567.0] class_Orderings_Obot(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,tc_fun(w,tc_bool)),v_x),c_Orderings_Obot__class_Obot(u),tc_bool)*.
% 299.64/300.38 11597[0:SpR:300.1,9567.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,tc_fun(w,tc_bool)),x),x,tc_bool)*.
% 299.64/300.38 11624[0:SpR:301.1,9567.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(u)),v,tc_bool)*.
% 299.64/300.38 11629[0:SpR:2935.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_in(t_a),v_x),u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)*.
% 299.64/300.38 11662[0:SSi:11656.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(u,v),w,tc_bool) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,x,tc_fun(y,tc_bool)),v),w,tc_bool)*.
% 299.64/300.38 11663[0:SSi:11655.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),y),tc_bool)* -> c_lessequals(u,hAPP(v,y),tc_bool).
% 299.64/300.38 11679[0:SSi:11673.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_Procs,u,tc_bool) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),v,tc_fun(w,tc_bool)),v_Procs),u,tc_bool)*.
% 299.64/300.38 11680[0:SSi:11672.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),v,tc_fun(w,tc_bool)),v_Procs),tc_bool)* -> c_lessequals(u,v_Procs,tc_bool).
% 299.64/300.38 11701[0:SSi:11692.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),c_Option_Ooption_OSome(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),u),x)),tc_bool)*.
% 299.64/300.38 11702[0:SSi:11691.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),c_Option_Ooption_OSome(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),y),x)),tc_bool)*.
% 299.64/300.38 11703[0:SSi:11688.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(x,w)),y,tc_bool)* -> c_lessequals(x,y,tc_bool).
% 299.64/300.38 11704[0:SSi:11687.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(w,x),c_Option_Othe(y)),c_Option_Ooption_OSome(v,y)),tc_bool)*.
% 299.64/300.38 12556[0:Res:9258.0,148.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)),v_x),tc_bool))* hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)).
% 299.64/300.38 12668[0:Res:3283.1,519.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v,v_Procs)) hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.38 12924[0:SSi:12908.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool),y,tc_bool),v,tc_bool)*.
% 299.64/300.38 12925[0:SSi:12907.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,w,tc_bool),x,tc_bool),y,tc_bool),tc_bool)* -> c_lessequals(u,v,tc_bool).
% 299.64/300.38 12950[0:SSi:12941.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u),y,z)),x1),tc_bool)*.
% 299.64/300.38 12951[0:SSi:12940.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x),y,z)),x1),tc_bool)*.
% 299.64/300.38 12952[0:SSi:12937.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(w,x,y)),z),x1,tc_bool)* -> c_lessequals(w,x1,tc_bool).
% 299.64/300.38 12953[0:SSi:12936.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(w,x),c_COMBK(v,y,z)),x1),tc_bool)*.
% 299.64/300.38 13033[0:SpR:10090.1,517.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v))*.
% 299.64/300.38 13043[0:SpR:10090.1,585.0] || equal(c_COMBC(u,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(u,c_Orderings_Otop__class_Otop(tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 13044[0:SpR:10090.1,586.0] || equal(c_COMBB(u,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(u,hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 13055[0:SpR:3229.1,10090.1] || equal(u,v)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)* -> equal(hAPP(hAPP(v,v_x),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 13059[0:SpR:525.1,10090.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.38 13239[0:SpR:9493.1,3317.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_in(t_a),v) -> hBOOL(hAPP(hAPP(v,v_x),u))*.
% 299.64/300.38 13392[0:Res:13385.1,431.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) c_Fun_Oinj__on(w,u,v,x)* -> c_Fun_Oinj__on(w,y,v,x)*.
% 299.64/300.38 13434[0:Res:13387.1,431.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) c_Fun_Oinj__on(w,x,v,y)* -> c_Fun_Oinj__on(w,u,v,y)*.
% 299.64/300.38 13496[0:SpR:3229.1,10921.1] || equal(hAPP(c_Set_Oinsert(u,v),v_Procs),w)* equal(c_in(tc_Com_Opname),c_in(v)) -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 13514[0:SpR:3229.1,11030.1] || equal(u,v)* equal(c_in(t_a),u)* -> hBOOL(hAPP(hAPP(v,v_x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.38 13518[0:SpR:525.1,11030.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 13554[0:SpR:585.0,11030.1] || equal(c_COMBC(u,v,w,x),c_in(t_a))** -> hBOOL(hAPP(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),v_x))*.
% 299.64/300.38 13555[0:SpR:586.0,11030.1] || equal(c_COMBB(u,v,w,x),c_in(t_a))** -> hBOOL(hAPP(u,hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.64/300.38 13602[0:SpR:11473.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_Com_Opname,w),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.38 13605[0:SpR:11473.0,3229.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w)* -> equal(hAPP(w,v_x),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 13606[0:SpR:11473.0,3283.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_Procs)).
% 299.64/300.38 13683[0:SpR:3229.1,11499.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(u,v_x)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 13848[0:SpL:3229.1,11759.0] || equal(u,v)* hBOOL(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),tc_bool))* -> hBOOL(hAPP(u,v_x))*.
% 299.64/300.38 14261[0:SpR:14216.0,9566.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),z),tc_bool)*.
% 299.64/300.38 14284[0:SpL:14216.0,3506.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(x,y),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.38 14324[0:SpR:11695.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.38 14399[0:SpR:12944.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),tc_Com_Opname,y),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.38 14402[0:SpR:12944.0,3229.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y)* -> equal(hAPP(y,v_x),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 14403[0:SpR:12944.0,3283.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_Procs)).
% 299.64/300.38 14796[0:Rew:79.0,14757.0] || -> equal(hAPP(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))**.
% 299.64/300.38 14902[0:Obv:14883.1] class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),u),v,u)*.
% 299.64/300.38 15029[0:Obv:15009.1] class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),u),u)*.
% 299.64/300.38 15145[0:MRR:15144.2,10475.0] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)).
% 299.64/300.38 15164[0:SpR:3229.1,11611.0] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),z)* -> c_lessequals(hAPP(z,v_x),u,tc_bool)*.
% 299.64/300.38 15268[0:SpR:10063.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.38 15280[0:SpL:10063.0,214.0] || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,tc_fun(t_a,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)).
% 299.64/300.38 15494[0:Rew:15475.0,15467.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(v,w),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* -> .
% 299.64/300.38 15496[0:Rew:15475.0,15437.0] || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(hAPP(c_Set_Oinsert(v,w),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool))),v_x),tc_bool)*.
% 299.64/300.38 15636[0:Res:526.1,278.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(w,v))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,x,w,y)))*.
% 299.64/300.38 15778[0:SpR:3229.1,15482.1] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))*.
% 299.64/300.38 15832[0:SSi:15820.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(v,v_x))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))*.
% 299.64/300.38 15864[0:Res:526.1,277.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(w,v))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,u,w,y)))*.
% 299.64/300.38 15918[2:SpR:3229.1,15483.1] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))*.
% 299.64/300.38 15923[2:SpR:525.1,15483.1] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.38 15967[2:Rew:3014.0,15948.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.38 15969[2:SSi:15960.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(v,v_x))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(u,tc_bool))*.
% 299.64/300.38 15970[2:SSi:15956.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.38 15971[2:SSi:15955.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.38 15983[2:SpL:2267.1,15964.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.38 16021[2:SpL:2267.1,15965.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.38 16140[0:SpR:524.0,15262.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.38 16149[0:SpR:414.0,15262.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_in(t_a))** -> hBOOL(hAPP(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.38 16164[0:SpR:9924.0,15262.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(t_a)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.38 16182[0:Res:15262.1,2629.1] || equal(c_in(tc_Com_Opname),c_in(t_a)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.38 16188[0:Res:15262.1,33.0] || equal(c_Set_Ovimage(u,v,w),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))))*.
% 299.64/300.38 16223[0:SpL:2097.1,16217.0] || hBOOL(hAPP(v_x,u))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(u,v),v_Procs)** -> .
% 299.64/300.38 16228[0:SpL:397.1,16217.0] class_Orderings_Otop(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_Procs) -> .
% 299.64/300.38 16229[0:SpL:365.1,16217.0] class_Orderings_Obot(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_Procs)** -> .
% 299.64/300.38 16240[0:SpL:300.1,16217.0] class_Lattices_Obounded__lattice(u) || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v_Procs)** -> .
% 299.64/300.38 16348[0:SpL:88.1,16286.0] class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_Procs)** -> .
% 299.64/300.38 16359[0:SpL:9.0,16286.0] || equal(hAPP(u,hAPP(v,v_x)),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Fun_Ocomp(u,v,w,x,y),v_Procs)** -> .
% 299.64/300.38 16463[0:SpL:9935.1,3483.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 16676[0:SpR:9936.1,584.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),u),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 16701[0:SpL:9936.1,3483.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY) equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 16770[0:SpL:3229.1,16768.0] || equal(c_in(tc_Com_Opname),u) hBOOL(hAPP(v_G,v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v_na,hAPP(u,v_x))))* -> c_Hoare__Mirabelle_Otriple__valid(v_na,v_Procs,t_a).
% 299.64/300.38 16811[0:SpR:3229.1,16776.0] || equal(c_Set_Oimage(u,v,w),x) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_x,u,v,w),hAPP(x,v_x),w,v)*.
% 299.64/300.38 17110[0:SpR:17045.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),tc_Com_Opname,x),v_Procs),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.38 17115[0:SpR:17045.0,3229.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x)* -> equal(hAPP(x,v_x),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 17116[0:SpR:17045.0,3283.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_Procs)).
% 299.64/300.38 17287[0:SpL:414.0,13272.0] || equal(u,c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Fun_Ofun__upd(v,v_x,u,w,x),y)* -> hBOOL(hAPP(y,v_x))*.
% 299.64/300.38 17438[0:SpL:414.0,16327.1] || equal(u,c_Fun_Ofun__upd(v,v_x,w,x,y))* equal(w,c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_Procs) -> .
% 299.64/300.38 17620[0:Res:9567.0,17530.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(u,x),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.38 17632[0:Res:12621.0,17530.1] || equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),u).
% 299.64/300.38 17634[0:Res:11580.0,17530.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs).
% 299.64/300.38 17952[0:Res:149.1,11894.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) -> hBOOL(hAPP(hAPP(c_in(v),w),u))*.
% 299.64/300.38 18007[0:Res:8366.1,263.0] || equal(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v))* equal(v_x,u).
% 299.64/300.38 18013[0:Res:3346.1,263.0] || equal(c_Set_Oinsert(u,v),c_Set_Oinsert(w,v))* -> hBOOL(hAPP(hAPP(c_in(v),u),v_x))* equal(u,w).
% 299.64/300.38 18291[0:SpL:15172.0,3483.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 18448[0:Res:8366.1,156.0] || equal(hAPP(c_Set_Ovimage(u,tc_Com_Opname,v),w),v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(u,v_x)),w))*.
% 299.64/300.38 18453[0:Res:3346.1,156.0] || equal(c_Set_Oinsert(u,v),c_Set_Ovimage(w,v,x))* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,u)),v_x))*.
% 299.64/300.38 18626[0:SpR:584.0,9568.0] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,y,z,x1),u),v),tc_bool)*.
% 299.64/300.38 18661[0:SpR:524.0,9568.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u)),x),u),tc_bool)*.
% 299.64/300.38 18670[0:SpR:414.0,9568.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Fun_Ofun__upd(w,x,u,y,z)),x1),x),tc_bool)*.
% 299.64/300.38 18769[0:SpR:584.0,18644.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.38 18972[0:SpR:524.0,9569.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u)),u),tc_bool)*.
% 299.64/300.38 18981[0:SpR:414.0,9569.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Fun_Ofun__upd(x,y,u,z,x1)),y),tc_bool)*.
% 299.64/300.38 19190[0:Res:12533.1,12626.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,w,tc_bool),x,tc_bool),tc_bool)* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,y,tc_bool),v,tc_bool)*.
% 299.64/300.38 19247[0:Res:12627.1,12532.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_bool),tc_bool)* -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,x,tc_bool),y,tc_bool),v,tc_bool)*.
% 299.64/300.38 19437[0:SpR:9493.1,9067.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(c_Set_Oinsert(v,t_a),u)))*.
% 299.64/300.38 19448[0:SpR:3586.1,9067.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),v_x)))*.
% 299.64/300.38 19487[0:SpR:3229.1,19451.0] || equal(c_in(t_a),u) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oinsert(v,t_a),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.38 19501[0:SpR:3229.1,19440.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),hAPP(c_Set_Oinsert(w,v),hAPP(u,v_x))))*.
% 299.64/300.38 19704[0:SpL:337.0,19641.0] || hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,t_a)*.
% 299.64/300.38 19726[0:Res:9258.0,19641.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_in(t_a),v_x),u),v_x),tc_bool))* c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_in(t_a),v_x),u,t_a).
% 299.64/300.38 19733[0:Res:12687.1,19641.0] || -> hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w)))* c_Hoare__Mirabelle_Ohoare__valids(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w,t_a).
% 299.64/300.38 19745[0:MRR:19708.1,820.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool)* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,t_a).
% 299.64/300.38 20205[0:Res:20152.0,436.1] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),x))* -> hBOOL(hAPP(v,x)).
% 299.64/300.38 20259[0:Res:20186.0,436.1] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),x)).
% 299.64/300.38 20386[0:Rew:438.1,20299.1] || c_Fun_Oinj__on(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> equal(hAPP(c_Set_Oinsert(u,v),y),y)**.
% 299.64/300.38 20390[0:AED:24.0,20348.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> .
% 299.64/300.38 20402[0:AED:24.0,20375.1] || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,z)* -> .
% 299.64/300.38 20653[0:SSi:20619.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_bool),u),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,tc_fun(w,tc_bool)),u),tc_bool)*.
% 299.64/300.38 20654[0:SSi:20618.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(hAPP(c_Orderings_Otop__class_Otop(tc_bool),u),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,tc_fun(w,tc_bool)),u),tc_bool)*.
% 299.64/300.38 20884[0:SpR:317.0,267.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(v,x,u),hAPP(c_Set_Oinsert(w,x),y))))*.
% 299.64/300.38 21056[0:SpR:524.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(v,w),y)),v))*.
% 299.64/300.38 21065[0:SpR:414.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),z,x1),hAPP(c_Set_Oinsert(v,z),x2)),w))*.
% 299.64/300.38 21089[0:SpR:9924.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,v),hAPP(c_Set_Oinsert(w,u),x)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.38 21110[0:SpR:9925.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),v),x)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.38 21125[0:SpR:8498.1,20881.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,v,x),u),hAPP(w,y)))*.
% 299.64/300.38 21127[0:SpR:9493.1,20881.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,t_a,w),u),hAPP(v,v_x)))*.
% 299.64/300.38 21138[0:SpR:3586.1,20881.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,u,x),v_x),hAPP(w,v)))*.
% 299.64/300.38 21139[0:SpR:2098.1,20881.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) hBOOL(hAPP(hAPP(c_Set_Oimage(w,tc_Hoare__Mirabelle_Otriple(t_a),x),v),hAPP(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v))))*.
% 299.64/300.38 21157[0:SpR:525.1,21130.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_Procs),v,w),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.38 21196[0:SpR:3229.1,21130.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,w,x),hAPP(u,v_x)),hAPP(v,v_Procs)))*.
% 299.64/300.38 21200[0:SpR:3229.1,21152.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,w),hAPP(u,v_x)),v_Procs))*.
% 299.64/300.38 21213[0:SpR:3229.1,21141.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(v,v_x)))*.
% 299.64/300.38 21218[0:SpR:525.1,21141.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.38 21271[0:Res:3284.1,469.0] || equal(c_Set_Oimage(u,v,w),c_in(tc_Com_Opname)) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_x,u,v_Procs,v,w)),v_Procs)**.
% 299.64/300.38 21515[0:SpR:3229.1,21267.0] || equal(u,v) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(v,v_x),tc_Com_Opname,w)),hAPP(v,v_x))**.
% 299.64/300.38 21563[0:SpL:21267.0,541.0] || equal(hAPP(c_Com_Ocom_OBODY,v_x),hAPP(c_Com_Ocom_OBODY,u))* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,v_x),tc_Com_Opname,v),u)*.
% 299.64/300.38 21764[0:SpR:524.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.38 21773[0:SpR:414.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v_x,v,w,x),t_a,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v))*.
% 299.64/300.38 21791[0:SpR:9924.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),t_a,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.38 21805[0:SpR:8498.1,21035.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,w),u),v_Procs))*.
% 299.64/300.38 21813[0:SpR:3586.1,21035.0] || equal(hAPP(c_in(u),v_Procs),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),v_x),v_Procs))*.
% 299.64/300.38 21833[0:SpR:524.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.38 21842[0:SpR:414.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v_x,v,w,x),tc_Com_Opname,y),hAPP(c_Set_Oinsert(z,tc_Com_Opname),v_Procs)),v))*.
% 299.64/300.38 21897[0:Res:3284.1,464.0] || equal(c_Set_Oimage(u,v,w),c_in(tc_Com_Opname)) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_x,v_Procs,u,v,w)),v_Procs)**.
% 299.64/300.38 22142[0:SpR:3229.1,21893.0] || equal(u,v) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),u,tc_Com_Opname,w)),hAPP(v,v_x))**.
% 299.64/300.38 22190[0:SpL:21893.0,541.0] || equal(hAPP(c_Com_Ocom_OBODY,v_x),hAPP(c_Com_Ocom_OBODY,u))* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Ocom_OBODY,v_x),c_Com_Ocom_OBODY,tc_Com_Opname,v),u)*.
% 299.64/300.38 22465[0:SpR:524.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),tc_Com_Opname,w),u),v_x))*.
% 299.64/300.38 22474[0:SpR:414.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(v,v_x,w,x,y),tc_Com_Opname,z),u),w))*.
% 299.64/300.38 22492[0:SpR:9924.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname,v),u),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.38 22671[0:Rew:9.0,22519.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,tc_Com_Opname,v),v_Procs)),hAPP(u,hAPP(x,v_x))))*.
% 299.64/300.38 22722[0:SpR:3294.1,341.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_fun(u,tc_bool))*.
% 299.64/300.38 22767[0:SpR:3294.1,517.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a))** hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v))*.
% 299.64/300.38 22813[0:SpR:9911.0,3294.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(t_a))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 22814[0:SpR:10463.0,3294.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_in(t_a))** -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 22899[0:MRR:22898.3,826.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a))** hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v))* -> hBOOL(hAPP(v_x,v)).
% 299.64/300.38 23193[0:SpL:9911.0,3487.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.38 23194[0:SpL:10463.0,3487.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.38 23270[0:SpL:9911.0,3489.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname))** hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.38 23271[0:SpL:10463.0,3489.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_in(tc_Com_Opname))** hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.38 23325[0:Res:10930.1,3489.1] || equal(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))),v_Procs)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname))** -> .
% 299.64/300.38 23333[4:MRR:23301.3,6340.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_x,u)* equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) -> .
% 299.64/300.38 23752[0:SpR:23682.0,3294.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(t_a)) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 23812[0:SpR:23682.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,w,x),y),hAPP(hAPP(u,y),y))*.
% 299.64/300.38 23813[0:SpR:23682.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v,w,x),y),hAPP(y,hAPP(u,y)))*.
% 299.64/300.38 23825[0:SpL:23682.0,3489.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.38 23879[0:SpR:23840.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.38 24525[0:SpR:24020.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(v,v_x),tc_Com_Opname,u),u)*.
% 299.64/300.38 24565[0:SpR:24020.1,9567.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),v,tc_fun(w,tc_bool)),v_x),v_x,tc_bool)*.
% 299.64/300.38 24621[0:SpR:15476.0,24020.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v_x),v_x)**.
% 299.64/300.38 24634[0:SpR:302.1,24020.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),v_x),v_x).
% 299.64/300.38 24635[0:SpR:331.0,24020.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.38 24658[0:SpR:11177.1,24020.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.38 24662[0:SpR:11176.1,24020.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(u,v_x),v_x).
% 299.64/300.38 24663[0:SpR:14216.0,24020.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x),v_x).
% 299.64/300.38 24674[0:SpL:24020.1,16217.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(u,v_x),v_Procs)** -> .
% 299.64/300.38 24742[0:Rew:9943.1,24613.2] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.38 24915[0:Res:474.0,467.0] || -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(u,x))),hAPP(u,x))**.
% 299.64/300.38 24945[0:SpR:23902.1,415.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(c_Fun_Ofun__upd(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_bool),v_x,v,w),hAPP(u,v_x))**.
% 299.64/300.38 24982[0:SpR:23902.1,518.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v))* -> hBOOL(hAPP(v_x,v)).
% 299.64/300.38 25004[0:SpR:2097.1,23902.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.38 25010[0:SpR:397.1,23902.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.38 25011[0:SpR:365.1,23902.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.38 25022[0:SpR:300.1,23902.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.38 25055[0:SpR:24020.1,23902.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.38 25633[0:Res:11610.0,24120.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) -> equal(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(v),w,tc_fun(x,tc_bool)),c_Option_Ooption_OSome(u,v)),u)**.
% 299.64/300.38 25634[0:Res:11611.0,24120.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) -> equal(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),z),u)**.
% 299.64/300.38 25659[0:SSi:25582.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool),hAPP(u,v_x)).
% 299.64/300.38 25660[0:SSi:25574.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),v).
% 299.64/300.38 25674[0:SSi:25673.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(u,w)*.
% 299.64/300.38 25676[0:SSi:25675.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(u,v).
% 299.64/300.38 25770[0:SpL:584.0,25662.0] || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),y),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(u,y),y).
% 299.64/300.38 25802[0:Obv:25799.0] || equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(v_Procs,v_x) -> .
% 299.64/300.38 25827[0:SpR:339.0,649.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs))))*.
% 299.64/300.38 25830[0:SpR:339.0,676.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_in(tc_Com_Opname),v_x))),v_Procs))*.
% 299.64/300.38 26027[0:SpR:338.0,650.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v))))*.
% 299.64/300.38 26040[0:SpR:338.0,675.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),w)),v_Procs))*.
% 299.64/300.38 26321[0:SSi:26308.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(v,tc_bool)),u))*.
% 299.64/300.38 26381[0:Res:13387.1,85.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),x,tc_fun(v,tc_bool))*.
% 299.64/300.38 26554[0:SpL:3229.1,24122.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(hAPP(u,v_x),v),c_Orderings_Obot__class_Obot(tc_bool))** -> c_lessequals(v_x,w,tc_bool)*.
% 299.64/300.38 26559[0:SpL:3229.1,24122.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> c_lessequals(u,w,tc_bool)*.
% 299.64/300.38 26709[0:SpL:3229.1,24123.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(hAPP(u,v_x),v),c_Orderings_Obot__class_Obot(tc_bool))** -> c_lessequals(v,w,tc_bool)*.
% 299.64/300.38 26714[0:SpL:3229.1,24123.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> c_lessequals(v_x,w,tc_bool)*.
% 299.64/300.38 26774[0:SpR:3229.1,23997.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(v,tc_bool)),w)* -> c_lessequals(hAPP(w,v_x),v_x,tc_bool)*.
% 299.64/300.38 26789[0:Res:23997.0,24120.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),u),u)**.
% 299.64/300.38 27050[0:Res:23946.1,454.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,u,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v_x,u),v_Procs,t_a)*.
% 299.64/300.38 27248[7:SpR:538.0,27207.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))*.
% 299.64/300.38 27253[7:SpR:328.1,27207.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)** -> hBOOL(u).
% 299.64/300.38 27292[7:Res:27207.1,454.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v_x,v),u,t_a)*.
% 299.64/300.38 27298[7:MRR:11289.2,27297.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) equal(hAPP(hAPP(u,v_x),w),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.38 27299[7:MRR:11420.2,27297.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.38 27665[7:SpL:117.0,27293.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x))*.
% 299.64/300.38 27825[7:SpR:3229.1,27219.1] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))*.
% 299.64/300.38 27894[7:SSi:27882.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(v,v_x))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))*.
% 299.64/300.38 27972[0:SpR:3229.1,27381.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),u,tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.38 27977[0:SpR:525.1,27381.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.38 28042[0:SpR:8498.1,28032.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v,u),tc_Com_Opname,w)))*.
% 299.64/300.38 28055[0:SpR:3586.1,28032.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v,u),tc_Com_Opname,w)))*.
% 299.64/300.38 28066[0:SpR:2098.1,28032.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,v)))*.
% 299.64/300.38 28075[0:SpR:17045.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),tc_Com_Opname,x)))*.
% 299.64/300.38 28078[0:SpR:88.1,28032.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,v)))*.
% 299.64/300.38 28095[0:SpR:11473.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_Com_Opname,w)))*.
% 299.64/300.38 28096[0:SpR:9.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,hAPP(v,v_x)),c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname,z)))*.
% 299.64/300.38 28102[0:SpR:12944.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),tc_Com_Opname,y)))*.
% 299.64/300.38 28260[0:SpR:3229.1,28056.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(v,v_x),tc_Com_Opname,w)))*.
% 299.64/300.38 28274[0:SpR:3229.1,27441.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(v,v_x),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.38 28279[0:SpR:525.1,27441.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_x,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.38 28345[0:SpR:8498.1,28335.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),v_x,tc_Com_Opname,w)))*.
% 299.64/300.38 28358[0:SpR:3586.1,28335.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),v_x,tc_Com_Opname,w)))*.
% 299.64/300.38 28369[0:SpR:2098.1,28335.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),v_x,tc_Com_Opname,v)))*.
% 299.64/300.38 28379[0:SpR:17045.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,x)))*.
% 299.64/300.38 28382[0:SpR:88.1,28335.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v)))*.
% 299.64/300.38 28399[0:SpR:11473.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))*.
% 299.64/300.38 28400[0:SpR:9.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ocomp(u,v,w,x,y),hAPP(u,hAPP(v,v_x)),tc_Com_Opname,z)))*.
% 299.64/300.38 28406[0:SpR:12944.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,y)))*.
% 299.64/300.38 28572[0:SpL:118.0,3577.0] || equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,v_x,w,x,y),y,z,x),v_Procs)** -> hBOOL(hAPP(u,w)).
% 299.64/300.38 28574[2:SpL:118.0,4268.0] || equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,v_x,w,x,y),y,z,x),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(u,w)).
% 299.64/300.38 28578[7:SpL:118.0,27234.0] || equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,v_x,w,x,y),y,z,x),v_x)** -> hBOOL(hAPP(u,w)).
% 299.64/300.38 28659[0:SpR:3229.1,28359.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(v,v_x),v_x,tc_Com_Opname,w)))*.
% 299.64/300.38 28713[0:SpR:28031.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(w,v_x),w,tc_Com_Opname,x))))*.
% 299.64/300.38 28715[0:SpR:28031.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.38 28733[0:SpR:3229.1,28031.0] || equal(u,v) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),u,tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 28738[0:SpR:525.1,28031.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 28868[0:SpR:28334.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,hAPP(w,v_x),tc_Com_Opname,x))))*.
% 299.64/300.38 28870[0:SpR:28334.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.38 28888[0:SpR:3229.1,28334.0] || equal(u,v) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(v,v_x),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 28893[0:SpR:525.1,28334.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_x,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 29208[0:SSi:28973.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)),v_x))*.
% 299.64/300.38 29325[7:SpR:27278.1,1158.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.38 29331[7:SpR:27278.1,3229.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),w)* -> equal(hAPP(w,v_x),v_x)**.
% 299.64/300.38 29332[7:SpR:27278.1,3283.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.38 29346[7:SpR:27278.1,28335.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),v_x,tc_Com_Opname,w)))*.
% 299.64/300.38 29352[7:SpR:27278.1,28032.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v,u),tc_Com_Opname,w)))*.
% 299.64/300.38 29407[7:SpR:27278.1,20881.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,u,x),v_x),hAPP(w,v)))*.
% 299.64/300.38 29408[7:SpR:27278.1,9067.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),v_x)))*.
% 299.64/300.38 29416[7:SpR:27278.1,21035.0] || equal(hAPP(c_in(u),v_Procs),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),v_x),v_Procs))*.
% 299.64/300.38 29942[0:SpL:27043.1,3483.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 30337[0:SSi:30062.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)),v_x))*.
% 299.64/300.38 31458[0:SpL:524.0,24254.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 31467[0:SpL:414.0,24254.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(v,c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 31491[0:SpL:9924.0,24254.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 31784[7:SpL:2097.1,31778.0] || hBOOL(hAPP(v_x,u))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(u,v),v_x)** -> .
% 299.64/300.38 31790[7:SpL:397.1,31778.0] class_Orderings_Otop(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x) -> .
% 299.64/300.38 31791[7:SpL:365.1,31778.0] class_Orderings_Obot(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x)** -> .
% 299.64/300.38 31803[7:SpL:300.1,31778.0] class_Lattices_Obounded__lattice(u) || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v_x)** -> .
% 299.64/300.38 31840[7:SpL:24020.1,31778.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(u,v_x),v_x)** -> .
% 299.64/300.38 31913[7:SpL:88.1,31868.0] class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_x)** -> .
% 299.64/300.38 31933[7:SpL:9.0,31868.0] || equal(hAPP(u,hAPP(v,v_x)),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Fun_Ocomp(u,v,w,x,y),v_x)** -> .
% 299.64/300.38 32272[0:SSi:32256.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(hAPP(v_x,u),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),u),tc_bool)*.
% 299.64/300.38 32610[0:SpR:524.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,v),v_x)),v_Procs))*.
% 299.64/300.38 32619[0:SpR:414.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ofun__upd(u,v_x,v,w,x),tc_Com_Opname,y),v)),v_Procs))*.
% 299.64/300.38 32643[0:SpR:9924.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_bool))),v_Procs))*.
% 299.64/300.38 32684[0:SpR:15476.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),tc_Com_Opname,v),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))))*.
% 299.64/300.38 32698[0:SpR:302.1,32669.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u))))*.
% 299.64/300.38 32726[0:SpR:11177.1,32669.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),v_x)))*.
% 299.64/300.38 32730[0:SpR:11176.1,32669.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),u)))*.
% 299.64/300.38 32732[0:SpR:14216.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_Com_Opname,x),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.38 33158[0:SSi:33134.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u,v,w,x),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.38 33266[0:SpR:524.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,v),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 33275[0:SpR:414.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ofun__upd(u,v_x,v,w,x),tc_Com_Opname,y),v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 33299[0:SpR:9924.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 33369[0:Res:23789.0,12532.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(w,x,tc_bool)),w,tc_bool)*.
% 299.64/300.38 33467[0:Res:23882.0,12532.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ominus__class_Ominus(u,v,tc_bool)),w,tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_bool)*.
% 299.64/300.38 33552[0:SpR:524.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),tc_Com_Opname,w)))*.
% 299.64/300.38 33561[0:SpR:414.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_Fun_Ofun__upd(w,v_x,v,x,y),tc_Com_Opname,z)))*.
% 299.64/300.38 33585[0:SpR:9924.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname,v)))*.
% 299.64/300.38 33643[0:SpR:524.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),v_x,tc_Com_Opname,w)))*.
% 299.64/300.38 33652[0:SpR:414.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ofun__upd(v,v_x,w,x,y),w,tc_Com_Opname,z)))*.
% 299.64/300.38 33676[0:SpR:9924.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v)))*.
% 299.64/300.38 33743[7:SpL:414.0,31886.1] || equal(u,c_Fun_Ofun__upd(v,v_x,w,x,y))* equal(w,c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_x) -> .
% 299.64/300.38 33905[0:SpR:24914.0,451.0] || -> c_Com_OWT(hAPP(c_Com_Ocom_OBODY,v_x)) equal(hAPP(c_Com_Obody,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Ocom_OBODY,tc_Com_Opname,u),hAPP(c_Com_Ocom_OBODY,v_x))),c_Option_Ooption_ONone(tc_Com_Ocom))**.
% 299.64/300.38 34015[0:SpR:24914.0,415.0] || -> equal(c_Fun_Ofun__upd(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),hAPP(u,v_x),w,x),u)**.
% 299.64/300.38 34549[0:SpR:34427.0,9566.0] || -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(u,v),c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,w)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),tc_bool)*.
% 299.64/300.38 34692[0:SpR:34428.0,24020.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.38 34714[0:SpR:34428.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_Com_Opname,v),v_x)))*.
% 299.64/300.38 34732[0:SpR:34428.0,9566.0] || -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(u,v),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,w)),v_x),tc_bool)*.
% 299.64/300.38 34754[0:SpL:34428.0,3506.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.38 34861[0:SpR:524.0,28053.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,w)))*.
% 299.64/300.38 34870[0:SpR:414.0,28053.1] || equal(u,c_Fun_Ofun__upd(v,v_x,w,x,y))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,w,u,tc_Com_Opname,z)))*.
% 299.64/300.38 34894[0:SpR:9924.0,28053.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),u,tc_Com_Opname,v)))*.
% 299.64/300.38 34940[0:SpR:524.0,28356.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,w)))*.
% 299.64/300.38 34949[0:SpR:414.0,28356.1] || equal(u,c_Fun_Ofun__upd(v,v_x,w,x,y))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,w,tc_Com_Opname,z)))*.
% 299.64/300.38 34973[0:SpR:9924.0,28356.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v)))*.
% 299.64/300.38 35213[0:SpR:410.0,342.0] || -> c_lessequals(hAPP(u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),u,w,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.64/300.38 35438[0:Rew:330.0,35277.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w,v,tc_fun(x,tc_bool)),hAPP(w,u))**.
% 299.64/300.38 35448[0:SpR:8498.1,35192.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_in(tc_Com_Opname),v,tc_fun(w,tc_bool)),v_Procs))*.
% 299.64/300.38 35450[0:SpR:9493.1,35192.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_in(tc_Com_Opname),t_a,tc_fun(v,tc_bool)),v_Procs))*.
% 299.64/300.38 35595[7:Res:29397.1,3489.1] || equal(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))),v_x)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname))** -> .
% 299.64/300.38 35655[0:SpR:8498.1,26119.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),x))*.
% 299.64/300.38 35668[7:SpR:27278.1,26119.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x),v))*.
% 299.64/300.38 35669[0:SpR:3586.1,26119.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x),v))*.
% 299.64/300.38 35670[0:SpR:2098.1,26119.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),v),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v)))*.
% 299.64/300.38 35684[0:SpR:28031.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)))*.
% 299.64/300.38 35687[0:SpR:28334.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)))*.
% 299.64/300.38 35878[0:SpR:3229.1,35795.0] || equal(c_HOL_Ominus__class_Ominus(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(t_a,tc_bool)),w)* -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool))*.
% 299.64/300.38 35898[0:SSi:35887.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(c_HOL_Ominus__class_Ominus(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_fun(t_a,tc_bool)),v_x))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))*.
% 299.64/300.38 36408[0:SSi:36390.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Set_Oinsert(v_x,t_a),w),v_x))))*.
% 299.64/300.38 36482[0:SSi:36456.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(v_x,t_a),v),v_x)),w)))*.
% 299.64/300.38 36613[0:SSi:36587.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Set_Oinsert(v_x,t_a),w),u,tc_bool))*.
% 299.64/300.38 36614[0:SSi:36574.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),u),v_x),v,tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w))*.
% 299.64/300.38 36615[0:SSi:36571.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),u),v_x),v,tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v))*.
% 299.64/300.38 36724[0:SpR:67.0,35795.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,t_a),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_fun(t_a,tc_bool)),v_x),tc_bool))*.
% 299.64/300.38 36769[0:SpL:67.0,3497.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),w)* hBOOL(hAPP(w,v_x))* -> .
% 299.64/300.38 37399[0:SpR:353.0,36687.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Set_Oinsert(v_x,t_a),w))),tc_Com_Opname,tc_bool))*.
% 299.64/300.38 37651[4:MRR:37642.2,6340.0] || equal(v_Procs,v_x) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> .
% 299.64/300.38 37668[0:SpR:3229.1,36804.1] || equal(hAPP(c_Set_Oinsert(u,v),v_Procs),w)* equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 37709[0:SpR:3229.1,36342.1] || equal(u,v)* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(v,v_x)))*.
% 299.64/300.38 38681[4:SpR:8498.1,37987.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.38 38694[7:SpR:27278.1,37987.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.38 38695[4:SpR:3586.1,37987.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.38 38707[4:SpR:2098.1,37987.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(v_x,v))*.
% 299.64/300.38 38717[4:SpR:17045.0,37987.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),x))*.
% 299.64/300.38 38720[4:SpR:88.1,37987.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v))*.
% 299.64/300.38 38739[4:SpR:11473.0,37987.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),w))*.
% 299.64/300.38 38740[4:SpR:9.0,37987.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(u,hAPP(v,v_x)),z))*.
% 299.64/300.38 38746[4:SpR:12944.0,37987.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),y))*.
% 299.64/300.38 38841[4:Res:37987.1,519.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v,w))* hBOOL(hAPP(v_x,w))*.
% 299.64/300.38 38883[7:SpR:27278.1,38042.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,w,t_a)*.
% 299.64/300.38 38884[4:SpR:3586.1,38042.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,w,t_a)*.
% 299.64/300.38 38896[4:SpR:2098.1,38042.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.38 38906[4:SpR:17045.0,38042.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_bool),x,t_a)*.
% 299.64/300.38 38909[4:SpR:88.1,38042.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Otop__class_Otop(u),v,t_a)*.
% 299.64/300.38 38928[4:SpR:11473.0,38042.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Otop__class_Otop(tc_bool),w,t_a)*.
% 299.64/300.38 38929[4:SpR:9.0,38042.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(u,hAPP(v,v_x)),z,t_a)*.
% 299.64/300.38 38935[4:SpR:12944.0,38042.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Otop__class_Otop(tc_bool),y,t_a)*.
% 299.64/300.38 40369[4:Res:10705.0,40016.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v_x),z,x1)),x))*.
% 299.64/300.38 40588[4:Res:10705.0,40105.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),y),z,x1)),x))*.
% 299.64/300.38 40661[4:Res:10697.0,40433.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x)),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(x)*.
% 299.64/300.38 40664[4:Res:10705.0,40433.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,v_x,y,z)),x),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(x1)*.
% 299.64/300.38 40795[4:Res:18644.0,40171.0] || c_lessequals(v_x,v_Procs,tc_bool) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),v),v_Procs))*.
% 299.64/300.38 40796[4:Res:18763.0,40171.0] || c_lessequals(v_x,v_Procs,tc_bool) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs))*.
% 299.64/300.38 40802[4:Res:10697.0,40171.0] || c_lessequals(v_x,u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u)),u))*.
% 299.64/300.38 40805[4:Res:10705.0,40171.0] || c_lessequals(v_x,u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Fun_Ofun__upd(x,y,u,z,x1)),y))*.
% 299.64/300.38 40813[4:Res:12627.1,40171.0] || c_lessequals(u,v,tc_bool)* c_lessequals(v_x,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool),tc_bool)* -> hBOOL(v).
% 299.64/300.38 40815[4:Res:23789.0,40171.0] || c_lessequals(v_x,hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w),tc_bool)* -> hBOOL(w).
% 299.64/300.38 40819[4:Res:23882.0,40171.0] || c_lessequals(v_x,hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool)* -> hBOOL(u).
% 299.64/300.38 40820[4:Res:9568.0,40171.0] || c_lessequals(v_x,hAPP(u,v),tc_bool) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v))*.
% 299.64/300.38 40821[4:Res:9569.0,40171.0] || c_lessequals(v_x,hAPP(u,v),tc_bool) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),v))*.
% 299.64/300.38 40822[4:Res:31323.0,40171.0] || c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u),tc_bool)* -> hBOOL(hAPP(v_Procs,u)).
% 299.64/300.38 41074[4:Res:12627.1,40323.1] || c_lessequals(u,v,tc_bool)* equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(v).
% 299.64/300.38 41076[4:Res:23789.0,40323.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(w).
% 299.64/300.38 41080[4:Res:23882.0,40323.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(u).
% 299.64/300.38 41446[4:SpR:397.1,38236.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(u),tc_Com_Opname,tc_bool))*.
% 299.64/300.38 41447[4:SpR:365.1,38236.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(u),tc_Com_Opname,tc_bool))*.
% 299.64/300.38 42292[4:SpL:3229.1,40680.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(u,v_x),tc_Com_Opname,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(v)*.
% 299.64/300.38 42307[4:SpL:3229.1,38697.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* equal(hAPP(v,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.38 42320[4:SpL:3229.1,38886.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* equal(hAPP(v,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,w,t_a)*.
% 299.64/300.38 42351[4:SpR:338.0,40371.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x)),v_x))*.
% 299.64/300.38 42367[4:SpR:3229.1,40371.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v)),w),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.38 42410[4:SpR:339.0,40372.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x))),v_x))*.
% 299.64/300.38 42416[4:SpR:3229.1,40372.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.38 42515[4:SpR:3229.1,40383.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(v,v_x),w,x),tc_Com_Opname,tc_bool))*.
% 299.64/300.38 42552[4:SpR:3229.1,40590.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(u,v_x)),w),x))*.
% 299.64/300.38 42555[4:SpR:3229.1,40590.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)* -> hBOOL(hAPP(hAPP(v,v_x),w))*.
% 299.64/300.38 42577[4:SpR:338.0,40590.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w)),x))*.
% 299.64/300.38 42788[4:SpR:3229.1,40591.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(u,v_x)),x))*.
% 299.64/300.38 42791[4:SpR:3229.1,40591.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* -> hBOOL(hAPP(hAPP(hAPP(v,v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w))*.
% 299.64/300.38 42815[4:SpR:339.0,40591.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))),x))*.
% 299.64/300.38 42838[4:SpR:3229.1,40601.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(hAPP(u,v_x),v),w,x),tc_Com_Opname,tc_bool))*.
% 299.64/300.38 43146[4:SpR:3229.1,42609.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(u,v_x)),w),x,t_a)*.
% 299.64/300.38 43149[4:SpR:3229.1,42609.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(v,v_x),w,t_a)*.
% 299.64/300.38 43171[4:SpR:338.0,42609.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w)),x,t_a)*.
% 299.64/300.38 43189[4:SpR:3229.1,42829.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(u,v_x)),x,t_a)*.
% 299.64/300.38 43192[4:SpR:3229.1,42829.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(v,v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w,t_a)*.
% 299.64/300.38 43216[4:SpR:339.0,42829.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))),x,t_a)*.
% 299.64/300.38 43267[4:Res:364.1,42356.0] || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,w),v),v_x))*.
% 299.64/300.38 43281[4:Res:448.2,42356.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),tc_fun(u,tc_bool))* hBOOL(hAPP(v,v_x)).
% 299.64/300.38 43365[4:SpL:3229.1,42582.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) c_lessequals(hAPP(u,v_x),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(v,x))*.
% 299.64/300.38 43373[4:Res:364.1,42582.0] || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,v),u),x))*.
% 299.64/300.38 43387[4:Res:448.2,42582.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(u,tc_bool))* hBOOL(hAPP(v,w))*.
% 299.64/300.38 43601[4:SpL:3229.1,43176.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) c_lessequals(hAPP(u,v_x),v,tc_fun(w,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(v,x,t_a)*.
% 299.64/300.38 43609[4:Res:364.1,43176.0] || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(v,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,v),u),x,t_a)*.
% 299.64/300.38 43623[4:Res:448.2,43176.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(u,tc_bool))* c_Hoare__Mirabelle_Ohoare__valids(v,w,t_a)*.
% 299.64/300.38 44041[4:SpR:3229.1,39033.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(v,w),x,y,z,x1),hAPP(u,v_x)))*.
% 299.64/300.38 44104[0:SpR:3229.1,38134.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(w,x,y)),z)* hBOOL(w) -> hBOOL(hAPP(z,v_x))*.
% 299.64/300.38 44260[0:SpR:584.0,36412.1] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),hAPP(v_Procs,v_x)))*.
% 299.64/300.38 44381[4:Res:37988.2,6935.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_in(u),c_Set_Oinsert(v,w))* -> .
% 299.64/300.38 44703[0:SpR:8498.1,36599.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x))*.
% 299.64/300.38 44753[0:SpR:584.0,36599.0] || -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),hAPP(c_Set_Oinsert(v_x,t_a),z)),v_x))*.
% 299.64/300.38 44827[0:SpR:338.0,44716.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)),v_x))*.
% 299.64/300.38 44844[0:SpR:3229.1,44716.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.38 44892[0:SpR:339.0,44824.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))),v_x))*.
% 299.64/300.38 44900[0:SpR:3229.1,44824.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.38 44927[0:Res:364.1,44833.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,w),v),v_x))*.
% 299.64/300.38 44939[0:Res:448.2,44833.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_fun(u,tc_bool))* hBOOL(hAPP(v,v_x)).
% 299.64/300.38 45145[0:SpR:8498.1,36600.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x))*.
% 299.64/300.38 45451[0:Res:45357.1,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),v))*.
% 299.64/300.38 45716[0:SpR:584.0,44625.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v,w,x,y),u),v_x))*.
% 299.64/300.38 45961[0:Res:526.1,45899.0] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),v))* -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)).
% 299.64/300.38 46355[0:SpR:584.0,37989.1] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,x,y,z),u)))*.
% 299.64/300.38 46616[4:SpL:3229.1,46565.1] || equal(u,v)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)* equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),hAPP(v,v_x))* -> .
% 299.64/300.38 46696[0:Res:83.0,44639.0] || equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),hAPP(c_Set_Ovimage(u,v,tc_Com_Opname),w)),v_Procs)** -> hBOOL(hAPP(w,v_x)).
% 299.64/300.38 46802[0:SSi:46754.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Orderings_Obot__class_Obot(tc_bool),v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.38 46803[0:SSi:46753.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.38 46831[0:SpL:8498.1,44750.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool))) c_lessequals(u,v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(v,v_x)).
% 299.64/300.38 46832[0:SpL:9493.1,44750.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(u,v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(v,v_x)).
% 299.64/300.38 47093[0:Res:9566.0,38189.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Set_Oinsert(x,y),u),v)))*.
% 299.64/300.38 47095[0:Res:10684.0,38189.0] || hBOOL(v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs)))*.
% 299.64/300.38 47113[0:Res:12533.1,38189.0] || c_lessequals(u,v,tc_bool)* hBOOL(c_HOL_Ominus__class_Ominus(u,w,tc_bool))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v))*.
% 299.64/300.38 47288[4:SpR:3229.1,47138.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(u,v_x),tc_Com_Opname,tc_bool)))*.
% 299.64/300.38 47421[4:SpR:3229.1,47319.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(u,v_x),tc_Com_Opname,tc_bool)),v))*.
% 299.64/300.38 47465[4:SpR:3229.1,47458.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(u,v_x),tc_Com_Opname,tc_bool)),v,t_a)*.
% 299.64/300.38 47469[4:SpL:3229.1,47318.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(u,v_x),tc_Com_Opname,tc_bool),v,tc_bool)* -> hBOOL(v).
% 299.64/300.38 47506[4:Res:10745.0,47318.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool))),w))*.
% 299.64/300.38 47507[4:Res:10746.0,47318.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool)))*.
% 299.64/300.38 47509[4:Res:10712.0,47318.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool),w)))*.
% 299.64/300.38 47510[4:Res:10713.0,47318.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool),w,x)),y))*.
% 299.64/300.38 47671[4:SpR:584.0,47550.0] || -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool)))*.
% 299.64/300.38 47813[0:Res:9566.0,38190.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(w,x),u),v)),y))*.
% 299.64/300.38 47815[0:Res:10684.0,38190.0] || hBOOL(v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs)),w))*.
% 299.64/300.38 47833[0:Res:12533.1,38190.0] || c_lessequals(u,v,tc_bool)* hBOOL(c_HOL_Ominus__class_Ominus(u,w,tc_bool))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),x))*.
% 299.64/300.38 47882[0:SSi:47772.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),u)),z))*.
% 299.64/300.38 48115[4:SpR:524.0,39023.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),x))*.
% 299.64/300.38 48124[4:SpR:414.0,39023.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,z),v),x1))*.
% 299.64/300.38 48149[4:SpR:9924.0,39023.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_bool)),w))*.
% 299.64/300.38 48230[4:SpR:524.0,39064.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),v_x),x,t_a)*.
% 299.64/300.38 48239[4:SpR:414.0,39064.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(y,z),v),x1,t_a)*.
% 299.64/300.38 48264[4:SpR:9924.0,39064.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_bool)),w,t_a)*.
% 299.64/300.38 48741[4:SpR:3229.1,48706.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(u,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(w,tc_bool)),v_x))*.
% 299.64/300.38 48744[4:SpR:3229.1,48706.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_in(tc_Com_Opname),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(v,tc_bool)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 48748[4:SpR:3229.1,48719.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 48752[4:SpR:3229.1,48718.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(v,tc_bool)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 48864[4:SpR:8498.1,42583.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(w,tc_bool)),x))*.
% 299.64/300.38 48866[4:SpR:9493.1,42583.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w))*.
% 299.64/300.38 49088[0:SpR:49017.1,20881.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname))))*.
% 299.64/300.38 49090[0:SpR:49017.1,9067.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.38 49094[0:SpR:49017.1,26119.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.38 50093[4:SpR:8498.1,43177.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(w,tc_bool)),x,t_a)*.
% 299.64/300.38 50095[4:SpR:9493.1,43177.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(v,tc_bool)),w,t_a)*.
% 299.64/300.38 50201[4:SpR:584.0,43372.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),hAPP(c_Set_Oinsert(x1,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))))*.
% 299.64/300.38 50376[0:SSi:50334.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(u) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),u)))*.
% 299.64/300.38 50579[0:Rew:25770.1,50557.1] || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),y),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(y) -> hBOOL(z)*.
% 299.64/300.38 50682[0:SpL:584.0,46413.0] || c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),y),z,tc_bool)* hBOOL(y) -> hBOOL(z).
% 299.64/300.38 50758[0:SSi:50717.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(u) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),z)))*.
% 299.64/300.38 50913[4:SpR:8498.1,48288.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,w,t_a)*.
% 299.64/300.38 50999[0:Res:9566.0,50575.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),w),x),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(hAPP(w,x)) -> hBOOL(y)*.
% 299.64/300.38 51001[0:Res:10684.0,50575.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(v_Procs) -> hBOOL(w)*.
% 299.64/300.38 51019[0:Res:12533.1,50575.0] || c_lessequals(u,v,tc_bool)* equal(v,c_Orderings_Obot__class_Obot(tc_bool)) hBOOL(c_HOL_Ominus__class_Ominus(u,w,tc_bool))* -> hBOOL(x)*.
% 299.64/300.38 51327[0:SpR:524.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 51336[0:SpR:414.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(u,hAPP(hAPP(c_Set_Oinsert(v,t_a),c_Fun_Ofun__upd(w,v_x,u,x,y)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 51468[0:SpL:8498.1,33513.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* c_Finite__Set_Ofinite(u,v) equal(c_Finite__Set_Ocard(u,v),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.38 51470[0:SpL:9493.1,33513.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool))** c_Finite__Set_Ofinite(u,t_a) equal(c_Finite__Set_Ocard(u,t_a),c_HOL_Ozero__class_Ozero(tc_nat)) -> .
% 299.64/300.38 51777[4:SpL:2098.1,39448.0] || equal(c_COMBK(v_x,u,v),w)* -> c_Hoare__Mirabelle_Ohoare__valids(x,c_COMBK(v_x,u,v),t_a)* hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 51853[4:Res:40792.1,3489.1] || c_lessequals(v_x,hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))),tc_bool)* equal(c_Set_Oinsert(u,v),c_in(tc_Com_Opname))** -> .
% 299.64/300.38 52010[4:MRR:17122.2,52007.0] || equal(v_Procs,v_x) equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> .
% 299.64/300.38 52014[4:MRR:23151.4,52007.0] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v_x,u)* -> .
% 299.64/300.38 52018[4:MRR:26448.4,52007.0] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v_x,c_Orderings_Obot__class_Obot(tc_bool),u)* -> .
% 299.64/300.38 52108[0:Res:9566.0,50366.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),w),x),y,tc_bool)* hBOOL(hAPP(w,x)) -> hBOOL(y).
% 299.64/300.38 52110[0:Res:10684.0,50366.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),w,tc_bool)* hBOOL(v_Procs) -> hBOOL(w).
% 299.64/300.38 52127[0:Res:12533.1,50366.0] || c_lessequals(u,v,tc_bool)* c_lessequals(v,w,tc_bool)* hBOOL(c_HOL_Ominus__class_Ominus(u,x,tc_bool))* -> hBOOL(w).
% 299.64/300.38 52248[0:SpL:8498.1,35720.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) c_lessequals(u,w,tc_fun(v,tc_bool))* -> hBOOL(hAPP(w,x))*.
% 299.64/300.38 52261[7:SpL:27278.1,35720.0] || equal(hAPP(c_in(u),v),v_x)** c_lessequals(v_x,w,tc_fun(u,tc_bool))* -> hBOOL(hAPP(w,v))*.
% 299.64/300.38 52262[0:SpL:3586.1,35720.0] || equal(hAPP(c_in(u),v),v_Procs)** c_lessequals(v_x,w,tc_fun(u,tc_bool))* -> hBOOL(hAPP(w,v))*.
% 299.64/300.38 52263[0:SpL:2098.1,35720.0] || c_lessequals(u,v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(w,u,t_a) hBOOL(hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,u)))*.
% 299.64/300.38 52273[0:SpL:28031.0,35720.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)))*.
% 299.64/300.38 52276[0:SpL:28334.0,35720.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)))*.
% 299.64/300.38 52280[0:SpL:49017.1,35720.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,v,tc_Com_Opname)))*.
% 299.64/300.38 52346[0:SSi:52323.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),hAPP(c_Set_Oinsert(z,u),x1)),z))*.
% 299.64/300.38 53068[0:SpR:23955.0,9935.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_bool)* -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.38 53200[0:SpR:23958.0,9935.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_bool)* -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.38 53528[0:Res:1145.0,4247.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w),tc_Com_Opname,tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.38 54502[0:SpR:2771.1,54406.0] || equal(u,v) -> equal(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),tc_bool),hAPP(u,v_x))**.
% 299.64/300.38 55571[0:Res:54593.1,16481.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(hAPP(u,v_x),v,tc_bool)* -> equal(c_Orderings_Otop__class_Otop(tc_bool),v).
% 299.64/300.38 55615[0:SSi:55556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(hAPP(u,v_x),v,tc_bool)* -> c_lessequals(w,v,tc_bool)*.
% 299.64/300.38 55691[0:Res:54983.1,16481.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v,tc_bool)* -> equal(c_Orderings_Otop__class_Otop(tc_bool),v).
% 299.64/300.38 55717[0:SSi:55671.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v,tc_bool)* -> c_lessequals(w,v,tc_bool)*.
% 299.64/300.38 55737[0:SpL:3229.1,55605.1] || equal(u,v)* equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.38 55807[0:Rew:9.0,55789.0] || equal(hAPP(u,hAPP(v,v_x)),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(u,hAPP(v,v_x)),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.38 55814[0:Rew:585.0,55790.0] || equal(hAPP(hAPP(u,v_x),v),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(hAPP(u,v_x),v),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.38 55864[0:SSi:55849.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.38 55884[0:SpL:3229.1,55174.1] || equal(u,v)* equal(u,w)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),hAPP(w,v_x))* -> .
% 299.64/300.38 56073[0:SSi:55951.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(v,v_x))* equal(v,w)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(w,v_x))* -> .
% 299.64/300.38 56397[0:SpL:30368.2,19641.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.38 56839[0:SpL:30928.2,19641.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.38 57053[0:Rew:56980.1,11148.3] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(u,c_HOL_Ozero__class_Ozero(tc_bool),tc_bool)* equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(c_Orderings_Obot__class_Obot(tc_bool),u).
% 299.64/300.38 57092[0:SSi:57005.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(w,v)* -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(u,tc_bool),w,tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_bool))**.
% 299.64/300.38 57093[0:MRR:57043.1,826.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))**.
% 299.64/300.38 57094[0:MRR:57049.1,826.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))**.
% 299.64/300.38 57918[0:SpL:524.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) -> .
% 299.64/300.38 57929[0:SpL:414.0,55910.1] || equal(c_COMBK(u,v,w),c_Fun_Ofun__upd(x,v_x,y,z,x1))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),y) -> .
% 299.64/300.38 57955[0:SpL:9924.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> .
% 299.64/300.38 58075[0:SpL:524.0,55992.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v) -> .
% 299.64/300.38 58086[0:SpL:414.0,55992.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_COMBK(y,z,x1))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),y) -> .
% 299.64/300.38 58159[0:SpL:8498.1,58055.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v,w),c_Set_Oinsert(x,u))* -> .
% 299.64/300.38 58173[7:SpL:27278.1,58055.0] || equal(hAPP(c_in(u),v),v_x)** equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),c_Set_Oinsert(v,u))* -> .
% 299.64/300.38 58174[0:SpL:3586.1,58055.0] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),c_Set_Oinsert(v,u))* -> .
% 299.64/300.38 58189[0:SpL:2098.1,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u,v),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,v_x),tc_Hoare__Mirabelle_Otriple(t_a)))* -> c_Hoare__Mirabelle_Ohoare__valids(w,v_x,t_a).
% 299.64/300.38 58203[0:SpL:88.1,58055.0] class_Lattices_Oboolean__algebra(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* -> .
% 299.64/300.38 58224[0:SpL:9.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),w,x),c_Fun_Ocomp(u,v,y,z,x1))* -> .
% 299.64/300.38 58433[0:SpL:2097.1,58248.0] || hBOOL(hAPP(v_x,u)) equal(c_COMBK(v_x,v,w),c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(u,x),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.38 58439[0:SpL:397.1,58248.0] class_Orderings_Otop(u) || equal(c_COMBK(c_Orderings_Otop__class_Otop(u),v,w),c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.38 58440[0:SpL:365.1,58248.0] class_Orderings_Obot(u) || equal(c_COMBK(c_Orderings_Obot__class_Obot(u),v,w),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.38 58455[0:SpL:300.1,58248.0] class_Lattices_Obounded__lattice(u) || equal(c_COMBK(v_x,v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.38 58496[0:SpL:24020.1,58248.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_COMBK(v_x,v,w),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.38 58521[0:SpL:2267.1,58493.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) equal(c_COMBK(v_x,v,w),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.38 58532[0:SpL:56980.1,58177.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x))* -> .
% 299.64/300.38 58535[0:SpL:3229.1,58177.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),hAPP(v,v_x))* -> .
% 299.64/300.38 58537[0:SSi:58530.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v_x) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x))* -> .
% 299.64/300.38 58596[0:Res:10771.1,3499.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x))* equal(c_in(v),c_Set_Oinsert(w,u))* -> .
% 299.64/300.38 58614[0:SpL:2267.1,58473.0] || equal(u,c_COMBK(v,w,x))* equal(c_COMBK(v,y,z),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.38 58634[0:SpL:56980.1,58188.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),c_Fun_Ofun__upd(x,v_x,u,y,z))* -> .
% 299.64/300.38 58635[0:SpL:57059.1,58188.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),v,w),c_Fun_Ofun__upd(x,v_x,u,y,z))* -> .
% 299.64/300.38 58654[0:SSi:58631.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(u,tc_bool),w,x),c_Fun_Ofun__upd(y,v_x,v,z,x1))* -> .
% 299.64/300.38 59151[0:SpL:56980.1,58636.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_COMBK(u,v,w),c_Fun_Ofun__upd(x,v_x,c_Orderings_Obot__class_Obot(tc_bool),y,z))* -> .
% 299.64/300.38 59152[0:SpL:57059.1,58636.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(c_COMBK(u,v,w),c_Fun_Ofun__upd(x,v_x,c_Orderings_Otop__class_Otop(tc_bool),y,z))* -> .
% 299.64/300.38 59162[0:SSi:59148.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v) equal(c_COMBK(v,w,x),c_Fun_Ofun__upd(y,v_x,c_HOL_Ouminus__class_Ouminus(u,tc_bool),z,x1))* -> .
% 299.64/300.38 59736[0:SpL:3744.1,21018.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Oimage(v,u,w),v_Procs),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.38 60040[0:SpL:2771.1,60015.1] || equal(u,v)* equal(w,hAPP(u,v_x))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),w)* -> .
% 299.64/300.38 60159[0:SpL:56980.1,60048.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u)* equal(v,u)* equal(w,v)* equal(c_Orderings_Obot__class_Obot(tc_bool),w)* -> .
% 299.64/300.38 60166[0:SSi:60156.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(w,v)* equal(x,w)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),x)* -> .
% 299.64/300.38 60187[0:SpL:524.0,58170.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),u)* -> .
% 299.64/300.38 60198[0:SpL:414.0,58170.1] || equal(u,c_Fun_Ofun__upd(v,v_x,w,x,y))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(w,tc_bool),z,x1),u)* -> .
% 299.64/300.38 60810[0:SpL:2267.1,60715.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** -> c_Finite__Set_Ofinite(v,w)*.
% 299.64/300.38 61481[4:Obv:61437.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u))* -> .
% 299.64/300.38 61953[0:SpL:23682.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 62387[0:SSi:62204.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oinsert(u,v),w),w) -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),w,tc_fun(v,tc_bool))*.
% 299.64/300.38 62524[0:SSi:62476.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),u)* -> c_lessequals(w,u,tc_bool)*.
% 299.64/300.38 62525[0:SSi:62475.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),u)* -> c_lessequals(v,u,tc_bool)*.
% 299.64/300.38 62531[0:SSi:62460.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(v,u)* c_lessequals(w,v,tc_bool)* -> c_lessequals(w,u,tc_bool)*.
% 299.64/300.38 63764[0:Obv:63674.1] class_Orderings_Olinorder(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(u),v) -> c_lessequals(w,v,u)*.
% 299.64/300.38 63774[0:SSi:63625.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(v,w)* hBOOL(hAPP(v,x))* -> hBOOL(hAPP(w,x))*.
% 299.64/300.38 64000[0:SpL:647.0,3863.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v)).
% 299.64/300.38 64109[0:Res:679.1,437.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),tc_Com_Opname)*.
% 299.64/300.38 64520[0:SpL:9911.0,24257.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_in(tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.38 64521[0:SpL:10463.0,24257.1] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_bool),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.38 65942[0:SpR:65404.1,21130.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_Procs),v,w),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.38 65946[0:SpR:65404.1,651.0] class_Lattices_Olattice(u) || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.38 65952[2:SpR:65404.1,15483.1] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.38 65957[0:SpR:65404.1,3284.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),v_x))*.
% 299.64/300.38 65966[0:SpR:65404.1,10090.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.38 65967[0:SpR:65404.1,11030.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 65969[0:SpR:65404.1,21141.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.38 65970[0:SpR:65404.1,27441.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_x,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.38 65972[0:SpR:65404.1,28334.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_x,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 65976[0:SpR:65404.1,27381.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.38 65978[0:SpR:65404.1,28031.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 65993[0:SpR:65404.1,648.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.38 65996[0:SpR:65404.1,3316.1] class_Lattices_Olattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 65997[0:SpR:65404.1,3339.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> equal(c_Fun_Ofun__upd(v,v_x,v_x,w,x),v)**.
% 299.64/300.38 66045[0:SpR:65404.1,7253.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v))*.
% 299.64/300.38 66203[0:SpL:65404.1,3698.2] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* equal(c_Com_Ocom_OBODY,v) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 66495[0:Res:66448.1,15857.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),v)))*.
% 299.64/300.38 66496[0:Res:66448.1,15629.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Orderings_Otop__class_Otop(tc_bool),u)))*.
% 299.64/300.38 66501[0:Res:66449.1,15857.0] || equal(c_Orderings_Obot__class_Obot(tc_bool),v_Procs) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),v)))*.
% 299.64/300.38 66502[0:Res:66449.1,15629.0] || equal(c_Orderings_Obot__class_Obot(tc_bool),v_Procs) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Orderings_Obot__class_Obot(tc_bool),u)))*.
% 299.64/300.38 66536[0:SpL:3229.1,66188.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v)* equal(hAPP(v,v_x),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 66676[0:Obv:66634.1] class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),u),v,u)*.
% 299.64/300.38 67120[4:Obv:66938.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> hBOOL(c_HOL_Ozero__class_Ozero(u))*.
% 299.64/300.38 67421[4:Obv:67238.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> hBOOL(c_HOL_Ozero__class_Ozero(u))*.
% 299.64/300.38 68750[4:Obv:68566.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> hBOOL(c_HOL_Ozero__class_Ozero(u))*.
% 299.64/300.38 69053[4:Obv:68868.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> hBOOL(c_HOL_Ozero__class_Ozero(u))*.
% 299.64/300.38 70286[0:Obv:70252.1] class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),u),u)*.
% 299.64/300.38 70979[0:Res:36017.0,70856.2] || equal(u,hAPP(c_HOL_Ominus__class_Ominus(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),v_x))* hBOOL(u)* -> .
% 299.64/300.38 71319[0:Res:7538.0,682.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_in(tc_Com_Opname),v_x))),v_Procs))*.
% 299.64/300.38 71320[0:Res:7538.0,437.1] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),u)* -> c_Finite__Set_Ofinite(x,u).
% 299.64/300.38 71326[4:Res:7538.0,43176.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))),x,t_a)*.
% 299.64/300.38 71327[4:Res:7538.0,42582.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))),x))*.
% 299.64/300.38 71330[4:Res:7538.0,42356.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x))),v_x))*.
% 299.64/300.38 71332[0:Res:7538.0,44833.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))),v_x))*.
% 299.64/300.38 71411[7:SpL:88.1,71221.0] class_Lattices_Oboolean__algebra(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_x)** -> .
% 299.64/300.38 71432[7:SpL:9.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool))* equal(c_Fun_Ocomp(u,v,w,x,y),v_x)** -> .
% 299.64/300.38 71619[7:SpR:71455.1,7253.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),u))*.
% 299.64/300.38 71770[7:SpL:71455.1,214.0] || equal(u,v_x) c_lessequals(u,v,tc_fun(t_a,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v))*.
% 299.64/300.38 72607[7:SSi:72582.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(hAPP(v_x,v_x),tc_bool),u),tc_bool,tc_bool))*.
% 299.64/300.38 73040[7:Res:71608.1,263.0] || equal(hAPP(c_Set_Oinsert(u,t_a),v),v_x)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v))* equal(v_x,u).
% 299.64/300.38 73057[7:Res:71608.1,156.0] || equal(hAPP(c_Set_Ovimage(u,t_a,v),w),v_x) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(u,v_x)),w))*.
% 299.64/300.38 73231[7:SpR:71835.1,16776.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_x,u,v,w),v_x,w,v)*.
% 299.64/300.38 73238[7:SpR:71835.1,649.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(v_x,v_Procs)))*.
% 299.64/300.38 73264[7:SpR:71835.1,23997.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(v_x,u,tc_fun(v,tc_bool)),v_x),v_x,tc_bool)*.
% 299.64/300.38 73303[7:SpR:71835.1,650.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u)))*.
% 299.64/300.38 73304[7:SpR:71835.1,649.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs)))*.
% 299.64/300.38 73306[7:SpR:71835.1,652.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(v_x,u)).
% 299.64/300.38 73307[7:SpR:71835.1,675.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),v_Procs))*.
% 299.64/300.38 73308[7:SpR:71835.1,676.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),v_Procs))*.
% 299.64/300.38 73314[7:SpR:71835.1,19440.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oinsert(v,u),v_x)))*.
% 299.64/300.38 73318[7:SpR:71835.1,21130.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),v_x),hAPP(u,v_Procs)))*.
% 299.64/300.38 73319[7:SpR:71835.1,21152.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),v_x),v_Procs))*.
% 299.64/300.38 73328[7:SpR:71835.1,13238.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(t_a)) equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(v_x,u))*.
% 299.64/300.38 73332[7:SpR:71835.1,19451.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(t_a)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))))*.
% 299.64/300.38 73357[7:SpR:71835.1,651.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.38 73363[7:SpR:71835.1,15483.1] || equal(c_Set_Oinsert(v_x,t_a),u) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.38 73368[7:SpR:71835.1,3284.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),v_x))*.
% 299.64/300.38 73379[7:SpR:71835.1,10090.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 73380[7:SpR:71835.1,11030.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_in(t_a),u) -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 73382[7:SpR:71835.1,21141.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.38 73383[7:SpR:71835.1,27441.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.38 73385[7:SpR:71835.1,28334.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 73389[7:SpR:71835.1,27381.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.38 73391[7:SpR:71835.1,28031.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 73406[7:SpR:71835.1,648.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.38 73409[7:SpR:71835.1,3316.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_in(v),u)* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 73410[7:SpR:71835.1,3339.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(v,u)* -> equal(c_Fun_Ofun__upd(v,v_x,v_x,w,x),v)**.
% 299.64/300.38 73418[7:SpR:71835.1,1161.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.38 73419[7:SpR:71835.1,28056.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,v)))*.
% 299.64/300.38 73420[7:SpR:71835.1,28359.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,v)))*.
% 299.64/300.38 73434[7:SpR:71835.1,23960.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,u),u)*.
% 299.64/300.38 73436[7:SpR:71835.1,47138.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,tc_bool)))*.
% 299.64/300.38 73437[7:SpR:71835.1,47319.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,tc_bool)),u))*.
% 299.64/300.38 73438[7:SpR:71835.1,47458.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,tc_bool)),u,t_a)*.
% 299.64/300.38 73455[7:SpR:71835.1,40601.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(v_x,u),v,w),tc_Com_Opname,tc_bool))*.
% 299.64/300.38 73462[7:SpR:71835.1,40590.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),w))*.
% 299.64/300.38 73463[7:SpR:71835.1,42609.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),w,t_a)*.
% 299.64/300.38 73464[7:SpR:71835.1,40591.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),w))*.
% 299.64/300.38 73465[7:SpR:71835.1,42829.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),w,t_a)*.
% 299.64/300.38 73516[7:SpR:71835.1,676.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(hAPP(v_x,hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.38 73521[7:SpR:71835.1,542.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(v_x,hAPP(v_x,v)),hAPP(v_x,v))**.
% 299.64/300.38 73527[7:SpR:71835.1,40591.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v))*.
% 299.64/300.38 73528[7:SpR:71835.1,42829.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v,t_a)*.
% 299.64/300.38 73545[7:SpR:71835.1,87.1] class_Lattices_Oboolean__algebra(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.38 73575[7:SpR:71835.1,675.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.38 73586[7:SpR:71835.1,499.0] || equal(c_Set_Oinsert(v_x,t_a),c_Hoare__Mirabelle_Otriple_Otriple(u)) -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(v_x,hAPP(c_Com_Ocom_OBODY,v)),w),u)*.
% 299.64/300.38 73620[7:SpR:71835.1,499.0] || equal(c_Set_Oinsert(v_x,t_a),c_Com_Ocom_OBODY) -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),v_x),w),u)*.
% 299.64/300.38 73657[7:SpR:71835.1,11499.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 73662[7:SpR:71835.1,8375.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) equal(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))* -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.38 73697[7:SpR:71835.1,7253.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x))*.
% 299.64/300.38 73727[7:SpR:71835.1,499.0] || equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),c_Set_Oinsert(v_x,t_a))** -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),v_x,u).
% 299.64/300.38 73749[7:SpR:71835.1,88.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Set_Oinsert(v_x,t_a))** -> equal(c_Orderings_Otop__class_Otop(u),v_x).
% 299.64/300.38 73766[7:SpR:71835.1,40590.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.38 73767[7:SpR:71835.1,42609.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),c_Set_Oinsert(v_x,t_a))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.38 73842[7:SpR:71835.1,11473.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Set_Oinsert(v_x,t_a))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.38 73885[7:SpR:71835.1,9.0] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(u,hAPP(v,v_x)),v_x).
% 299.64/300.38 73892[7:SpR:71835.1,11611.0] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(v_x,u,tc_bool).
% 299.64/300.38 73902[7:SpR:71835.1,12944.0] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Set_Oinsert(v_x,t_a))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.38 73952[7:SpL:71835.1,591.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(v_x,v_G)) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),v_x,t_a)*.
% 299.64/300.38 73988[7:SpL:71835.1,24123.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(v_x,u),c_Orderings_Obot__class_Obot(tc_bool)) -> c_lessequals(u,v,tc_bool)*.
% 299.64/300.38 73989[7:SpL:71835.1,24122.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(v_x,u),c_Orderings_Obot__class_Obot(tc_bool))** -> c_lessequals(v_x,v,tc_bool)*.
% 299.64/300.38 74012[7:SpL:71835.1,682.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) c_lessequals(v_x,u,tc_fun(v,tc_bool))* -> hBOOL(hAPP(u,v_Procs)).
% 299.64/300.38 74017[7:SpL:71835.1,16768.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) hBOOL(hAPP(v_G,v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v_na,v_x)))* -> c_Hoare__Mirabelle_Otriple__valid(v_na,v_Procs,t_a).
% 299.64/300.38 74050[7:SpL:71835.1,3698.2] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(v,u)* equal(c_Com_Ocom_OBODY,v)* equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 74057[7:SpL:71835.1,3726.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** equal(c_in(tc_Com_Opname),v_x) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.38 74058[7:SpL:71835.1,3330.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** equal(v_x,v) -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.38 74061[7:SpL:71835.1,38886.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.38 74062[7:SpL:71835.1,38697.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.38 74065[7:SpL:71835.1,66188.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 74066[7:SpL:71835.1,3701.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 74090[7:SpL:71835.1,58493.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_COMBK(v_x,u,v),c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.38 74091[7:SpL:71835.1,40680.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(u)*.
% 299.64/300.38 74092[7:SpL:71835.1,47318.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,tc_bool),u,tc_bool)* -> hBOOL(u).
% 299.64/300.38 74100[7:SpL:71835.1,43176.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(v_x,u,tc_fun(v,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(u,w,t_a)*.
% 299.64/300.38 74101[7:SpL:71835.1,42582.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(v_x,u,tc_fun(v,tc_bool))* -> hBOOL(hAPP(u,w))*.
% 299.64/300.38 74155[7:SpL:71835.1,332.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) c_Finite__Set_Ofinite(hAPP(v_x,v),u)* -> c_Finite__Set_Ofinite(v,u).
% 299.64/300.38 74156[7:SpL:71835.1,333.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) c_Finite__Set_Ofinite(hAPP(v_x,v),u)* -> c_Finite__Set_Ofinite(v_x,u).
% 299.64/300.38 74282[7:SpL:71835.1,333.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a))** c_Finite__Set_Ofinite(v_x,u) -> c_Finite__Set_Ofinite(v,u).
% 299.64/300.38 74375[7:SpL:71835.1,58177.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v,w),v_x)** -> .
% 299.64/300.38 74462[7:MRR:74243.1,6340.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(hAPP(c_in(w),v_x),u))*.
% 299.64/300.38 74463[7:MRR:74228.1,6340.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(v),v_x),u))* -> .
% 299.64/300.38 74471[7:MRR:74159.2,27297.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) equal(hAPP(v_x,v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))* -> .
% 299.64/300.38 74484[7:MRR:73977.2,429.0] || equal(c_Set_Oimage(u,v,v),c_Set_Oinsert(v_x,t_a)) c_Finite__Set_Ofinite(v_x,v) -> c_Fun_Oinj__on(u,v_x,v,v)*.
% 299.64/300.38 74489[7:MRR:73667.1,74485.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_Set_Oinsert(v_x,t_a))** -> equal(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_x).
% 299.64/300.38 74633[7:SpR:532.0,71906.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),w)),v_x))*.
% 299.64/300.38 74703[7:SpR:533.0,71907.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),v_x))*.
% 299.64/300.38 74780[7:Res:23320.1,72021.1] || equal(c_in(tc_Com_Opname),c_in(t_a)) equal(hAPP(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_x),hAPP(v_x,v_x))** -> .
% 299.64/300.38 74781[7:Res:9267.0,72021.1] || equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x),hAPP(v_x,v_x))** -> equal(v_x,u).
% 299.64/300.38 74866[7:SpR:17045.0,72297.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_x)).
% 299.64/300.38 74870[7:SpR:88.1,72297.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_x)).
% 299.64/300.38 74890[7:SpR:11473.0,72297.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x)).
% 299.64/300.38 74891[7:SpR:9.0,72297.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_in(t_a))** -> hBOOL(hAPP(hAPP(u,hAPP(v,v_x)),v_x))*.
% 299.64/300.38 74897[7:SpR:12944.0,72297.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x)).
% 299.64/300.38 75222[7:SSi:75189.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x))*.
% 299.64/300.38 75223[7:SSi:75186.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x))*.
% 299.64/300.38 75581[0:SSi:75489.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),tc_fun(w,tc_bool))*.
% 299.64/300.38 75679[7:SpR:71883.1,24914.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(v_x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_x,tc_Com_Opname,u),v_x)),v_x)**.
% 299.64/300.38 76039[0:SSi:75943.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),tc_fun(w,tc_bool))*.
% 299.64/300.38 76076[0:SSi:76075.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(w,v).
% 299.64/300.38 77141[7:SpL:15476.0,74788.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v)* -> hBOOL(v)*.
% 299.64/300.38 77162[7:SpL:302.1,74788.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** equal(c_Orderings_Otop__class_Otop(u),v)* -> hBOOL(v)*.
% 299.64/300.38 77196[7:SpL:11176.1,74788.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x)** equal(u,v)* -> hBOOL(v)*.
% 299.64/300.38 77232[7:SpR:71835.1,801.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* -> equal(c_Fun_Ofun__upd(v_x,v_x,v_x,v,w),v_x)**.
% 299.64/300.38 77629[7:SpR:8415.2,77503.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,v_x,tc_Com_Opname),v_x))*.
% 299.64/300.38 77907[0:Res:8375.1,5892.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> hBOOL(hAPP(c_COMBS(c_in(w),c_in(v),x,y,z),u))*.
% 299.64/300.38 77921[0:Res:38134.1,5892.0] || hBOOL(u) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Set_Oinsert(w,x),y,z,x1),c_COMBK(u,x2,x3)))*.
% 299.64/300.38 77928[4:Res:40591.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))*.
% 299.64/300.38 77934[4:Res:47138.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool)))*.
% 299.64/300.38 77936[4:Res:40590.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w,x,y),z))*.
% 299.64/300.38 77980[0:Res:38130.1,5892.0] || hBOOL(u) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Set_Oinsert(w,x),y,z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)))*.
% 299.64/300.38 78036[0:Rew:538.0,77944.0,584.0,77944.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),hAPP(c_Set_Oinsert(v_x,t_a),w))))*.
% 299.64/300.38 78123[0:MRR:78122.1,820.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),w),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))))*.
% 299.64/300.38 78163[7:Res:77996.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_x),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.64/300.38 78206[7:MRR:78187.1,6340.0] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname))*.
% 299.64/300.38 78207[7:MRR:78188.1,6340.0] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname))*.
% 299.64/300.38 78437[7:SpL:78167.0,215.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,v_x,v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.64/300.38 78533[4:MRR:9459.1,78524.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))**.
% 299.64/300.38 78534[4:MRR:9456.1,78524.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(v,u)),c_Set_Oinsert(v,u))**.
% 299.64/300.38 78535[4:MRR:9445.1,78524.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(v,u)),c_Set_Oinsert(v,u))**.
% 299.64/300.38 78570[7:MRR:29329.1,78524.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(v,u)),c_Set_Oinsert(v,u))**.
% 299.64/300.38 78572[4:MRR:29853.2,78524.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_Procs,u),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.38 78573[7:MRR:29852.2,78524.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_Procs,u),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.38 78578[4:MRR:35877.2,78524.0] || equal(v_Procs,v_x) equal(c_HOL_Ominus__class_Ominus(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> .
% 299.64/300.38 78581[4:MRR:52636.2,78524.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_Procs) -> .
% 299.64/300.38 78583[7:MRR:52869.2,78524.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) -> .
% 299.64/300.38 78741[4:Res:78665.1,5892.0] || equal(hAPP(hAPP(u,v),v),v_x)** -> hBOOL(hAPP(c_COMBS(c_in(w),u,x,y,z),v))*.
% 299.64/300.38 78751[4:Res:78665.1,12554.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),v_x)** -> hBOOL(hAPP(hAPP(c_in(w),x),u)).
% 299.64/300.38 78758[4:Res:78665.1,5986.0] || equal(hAPP(c_COMBS(c_in(u),v,w,x,y),z),v_x)** -> hBOOL(hAPP(hAPP(v,z),z))*.
% 299.64/300.38 78765[4:Res:78665.1,11883.0] || equal(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w),v_x)** hBOOL(hAPP(hAPP(c_in(v),w),u)) -> .
% 299.64/300.38 79309[4:SpR:2771.1,78846.1] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))*.
% 299.64/300.38 80323[0:Rew:300.1,79866.1] class_Lattices_Obounded__lattice(u) || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,v,x),w)**.
% 299.64/300.38 80324[0:Rew:301.1,79486.1] class_Lattices_Obounded__lattice(u) || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x),w)**.
% 299.64/300.38 80382[0:Rew:525.1,80381.1] class_Lattices_Oupper__semilattice(u) || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x),w)**.
% 299.64/300.38 80392[0:Rew:65404.1,80391.1] class_Lattices_Olattice(u) || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x),w)**.
% 299.64/300.38 81518[0:Rew:300.1,81060.1] class_Lattices_Obounded__lattice(u) || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,x),w)**.
% 299.64/300.38 81519[0:Rew:301.1,80679.1] class_Lattices_Obounded__lattice(u) || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Lattices_Oupper__semilattice__class_Osup(u),v,x),w)**.
% 299.64/300.38 81577[0:Rew:525.1,81576.1] class_Lattices_Oupper__semilattice(u) || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Lattices_Oupper__semilattice__class_Osup(u),v,x),w)**.
% 299.64/300.38 81587[0:Rew:65404.1,81586.1] class_Lattices_Olattice(u) || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Lattices_Oupper__semilattice__class_Osup(u),v,x),w)**.
% 299.64/300.38 81837[0:SpR:456.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Option_Othe(w),x,y,z),c_Option_Ooption_OSome(v,w)),u)*.
% 299.64/300.38 82309[0:SpR:456.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Option_Othe(w),x,y,z),c_Option_Ooption_OSome(v,w)),u)*.
% 299.64/300.38 82838[7:Res:77991.0,255.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),v_x),w,tc_fun(x,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(x),v_x),w)).
% 299.64/300.38 82853[7:Res:77991.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),v_x),w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oinsert(u,v),v_x),w),v_x,t_a)*.
% 299.64/300.38 82968[7:SpR:5924.0,27207.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_x)** -> hBOOL(hAPP(hAPP(u,v_x),v)).
% 299.64/300.38 82969[0:SpR:5924.0,3282.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_Procs)** -> hBOOL(hAPP(hAPP(u,v_x),v)).
% 299.64/300.38 82979[2:SpR:5924.0,4250.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(hAPP(u,v_x),v)).
% 299.64/300.38 83199[7:SpR:8498.1,78357.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,x),v_x),v_x))*.
% 299.64/300.38 83213[7:SpR:27278.1,78357.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,x),v_x),v_x))*.
% 299.64/300.38 83214[7:SpR:3586.1,78357.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,x),v_x),v_x))*.
% 299.64/300.38 83228[7:SpR:2098.1,78357.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),v,w),v_x),v_x))*.
% 299.64/300.38 83238[7:SpR:17045.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x,y),v_x),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.38 83242[7:SpR:88.1,78357.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v,w),v_x),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.38 83262[7:SpR:11473.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,x),v_x),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.38 83263[7:SpR:9.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),z,x1),v_x),hAPP(u,hAPP(v,v_x))))*.
% 299.64/300.38 83269[7:SpR:12944.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y,z),v_x),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.38 83283[7:Rew:9.0,83279.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),hAPP(u,hAPP(x,v_x))))*.
% 299.64/300.38 83298[7:SpR:5961.0,27207.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_x)** -> hBOOL(hAPP(u,hAPP(x,v_x))).
% 299.64/300.38 83299[0:SpR:5961.0,3282.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_Procs)** -> hBOOL(hAPP(u,hAPP(x,v_x))).
% 299.64/300.38 83309[2:SpR:5961.0,4250.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(u,hAPP(x,v_x))).
% 299.64/300.38 84176[7:SpL:302.1,78767.0] class_Lattices_Obounded__lattice(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> .
% 299.64/300.38 84285[0:SpL:3339.1,10287.0] || equal(u,v)* equal(c_Fun_Ofun__upd(u,v_x,w,x,y),u)** -> equal(w,hAPP(v,v_x))*.
% 299.64/300.38 84289[0:SpL:771.0,10287.0] || equal(c_Fun_Ofun__upd(c_COMBK(u,v,w),x,y,z,x1),c_COMBK(u,v,w))** -> equal(y,u).
% 299.64/300.38 84293[0:SpL:23979.0,10287.0] || equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),u,v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))** -> equal(v,u).
% 299.64/300.38 84916[4:SpL:23682.0,78744.0] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,t_a)*.
% 299.64/300.38 84994[0:Res:84957.0,255.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),u),w,tc_fun(x,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(x),u),w)).
% 299.64/300.38 85009[0:Res:84957.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),u),w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oinsert(u,v),u),w),u,t_a)*.
% 299.64/300.38 85298[0:SpL:8385.1,26240.0] || equal(u,v_Procs) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))** -> .
% 299.64/300.38 85299[7:SpL:71455.1,26240.0] || equal(u,v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** -> .
% 299.64/300.38 85319[0:SpL:10063.0,26240.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** -> .
% 299.64/300.38 85375[0:SpL:328.1,26240.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* equal(x,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) -> .
% 299.64/300.38 85427[4:SpR:78507.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,w),c_Set_Oinsert(v_x,u))**.
% 299.64/300.38 85429[4:SpR:78507.0,9566.0] || -> c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,w)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),tc_bool)*.
% 299.64/300.38 85625[4:SSi:85603.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),v_x,tc_bool)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),v_x).
% 299.64/300.38 85722[4:SSi:85678.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),u,tc_bool)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),u).
% 299.64/300.38 85728[0:SpR:8385.1,9066.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u)))*.
% 299.64/300.38 85729[7:SpR:71455.1,9066.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u)))*.
% 299.64/300.38 85734[0:SpR:2089.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))))*.
% 299.64/300.38 85749[0:SpR:10063.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))))*.
% 299.64/300.38 85962[0:SSi:85931.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),hAPP(v,v_x),tc_bool))* hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)) -> .
% 299.64/300.38 85981[4:Res:85725.0,17530.1] || equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.38 85984[4:SSi:85972.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,u,tc_bool) -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x),u,tc_bool)*.
% 299.64/300.38 85985[4:SSi:85971.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x),tc_bool)* -> c_lessequals(u,v_x,tc_bool).
% 299.64/300.38 86059[0:SpL:88.1,86011.0] class_Lattices_Oboolean__algebra(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_Procs)** -> .
% 299.64/300.38 86080[0:SpL:9.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool))* equal(c_Fun_Ocomp(u,v,w,x,y),v_Procs)** -> .
% 299.64/300.38 86277[0:SpR:86109.1,7253.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),u))*.
% 299.64/300.38 86335[0:SpR:86109.1,9066.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u)))*.
% 299.64/300.38 86455[0:SpL:86109.1,214.0] || equal(u,v_Procs) c_lessequals(u,v,tc_fun(t_a,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v))*.
% 299.64/300.38 86497[0:SpL:86109.1,26240.0] || equal(u,v_Procs) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** -> .
% 299.64/300.38 86545[7:MRR:86544.1,6340.0] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname))*.
% 299.64/300.38 86547[7:MRR:86546.1,6340.0] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,c_Set_Oinsert(v_x,t_a),tc_Com_Opname),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,c_Set_Oinsert(v_x,t_a),tc_Com_Opname))*.
% 299.64/300.38 86600[0:Res:19823.1,11883.0] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool))))* -> .
% 299.64/300.38 86634[0:Res:86261.1,263.0] || equal(hAPP(c_Set_Oinsert(u,t_a),v),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v))* equal(v_x,u).
% 299.64/300.38 86651[0:Res:86261.1,156.0] || equal(hAPP(c_Set_Ovimage(u,t_a,v),w),v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(u,v_x)),w))*.
% 299.64/300.38 86721[4:SpL:302.1,86106.0] class_Lattices_Obounded__lattice(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> .
% 299.64/300.38 87088[0:SSi:87087.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_fun(t_a,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),hAPP(v,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 87206[0:Res:13385.1,32820.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.64/300.38 87277[7:SpR:397.1,71492.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v))*.
% 299.64/300.38 87278[7:SpR:365.1,71492.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(u)),v))*.
% 299.64/300.38 87410[7:SSi:87366.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),w)))*.
% 299.64/300.38 87425[7:SpR:397.1,71493.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.38 87426[7:SpR:365.1,71493.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(u)),v,t_a)*.
% 299.64/300.38 87555[7:SpR:397.1,71679.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.38 87556[7:SpR:365.1,71679.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.38 87682[7:SSi:87655.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(u,v_x))))*.
% 299.64/300.38 88322[0:Res:7227.0,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(c_COMBK(v_x,u,v),w,t_a),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x),tc_bool))* -> .
% 299.64/300.38 88554[0:Res:13385.1,8306.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** -> c_lessequals(x,u,tc_fun(w,tc_bool))*.
% 299.64/300.38 88611[7:SpL:15476.0,88086.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x) hBOOL(c_HOL_Ominus__class_Ominus(v,c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),tc_bool))* -> .
% 299.64/300.38 88618[7:SpL:34428.0,88086.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,v_x,tc_bool))* -> .
% 299.64/300.38 88628[7:SpL:302.1,88086.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,c_Orderings_Otop__class_Otop(u),tc_bool))* -> .
% 299.64/300.38 88629[7:SpL:331.0,88086.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,v_x,tc_bool))* -> .
% 299.64/300.38 88658[7:SpL:11177.1,88086.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,v_x,tc_bool))* -> .
% 299.64/300.38 88662[7:SpL:11176.1,88086.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x) hBOOL(c_HOL_Ominus__class_Ominus(v,u,tc_bool))* -> .
% 299.64/300.38 88832[0:SpR:659.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),hAPP(c_Set_Oinsert(v_Procs,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),v_Procs))*.
% 299.64/300.38 88984[7:SpR:78167.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,u),v,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_x))*.
% 299.64/300.38 89057[0:Res:78099.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),t_a)*.
% 299.64/300.38 89092[7:Res:78350.0,17530.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,u),v,tc_fun(w,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.38 89102[7:SSi:89083.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,u,tc_bool) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,v),w,tc_fun(x,tc_bool)),v_x),u,tc_bool)*.
% 299.64/300.38 89103[7:SSi:89082.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,v),w,tc_fun(x,tc_bool)),v_x),tc_bool)* -> c_lessequals(u,v_x,tc_bool).
% 299.64/300.38 89235[7:SpR:78590.1,10745.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Set_Oinsert(v_x,t_a)) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool)*.
% 299.64/300.38 89248[7:SpR:78590.1,10746.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Set_Oinsert(v_x,t_a)) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool)*.
% 299.64/300.38 89322[7:SpR:78590.1,415.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,t_a),u,u,v,w),c_Set_Oinsert(v_x,t_a))**.
% 299.64/300.38 89324[7:SpR:78590.1,9566.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,t_a)),u),tc_bool)*.
% 299.64/300.38 89582[7:SpL:78590.1,21018.0] || equal(c_Set_Oinsert(v_x,t_a),u) equal(hAPP(c_Set_Oimage(v,t_a,w),u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.38 89657[7:MRR:89656.1,6340.0] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname),c_Set_Oinsert(v_x,t_a)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname))*.
% 299.64/300.38 89737[7:Res:89344.1,19641.0] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_in(t_a),v_x),u),c_Set_Oinsert(v_x,t_a)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_in(t_a),v_x),u,t_a)*.
% 299.64/300.38 90025[4:SpR:78660.1,10745.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),v_x) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool)*.
% 299.64/300.38 90038[4:SpR:78660.1,10746.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),v_x) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool)*.
% 299.64/300.38 90112[4:SpR:78660.1,415.0] || equal(hAPP(u,v_x),v_x) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,t_a),u,u,v,w),c_Set_Oinsert(v_x,t_a))**.
% 299.64/300.38 90114[4:SpR:78660.1,9566.0] || equal(hAPP(u,v_x),v_x) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,t_a)),u),tc_bool)*.
% 299.64/300.38 90373[4:SpL:78660.1,21018.0] || equal(hAPP(u,v_x),v_x) equal(hAPP(c_Set_Oimage(v,t_a,w),u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.38 90431[7:MRR:90430.1,6340.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname),v_x),v_x)** -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname)).
% 299.64/300.38 90777[0:Res:13387.1,26480.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> c_lessequals(u,v,tc_fun(w,tc_bool)).
% 299.64/300.38 90881[4:Res:90134.1,19641.0] || equal(hAPP(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_in(t_a),v_x),u),v_x),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_in(t_a),v_x),u,t_a).
% 299.64/300.38 91097[0:SpR:44588.1,7253.0] class_Complete__Lattice_Ocomplete__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v))*.
% 299.64/300.38 91298[0:Rew:91288.1,91098.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(u)),v,tc_bool)*.
% 299.64/300.38 91300[0:Rew:91288.1,91068.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(u),v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.64/300.38 91322[0:Rew:91289.1,91208.1,91288.1,91208.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Lattices_Oupper__semilattice__class_Osup(u),v,x),w)**.
% 299.64/300.38 91323[0:Rew:91289.1,91206.1,91288.1,91206.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x),w)**.
% 299.64/300.38 91908[0:SpR:79073.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_Procs,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,x),c_Set_Oinsert(v_Procs,u))**.
% 299.64/300.38 91910[0:SpR:79073.0,9566.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_Procs,x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_bool)*.
% 299.64/300.38 92057[7:SpR:79101.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,u),hAPP(c_in(v),v_x),hAPP(c_in(v),v_x),w,x),c_Set_Oinsert(v_x,u))**.
% 299.64/300.38 92059[7:SpR:79101.0,9566.0] || -> c_lessequals(hAPP(c_in(u),v_x),hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,x)),hAPP(c_in(u),v_x)),tc_bool)*.
% 299.64/300.38 92234[0:Obv:92221.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),u)*.
% 299.64/300.38 92534[7:Res:10705.0,92132.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,hAPP(hAPP(c_in(y),v_x),v_x),z,x1)),x))*.
% 299.64/300.38 92580[0:SpL:5227.1,509.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x)* equal(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),c_Suc(w)) -> .
% 299.64/300.38 92591[7:SpR:2097.1,82151.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,w)))*.
% 299.64/300.38 92601[7:SpR:397.1,82151.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Set_Oinsert(v_x,v)))*.
% 299.64/300.38 92602[7:SpR:365.1,82151.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(u),c_Set_Oinsert(v_x,v)))*.
% 299.64/300.38 92615[7:SpR:300.1,82151.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,v)))*.
% 299.64/300.38 92656[7:SpR:24020.1,82151.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,v)))*.
% 299.64/300.38 92696[7:Res:82151.1,371.0] || equal(c_Set_Oinsert(u,v),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,w)))* equal(u,c_Set_Oinsert(v_x,w))*.
% 299.64/300.38 93251[4:SpR:2097.1,85556.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v_x,w),tc_bool)*.
% 299.64/300.38 93261[4:SpR:397.1,85556.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(c_Orderings_Otop__class_Otop(u),v),tc_bool)*.
% 299.64/300.38 93262[4:SpR:365.1,85556.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(c_Orderings_Obot__class_Obot(u),v),tc_bool)*.
% 299.64/300.38 93275[4:SpR:300.1,85556.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v_x,v),tc_bool)*.
% 299.64/300.38 93316[4:SpR:24020.1,85556.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v_x,v),tc_bool)*.
% 299.64/300.38 93340[4:SpR:539.1,85556.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_bool)*.
% 299.64/300.38 93341[4:SpR:540.1,85556.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_bool)*.
% 299.64/300.38 93342[4:SpR:297.2,85556.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,v,tc_bool)*.
% 299.64/300.38 93429[4:SSi:93396.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) c_lessequals(hAPP(hAPP(u,v_x),v),w,tc_bool)* -> c_lessequals(v_x,w,tc_bool).
% 299.64/300.38 93430[4:SSi:93395.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) c_lessequals(v,v_x,tc_bool) -> c_lessequals(v,hAPP(hAPP(u,v_x),w),tc_bool)*.
% 299.64/300.38 93449[0:SpR:397.1,86147.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v))*.
% 299.64/300.38 93450[0:SpR:365.1,86147.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(u)),v))*.
% 299.64/300.38 93583[0:SSi:93538.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),w)))*.
% 299.64/300.38 93600[0:SpR:397.1,86148.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.38 93601[0:SpR:365.1,86148.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(u)),v,t_a)*.
% 299.64/300.38 93744[0:SpR:397.1,86342.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.38 93745[0:SpR:365.1,86342.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.38 93871[0:SSi:93844.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(u,v_x))))*.
% 299.64/300.38 94331[7:Res:14491.3,71881.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,hAPP(v_x,v_x)))* c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.64/300.38 643[0:Res:589.0,151.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),u)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_HOL_Ominus__class_Ominus(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.64/300.38 639[0:Res:589.0,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v),u,tc_Com_Opname)))* -> hBOOL(hAPP(u,v_x)).
% 299.64/300.38 640[0:Res:589.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs),u,tc_Com_Opname)))* -> hBOOL(hAPP(u,v_x)).
% 299.64/300.38 666[0:Res:589.0,280.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_in(tc_Com_Opname),u,tc_fun(w,tc_bool)),v_Procs))*.
% 299.64/300.38 830[0:SpR:300.1,415.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))**.
% 299.64/300.38 927[0:Res:686.1,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_in(u),v),tc_Com_Opname),v))*.
% 299.64/300.38 935[0:Res:687.1,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_in(u),v),tc_Com_Opname),v))*.
% 299.64/300.38 961[0:SpR:303.1,415.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(u),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.64/300.38 986[0:SpR:302.1,683.1] class_Lattices_Obounded__lattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),v)*.
% 299.64/300.38 987[0:SpR:331.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_Com_Opname,u),u)*.
% 299.64/300.38 1105[0:SpR:300.1,1103.1] class_Lattices_Obounded__lattice(u) || -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),t_a)* hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))).
% 299.64/300.38 1137[0:SpR:397.1,651.0] class_Orderings_Otop(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.38 1138[0:SpR:365.1,651.0] class_Orderings_Obot(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.38 1141[0:SpR:300.1,651.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.38 1149[0:SpR:397.1,648.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.38 1150[0:SpR:365.1,648.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.38 1153[0:SpR:300.1,648.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.38 1940[0:SSi:1934.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,v)* equal(v,v_Procs)* c_lessequals(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* -> .
% 299.64/300.38 1951[0:Res:448.2,1937.1] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.38 2026[0:SSi:2022.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.38 2043[0:SSi:2039.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.38 2112[0:SpR:2097.1,651.0] || hBOOL(hAPP(v_x,u)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.38 2115[0:SpR:2097.1,648.0] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(u,w),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.38 2143[0:SpR:74.1,47.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.38 2144[0:SpR:73.1,47.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u) -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.38 2218[0:SpR:74.1,43.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.38 2219[0:SpR:73.1,43.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u) -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.38 2297[0:SpR:2267.1,2267.1] || equal(u,v)* equal(w,u)* -> equal(c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(x,tc_bool)))*.
% 299.64/300.38 2336[0:SpL:2267.1,16.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)))* -> equal(u,x)*.
% 299.64/300.38 2349[0:SpL:2267.1,2063.0] || equal(u,v)* equal(w,c_HOL_Ouminus__class_Ouminus(v,tc_fun(x,tc_bool)))* -> equal(c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool)),u)*.
% 299.64/300.38 2378[0:SpL:74.1,48.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u).
% 299.64/300.38 2379[0:SpL:73.1,48.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u).
% 299.64/300.38 2408[0:SpL:74.1,44.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u).
% 299.64/300.38 2409[0:SpL:73.1,44.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u).
% 299.64/300.38 2438[0:SpR:74.1,49.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.38 2439[0:SpR:73.1,49.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.38 2466[0:SpR:74.1,45.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.38 2467[0:SpR:73.1,45.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.38 2494[0:SpL:74.1,50.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u),u)* -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.38 2495[0:SpL:73.1,50.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.38 2520[0:SpL:74.1,46.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u),u)* -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.38 2521[0:SpL:73.1,46.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.38 2566[0:SpR:585.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBC(u,v,w,x),y),tc_Com_Opname,z),v_Procs),hAPP(hAPP(u,v_x),y)))*.
% 299.64/300.38 2577[0:SpR:586.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),tc_Com_Opname,z),v_Procs),hAPP(u,hAPP(y,v_x))))*.
% 299.64/300.38 2596[0:SpR:445.1,1158.0] || -> equal(v_x,u) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(v,u,w,x,y),tc_Com_Opname,z),v_Procs),hAPP(v,v_x)))*.
% 299.64/300.38 2773[0:Rew:25.1,2757.2] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_HOL_Ouminus(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),u),hAPP(v,v_x))**.
% 299.64/300.38 2774[0:Rew:25.1,2756.2] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_HOL_Ouminus(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),u),hAPP(v,v_x))**.
% 299.64/300.38 3141[0:SpR:2771.1,2771.1] || equal(u,v)* equal(v,w)* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.38 3239[0:SSi:3227.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(w,c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))* -> equal(c_HOL_Ouminus__class_Ouminus(w,tc_bool),hAPP(u,v_x))*.
% 299.64/300.38 3240[0:SSi:3225.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(w,tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))* -> equal(w,hAPP(u,v_x))*.
% 299.64/300.38 3241[0:SSi:3220.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 3242[0:SSi:3219.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 3243[0:SSi:3156.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(w,hAPP(u,v_x))* -> equal(c_HOL_Ouminus__class_Ouminus(w,tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))*.
% 299.64/300.38 3244[0:SSi:3151.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 3245[0:SSi:3150.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 3246[0:SSi:3146.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 3281[0:SpR:3229.1,445.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),z)* -> equal(v_x,v) equal(hAPP(z,v_x),hAPP(u,v_x))*.
% 299.64/300.38 3313[0:SpR:3229.1,1162.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v)* -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(v,v_x),tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.38 3318[0:SpR:3229.1,1157.0] || equal(c_in(u),v) -> hBOOL(hAPP(hAPP(v,v_x),hAPP(c_Set_Oimage(c_COMBK(v_x,w,x),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.38 3366[0:SpR:3229.1,1162.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_Procs),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 3368[0:SpR:3229.1,585.0] || equal(hAPP(c_COMBC(u,v,w,x),y),z)* -> equal(hAPP(z,v_x),hAPP(hAPP(u,v_x),y))*.
% 299.64/300.38 3369[0:SpR:3229.1,586.0] || equal(hAPP(c_COMBB(u,v,w,x),y),z)* -> equal(hAPP(z,v_x),hAPP(u,hAPP(y,v_x)))*.
% 299.64/300.38 3370[0:SpR:3229.1,585.0] || equal(c_COMBC(u,v,w,x),y)* -> equal(hAPP(hAPP(y,v_x),z),hAPP(hAPP(u,z),v_x))*.
% 299.64/300.38 3371[0:SpR:3229.1,586.0] || equal(c_COMBB(u,v,w,x),y)* -> equal(hAPP(hAPP(y,v_x),z),hAPP(u,hAPP(v_x,z)))*.
% 299.64/300.38 3485[0:SpL:3229.1,1943.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.38 3488[0:SpL:3229.1,1944.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.38 3500[0:SpL:3229.1,279.0] || equal(c_in(u),v)* hBOOL(hAPP(hAPP(v,v_x),w))* -> equal(hAPP(c_Set_Oinsert(v_x,u),w),w)**.
% 299.64/300.38 3510[0:SpL:3229.1,360.0] || equal(c_Set_Oinsert(u,v),w)* c_Fun_Oinj__on(x,hAPP(w,v_x),v,y)* -> c_Fun_Oinj__on(x,v_x,v,y).
% 299.64/300.38 3511[0:SpL:3229.1,279.0] || equal(hAPP(c_in(u),v),w)* hBOOL(hAPP(w,v_x))* -> equal(hAPP(c_Set_Oinsert(v,u),v_x),v_x)**.
% 299.64/300.38 3697[0:SpL:25.1,3483.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Com_Ocom_OBODY) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.38 3703[0:SpL:540.1,3483.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.38 3711[0:SpL:337.0,3483.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 3718[0:SpR:445.1,3283.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_in(tc_Com_Opname))** -> equal(v_x,v) hBOOL(hAPP(hAPP(u,v_x),v_Procs)).
% 299.64/300.38 3739[0:SpR:585.0,3283.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),y),v_Procs))*.
% 299.64/300.38 3740[0:SpR:586.0,3283.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(u,hAPP(y,v_x)),v_Procs))*.
% 299.64/300.38 3835[0:SpL:539.1,3483.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.38 3899[0:SpR:74.1,53.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.38 3900[0:SpR:73.1,53.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u) -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.38 3953[0:SpL:2098.1,3506.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a).
% 299.64/300.38 3957[0:SpL:88.1,3506.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),c_Orderings_Otop__class_Otop(u))* -> .
% 299.64/300.38 3959[0:SpL:9.0,3506.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(z,x1),hAPP(u,hAPP(v,v_x)))* -> .
% 299.64/300.38 3963[0:SpR:74.1,41.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u).
% 299.64/300.38 3964[0:SpR:73.1,41.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u).
% 299.64/300.38 4111[0:SpL:87.1,298.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.38 4145[0:SpL:302.1,3929.0] class_Lattices_Obounded__lattice(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.38 4218[0:SpR:299.2,88.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)).
% 299.64/300.38 4238[0:SpL:299.2,3483.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Com_Ocom_OBODY)** equal(v,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 4333[0:SpL:297.2,3483.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 4399[0:SpR:2097.1,3284.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),v_x))*.
% 299.64/300.38 4401[0:SpR:397.1,3284.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.38 4403[0:SpR:365.1,3284.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.38 4410[0:SpR:300.1,3284.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),v_x))*.
% 299.64/300.38 4449[0:SpL:397.1,3493.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_in(tc_Com_Opname))** equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.38 4451[0:SpL:365.1,3493.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_in(tc_Com_Opname))** equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.38 4496[0:SpR:2097.1,3316.1] || hBOOL(hAPP(v_x,u))* equal(c_in(v),c_Set_Oinsert(u,w))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 4498[0:SpR:397.1,3316.1] class_Orderings_Otop(u) || equal(c_in(v),c_Orderings_Otop__class_Otop(tc_fun(t_a,u))) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 4500[0:SpR:365.1,3316.1] class_Orderings_Obot(u) || equal(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(t_a,u))) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 4507[0:SpR:300.1,3316.1] class_Lattices_Obounded__lattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 4531[0:Res:3316.1,279.0] || equal(c_in(u),c_in(v)) -> equal(hAPP(c_Set_Oinsert(v_x,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.38 4553[0:SpR:3586.1,415.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v,u),v_x,v_x,w,x),c_Set_Oinsert(v,u))**.
% 299.64/300.38 4561[0:SpL:3586.1,3506.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(w,x),v_x)** -> .
% 299.64/300.38 4573[0:SpR:74.1,111.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_Orderings_Obot__class_Obot(u),v,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.38 4574[0:SpR:73.1,111.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.38 4598[0:SpR:74.1,111.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.38 4599[0:SpR:73.1,111.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,c_Orderings_Otop__class_Otop(u),u) -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.38 4631[0:SpL:2097.1,3698.2] || hBOOL(hAPP(v_x,u))* equal(v,c_Set_Oinsert(u,w))* equal(c_Com_Ocom_OBODY,v) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 4633[0:SpL:397.1,3698.2] class_Orderings_Otop(u) || equal(v,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)))* equal(c_Com_Ocom_OBODY,v) equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 4635[0:SpL:365.1,3698.2] class_Orderings_Obot(u) || equal(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)))* equal(c_Com_Ocom_OBODY,v) equal(c_Orderings_Obot__class_Obot(u),c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 4643[0:SpL:300.1,3698.2] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))* equal(c_Com_Ocom_OBODY,v) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 4705[0:Res:305.1,146.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),w),u),v,u)*.
% 299.64/300.38 4706[0:Res:310.1,146.1] class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),w),u),v,u)*.
% 299.64/300.38 4707[0:Res:306.1,146.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ouminus__class_Ouminus(w,u)),u),w,u)*.
% 299.64/300.38 4708[0:Res:309.1,146.1] class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ouminus__class_Ouminus(w,u)),u),w,u)*.
% 299.64/300.38 4881[0:SpL:74.1,112.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u),u)* -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u).
% 299.64/300.38 4882[0:SpL:73.1,112.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(c_Orderings_Otop__class_Otop(u),v,u).
% 299.64/300.38 4906[0:SpL:74.1,112.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(v,c_Orderings_Obot__class_Obot(u),u).
% 299.64/300.38 4907[0:SpL:73.1,112.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(v,c_Orderings_Otop__class_Otop(u),u).
% 299.64/300.38 4995[0:Res:858.2,405.1] class_Lattices_Obounded__lattice(u) class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> equal(v,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.38 5001[0:Res:1177.2,405.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> equal(c_Orderings_Otop__class_Otop(u),v).
% 299.64/300.38 5003[0:Res:943.2,405.1] class_Lattices_Obounded__lattice(u) class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> equal(c_Orderings_Otop__class_Otop(u),v).
% 299.64/300.38 5074[0:Res:83.0,436.1] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),x)),y))* -> hBOOL(hAPP(x,y)).
% 299.64/300.38 5087[0:SpR:2097.1,3339.1] || hBOOL(hAPP(v_x,u))* equal(v,c_Set_Oinsert(u,w))* -> equal(c_Fun_Ofun__upd(v,v_x,v_x,x,y),v)**.
% 299.64/300.38 5089[0:SpR:397.1,3339.1] class_Orderings_Otop(u) || equal(v,c_Orderings_Otop__class_Otop(tc_fun(t_a,u))) -> equal(c_Fun_Ofun__upd(v,v_x,c_Orderings_Otop__class_Otop(u),w,x),v)**.
% 299.64/300.38 5091[0:SpR:365.1,3339.1] class_Orderings_Obot(u) || equal(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,u))) -> equal(c_Fun_Ofun__upd(v,v_x,c_Orderings_Obot__class_Obot(u),w,x),v)**.
% 299.64/300.38 5099[0:SpR:300.1,3339.1] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))* -> equal(c_Fun_Ofun__upd(v,v_x,v_x,w,x),v)**.
% 299.64/300.38 5896[0:SpR:584.0,337.0] || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.38 5898[0:SpR:584.0,517.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,y,z,x1),u),v))*.
% 299.64/300.38 5910[0:SpR:524.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y,z),w),hAPP(hAPP(u,w),w))**.
% 299.64/300.38 5918[0:SpR:414.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Fun_Ofun__upd(v,w,x,y,z),x1,x2,x3),w),hAPP(hAPP(u,w),x))**.
% 299.64/300.38 5923[0:SpR:456.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Option_Othe(v),w,x,y),c_Option_Ooption_OSome(z,v)),hAPP(hAPP(u,c_Option_Ooption_OSome(z,v)),z))*.
% 299.64/300.38 5947[0:SpR:524.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y,z),v),hAPP(v,hAPP(w,v)))**.
% 299.64/300.38 5955[0:SpR:414.0,584.0] || -> equal(hAPP(c_COMBS(c_Fun_Ofun__upd(u,v,w,x,y),z,x1,x2,x3),v),hAPP(w,hAPP(z,v)))**.
% 299.64/300.38 5960[0:SpR:456.0,584.0] || -> equal(hAPP(c_COMBS(c_Option_Othe(u),v,w,x,y),c_Option_Ooption_OSome(z,u)),hAPP(z,hAPP(v,c_Option_Ooption_OSome(z,u))))*.
% 299.64/300.38 5980[0:SpL:584.0,3483.1] || equal(c_COMBS(u,v,w,x,y),c_Com_Ocom_OBODY)** equal(hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.38 5987[0:SpL:584.0,332.0] || c_Finite__Set_Ofinite(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),u)* -> c_Finite__Set_Ofinite(hAPP(v,z),u).
% 299.64/300.38 6018[0:SpR:331.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x,y,z),u))*.
% 299.64/300.38 6310[0:SpR:3229.1,3279.1] || equal(u,v)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u)* -> hBOOL(hAPP(hAPP(hAPP(v,v_x),v_Procs),v_x))*.
% 299.64/300.38 6314[0:SpR:525.1,3279.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.38 6335[0:SpR:585.0,3279.1] || equal(c_COMBC(u,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(hAPP(u,v_Procs),v_x),v_x))*.
% 299.64/300.38 6336[0:SpR:586.0,3279.1] || equal(c_COMBB(u,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(u,hAPP(v_x,v_Procs)),v_x))*.
% 299.64/300.38 6337[0:SpR:3229.1,3279.1] || equal(hAPP(hAPP(u,v_x),v_Procs),v)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u) -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.38 6348[0:SpL:3229.1,3727.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v)* equal(hAPP(v,v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs))*.
% 299.64/300.38 6491[0:SpR:3229.1,3285.1] || equal(u,v)* equal(c_in(tc_Com_Opname),u)* -> hBOOL(hAPP(hAPP(v,v_x),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.38 6495[0:SpR:525.1,3285.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.38 6518[0:SpR:585.0,3285.1] || equal(c_COMBC(u,v,w,x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(u,hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.38 6519[0:SpR:586.0,3285.1] || equal(c_COMBB(u,v,w,x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(u,hAPP(v_x,hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs))))*.
% 299.64/300.38 6528[0:SpL:3229.1,3302.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u)* equal(hAPP(u,v_x),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.38 6718[0:SpL:3229.1,3945.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* equal(hAPP(v,v_x),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(w,x),v_x)** -> .
% 299.64/300.38 6729[0:SpR:3229.1,3291.1] || equal(u,v)* equal(c_in(tc_Com_Opname),u)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(v,v_x)),v_Procs))*.
% 299.64/300.38 6733[0:SpR:525.1,3291.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),v_Procs))*.
% 299.64/300.38 6849[0:SpL:3229.1,3331.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v)* equal(hAPP(v,v_x),w)* -> equal(hAPP(w,v_x),v_x)**.
% 299.64/300.38 6859[0:SpL:3229.1,3484.1] || equal(u,v)* equal(c_Com_Ocom_OBODY,u)* equal(hAPP(v,v_x),hAPP(c_Com_Ocom_OBODY,w))* -> equal(v_x,w).
% 299.64/300.38 6863[0:SpL:525.1,3484.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,v),v_x)** -> equal(v_x,v).
% 299.64/300.38 6895[0:SpL:3229.1,3499.1] || equal(u,v)* equal(c_in(w),u)* hBOOL(hAPP(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))* -> .
% 299.64/300.38 6899[0:SpL:525.1,3499.1] class_Lattices_Oupper__semilattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* hBOOL(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.38 6929[0:SpL:585.0,3499.1] || equal(c_in(u),c_COMBC(v,w,x,y))* hBOOL(hAPP(hAPP(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_x))* -> .
% 299.64/300.38 6930[0:SpL:586.0,3499.1] || equal(c_in(u),c_COMBB(v,w,x,y))* hBOOL(hAPP(v,hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> .
% 299.64/300.38 6986[0:Obv:6982.0] class_Lattices_Oboolean__algebra(u) || equal(v,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),v_Procs)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.38 6988[0:Obv:6978.0] class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Obot__class_Obot(u),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.38 7038[2:Obv:7034.0] class_Lattices_Oboolean__algebra(u) || equal(v,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.38 7040[2:Obv:7030.0] class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Obot__class_Obot(u),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.38 7041[2:Obv:7029.0] class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Otop__class_Otop(u),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.38 7053[0:Res:448.2,6546.0] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) || equal(u,v)* -> c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(v,v_x))*.
% 299.64/300.38 7116[0:SpR:3229.1,3305.1] || equal(u,v)* equal(w,u)* -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,tc_Com_Opname,x),v_Procs),hAPP(v,v_x)))*.
% 299.64/300.38 7120[0:SpR:525.1,3305.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.38 7159[0:SpR:3229.1,3317.1] || equal(u,v)* equal(c_in(w),u)* -> hBOOL(hAPP(hAPP(v,v_x),hAPP(c_Set_Oinsert(v_x,w),x)))*.
% 299.64/300.38 7163[0:SpR:525.1,3317.1] class_Lattices_Oupper__semilattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,v),w)))*.
% 299.64/300.38 7190[0:SpR:585.0,3317.1] || equal(c_in(u),c_COMBC(v,w,x,y))* -> hBOOL(hAPP(hAPP(v,hAPP(c_Set_Oinsert(v_x,u),z)),v_x))*.
% 299.64/300.38 7191[0:SpR:586.0,3317.1] || equal(c_in(u),c_COMBB(v,w,x,y))* -> hBOOL(hAPP(v,hAPP(v_x,hAPP(c_Set_Oinsert(v_x,u),z))))*.
% 299.64/300.38 7242[0:SpR:2935.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_in(t_a),v_x),v,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))))*.
% 299.64/300.38 7254[0:SpR:2097.1,7253.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),u))*.
% 299.64/300.38 7262[0:SpR:397.1,7253.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.38 7264[0:SpR:365.1,7253.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.38 7272[0:SpR:300.1,7253.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),x))*.
% 299.64/300.38 7286[0:SpR:87.1,7253.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.38 7300[0:SpR:303.1,7253.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.38 7321[0:SpL:3229.1,3507.1] || equal(u,v)* equal(c_Set_Oinsert(w,x),u)* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> .
% 299.64/300.38 7457[0:Res:364.1,6546.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool))* equal(hAPP(c_Set_Oinsert(v,tc_Com_Opname),u),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 7459[0:Res:364.1,1937.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,tc_Com_Opname),u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.38 7492[0:SpR:3229.1,3346.1] || equal(u,v)* equal(c_Set_Oinsert(w,x),u)* -> hBOOL(hAPP(hAPP(c_in(x),w),hAPP(v,v_x)))*.
% 299.64/300.38 7496[0:SpR:525.1,3346.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x))*.
% 299.64/300.38 7541[0:Res:1145.0,363.0] || -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_Set_Oinsert(v,w),u),x,y),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.38 7616[0:SpR:3229.1,7599.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),hAPP(u,v_x))),v_Procs))*.
% 299.64/300.38 7685[0:SpL:3229.1,4439.0] || equal(c_Set_Ovimage(u,v,w),x)* equal(hAPP(x,v_x),v_Procs)** -> hBOOL(hAPP(v_x,hAPP(u,v_x)))*.
% 299.64/300.38 7795[0:Res:448.2,296.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),u)* c_lessequals(x,v,u).
% 299.64/300.38 7990[0:SpR:3229.1,5877.0] || equal(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Com_Ocom_OBODY,v,w,x),y)* -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(y,v_x),z),u)*.
% 299.64/300.38 7993[0:SpR:3229.1,5877.0] || equal(hAPP(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Com_Ocom_OBODY,v,w,x),y),z)* -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(z,v_x),u)*.
% 299.64/300.38 8040[0:Res:448.2,295.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),u)* c_lessequals(w,v,u).
% 299.64/300.38 8081[0:SpR:3229.1,7284.0] || equal(hAPP(c_Set_Oimage(c_COMBK(v_x,u,v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),y)* -> hBOOL(hAPP(y,v_x))*.
% 299.64/300.38 8093[0:SpL:3229.1,7600.0] || equal(c_Set_Oinsert(u,v),w)* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(x,v),hAPP(w,v_x)),v)* -> c_Finite__Set_Ofinite(v_x,v).
% 299.64/300.38 8128[0:Res:448.2,427.1] class_Orderings_Olinorder(u) class_Orderings_Opreorder(u) || c_lessequals(v,w,u)* -> c_lessequals(v,x,u)* c_lessequals(x,w,u)*.
% 299.64/300.38 8137[0:Res:1177.2,427.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_Orderings_Opreorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> c_lessequals(w,v,u)*.
% 299.64/300.38 8139[0:Res:943.2,427.1] class_Lattices_Obounded__lattice(u) class_Lattices_Olattice(u) class_Orderings_Opreorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> c_lessequals(w,v,u)*.
% 299.64/300.38 8171[0:Obv:8167.0] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),w,u)* -> c_lessequals(v,w,u).
% 299.64/300.38 8173[0:Obv:8163.0] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),v,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u).
% 299.64/300.38 8183[0:SpR:3229.1,5887.1] class_Lattices_Oupper__semilattice(u) || equal(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z)* -> c_lessequals(v_x,hAPP(z,v_x),u)*.
% 299.64/300.38 8208[0:SpR:3229.1,5888.1] class_Lattices_Olattice(u) || equal(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z)* -> c_lessequals(v_x,hAPP(z,v_x),u)*.
% 299.64/300.38 8251[0:Res:858.2,426.1] class_Lattices_Obounded__lattice(u) class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(v,w,u)*.
% 299.64/300.38 8253[0:Res:448.2,426.1] class_Orderings_Olinorder(u) class_Orderings_Oorder(u) || c_lessequals(v,w,u)* -> c_lessequals(x,w,u)* c_lessequals(v,x,u)*.
% 299.64/300.38 8491[0:SpR:584.0,8375.1] || equal(hAPP(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) -> hBOOL(hAPP(c_COMBS(c_in(w),u,x,y,z),v))*.
% 299.64/300.38 8590[0:SpR:8498.1,415.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(w,v),u,u,x,y),c_Set_Oinsert(w,v))**.
% 299.64/300.38 8617[0:SpL:8498.1,3506.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(w,x),v_x)** -> .
% 299.64/300.38 8624[0:SpL:8498.1,2693.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)))* equal(v,u)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.38 8786[0:SpR:8415.2,3229.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(u,v)* -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.38 8787[0:SpR:8415.2,3283.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(v_x,v_Procs))*.
% 299.64/300.38 8822[0:SpR:8415.2,525.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* -> equal(hAPP(v_x,v_x),v_x)**.
% 299.64/300.38 9011[4:MRR:8989.2,6340.0] || equal(v_Procs,v_x) equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(u,v_x)).
% 299.64/300.38 9014[0:Obv:8988.0] || equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(v_Procs,v_x) -> hBOOL(hAPP(v_x,hAPP(u,v_x)))*.
% 299.64/300.38 9049[0:SpL:2097.1,214.0] || hBOOL(hAPP(u,v))* c_lessequals(u,w,tc_fun(x,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(x),v),w))*.
% 299.64/300.38 9068[0:Res:7539.0,214.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(x,u),hAPP(c_Set_Oinsert(v,u),y)))))*.
% 299.64/300.38 9132[0:SpL:2267.1,8494.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)))** equal(v,v_Procs)* -> .
% 299.64/300.38 9150[0:SpR:3229.1,8376.2] || equal(u,v)* equal(c_in(tc_Com_Opname),u)* equal(w,v_Procs) -> hBOOL(hAPP(hAPP(v,v_x),w))*.
% 299.64/300.38 9154[0:SpR:525.1,8376.2] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.38 9199[0:SpR:585.0,8376.2] || equal(c_COMBC(u,v,w,x),c_in(tc_Com_Opname))** equal(y,v_Procs) -> hBOOL(hAPP(hAPP(u,y),v_x))*.
% 299.64/300.38 9200[0:SpR:586.0,8376.2] || equal(c_COMBB(u,v,w,x),c_in(tc_Com_Opname))** equal(y,v_Procs) -> hBOOL(hAPP(u,hAPP(v_x,y)))*.
% 299.64/300.38 9221[0:SpR:3229.1,9071.0] || equal(c_in(u),v) -> hBOOL(hAPP(hAPP(v,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_x,u),tc_Com_Opname,tc_fun(u,tc_bool))))*.
% 299.64/300.38 9249[0:SpR:2267.1,8369.1] || equal(u,v)* -> hBOOL(hAPP(hAPP(c_in(w),x),v))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),x))*.
% 299.64/300.38 9253[0:SpR:3229.1,8369.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w)* -> hBOOL(hAPP(hAPP(c_in(v),v_x),u))* hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 9291[0:SpR:539.1,9269.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)).
% 299.64/300.38 9292[0:SpR:540.1,9269.0] class_Lattices_Olattice(u) || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)).
% 299.64/300.38 9517[0:Res:367.1,251.1] class_Orderings_Obot(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,v)),w),hAPP(x,w),v)*.
% 299.64/300.38 9531[0:Res:421.1,251.1] class_Orderings_Otop(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,v)),x),v)*.
% 299.64/300.38 9575[0:SSi:9500.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(u,x),hAPP(hAPP(c_Set_Oinsert(y,w),v),x),tc_bool)*.
% 299.64/300.38 9916[0:Rew:9911.0,5964.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,w,x,y),z),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 9918[0:Rew:9911.0,5975.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y,z),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 9964[0:SpR:9911.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.38 10038[0:SpR:9924.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v,w,x),y),hAPP(hAPP(u,y),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.64/300.38 10039[0:SpR:9924.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,v,w,x),y),hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(u,y)))**.
% 299.64/300.38 10079[0:SpR:9925.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.38 10105[0:Res:7539.0,431.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),y)),w,z)* -> c_Fun_Oinj__on(u,y,w,z).
% 299.64/300.38 10110[0:Res:651.0,431.0] || c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,tc_fun(w,tc_bool)),w,x)* -> c_Fun_Oinj__on(u,hAPP(v,v_x),w,x).
% 299.64/300.38 10111[0:Res:7542.0,431.0] || c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,tc_fun(w,tc_bool)),w,x)* -> c_Fun_Oinj__on(u,v_x,w,x).
% 299.64/300.38 10501[0:Res:3284.1,454.0] || equal(c_in(tc_Com_Opname),u) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(u,v_x),v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(u,v_x),v),v_Procs,t_a)*.
% 299.64/300.38 10543[0:SpR:10463.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.38 10598[0:SpL:300.1,57.1] class_Lattices_Obounded__lattice(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),c_HOL_Ozero__class_Ozero(u))** -> equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.38 10621[0:Rew:3246.1,10594.2] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || equal(u,v)* equal(c_Orderings_Otop__class_Otop(tc_bool),c_HOL_Ozero__class_Ozero(tc_bool)) -> equal(hAPP(v,v_x),c_HOL_Ozero__class_Ozero(tc_bool))**.
% 299.64/300.38 10681[0:SpR:8498.1,9566.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(w,x),c_Set_Oinsert(y,v)),u),tc_bool)*.
% 299.64/300.38 10686[0:SpR:653.0,9566.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.38 10696[0:SpR:3586.1,9566.0] || equal(hAPP(c_in(u),v),v_Procs) -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(w,x),c_Set_Oinsert(v,u)),v_x),tc_bool)*.
% 299.64/300.38 10706[0:SpR:2098.1,9566.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) c_lessequals(v,hAPP(hAPP(c_Set_Oinsert(w,x),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a))),v),tc_bool)*.
% 299.64/300.38 10714[0:SpR:88.1,9566.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(x,u))),x),tc_bool)*.
% 299.64/300.38 10715[0:SpR:87.1,9566.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x)),c_HOL_Ouminus__class_Ouminus(x,u)),tc_bool)*.
% 299.64/300.38 10725[0:SpR:1195.1,9566.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),c_Orderings_Obot__class_Obot(u)),tc_bool)*.
% 299.64/300.38 10727[0:SpR:321.0,9566.0] || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oimage(x,y,u)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_bool)*.
% 299.64/300.38 10728[0:SpR:38.0,9566.0] || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Ovimage(x,u,y)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_bool)*.
% 299.64/300.38 10731[0:SpR:1196.1,9566.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u))),c_Orderings_Otop__class_Otop(u)),tc_bool)*.
% 299.64/300.38 10732[0:SpR:105.0,9566.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Ovimage(x,u,y)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),tc_bool)*.
% 299.64/300.38 10736[0:SpR:9.0,9566.0] || -> c_lessequals(hAPP(u,hAPP(v,w)),hAPP(hAPP(c_Set_Oinsert(x,y),c_Fun_Ocomp(u,v,z,x1,x2)),w),tc_bool)*.
% 299.64/300.38 10794[0:SpR:353.0,378.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(x,v),w)),v)*.
% 299.64/300.38 10807[0:SpR:353.0,3291.1] || equal(c_Set_Oinsert(u,v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),v_Procs))*.
% 299.64/300.38 10816[0:SpR:353.0,3317.1] || equal(c_in(u),v) -> hBOOL(hAPP(hAPP(v,v_x),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(v_x,u),x))))*.
% 299.64/300.38 10859[0:SpR:8385.1,353.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),u)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),u))**.
% 299.64/300.38 10890[0:SpL:353.0,377.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),x),v).
% 299.64/300.38 11210[0:SpR:11176.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Orderings_Otop__class_Otop(tc_bool),v) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),tc_Com_Opname,u),u)*.
% 299.64/300.38 11227[0:SpR:11176.1,415.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,u,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))**.
% 299.64/300.38 11338[0:SpR:11177.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),tc_Com_Opname,u),u)*.
% 299.64/300.38 11355[0:SpR:11177.1,415.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,u,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))**.
% 299.64/300.38 11356[0:SpR:11177.1,5875.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,y,z),u))*.
% 299.64/300.38 11458[0:SpR:8498.1,10745.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),tc_bool)*.
% 299.64/300.38 11484[0:SpR:8498.1,10746.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),tc_bool)*.
% 299.64/300.38 11581[0:SpR:3744.1,9567.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,u),v,tc_fun(w,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.38 11583[0:SpR:2093.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_Procs,u),v,tc_fun(w,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_in(tc_Com_Opname),v_x),tc_bool)*.
% 299.64/300.38 11601[0:SpR:302.1,9567.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(w,tc_bool)),x),c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.38 11602[0:SpR:331.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,tc_fun(w,tc_bool)),x),x,tc_bool)*.
% 299.64/300.38 11626[0:SpR:330.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,tc_bool)*.
% 299.64/300.38 11630[0:SpR:303.1,9567.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.38 11633[0:SpR:2095.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(u,v),w,tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_bool)*.
% 299.64/300.38 11635[0:SpR:9987.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,t_a),u,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool)*.
% 299.64/300.38 11881[0:Res:652.1,150.1] || c_lessequals(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),u)) -> .
% 299.64/300.38 11884[0:Res:8375.1,150.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_in(v),w),u))* -> .
% 299.64/300.38 12553[0:Res:652.1,148.0] || c_lessequals(v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),u)).
% 299.64/300.38 12555[0:Res:8375.1,148.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(w),x),u))*.
% 299.64/300.38 12675[0:Res:3282.1,519.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_Procs)** -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(w,v_x)).
% 299.64/300.38 12689[0:MRR:3875.2,12687.1] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* -> hBOOL(hAPP(v,w))*.
% 299.64/300.38 12724[0:SSi:12711.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) c_lessequals(v,c_HOL_Ominus__class_Ominus(u,w,tc_bool),tc_bool)* -> equal(v,c_HOL_Ominus__class_Ominus(u,w,tc_bool)).
% 299.64/300.38 12989[0:Res:3284.1,501.0] || equal(c_in(tc_Com_Opname),u) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,hAPP(u,v_x)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,v_Procs,t_a).
% 299.64/300.38 12992[0:Res:3283.1,501.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,v_Procs),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.38 13009[0:SpR:10090.1,299.2] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,u)* -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.38 13012[0:SpR:10090.1,415.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(c_Fun_Ofun__upd(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_bool),v,w),hAPP(u,v_x))**.
% 299.64/300.38 13030[0:SpR:10090.1,293.2] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v,v_x,u) -> c_lessequals(v,c_Orderings_Otop__class_Otop(tc_bool),u)*.
% 299.64/300.38 13046[0:SpR:2097.1,10090.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 13050[0:SpR:397.1,10090.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 13051[0:SpR:365.1,10090.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 13060[0:SpR:300.1,10090.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.38 13088[0:SpL:10090.1,311.1] class_Lattices_Obounded__lattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Obot__class_Obot(u),v_x).
% 299.64/300.38 13090[0:SpL:10090.1,295.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v,u)* -> c_lessequals(v_x,v,u).
% 299.64/300.38 13196[0:SpR:9493.1,10745.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool)*.
% 299.64/300.38 13205[0:SpR:9493.1,10746.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool)*.
% 299.64/300.38 13232[0:SpR:9493.1,415.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,t_a),u,u,v,w),c_Set_Oinsert(v_x,t_a))**.
% 299.64/300.38 13234[0:SpR:9493.1,9566.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,t_a)),u),tc_bool)*.
% 299.64/300.38 13309[0:Res:13238.1,148.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)).
% 299.64/300.38 13411[0:Res:13385.1,357.1] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** c_Finite__Set_Ofinite(x,v) -> c_Finite__Set_Ofinite(y,w)*.
% 299.64/300.38 13504[0:SpR:2097.1,11030.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.38 13509[0:SpR:397.1,11030.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 13510[0:SpR:365.1,11030.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 13519[0:SpR:300.1,11030.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 13557[0:Res:11030.1,279.0] || equal(c_in(t_a),c_in(u)) -> equal(hAPP(c_Set_Oinsert(v_x,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.64/300.38 13585[0:Res:9258.0,147.1] || hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ominus__class_Ominus(v,u,tc_fun(t_a,tc_bool)),v_x),tc_bool))*.
% 299.64/300.38 13629[0:SpR:11473.0,9566.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))),y),tc_bool)*.
% 299.64/300.38 13651[0:SpL:11473.0,3506.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(w,x),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.38 13674[0:SpR:11499.0,9566.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y))),c_Orderings_Otop__class_Otop(tc_bool)),tc_bool)*.
% 299.64/300.38 14248[0:SpR:14216.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),tc_Com_Opname,u),u)*.
% 299.64/300.38 14321[0:SpR:11695.0,9566.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,x),c_Option_Othe(y))),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),y)),tc_bool)*.
% 299.64/300.38 14354[0:Res:678.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_in(tc_Com_Opname),v_x),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_in(tc_Com_Opname),v_x),u),v_Procs,u)*.
% 299.64/300.38 14357[0:Res:264.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u),v,u)*.
% 299.64/300.38 14368[0:Res:3283.1,170.1] class_Orderings_Olinorder(u) || equal(c_in(tc_Com_Opname),c_in(u)) c_Finite__Set_Ofinite(v_Procs,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,u),v_x,u)*.
% 299.64/300.38 14374[0:Res:9258.0,170.1] class_Orderings_Olinorder(t_a) || c_Finite__Set_Ofinite(u,t_a) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* c_lessequals(c_Finite__Set_Olinorder__class_OMin(u,t_a),v_x,t_a).
% 299.64/300.38 14375[0:Res:11029.0,170.1] class_Orderings_Olinorder(t_a) || c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),t_a) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),t_a),v_x,t_a)*.
% 299.64/300.38 14426[0:SpR:12944.0,9566.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,x),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),y,z))),x1),tc_bool)*.
% 299.64/300.38 14448[0:SpL:12944.0,3506.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(y,z),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.38 14481[0:Res:678.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_in(tc_Com_Opname),v_x),u) -> c_lessequals(v_Procs,c_Finite__Set_Olinorder__class_OMax(hAPP(c_in(tc_Com_Opname),v_x),u),u)*.
% 299.64/300.38 14484[0:Res:264.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u),u)*.
% 299.64/300.38 14495[0:Res:3283.1,169.1] class_Orderings_Olinorder(u) || equal(c_in(tc_Com_Opname),c_in(u)) c_Finite__Set_Ofinite(v_Procs,u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(v_Procs,u),u)*.
% 299.64/300.38 14501[0:Res:9258.0,169.1] class_Orderings_Olinorder(t_a) || c_Finite__Set_Ofinite(u,t_a) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(u,t_a),t_a).
% 299.64/300.38 14502[0:Res:11029.0,169.1] class_Orderings_Olinorder(t_a) || c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),t_a) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),t_a),t_a)*.
% 299.64/300.38 14534[0:SSi:14521.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(w),x,tc_fun(y,tc_bool)),c_Option_Ooption_OSome(u,w)),v,tc_bool)*.
% 299.64/300.38 14535[0:SSi:14520.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(v),w,tc_fun(x,tc_bool)),c_Option_Ooption_OSome(y,v)),tc_bool)* -> c_lessequals(u,y,tc_bool).
% 299.64/300.38 15181[0:SSi:15167.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(u,w,x),y,tc_fun(z,tc_bool)),x1),v,tc_bool)*.
% 299.64/300.38 15182[0:SSi:15166.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(v,w,x),y,tc_fun(z,tc_bool)),x1),tc_bool)* -> c_lessequals(u,v,tc_bool).
% 299.64/300.38 15327[0:Rew:10.0,15324.0] || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v) -> c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(w,v),u),tc_fun(v,tc_bool)),v)*.
% 299.64/300.38 15368[0:Rew:10.0,15362.1] || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),w),tc_fun(v,tc_bool)),v)* -> c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)),v).
% 299.64/300.38 15497[0:Rew:15475.0,15465.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.38 15498[0:Rew:15475.0,15443.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v,tc_fun(w,tc_bool)),v_x),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),tc_bool)*.
% 299.64/300.38 15501[0:Rew:15475.0,15426.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),tc_Com_Opname,u),u)*.
% 299.64/300.38 15640[0:Res:3283.1,278.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,v,u)))*.
% 299.64/300.38 15646[0:Res:9258.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool)) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,w,u,t_a)))*.
% 299.64/300.38 15772[0:SpR:397.1,15482.1] class_Orderings_Otop(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)).
% 299.64/300.38 15773[0:SpR:365.1,15482.1] class_Orderings_Obot(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool)).
% 299.64/300.38 15868[0:Res:3283.1,277.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,v,u)))*.
% 299.64/300.38 15874[0:Res:9258.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool)) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v,u,t_a)))*.
% 299.64/300.38 15907[2:SpR:2097.1,15483.1] || hBOOL(hAPP(v_x,u)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(u,v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.38 15912[2:SpR:397.1,15483.1] class_Orderings_Otop(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)).
% 299.64/300.38 15913[2:SpR:365.1,15483.1] class_Orderings_Obot(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool)).
% 299.64/300.38 15924[2:SpR:300.1,15483.1] class_Lattices_Obounded__lattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.38 15972[2:Rew:3014.0,15954.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.38 15973[2:Rew:3014.0,15949.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.38 16031[2:SpL:2267.1,15966.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.38 16137[0:SpR:3229.1,15262.1] || equal(u,v)* equal(c_in(t_a),u)* -> hBOOL(hAPP(hAPP(v,v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.38 16142[0:SpR:525.1,15262.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.38 16180[0:SpR:585.0,15262.1] || equal(c_COMBC(u,v,w,x),c_in(t_a))** -> hBOOL(hAPP(hAPP(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.38 16181[0:SpR:586.0,15262.1] || equal(c_COMBB(u,v,w,x),c_in(t_a))** -> hBOOL(hAPP(u,hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))))*.
% 299.64/300.38 16215[0:SpL:2267.1,15834.1] || equal(u,v)* equal(hAPP(v,v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.38 16244[0:SpL:302.1,16217.0] class_Lattices_Obounded__lattice(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> .
% 299.64/300.38 16245[0:SpL:331.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_Procs)** -> .
% 299.64/300.38 16320[0:SpL:445.1,16286.0] || equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Fun_Ofun__upd(u,v,w,x,y),v_Procs)** -> equal(v_x,v).
% 299.64/300.38 16360[0:SpL:585.0,16286.0] || equal(hAPP(hAPP(u,v_x),v),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_COMBC(u,w,x,y),v),v_Procs)** -> .
% 299.64/300.38 16361[0:SpL:586.0,16286.0] || equal(hAPP(u,hAPP(v,v_x)),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_COMBB(u,w,x,y),v),v_Procs)** -> .
% 299.64/300.38 16379[0:SpR:9935.1,1158.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.38 16384[0:SpR:9935.1,3229.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* -> equal(hAPP(v,v_x),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 16385[0:SpR:9935.1,3283.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_Procs))*.
% 299.64/300.38 16459[0:SpR:3229.1,9935.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v,tc_bool) -> equal(hAPP(hAPP(u,v_x),v),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 16497[0:MRR:16496.1,826.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))**.
% 299.64/300.38 16615[0:SpR:9936.1,1158.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.38 16620[0:SpR:9936.1,3229.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* -> equal(hAPP(v,v_x),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 16621[0:SpR:9936.1,3283.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_Procs))*.
% 299.64/300.38 16697[0:SpR:3229.1,9936.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> equal(hAPP(hAPP(u,v_x),v),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 16715[0:SpL:9936.1,57.1] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(c_Orderings_Otop__class_Otop(tc_bool),c_HOL_Ozero__class_Ozero(tc_bool)) -> equal(u,c_HOL_Ozero__class_Ozero(tc_bool)).
% 299.64/300.38 16734[0:MRR:16733.1,826.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))**.
% 299.64/300.38 16759[0:Res:16753.1,346.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> c_Fun_Oinj__on(x,w,u,u)*.
% 299.64/300.38 16760[0:Res:16753.1,347.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> c_Fun_Oinj__on(x,v,u,u)*.
% 299.64/300.38 16778[0:Res:124.0,390.0] || -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(u,v,w,x),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(v,w,x),u),y,tc_fun(x,tc_bool)),x,w)*.
% 299.64/300.38 16815[0:SpR:8415.2,16814.1] class_Finite__Set_Ofinite_Ofinite(u) || equal(v_Procs,v_x) equal(c_Set_Oimage(v,u,w),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_Finite__Set_Ofinite(v_x,w).
% 299.64/300.38 16847[0:SpL:2267.1,15830.0] || equal(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.38 16873[0:SpL:2267.1,15896.1] || equal(u,v)* equal(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.38 16910[0:SpL:2267.1,16870.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))* equal(v,v_Procs)* -> .
% 299.64/300.38 16970[0:SpL:600.0,332.0] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),u).
% 299.64/300.38 17005[0:SSi:16991.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),u)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,tc_fun(w,tc_bool)),u))*.
% 299.64/300.38 17024[0:SSi:17016.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),u)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,tc_fun(w,tc_bool)),u))*.
% 299.64/300.38 17101[0:Res:511.1,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w),v))*.
% 299.64/300.38 17163[0:SpL:17045.0,3506.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(x,y),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.38 17180[2:Rew:2990.0,17114.1] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.38 17258[0:Res:510.1,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),v))*.
% 299.64/300.38 17275[0:SpL:3229.1,13272.0] || equal(u,v)* equal(hAPP(v,v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(u,w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 17359[0:Res:172.2,527.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(v,c_Finite__Set_Olinorder__class_OMax(v,u)))*.
% 299.64/300.38 17381[0:SpR:14526.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.38 17401[0:SpL:2267.1,15798.0] || equal(u,c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool)).
% 299.64/300.38 17411[2:SpL:2267.1,15938.0] || equal(u,c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v,tc_bool)).
% 299.64/300.38 17426[0:SpL:3229.1,16327.1] || equal(u,v)* equal(w,u)* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool))** equal(w,v_Procs)* -> .
% 299.64/300.38 17477[0:Res:171.2,527.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(v,c_Finite__Set_Olinorder__class_OMin(v,u)))*.
% 299.64/300.38 17635[0:Res:11610.0,17530.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Option_Ooption_OSome(x,u)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),x).
% 299.64/300.38 17636[0:Res:11611.0,17530.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),z),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),u).
% 299.64/300.38 17686[0:SSi:17587.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 17688[0:SSi:17584.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 17823[0:SpR:3229.1,10930.1] || equal(c_Set_Oinsert(u,v),w)* equal(hAPP(c_in(v),x),v_Procs)** -> hBOOL(hAPP(hAPP(w,v_x),x))*.
% 299.64/300.38 17928[0:SpL:3229.1,11894.1] || equal(c_in(u),v)* equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))* hBOOL(hAPP(hAPP(v,v_x),w))* -> .
% 299.64/300.38 17977[0:Res:1103.1,11894.1] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(v),w)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a)*.
% 299.64/300.38 18011[0:Res:526.1,263.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),x))* -> hBOOL(hAPP(hAPP(c_in(v),x),w)) equal(x,u).
% 299.64/300.38 18238[0:SpR:15172.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),tc_Com_Opname,y),v_Procs),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.38 18243[0:SpR:15172.0,3229.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y)* -> equal(hAPP(y,v_x),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 18244[0:SpR:15172.0,3283.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_Procs)).
% 299.64/300.38 18422[0:Res:545.1,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(x,u,y),w),hAPP(x,v)))*.
% 299.64/300.38 18451[0:Res:526.1,156.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,y)),x))*.
% 299.64/300.38 18469[0:SpL:3229.1,8513.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)* hBOOL(hAPP(w,v_x))* -> equal(v_x,u).
% 299.64/300.38 18515[0:SpR:2267.1,9246.0] || equal(u,v)* -> hBOOL(hAPP(hAPP(c_in(w),x),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))))* hBOOL(hAPP(v,x))*.
% 299.64/300.38 18518[0:SpR:3229.1,9246.0] || equal(c_in(u),v) -> hBOOL(hAPP(hAPP(v,v_x),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))))* hBOOL(hAPP(w,v_x)).
% 299.64/300.38 18526[0:Res:9246.0,279.0] || -> hBOOL(hAPP(u,v)) equal(hAPP(c_Set_Oinsert(v,w),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)))**.
% 299.64/300.38 18557[0:SpL:2267.1,18529.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> hBOOL(hAPP(v,x))*.
% 299.64/300.38 18589[0:Res:153.1,527.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,y,u),x),w))*.
% 299.64/300.38 18598[0:SpR:3229.1,9568.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* -> c_lessequals(hAPP(v_x,w),hAPP(hAPP(hAPP(v,v_x),x),w),tc_bool)*.
% 299.64/300.38 18601[0:SpR:3229.1,9568.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)* -> c_lessequals(hAPP(v,x),hAPP(hAPP(w,v_x),x),tc_bool)*.
% 299.64/300.38 18635[0:SpR:3229.1,9568.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)* -> c_lessequals(hAPP(v,v_x),hAPP(x,v_x),tc_bool)*.
% 299.64/300.38 18641[0:SpR:8385.1,9568.0] || equal(u,v_Procs) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),w),u),tc_bool)*.
% 299.64/300.38 18658[0:SpR:3229.1,9568.0] || equal(u,v) -> c_lessequals(hAPP(v,v_x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v_x),tc_bool)*.
% 299.64/300.38 18663[0:SpR:525.1,9568.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),x),v),tc_bool)*.
% 299.64/300.38 18749[0:SpR:3229.1,18644.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),v)* -> c_lessequals(v_Procs,hAPP(hAPP(v,v_x),v_Procs),tc_bool)*.
% 299.64/300.38 18778[0:Res:18644.0,10214.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),v),v_Procs),v_Procs)**.
% 299.64/300.38 18795[0:SpR:3229.1,18763.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(v,v_x),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.38 18819[0:Res:18763.0,10214.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),v_Procs)**.
% 299.64/300.38 18840[0:Res:364.1,18768.0] || c_lessequals(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)) -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(w,v),u),v_Procs),tc_bool)*.
% 299.64/300.38 18850[0:Res:448.2,18768.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,c_Set_Oinsert(v_x,tc_Com_Opname),tc_fun(u,tc_bool))* c_lessequals(v_Procs,hAPP(v,v_Procs),tc_bool).
% 299.64/300.38 18901[0:Res:463.1,12956.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x)* -> c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u))),v,x)*.
% 299.64/300.38 18909[0:SpR:3229.1,9569.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* -> c_lessequals(hAPP(w,x),hAPP(hAPP(hAPP(v,v_x),w),x),tc_bool)*.
% 299.64/300.38 18912[0:SpR:3229.1,9569.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)* -> c_lessequals(hAPP(v_x,x),hAPP(hAPP(w,v_x),x),tc_bool)*.
% 299.64/300.38 18946[0:SpR:3229.1,9569.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)* -> c_lessequals(hAPP(w,v_x),hAPP(x,v_x),tc_bool)*.
% 299.64/300.38 18952[0:SpR:8385.1,9569.0] || equal(u,v_Procs) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_x,tc_Com_Opname)),u),tc_bool)*.
% 299.64/300.38 18969[0:SpR:3229.1,9569.0] || equal(u,v) -> c_lessequals(hAPP(v,v_x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),v_x),tc_bool)*.
% 299.64/300.38 18974[0:SpR:525.1,9569.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),v),tc_bool)*.
% 299.64/300.38 19060[0:SpR:3229.1,10697.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(v,v_x)),v_x),tc_bool)*.
% 299.64/300.38 19068[0:SpR:3229.1,10697.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x)),x)* -> c_lessequals(v_x,hAPP(x,v_x),tc_bool)*.
% 299.64/300.38 19077[0:Res:10697.0,10214.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u)),u),u)**.
% 299.64/300.38 19131[0:SpR:3229.1,10931.1] || equal(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v)* -> c_Hoare__Mirabelle_Ohoare__valids(w,v_x,t_a) hBOOL(hAPP(hAPP(v,v_x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,v_x)))*.
% 299.64/300.38 19189[0:Res:12621.0,12626.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,tc_bool),y,tc_bool),z,tc_bool),u,tc_bool)*.
% 299.64/300.38 19427[0:Res:15188.1,401.0] || c_Natural_Oevalc(u,v,w)* c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSKIP)),u),v,x)* -> equal(x,w)*.
% 299.64/300.38 19446[0:SpR:3229.1,9067.0] || equal(c_Set_Oinsert(u,v),w) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oinsert(x,v),hAPP(w,v_x))))*.
% 299.64/300.38 19449[0:SpR:2098.1,9067.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v)),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),v)))*.
% 299.64/300.38 19526[0:SpR:3229.1,19452.0] || equal(c_in(t_a),u) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))))*.
% 299.64/300.38 19589[0:SpR:3229.1,19441.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))))*.
% 299.64/300.38 19621[0:SpR:3229.1,19436.1] || equal(c_in(tc_Com_Opname),u) equal(v,v_Procs) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v)))*.
% 299.64/300.38 19663[0:Res:526.1,496.0] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,u)),u))* c_Hoare__Mirabelle_Otriple__valid(w,v,t_a)*.
% 299.64/300.38 19720[0:Res:652.1,19641.0] || c_lessequals(v_Procs,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_in(tc_Com_Opname),v_x),u),tc_fun(tc_Com_Opname,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_in(tc_Com_Opname),v_x),u,t_a).
% 299.64/300.38 19722[0:Res:8375.1,19641.0] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_in(u),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_in(u),v),w,t_a)*.
% 299.64/300.38 19725[0:Res:13238.1,19641.0] || equal(hAPP(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_in(t_a),v_x),u),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_in(t_a),v_x),u,t_a).
% 299.64/300.38 19727[0:Res:212.1,19641.0] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Set_Oinsert(v,w),u),x)))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),u),x,t_a).
% 299.64/300.38 19730[0:Res:8376.2,19641.0] || equal(c_in(tc_Com_Opname),u) equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(u,v_x),v),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(u,v_x),v,t_a)*.
% 299.64/300.38 19802[0:SpR:104.0,342.0] || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.38 19900[0:Rew:19819.0,6229.1] || equal(u,v) -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.64/300.38 19919[0:SSi:19918.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),w)**.
% 299.64/300.38 19934[0:SpR:353.0,19744.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w)),hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),w),t_a)*.
% 299.64/300.38 20134[0:SpR:2267.1,19747.0] || equal(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)))* -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.38 20151[0:Res:19747.0,363.0] || -> c_lessequals(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),u),tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.38 20190[0:SpR:2267.1,20152.0] || equal(u,v) -> c_lessequals(c_HOL_Ominus__class_Ominus(w,c_HOL_Ouminus__class_Ouminus(u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),v,tc_fun(x,tc_bool))*.
% 299.64/300.38 20243[0:SpR:2267.1,20186.0] || equal(u,v) -> c_lessequals(c_HOL_Ominus__class_Ominus(w,v,tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.38 20589[0:Res:448.2,18625.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,w,tc_fun(u,tc_bool))* c_lessequals(hAPP(w,x),hAPP(v,x),tc_bool)*.
% 299.64/300.38 20693[0:SpR:3229.1,10705.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,v_x,x,y,z)),x1)* -> c_lessequals(x,hAPP(x1,v_x),tc_bool)*.
% 299.64/300.38 20702[0:Res:10705.0,10214.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(hAPP(c_Set_Oinsert(v,w),c_Fun_Ofun__upd(x,y,u,z,x1)),y),u)**.
% 299.64/300.38 20737[0:Res:313.1,357.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(v,w) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x,w,y),u),y)*.
% 299.64/300.38 20889[0:SpR:317.0,10813.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oimage(w,x,v),hAPP(c_Set_Oinsert(y,x),z))),hAPP(w,y)))*.
% 299.64/300.38 21032[0:SpR:8385.1,20881.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(u,v),x)),u))*.
% 299.64/300.38 21053[0:SpR:3229.1,20881.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(v_x,w),y)),hAPP(v,v_x)))*.
% 299.64/300.38 21058[0:SpR:525.1,20881.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(v,w),y)),v))*.
% 299.64/300.38 21133[0:SpR:353.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(y,v),z))),hAPP(u,y)))*.
% 299.64/300.38 21136[0:SpR:3229.1,20881.0] || equal(c_Set_Oinsert(u,v),w) -> hBOOL(hAPP(hAPP(c_Set_Oimage(x,v,y),hAPP(w,v_x)),hAPP(x,u)))*.
% 299.64/300.38 21147[0:SpR:2097.1,21130.0] || hBOOL(hAPP(v_Procs,u)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.38 21158[0:SpR:300.1,21130.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.38 21202[0:SpR:2097.1,21141.0] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),v_x))*.
% 299.64/300.38 21207[0:SpR:397.1,21141.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.38 21208[0:SpR:365.1,21141.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.38 21219[0:SpR:300.1,21141.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.38 21265[0:Res:8366.1,469.0] || equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),v_Procs) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,tc_Com_Opname)),v_x)**.
% 299.64/300.38 21272[0:Res:3346.1,469.0] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(w,x,v)) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_x,w,u,x,v)),u)**.
% 299.64/300.38 21372[0:SpR:21267.0,9566.0] || -> c_lessequals(hAPP(u,v_x),hAPP(hAPP(c_Set_Oinsert(v,w),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,x)),tc_bool)*.
% 299.64/300.38 21504[0:SpR:2097.1,21267.0] || hBOOL(hAPP(v_x,u)) -> equal(hAPP(c_Set_Oinsert(u,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),v_x,tc_Com_Opname,w)),v_x)**.
% 299.64/300.38 21520[0:SpR:525.1,21267.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_x,tc_Com_Opname,v)),v_x)**.
% 299.64/300.38 21719[0:Rew:99.1,21441.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,x),v_x)**.
% 299.64/300.38 21761[0:SpR:3229.1,21143.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(v,v_x)))*.
% 299.64/300.38 21766[0:SpR:525.1,21143.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.38 21808[0:SpR:353.0,21035.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(v_Procs,u),x))),v_Procs))*.
% 299.64/300.38 21811[0:SpR:3229.1,21035.0] || equal(c_Set_Oinsert(v_Procs,u),v) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,w),hAPP(v,v_x)),v_Procs))*.
% 299.64/300.38 21830[0:SpR:3229.1,21131.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),hAPP(v,v_x)))*.
% 299.64/300.38 21835[0:SpR:525.1,21131.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.38 21891[0:Res:8366.1,464.0] || equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),v_Procs) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,tc_Com_Opname)),v_x)**.
% 299.64/300.38 21898[0:Res:3346.1,464.0] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(w,x,v)) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_x,u,w,x,v)),u)**.
% 299.64/300.38 21998[0:SpR:21893.0,9566.0] || -> c_lessequals(hAPP(u,v_x),hAPP(hAPP(c_Set_Oinsert(v,w),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,x)),tc_bool)*.
% 299.64/300.38 22131[0:SpR:2097.1,21893.0] || hBOOL(hAPP(v_x,u)) -> equal(hAPP(c_Set_Oinsert(u,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(u,v),tc_Com_Opname,w)),v_x)**.
% 299.64/300.38 22147[0:SpR:525.1,21893.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v)),v_x)**.
% 299.64/300.38 22348[0:Rew:99.1,22067.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,x),v_x)**.
% 299.64/300.38 22383[0:SpR:3229.1,21689.1] class_Lattices_Obounded__lattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x),tc_Com_Opname,w),v_x)**.
% 299.64/300.38 22389[0:SpR:3229.1,21704.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x),tc_Com_Opname,w),v_x)**.
% 299.64/300.38 22443[0:SpR:3229.1,22318.1] class_Lattices_Obounded__lattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,w),v_x)**.
% 299.64/300.38 22449[0:SpR:3229.1,22333.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,w),v_x)**.
% 299.64/300.38 22462[0:SpR:3229.1,21126.1] || equal(u,v) equal(w,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x),w),hAPP(v,v_x)))*.
% 299.64/300.38 22467[0:SpR:525.1,21126.1] class_Lattices_Oupper__semilattice(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,w),v),v_x))*.
% 299.64/300.38 22512[0:Obv:22506.0] || equal(c_Set_Oimage(u,tc_Com_Opname,v),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(v_Procs,v_x) -> hBOOL(hAPP(v_x,hAPP(u,v_x)))*.
% 299.64/300.38 22687[0:SpR:3229.1,21173.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBK(v,w,x),y,z),hAPP(u,v_x)),v))*.
% 299.64/300.38 22690[0:SpR:3229.1,21173.0] || equal(hAPP(c_Set_Oimage(c_COMBK(v_x,u,v),w,x),hAPP(c_in(tc_Com_Opname),v_x)),y)* -> hBOOL(hAPP(y,v_x))*.
% 299.64/300.38 22695[0:SpR:3229.1,21234.0] || equal(hAPP(c_Set_Oimage(c_COMBK(v_x,u,v),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),y)* -> hBOOL(hAPP(y,v_x))*.
% 299.64/300.38 22739[0:SpR:3294.1,543.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 22740[0:SpR:3294.1,544.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 22761[0:SpR:3294.1,293.2] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) c_lessequals(v,v_x,u) -> c_lessequals(v,c_Orderings_Obot__class_Obot(tc_bool),u)*.
% 299.64/300.38 22802[0:SpR:524.0,3294.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_in(t_a))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.38 22811[0:SpR:414.0,3294.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_in(t_a))** -> equal(hAPP(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 22829[0:SpR:9924.0,3294.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(t_a)) -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 22846[0:SpL:3294.1,295.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v,u)* -> c_lessequals(v_x,v,u).
% 299.64/300.38 22868[0:SpL:3294.1,332.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_bool),u) -> c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),u)*.
% 299.64/300.38 23045[0:Rew:105.0,23009.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(c_COMBK(v_x,tc_Com_Opname,u),v,u,tc_Com_Opname,w),w,tc_Com_Opname),v_Procs),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.64/300.38 23191[0:SpL:414.0,3487.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> .
% 299.64/300.38 23209[0:SpL:9924.0,3487.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.38 23268[0:SpL:414.0,3489.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_in(tc_Com_Opname))** hBOOL(hAPP(v,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.38 23286[0:SpL:9924.0,3489.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.38 23318[0:Res:34.1,3489.1] || hBOOL(hAPP(v_x,hAPP(u,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)))))* equal(c_Set_Ovimage(u,v,w),c_in(tc_Com_Opname))** -> .
% 299.64/300.38 23322[0:Res:518.1,3489.1] || hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname))** -> .
% 299.64/300.38 23323[0:Res:517.1,3489.1] || hBOOL(hAPP(u,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(tc_Com_Opname))** -> .
% 299.64/300.38 23335[4:MRR:23303.2,6340.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_x,tc_fun(u,tc_bool))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(tc_Com_Opname)) -> .
% 299.64/300.38 23338[0:MRR:23337.2,820.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_in(tc_Com_Opname))** -> .
% 299.64/300.38 23446[0:SpL:2267.1,23416.1] || equal(u,v)* equal(v,v_Procs)* equal(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),w),c_in(tc_Com_Opname))** -> .
% 299.64/300.38 23467[0:SpL:2267.1,23443.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** equal(c_Set_Oinsert(v,w),c_in(tc_Com_Opname))** -> .
% 299.64/300.38 23786[0:SpR:23682.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.38 24500[0:SpR:24020.1,651.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(u,v_x),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.38 24505[2:SpR:24020.1,15483.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.38 24510[0:SpR:24020.1,3284.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),v_x))*.
% 299.64/300.38 24516[0:SpR:24020.1,10090.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 24517[0:SpR:24020.1,11030.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 24519[0:SpR:24020.1,21141.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(u,v_x),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.38 24520[0:SpR:24020.1,21267.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(u,v_x),v_x,tc_Com_Opname,v)),v_x)**.
% 299.64/300.38 24523[0:SpR:24020.1,21893.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(u,v_x),tc_Com_Opname,v)),v_x)**.
% 299.64/300.38 24526[0:SpR:24020.1,648.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(hAPP(u,v_x),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.38 24529[0:SpR:24020.1,3316.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_in(v),hAPP(u,v_x))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.38 24530[0:SpR:24020.1,3339.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(v,hAPP(u,v_x))* -> equal(c_Fun_Ofun__upd(v,v_x,v_x,w,x),v)**.
% 299.64/300.38 24564[0:SpR:24020.1,7253.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x))*.
% 299.64/300.38 24626[0:SpR:3586.1,24020.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.38 24637[0:SpR:2098.1,24020.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(hAPP(v_x,v_x),v_x).
% 299.64/300.38 24646[0:SpR:17045.0,24020.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_x),v_x).
% 299.64/300.38 24649[0:SpR:88.1,24020.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),v_x),v_x).
% 299.64/300.38 24664[0:SpR:11473.0,24020.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x),v_x).
% 299.64/300.38 24665[0:SpR:9.0,24020.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(u,hAPP(v,v_x)),v_x),v_x)**.
% 299.64/300.38 24671[0:SpR:12944.0,24020.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x),v_x).
% 299.64/300.38 24683[0:SpL:24020.1,3698.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(v,hAPP(u,v_x))* equal(c_Com_Ocom_OBODY,v) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 24918[0:Res:3284.1,467.0] || equal(c_Set_Oimage(u,v,w),c_in(tc_Com_Opname)) -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_x,u,v,w),v_Procs)),v_Procs)**.
% 299.64/300.38 24963[0:SpR:23902.1,9567.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),v_x,tc_bool)*.
% 299.64/300.38 24977[0:SpR:23902.1,294.2] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v,c_Orderings_Obot__class_Obot(tc_bool),u)* -> c_lessequals(v,v_x,u).
% 299.64/300.38 25013[0:SpR:15476.0,23902.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.38 25026[0:SpR:302.1,23902.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.38 25027[0:SpR:331.0,23902.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.38 25050[0:SpR:11177.1,23902.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.38 25054[0:SpR:11176.1,23902.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(u,c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.38 25056[0:SpR:14216.0,23902.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.38 25068[0:SpL:23902.1,312.1] class_Lattices_Obounded__lattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) equal(c_Orderings_Obot__class_Obot(u),v_x) -> equal(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(u))*.
% 299.64/300.38 25070[0:SpL:23902.1,296.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v_x,v,u) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v,u)*.
% 299.64/300.38 25612[0:Res:9567.0,24120.1] || equal(hAPP(u,v),c_Orderings_Obot__class_Obot(tc_bool)) -> equal(hAPP(c_HOL_Ominus__class_Ominus(u,w,tc_fun(x,tc_bool)),v),hAPP(u,v))**.
% 299.64/300.38 25631[0:Res:12627.1,24120.1] || c_lessequals(u,v,tc_bool)* equal(v,c_Orderings_Obot__class_Obot(tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool),v)*.
% 299.64/300.38 25699[0:Res:678.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(tc_Com_Opname),v_x),t_a)* c_Hoare__Mirabelle_Otriple__valid(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,v_Procs,t_a).
% 299.64/300.38 25910[0:SpR:339.0,18763.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_x,tc_Com_Opname))),v_Procs),tc_bool)*.
% 299.64/300.38 25917[0:SpR:339.0,9569.0] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u)),v),tc_bool)*.
% 299.64/300.38 25960[0:SpL:339.0,1944.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.38 25961[0:SpL:339.0,3303.0] || equal(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 26075[0:SpR:338.0,18644.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),w)),v_Procs),tc_bool)*.
% 299.64/300.38 26085[0:SpR:338.0,9568.0] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),y)),v),tc_bool)*.
% 299.64/300.38 26128[0:SpR:338.0,10813.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),y))),x))*.
% 299.64/300.38 26222[0:SpL:338.0,1943.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.38 26223[0:SpL:338.0,3302.0] || equal(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 26262[0:Rew:524.0,26088.0] || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v,u),w,x,y),z),hAPP(c_Set_Oinsert(v,u),z))**.
% 299.64/300.38 26783[0:Res:23997.0,17530.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),u),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),u).
% 299.64/300.38 26796[0:SSi:26777.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,tc_fun(x,tc_bool)),u),v,tc_bool)*.
% 299.64/300.38 26797[0:SSi:26776.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,tc_fun(x,tc_bool)),v),tc_bool)* -> c_lessequals(u,v,tc_bool).
% 299.64/300.38 26892[0:SpR:8415.2,23979.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_Fun_Ofun__upd(v_x,v_x,v_x,u,v),v_x)**.
% 299.64/300.38 26982[2:SpL:2267.1,23941.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.38 27035[0:SpR:3229.1,26317.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(u,v_x),tc_Com_Opname,tc_bool),v_x)**.
% 299.64/300.38 27038[0:SpR:3229.1,23946.1] || equal(hAPP(c_in(u),v_Procs),v)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.38 27130[0:SpL:3229.1,24627.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* equal(hAPP(v,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.38 27296[7:Res:27207.1,519.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x)** -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(w,v_x)).
% 299.64/300.38 27304[7:MRR:24291.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))*.
% 299.64/300.38 27305[7:MRR:24281.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_Procs)** -> hBOOL(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))*.
% 299.64/300.38 27361[7:MRR:27214.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_x)** -> hBOOL(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))*.
% 299.64/300.38 27819[7:SpR:397.1,27219.1] class_Orderings_Otop(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)).
% 299.64/300.38 27820[7:SpR:365.1,27219.1] class_Orderings_Obot(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool)).
% 299.64/300.38 27960[0:SpR:2097.1,27381.0] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(u,v),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.38 27966[0:SpR:397.1,27381.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.38 27967[0:SpR:365.1,27381.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.38 28012[0:SpR:24020.1,27381.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(u,v_x),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.38 28046[0:SpR:445.1,28032.0] || -> equal(v_x,u) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),c_Fun_Ofun__upd(v,u,w,x,y),tc_Com_Opname,z)))*.
% 299.64/300.38 28087[0:SpR:9935.1,28032.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v)))*.
% 299.64/300.38 28091[0:SpR:9936.1,28032.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v)))*.
% 299.64/300.38 28097[0:SpR:585.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(u,v_x),v),hAPP(c_COMBC(u,w,x,y),v),tc_Com_Opname,z)))*.
% 299.64/300.38 28098[0:SpR:586.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,hAPP(v,v_x)),hAPP(c_COMBB(u,w,x,y),v),tc_Com_Opname,z)))*.
% 299.64/300.38 28103[0:SpR:15172.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),tc_Com_Opname,y)))*.
% 299.64/300.38 28262[0:SpR:2097.1,27441.0] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),v_x,tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.38 28268[0:SpR:397.1,27441.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.38 28269[0:SpR:365.1,27441.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Orderings_Obot__class_Obot(u),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.38 28315[0:SpR:24020.1,27441.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(u,v_x),v_x,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.38 28349[0:SpR:445.1,28335.0] || -> equal(v_x,u) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ofun__upd(v,u,w,x,y),hAPP(v,v_x),tc_Com_Opname,z)))*.
% 299.64/300.38 28391[0:SpR:9935.1,28335.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v)))*.
% 299.64/300.38 28395[0:SpR:9936.1,28335.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v)))*.
% 299.64/300.38 28401[0:SpR:585.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_COMBC(u,v,w,x),y),hAPP(hAPP(u,v_x),y),tc_Com_Opname,z)))*.
% 299.64/300.38 28402[0:SpR:586.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_COMBB(u,v,w,x),y),hAPP(u,hAPP(y,v_x)),tc_Com_Opname,z)))*.
% 299.64/300.38 28407[0:SpR:15172.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,y)))*.
% 299.64/300.38 28682[0:SpR:28031.0,9566.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(w,v_x),w,tc_Com_Opname,x),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.38 28721[0:SpR:2097.1,28031.0] || hBOOL(hAPP(v_x,u)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(u,v),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 28727[0:SpR:397.1,28031.0] class_Orderings_Otop(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 28728[0:SpR:365.1,28031.0] class_Orderings_Obot(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 28774[0:SpR:24020.1,28031.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 28837[0:SpR:28334.0,9566.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,hAPP(w,v_x),tc_Com_Opname,x),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.38 28876[0:SpR:2097.1,28334.0] || hBOOL(hAPP(v_x,u)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),v_x,tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 28882[0:SpR:397.1,28334.0] class_Orderings_Otop(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 28883[0:SpR:365.1,28334.0] class_Orderings_Obot(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Orderings_Obot__class_Obot(u),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 28929[0:SpR:24020.1,28334.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(u,v_x),v_x,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 29202[0:SSi:29194.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),c_Orderings_Obot__class_Obot(tc_bool))** -> c_lessequals(w,x,tc_bool)*.
% 299.64/300.38 29336[7:SpR:27278.1,24020.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.38 29371[7:SpR:27278.1,415.0] || equal(hAPP(c_in(u),v),v_x) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v,u),v_x,v_x,w,x),c_Set_Oinsert(v,u))**.
% 299.64/300.38 29373[7:SpR:27278.1,9566.0] || equal(hAPP(c_in(u),v),v_x) -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(w,x),c_Set_Oinsert(v,u)),v_x),tc_bool)*.
% 299.64/300.38 29421[7:SpL:27278.1,3506.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(w,x),v_x)** -> .
% 299.64/300.38 29850[0:SpR:27043.1,1158.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.38 29856[0:SpR:27043.1,3229.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),v)* -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.38 29871[0:SpR:27043.1,28335.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_Procs,u),v_x,tc_Com_Opname,v)))*.
% 299.64/300.38 29877[0:SpR:27043.1,28032.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v)))*.
% 299.64/300.38 29930[0:SpR:27043.1,20881.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),v_x),hAPP(u,v_Procs)))*.
% 299.64/300.38 29931[0:SpR:27043.1,9067.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oinsert(v,u),v_x)))*.
% 299.64/300.38 29938[0:SpR:27043.1,21035.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),v_x),v_Procs))*.
% 299.64/300.38 30327[0:SSi:30317.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),c_Orderings_Obot__class_Obot(tc_bool))** -> c_lessequals(v,x,tc_bool)*.
% 299.64/300.38 31100[0:SpR:28771.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w))))*.
% 299.64/300.38 31102[0:SpR:28771.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.38 31186[0:SpR:28926.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w))))*.
% 299.64/300.38 31188[0:SpR:28926.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.38 31221[0:SpR:3229.1,23934.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_Procs),v,w),hAPP(u,v_x)),v_Procs))*.
% 299.64/300.38 31340[0:SpR:3229.1,23954.0] || equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),t_a,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 31347[0:SpR:3229.1,23961.0] || equal(c_in(u),v) -> hBOOL(hAPP(hAPP(v,v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.38 31454[0:SpL:3229.1,24254.1] || equal(u,v)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)* equal(hAPP(v,v_x),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 31460[0:SpL:525.1,24254.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.38 31640[0:SpR:3229.1,25828.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(hAPP(u,v_x),v_Procs)),v_x))*.
% 299.64/300.38 31663[0:SpR:339.0,25828.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs))),v_x))*.
% 299.64/300.38 31683[0:SpR:3229.1,26028.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(u,v_x)),v_x))*.
% 299.64/300.38 31704[0:SpR:338.0,26028.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w))),v_x))*.
% 299.64/300.38 31776[7:SpL:2267.1,27896.1] || equal(u,v)* equal(hAPP(v,v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.38 31807[7:SpL:302.1,31778.0] class_Lattices_Obounded__lattice(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> .
% 299.64/300.38 31808[7:SpL:331.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_x)** -> .
% 299.64/300.38 31879[7:SpL:445.1,31868.0] || equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Fun_Ofun__upd(u,v,w,x,y),v_x)** -> equal(v_x,v).
% 299.64/300.38 31934[7:SpL:585.0,31868.0] || equal(hAPP(hAPP(u,v_x),v),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_COMBC(u,w,x,y),v),v_x)** -> .
% 299.64/300.38 31935[7:SpL:586.0,31868.0] || equal(hAPP(u,hAPP(v,v_x)),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_COMBB(u,w,x,y),v),v_x)** -> .
% 299.64/300.38 32002[0:SpL:383.1,3577.0] || equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v_x,v,w,x),y,z,w,x),v_Procs)** -> equal(y,v_x) hBOOL(v).
% 299.64/300.38 32004[2:SpL:383.1,4268.0] || equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v_x,v,w,x),y,z,w,x),c_Com_Ocom_OBODY)** -> equal(y,v_x) c_Com_OWT(v).
% 299.64/300.38 32008[7:SpL:383.1,27234.0] || equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v_x,v,w,x),y,z,w,x),v_x)** -> equal(y,v_x) hBOOL(v).
% 299.64/300.38 32173[0:SpR:3229.1,31323.0] || equal(v_Procs,u) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v_x),hAPP(u,v_x),tc_bool)*.
% 299.64/300.38 32181[0:SpR:3229.1,31323.0] || equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u)* -> c_lessequals(hAPP(u,v_x),hAPP(v_Procs,v_x),tc_bool)*.
% 299.64/300.38 32231[0:SpR:339.0,31669.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))),v_x))*.
% 299.64/300.38 32235[0:SpR:3229.1,31669.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 32273[0:SSi:32260.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),u))*.
% 299.64/300.38 32428[7:SpL:2267.1,27892.0] || equal(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.38 32450[7:SpL:2267.1,27917.1] || equal(u,v)* equal(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.38 32456[0:SpR:3229.1,28058.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v)* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(v,v_x),tc_Com_Opname,w)))*.
% 299.64/300.38 32592[0:SpR:3229.1,28361.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v)* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(v,v_x),v_x,tc_Com_Opname,w)))*.
% 299.64/300.38 32606[0:SpR:3229.1,31533.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,w),hAPP(v,v_x))),v_Procs))*.
% 299.64/300.38 32612[0:SpR:525.1,31533.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x)),v_Procs))*.
% 299.64/300.38 32676[0:SpR:8498.1,32669.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x)))*.
% 299.64/300.38 32689[7:SpR:27278.1,32669.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x)))*.
% 299.64/300.38 32690[0:SpR:3586.1,32669.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x)))*.
% 299.64/300.38 32701[0:SpR:2098.1,32669.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,v),v_x)))*.
% 299.64/300.38 32711[0:SpR:17045.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),tc_Com_Opname,x),c_Orderings_Obot__class_Obot(tc_bool))))*.
% 299.64/300.38 32714[0:SpR:88.1,32669.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u))))*.
% 299.64/300.38 32733[0:SpR:11473.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_Com_Opname,w),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.38 32734[0:SpR:9.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname,z),hAPP(u,hAPP(v,v_x)))))*.
% 299.64/300.38 32740[0:SpR:12944.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),tc_Com_Opname,y),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.38 32819[0:MRR:32794.1,420.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(v,c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),u)**.
% 299.64/300.38 33054[0:SpR:3229.1,32691.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(v,v_x),tc_Com_Opname,w),v_x)))*.
% 299.64/300.38 33057[0:SpR:3229.1,32691.0] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,v),w)* -> hBOOL(hAPP(v_Procs,hAPP(w,v_x)))*.
% 299.64/300.38 33104[0:Res:364.1,32232.0] || c_lessequals(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),v,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v),v_x))*.
% 299.64/300.38 33119[0:Res:448.2,32232.0] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) || -> c_lessequals(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(u,v_x)).
% 299.64/300.38 33185[7:SpL:2267.1,32447.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))* equal(v,v_x)* -> .
% 299.64/300.38 33242[0:SpR:32668.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,w,tc_Com_Opname,x),hAPP(w,v_x)))))*.
% 299.64/300.38 33244[0:SpR:32668.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x))),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.38 33262[0:SpR:3229.1,32668.0] || equal(u,v) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,w),hAPP(v,v_x)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 33268[0:SpR:525.1,32668.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.38 33355[0:SpR:3229.1,23789.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w)* -> c_lessequals(hAPP(w,v_x),v_x,tc_bool)*.
% 299.64/300.38 33372[0:Res:23789.0,24120.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,tc_fun(w,tc_bool)),u),u)**.
% 299.64/300.38 33470[0:Res:23882.0,24120.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),u)**.
% 299.64/300.38 33490[7:Obv:33486.0] class_Lattices_Oboolean__algebra(u) || equal(v,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),v_x)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.38 33492[7:Obv:33482.0] class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Obot__class_Obot(u),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.38 33533[7:SpL:2267.1,27846.0] || equal(u,c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool)).
% 299.64/300.38 33548[0:SpR:3229.1,28704.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),u,tc_Com_Opname,x)))*.
% 299.64/300.38 33554[0:SpR:525.1,28704.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,w)))*.
% 299.64/300.38 33639[0:SpR:3229.1,28859.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(v,v_x),tc_Com_Opname,x)))*.
% 299.64/300.38 33645[0:SpR:525.1,28859.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_x,tc_Com_Opname,w)))*.
% 299.64/300.38 33730[7:SpL:3229.1,31886.1] || equal(u,v)* equal(w,u)* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool))** equal(w,v_x)* -> .
% 299.64/300.38 33837[0:SpR:3229.1,23881.0] || equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 34202[0:SpR:3229.1,24914.0] || equal(u,v) -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,w),hAPP(v,v_x))),hAPP(v,v_x))**.
% 299.64/300.38 34267[0:SpL:24914.0,541.0] || equal(hAPP(c_Com_Ocom_OBODY,v_x),hAPP(c_Com_Ocom_OBODY,u))* -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Ocom_OBODY,tc_Com_Opname,v),hAPP(c_Com_Ocom_OBODY,v_x)),u)*.
% 299.64/300.38 34561[0:SpR:34427.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v,tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v_x,tc_bool)*.
% 299.64/300.38 34712[0:SpR:34428.0,23902.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.38 34717[0:SpR:34428.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),tc_Com_Opname,u),u)*.
% 299.64/300.38 34744[0:SpR:34428.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v,tc_fun(w,tc_bool)),v_x),v_x,tc_bool)*.
% 299.64/300.38 34751[7:SpL:34428.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x)** -> .
% 299.64/300.38 34752[0:SpL:34428.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs)** -> .
% 299.64/300.38 34856[0:SpR:3229.1,28053.1] || equal(u,v)* equal(w,u)* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),w,tc_Com_Opname,x)))*.
% 299.64/300.38 34863[0:SpR:525.1,28053.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v,tc_Com_Opname,w)))*.
% 299.64/300.38 34935[0:SpR:3229.1,28356.1] || equal(u,v)* equal(w,u)* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,hAPP(v,v_x),tc_Com_Opname,x)))*.
% 299.64/300.38 34942[0:SpR:525.1,28356.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,v_x,tc_Com_Opname,w)))*.
% 299.64/300.38 35058[0:SpR:28755.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,w,c_COMBK(w,x,y),tc_Com_Opname,z))))*.
% 299.64/300.38 35060[0:SpR:28755.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x)),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)))*.
% 299.64/300.38 35147[0:SpR:28910.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(w,x,y),w,tc_Com_Opname,z))))*.
% 299.64/300.38 35149[0:SpR:28910.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x)),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)))*.
% 299.64/300.38 35426[0:SpL:410.0,333.0] || c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),y)* -> c_Finite__Set_Ofinite(hAPP(x,u),y).
% 299.64/300.38 35455[0:SpR:353.0,35192.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(v_x,v),w)),c_in(tc_Com_Opname),v,tc_fun(x,tc_bool)),v_Procs))*.
% 299.64/300.38 35541[0:Rew:80.0,35493.0] || -> equal(hAPP(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))**.
% 299.64/300.38 35576[7:SpR:3229.1,29397.1] || equal(c_Set_Oinsert(u,v),w)* equal(hAPP(c_in(v),x),v_x)** -> hBOOL(hAPP(hAPP(w,v_x),x))*.
% 299.64/300.38 35603[0:SpR:3229.1,23772.0] || equal(c_COMBS(c_Set_Oinsert(v_x,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,w,x),y)* -> hBOOL(hAPP(y,v_x))*.
% 299.64/300.38 35663[0:SpR:353.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(x,u),y))),x))*.
% 299.64/300.38 35666[0:SpR:3229.1,26119.0] || equal(c_Set_Oinsert(u,v),w) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(w,v_x)),u))*.
% 299.64/300.38 35683[0:SpR:27043.1,26119.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),v_Procs))*.
% 299.64/300.38 35685[0:SpR:28771.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)))*.
% 299.64/300.38 35686[0:SpR:28755.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y)))*.
% 299.64/300.38 35688[0:SpR:28926.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)))*.
% 299.64/300.38 35689[0:SpR:28910.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y)))*.
% 299.64/300.38 35690[0:SpR:32668.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))))*.
% 299.64/300.38 35694[0:SpR:3229.1,26119.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v) -> hBOOL(hAPP(hAPP(hAPP(v,v_x),hAPP(c_Set_Oinsert(w,u),x)),w))*.
% 299.64/300.38 36094[0:SpR:3229.1,36017.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),v)* -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))*.
% 299.64/300.38 36113[0:SSi:36103.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(c_HOL_Ominus__class_Ominus(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),v_x))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))*.
% 299.64/300.38 36597[0:Res:10705.0,36406.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,hAPP(hAPP(c_Set_Oinsert(v_x,t_a),y),v_x),z,x1)),x))*.
% 299.64/300.38 36721[0:SpR:67.0,20186.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.38 36725[0:SpR:67.0,36017.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_fun(t_a,tc_bool)),v_x),tc_bool))*.
% 299.64/300.38 36737[0:SpR:67.0,20152.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))*.
% 299.64/300.38 36771[4:SpL:67.0,9001.1] || equal(v_Procs,v_x) equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> .
% 299.64/300.38 38191[0:SSi:38108.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_bool))*.
% 299.64/300.38 38685[4:SpR:445.1,37987.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(v_x,v) hBOOL(hAPP(hAPP(u,v_x),z))*.
% 299.64/300.38 38691[4:SpR:8415.2,37987.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.38 38731[4:SpR:9935.1,37987.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v))*.
% 299.64/300.38 38735[4:SpR:9936.1,37987.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v))*.
% 299.64/300.38 38741[4:SpR:585.0,37987.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),y),z))*.
% 299.64/300.38 38742[4:SpR:586.0,37987.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(u,hAPP(y,v_x)),z))*.
% 299.64/300.38 38747[4:SpR:15172.0,37987.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),y))*.
% 299.64/300.38 38748[4:SpR:27043.1,37987.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.38 38874[4:SpR:445.1,38042.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(v_x,v) c_Hoare__Mirabelle_Ohoare__valids(hAPP(u,v_x),z,t_a)*.
% 299.64/300.38 38880[4:SpR:8415.2,38042.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.38 38920[4:SpR:9935.1,38042.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Otop__class_Otop(tc_bool),v,t_a)*.
% 299.64/300.38 38924[4:SpR:9936.1,38042.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Otop__class_Otop(tc_bool),v,t_a)*.
% 299.64/300.38 38930[4:SpR:585.0,38042.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(u,v_x),y),z,t_a)*.
% 299.64/300.38 38931[4:SpR:586.0,38042.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(u,hAPP(y,v_x)),z,t_a)*.
% 299.64/300.38 38936[4:SpR:15172.0,38042.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Obot__class_Obot(tc_bool),y,t_a)*.
% 299.64/300.38 38937[4:SpR:27043.1,38042.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.38 38977[0:SpR:354.2,16814.1] class_Finite__Set_Ofinite_Ofinite(u) || c_lessequals(v,w,tc_fun(x,tc_bool))* c_Fun_Oinj__on(y,w,x,u)* -> c_Finite__Set_Ofinite(v,x).
% 299.64/300.38 41449[4:SpR:15476.0,38236.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),tc_Com_Opname,tc_bool))*.
% 299.64/300.38 41464[4:SpR:302.1,38236.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(u),tc_Com_Opname,tc_bool))*.
% 299.64/300.38 41497[4:SpR:11176.1,38236.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool))*.
% 299.64/300.38 41499[4:SpR:14216.0,38236.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,tc_bool)).
% 299.64/300.38 42186[0:SSi:42140.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) hBOOL(v) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,hAPP(c_Set_Oinsert(v,tc_bool),u),tc_bool,tc_bool))*.
% 299.64/300.38 42187[0:SSi:42130.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),tc_bool),u),tc_bool,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.38 42549[4:SSi:42529.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),v_x)),w,x),tc_Com_Opname,tc_bool))*.
% 299.64/300.38 42606[4:Res:40590.0,449.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))),t_a)*.
% 299.64/300.38 42887[4:SSi:42857.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v)),w,x),tc_Com_Opname,tc_bool))*.
% 299.64/300.38 42943[4:SpR:486.1,40590.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(w,tc_bool)),x))*.
% 299.64/300.38 42945[4:SpR:486.1,40371.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(x,tc_bool)),v_x))*.
% 299.64/300.38 43178[4:SpR:486.1,42609.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(w,tc_bool)),x,t_a)*.
% 299.64/300.38 44428[0:SpL:3229.1,35900.0] || equal(c_HOL_Ominus__class_Ominus(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(t_a,tc_bool)),w)* equal(hAPP(w,v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.38 44510[0:Res:10745.0,36528.1] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v_Procs,v_x))),w))*.
% 299.64/300.38 44511[0:Res:10746.0,36528.1] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),hAPP(v_Procs,v_x)))*.
% 299.64/300.38 44513[0:Res:10712.0,36528.1] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(hAPP(v_Procs,v_x),w)))*.
% 299.64/300.38 44514[0:Res:10713.0,36528.1] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(hAPP(v_Procs,v_x),w,x)),y))*.
% 299.64/300.38 44633[0:SpR:339.0,35656.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),u)),v_x))*.
% 299.64/300.38 44658[0:SpR:3229.1,35656.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),w)* equal(v,v_Procs) -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 44707[0:SpR:353.0,36599.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Set_Oinsert(v_x,t_a),w))),x),v_x))*.
% 299.64/300.38 44744[0:SpR:338.0,36599.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),w)),x)),v_x))*.
% 299.64/300.38 44762[0:SpR:3229.1,36599.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v)),w),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.38 45149[0:SpR:353.0,36600.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Set_Oinsert(v_x,t_a),x))),v_x))*.
% 299.64/300.38 45189[0:SpR:339.0,36600.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(v_x,t_a),x))),v_x))*.
% 299.64/300.38 45195[0:SpR:3229.1,36600.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(v_x,t_a),w)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.38 45210[0:SpR:353.0,36608.0] || -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),v_x),w,x),tc_Com_Opname,tc_bool))*.
% 299.64/300.38 45225[0:SpR:3229.1,36608.0] || equal(hAPP(c_Set_Oinsert(v_x,t_a),u),v)* -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(v,v_x),w,x),tc_Com_Opname,tc_bool))*.
% 299.64/300.38 45517[4:SpL:3229.1,38699.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v)* equal(hAPP(v,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.38 45661[4:SpL:3229.1,38888.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v)* equal(hAPP(v,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,w,t_a)*.
% 299.64/300.38 45700[0:SpR:338.0,44625.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),w)),v_x))*.
% 299.64/300.38 45731[0:SpR:3229.1,44625.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),w)* equal(u,v_Procs) -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 45987[0:Res:12687.1,45899.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_Com_Opname)))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x)).
% 299.64/300.38 46092[0:SpR:3229.1,36802.1] || equal(hAPP(c_Set_Oinsert(u,v),w),x)* equal(w,c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool))) -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.38 46551[4:SpR:3229.1,42029.1] || equal(hAPP(c_Set_Oinsert(u,v),w),x)* equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.38 46610[4:SpL:397.1,46565.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(u))* -> .
% 299.64/300.38 46611[4:SpL:365.1,46565.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(u))* -> .
% 299.64/300.38 46682[0:Res:364.1,44639.0] || c_lessequals(u,v,tc_fun(tc_Com_Opname,tc_bool))* equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v),v_x))*.
% 299.64/300.38 46724[0:Res:448.2,44639.0] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) || equal(u,v_Procs) -> c_lessequals(v,u,tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(v,v_x)).
% 299.64/300.38 46835[0:SpL:353.0,44750.0] || c_lessequals(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),w,tc_fun(x,tc_bool))* -> hBOOL(hAPP(w,v_x)).
% 299.64/300.38 46855[0:Res:364.1,44750.0] || c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,w),v),v_x))*.
% 299.64/300.38 46871[0:Res:448.2,44750.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,hAPP(c_Set_Oinsert(v_x,t_a),w),tc_fun(u,tc_bool))* hBOOL(hAPP(v,v_x)).
% 299.64/300.38 46976[0:SpL:353.0,46860.0] || equal(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.38 47094[0:Res:9567.0,38189.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),hAPP(u,x)))*.
% 299.64/300.38 47101[0:Res:10745.0,38189.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),y)))*.
% 299.64/300.38 47102[0:Res:10746.0,38189.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y)),u)))*.
% 299.64/300.38 47104[0:Res:10712.0,38189.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Set_Oinsert(w,x),c_Option_Othe(y)),c_Option_Ooption_OSome(u,y))))*.
% 299.64/300.38 47105[0:Res:10713.0,38189.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Set_Oinsert(w,x),c_COMBK(u,y,z)),x1)))*.
% 299.64/300.38 47111[0:Res:12621.0,38189.0] || hBOOL(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,tc_bool))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),u))*.
% 299.64/300.38 47115[0:Res:11580.0,38189.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v_Procs))*.
% 299.64/300.38 47320[4:SSi:47309.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool))))*.
% 299.64/300.38 47462[4:SSi:47441.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool)),v)))*.
% 299.64/300.38 47520[4:SSi:47491.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool),u,tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v))*.
% 299.64/300.38 47521[4:SSi:47488.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool),u,tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u))*.
% 299.64/300.38 47721[4:Res:10745.0,47549.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool))),w))*.
% 299.64/300.38 47722[4:Res:10746.0,47549.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool)))*.
% 299.64/300.38 47724[4:Res:10712.0,47549.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool),w)))*.
% 299.64/300.38 47725[4:Res:10713.0,47549.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool),w,x)),y))*.
% 299.64/300.38 47814[0:Res:9567.0,38190.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,x)),y))*.
% 299.64/300.38 47821[0:Res:10745.0,38190.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),x)),y))*.
% 299.64/300.38 47822[0:Res:10746.0,38190.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),u)),y))*.
% 299.64/300.38 47824[0:Res:10712.0,38190.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),c_Option_Ooption_OSome(u,x))),y))*.
% 299.64/300.38 47825[0:Res:10713.0,38190.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(v,w),c_COMBK(u,x,y)),z)),x1))*.
% 299.64/300.38 47831[0:Res:12621.0,38190.0] || hBOOL(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,tc_bool))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),y))*.
% 299.64/300.38 47835[0:Res:11580.0,38190.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_Procs),w))*.
% 299.64/300.38 48110[4:SpR:3229.1,39023.1] || equal(u,v)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(v,v_x)),y))*.
% 299.64/300.38 48117[4:SpR:525.1,39023.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),x))*.
% 299.64/300.38 48174[4:SpR:353.0,39023.1] || equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),x))*.
% 299.64/300.38 48181[4:SpR:3229.1,39023.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(w,v_x)),x)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w) -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.38 48225[4:SpR:3229.1,39064.1] || equal(u,v)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),hAPP(v,v_x)),y,t_a)*.
% 299.64/300.38 48232[4:SpR:525.1,39064.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),v_x),x,t_a)*.
% 299.64/300.38 48289[4:SpR:353.0,39064.1] || equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),x,t_a)*.
% 299.64/300.38 48483[4:SpR:3229.1,40388.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,x,y,z),hAPP(v,v_x)))*.
% 299.64/300.38 48529[4:SpR:3229.1,40606.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),hAPP(hAPP(u,v_x),z)))*.
% 299.64/300.38 48712[4:SpR:3229.1,42357.0] || equal(c_Set_Oinsert(u,v),w)* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(w,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(x,tc_bool)),v_x))*.
% 299.64/300.38 48737[4:SpR:3229.1,42357.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(x,tc_bool)),y)* -> hBOOL(hAPP(y,v_x))*.
% 299.64/300.38 48843[4:SpR:3229.1,48723.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),t_a,tc_fun(u,tc_bool)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.38 48848[4:SpR:3229.1,48702.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,tc_fun(v,tc_bool)),w)* equal(u,v_Procs) -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.38 48852[4:SpR:3229.1,42414.0] || equal(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x),y)* -> hBOOL(hAPP(hAPP(y,v_x),v_x))*.
% 299.64/300.38 48859[4:SpR:3229.1,42414.0] || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x),y),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.64/300.38 48871[4:SpR:353.0,42583.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(v_x,v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(x,tc_bool)),y))*.
% 299.64/300.38 49055[0:SpR:49017.1,9566.0] || -> hBOOL(hAPP(u,v_x)) c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.38 49411[0:SpR:49342.1,20881.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname))))*.
% 299.64/300.38 49413[0:SpR:49342.1,9067.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.38 49417[0:SpR:49342.1,26119.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.38 50100[4:SpR:353.0,43177.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(v_x,v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(x,tc_bool)),y,t_a)*.
% 299.64/300.38 50136[4:SpR:3229.1,43266.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x))),y)* -> hBOOL(hAPP(y,v_x))*.
% 299.64/300.38 50183[4:SpR:3229.1,43372.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),hAPP(u,v_x))),y))*.
% 299.64/300.38 50214[4:SpR:3229.1,43608.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),hAPP(u,v_x))),y,t_a)*.
% 299.64/300.38 50245[0:SpR:3229.1,44926.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))),y)* -> hBOOL(hAPP(y,v_x))*.
% 299.64/300.38 50352[0:Res:10745.0,46309.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u))),y))*.
% 299.64/300.38 50353[0:Res:10746.0,46309.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),u)))*.
% 299.64/300.38 50355[0:Res:10712.0,46309.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),c_Option_Ooption_OSome(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),u),x)))*.
% 299.64/300.38 50356[0:Res:10713.0,46309.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u),y,z)),x1))*.
% 299.64/300.38 50735[0:Res:10745.0,46413.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x))),y))*.
% 299.64/300.38 50736[0:Res:10746.0,46413.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),y)))*.
% 299.64/300.38 50738[0:Res:10712.0,46413.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),c_Option_Ooption_OSome(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),y),x)))*.
% 299.64/300.38 50739[0:Res:10713.0,46413.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x),y,z)),x1))*.
% 299.64/300.38 51007[0:Res:10745.0,50575.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(w) -> hBOOL(y)*.
% 299.64/300.38 51008[0:Res:10746.0,50575.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(x) -> hBOOL(y)*.
% 299.64/300.38 51010[0:Res:10712.0,50575.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(x,w)),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(x) -> hBOOL(y)*.
% 299.64/300.38 51011[0:Res:10713.0,50575.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(w,x,y)),z),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(w) -> hBOOL(x1)*.
% 299.64/300.38 51165[0:SpR:3229.1,26873.0] || equal(c_Set_Oinsert(u,v),w)* -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(w,v_x),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.64/300.38 51235[0:Rew:26873.0,51121.0] || -> equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),u)),tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.64/300.38 51286[0:SpR:3229.1,51231.0] || equal(c_Set_Oinsert(u,t_a),v)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(v_x,v_x),hAPP(hAPP(v,v_x),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 51303[0:SpR:3229.1,51231.0] || equal(hAPP(c_Set_Oinsert(u,t_a),v),w)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 51321[0:SpR:3229.1,51231.0] || equal(u,v) -> equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(hAPP(c_Set_Oinsert(w,t_a),u),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 51329[0:SpR:525.1,51231.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 51421[0:Rew:15569.0,51370.0] || -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.38 51437[7:SpL:3229.1,27284.0] || equal(c_Set_Ovimage(u,v,w),x)* equal(hAPP(x,v_x),v_x)** -> hBOOL(hAPP(v_x,hAPP(u,v_x)))*.
% 299.64/300.38 51465[0:SpR:3229.1,32700.0] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ofun__upd(u,v_x,v_x,v,w),tc_Com_Opname,x),y)* -> hBOOL(hAPP(v_Procs,hAPP(y,v_x)))*.
% 299.64/300.38 51475[0:SpL:369.0,33513.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(u,v),w),v),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.38 51479[0:SpL:3229.1,33513.1] || equal(c_Set_Oinsert(u,v),w)* c_Finite__Set_Ofinite(v_x,v) equal(c_Finite__Set_Ocard(hAPP(w,v_x),v),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.38 51490[0:SpL:10063.0,33513.1] || c_Finite__Set_Ofinite(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),t_a) equal(c_Finite__Set_Ocard(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),t_a),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.38 51808[4:SpR:3229.1,40792.1] || equal(c_Set_Oinsert(u,v),w)* c_lessequals(v_x,hAPP(v_x,x),tc_bool) -> hBOOL(hAPP(hAPP(w,v_x),x))*.
% 299.64/300.38 51835[4:SpR:3229.1,40792.1] || equal(hAPP(c_Set_Oinsert(u,v),w),x)* c_lessequals(v_x,hAPP(w,v_x),tc_bool)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.38 51974[0:Rew:351.0,51934.1,351.0,51934.1] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(c_COMBK(u,v,w),x,y,z),u)** -> equal(c_List_Ofoldl(x1,u,x2,z,x3),u)**.
% 299.64/300.38 52011[4:MRR:18250.2,52007.0] || equal(v_Procs,v_x) equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> .
% 299.64/300.38 52109[0:Res:9567.0,50366.0] || c_lessequals(hAPP(u,v),w,tc_bool)* hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,x,tc_fun(y,tc_bool)),v))* -> hBOOL(w).
% 299.64/300.38 52116[0:Res:10745.0,50366.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),y,tc_bool)* hBOOL(w) -> hBOOL(y).
% 299.64/300.39 52117[0:Res:10746.0,50366.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),y,tc_bool)* hBOOL(x) -> hBOOL(y).
% 299.64/300.39 52119[0:Res:10712.0,50366.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(x,w)),y,tc_bool)* hBOOL(x) -> hBOOL(y).
% 299.64/300.39 52120[0:Res:10713.0,50366.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(w,x,y)),z),x1,tc_bool)* hBOOL(w) -> hBOOL(x1).
% 299.64/300.39 52126[0:Res:12621.0,50366.0] || c_lessequals(u,v,tc_bool)* hBOOL(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool),y,tc_bool))* -> hBOOL(v).
% 299.64/300.39 52129[0:Res:11580.0,50366.0] || c_lessequals(v_Procs,u,tc_bool)* hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),v,tc_fun(w,tc_bool)),v_Procs))* -> hBOOL(u).
% 299.64/300.39 52256[0:SpL:353.0,35720.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),y,tc_fun(v,tc_bool))* -> hBOOL(hAPP(y,w)).
% 299.64/300.39 52259[0:SpL:3229.1,35720.0] || equal(c_Set_Oinsert(u,v),w)* c_lessequals(hAPP(w,v_x),x,tc_fun(v,tc_bool))* -> hBOOL(hAPP(x,u))*.
% 299.64/300.39 52272[0:SpL:27043.1,35720.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) c_lessequals(v_x,u,tc_fun(v,tc_bool))* -> hBOOL(hAPP(u,v_Procs)).
% 299.64/300.39 52274[0:SpL:28771.0,35720.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)))*.
% 299.64/300.39 52275[0:SpL:28755.0,35720.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y)))*.
% 299.64/300.39 52277[0:SpL:28926.0,35720.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)))*.
% 299.64/300.39 52278[0:SpL:28910.0,35720.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y)))*.
% 299.64/300.39 52279[0:SpL:32668.0,35720.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))))*.
% 299.64/300.39 52281[0:SpL:49342.1,35720.0] || hBOOL(hAPP(u,v_x)) c_lessequals(v_Procs,v,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.39 52291[0:Res:364.1,35720.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,v),x),u))*.
% 299.64/300.39 52308[0:Res:448.2,35720.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,hAPP(c_Set_Oinsert(w,u),x),tc_fun(u,tc_bool))* hBOOL(hAPP(v,w)).
% 299.64/300.39 52498[0:SpL:3229.1,38147.0] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),z)* hBOOL(hAPP(z,v_x))* -> hBOOL(u).
% 299.64/300.39 53006[0:Res:23739.1,454.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,u,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v_x,u),v_Procs,t_a)*.
% 299.64/300.39 53789[0:SpR:53771.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Option_Othe(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Option_Othe(u),v,x),w,y,z),c_Option_Othe(u))**.
% 299.64/300.39 53820[0:SpR:53772.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Option_Othe(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(u),w,v,x),w,y,z),c_Option_Othe(u))**.
% 299.64/300.39 54158[0:SpL:52997.1,3483.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 55622[0:SSi:55557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(hAPP(u,v_x),v,tc_bool)* -> equal(hAPP(u,v_x),v).
% 299.64/300.39 55722[0:SSi:55672.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v,tc_bool)* -> equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v).
% 299.64/300.39 55878[0:SpL:397.1,55174.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v) equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),hAPP(v,v_x))* -> .
% 299.64/300.39 55879[0:SpL:365.1,55174.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v)* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool),hAPP(v,v_x))* -> .
% 299.64/300.39 55961[0:SpL:397.1,55174.1] class_Orderings_Otop(u) || equal(v,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Otop__class_Otop(u))* -> .
% 299.64/300.39 55962[0:SpL:365.1,55174.1] class_Orderings_Obot(u) || equal(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Obot__class_Obot(u))* -> .
% 299.64/300.39 56305[0:SpR:30368.2,584.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 56335[0:SpL:30368.2,3483.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 56468[0:AED:24.0,56223.3] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> .
% 299.64/300.39 56536[0:Res:55596.2,16481.0] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(c_Orderings_Obot__class_Obot(u),v,tc_bool)* -> equal(c_Orderings_Otop__class_Otop(tc_bool),v).
% 299.64/300.39 56558[0:SSi:56518.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(c_Orderings_Obot__class_Obot(u),v,tc_bool)* -> equal(c_Orderings_Obot__class_Obot(u),v).
% 299.64/300.39 56559[0:SSi:56517.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(c_Orderings_Obot__class_Obot(u),v,tc_bool)* -> c_lessequals(w,v,tc_bool)*.
% 299.64/300.39 56747[0:SpR:30928.2,584.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 56777[0:SpL:30928.2,3483.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 56915[0:AED:24.0,56665.3] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> .
% 299.64/300.39 57044[2:Rew:56980.1,15946.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.39 57056[2:Rew:56980.1,15947.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.39 57057[0:Rew:56980.1,55932.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.39 57135[0:SpR:56980.1,49.2] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || equal(c_Orderings_Otop__class_Otop(tc_bool),u) c_lessequals(u,c_HOL_Ozero__class_Ozero(tc_bool),tc_bool) -> c_lessequals(u,c_Orderings_Obot__class_Obot(tc_bool),tc_bool)*.
% 299.64/300.39 57685[4:SpL:3229.1,55477.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(v,t_a),hAPP(u,v_x)),v_x),tc_bool),v_x)** -> .
% 299.64/300.39 57691[4:SpL:3229.1,55477.0] || equal(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),v_x)** -> .
% 299.64/300.39 57708[4:SSi:57698.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v_x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x)** -> .
% 299.64/300.39 57759[4:SpL:3229.1,57560.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(hAPP(c_Set_Oinsert(v,t_a),hAPP(u,v_x)),v_x),c_HOL_Ouminus__class_Ouminus(v_x,tc_bool))** -> .
% 299.64/300.39 57765[4:SpL:3229.1,57560.0] || equal(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)* equal(hAPP(v,v_x),c_HOL_Ouminus__class_Ouminus(v_x,tc_bool))** -> .
% 299.64/300.39 57836[0:Res:4703.2,4203.2] class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),c_Orderings_Obot__class_Obot(u))**.
% 299.64/300.39 57892[0:SpL:56980.1,55910.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_COMBK(u,v,w),x)* equal(hAPP(x,v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.39 57893[0:SpL:57059.1,55910.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(c_COMBK(u,v,w),x)* equal(hAPP(x,v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.39 57911[0:SpL:3229.1,55910.1] || equal(u,v)* equal(c_COMBK(w,x,y),u)* equal(c_HOL_Ouminus__class_Ouminus(w,tc_bool),hAPP(v,v_x))* -> .
% 299.64/300.39 57920[0:SpL:525.1,55910.1] class_Lattices_Oupper__semilattice(u) || equal(c_COMBK(v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),v_x) -> .
% 299.64/300.39 57975[0:SSi:57889.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(c_COMBK(v,w,x),y)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(y,v_x))* -> .
% 299.64/300.39 58019[0:Res:4790.2,4229.2] class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 58045[0:Rew:57836.4,58026.4] class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 58068[0:SpL:3229.1,55992.1] || equal(u,v)* equal(u,c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),w)* -> .
% 299.64/300.39 58077[0:SpL:525.1,55992.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v) -> .
% 299.64/300.39 58146[0:Rew:3014.0,58120.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBK(x,y,z))* equal(c_Orderings_Obot__class_Obot(tc_bool),x) -> .
% 299.64/300.39 58150[0:SSi:58137.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(v,v_x))* equal(v,c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),w)* -> .
% 299.64/300.39 58163[0:SpL:445.1,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v,w),c_Fun_Ofun__upd(u,x,y,z,x1))* -> equal(v_x,x).
% 299.64/300.39 58225[0:SpL:585.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool),w,x),hAPP(c_COMBC(u,y,z,x1),v))* -> .
% 299.64/300.39 58226[0:SpL:586.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),w,x),hAPP(c_COMBB(u,y,z,x1),v))* -> .
% 299.64/300.39 58233[0:SpL:27043.1,58055.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u,v),c_Set_Oinsert(v_Procs,w))* -> .
% 299.64/300.39 58285[0:Res:4703.2,4996.2] class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),c_Orderings_Obot__class_Obot(u))**.
% 299.64/300.39 58383[0:Res:305.1,5005.2] class_Lattices_Oupper__semilattice(u) class_Orderings_Otop(u) class_Orderings_Oorder(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 58384[0:Res:310.1,5005.2] class_Lattices_Olattice(u) class_Orderings_Otop(u) class_Orderings_Oorder(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 58386[0:Res:306.1,5005.2] class_Lattices_Oupper__semilattice(u) class_Orderings_Otop(u) class_Orderings_Oorder(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 58387[0:Res:309.1,5005.2] class_Lattices_Olattice(u) class_Orderings_Otop(u) class_Orderings_Oorder(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 58394[0:Res:4790.2,5005.2] class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Otop(u) class_Orderings_Oorder(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 58451[0:SpL:34428.0,58248.0] || equal(c_COMBK(v_x,u,v),c_HOL_Ouminus__class_Ouminus(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,w),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 58461[0:SpL:302.1,58248.0] class_Lattices_Obounded__lattice(u) || equal(c_COMBK(c_Orderings_Otop__class_Otop(u),v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 58462[0:SpL:331.0,58248.0] || equal(c_COMBK(v_x,u,v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 58491[0:SpL:11177.1,58248.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_COMBK(v_x,u,v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 58495[0:SpL:11176.1,58248.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_COMBK(u,v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 58497[0:SpL:14216.0,58248.0] || equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),u,v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(w,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 58597[0:Res:10771.1,3489.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))),v_x))* equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname))** -> .
% 299.64/300.39 58856[0:Res:423.0,15629.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Set_Oinsert(u,v),w),x)))*.
% 299.64/300.39 59116[0:Rew:300.1,58707.2] class_Lattices_Obounded__lattice(u) || hBOOL(v)* -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w))*.
% 299.64/300.39 59364[0:Res:423.0,15857.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),y)))*.
% 299.64/300.39 59626[0:Rew:300.1,59215.2] class_Lattices_Obounded__lattice(u) || hBOOL(v)* -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x))*.
% 299.64/300.39 59654[0:SpL:2267.1,58492.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)))* equal(c_COMBK(v_x,v,w),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 59667[0:SpL:2267.1,58465.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 59716[0:SpL:2267.1,58466.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 59725[0:SpL:56980.1,58179.1] class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> .
% 299.64/300.39 59728[0:SpL:3229.1,58179.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v)* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),hAPP(v,v_x))* -> .
% 299.64/300.39 59730[0:SSi:59723.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Lattices_Oupper__semilattice(u) || equal(v,v_x) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v,tc_bool),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> .
% 299.64/300.39 59732[0:SpL:8498.1,21018.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) equal(hAPP(c_Set_Oimage(w,v,x),u),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))** -> .
% 299.64/300.39 59734[0:SpL:9493.1,21018.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Set_Oimage(v,t_a,w),u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.39 59776[0:SpL:3229.1,59737.0] || equal(c_in(tc_Com_Opname),u) equal(hAPP(c_Set_Oimage(v,w,x),hAPP(u,v_x)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))** -> .
% 299.64/300.39 59892[0:SpL:10090.1,4126.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,u)*.
% 299.64/300.39 59977[0:SpL:56980.1,57894.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x)* equal(u,hAPP(x,v_x))* -> .
% 299.64/300.39 59978[0:SpL:57059.1,57894.0] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),v,w),x)* equal(u,hAPP(x,v_x))* -> .
% 299.64/300.39 59988[0:SSi:59974.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v)* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(u,tc_bool),w,x),y)* equal(v,hAPP(y,v_x))* -> .
% 299.64/300.39 60180[0:SpL:3229.1,58170.1] || equal(u,v)* equal(w,u)* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),x,y),w)* -> .
% 299.64/300.39 60189[0:SpL:525.1,58170.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),v)* -> .
% 299.64/300.39 60251[0:SpL:56980.1,58170.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(v,u)* equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),v)* -> .
% 299.64/300.39 60252[0:SpL:57059.1,58170.1] || equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_bool))** equal(v,u)* equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x),v)* -> .
% 299.64/300.39 60258[0:Rew:3014.0,60232.1] || equal(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))* equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),y,z),u)* -> .
% 299.64/300.39 60262[0:SSi:60249.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(v,v_x))* equal(w,v)* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(u,tc_bool),x,y),w)* -> .
% 299.64/300.39 61431[0:Res:61338.3,51.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(v,w,u)*.
% 299.64/300.39 61651[0:Res:305.1,8141.2] class_Lattices_Oupper__semilattice(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w),u)*.
% 299.64/300.39 61652[0:Res:310.1,8141.2] class_Lattices_Olattice(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w),u)*.
% 299.64/300.39 61654[0:Res:306.1,8141.2] class_Lattices_Oupper__semilattice(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Orderings_Otop__class_Otop(u)),u)*.
% 299.64/300.39 61655[0:Res:309.1,8141.2] class_Lattices_Olattice(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Orderings_Otop__class_Otop(u)),u)*.
% 299.64/300.39 61913[0:SpL:524.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 61924[0:SpL:414.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Fun_Ofun__upd(u,v_x,v,w,x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 62082[2:Res:54983.1,16623.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 62083[2:Res:54593.1,16623.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 62104[2:SpL:3229.1,62081.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(u,v_x),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 62374[0:SSi:62356.1,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Orderings_Obot__class_Obot(u),v) -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,tc_bool)*.
% 299.64/300.39 62375[0:SSi:62355.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(u,v_x),v) -> c_lessequals(hAPP(u,v_x),v,tc_bool)*.
% 299.64/300.39 62376[0:SSi:62354.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v,tc_bool)*.
% 299.64/300.39 62377[0:SSi:62341.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) equal(v,c_HOL_Ominus__class_Ominus(u,w,tc_bool)) -> c_lessequals(v,c_HOL_Ominus__class_Ominus(u,w,tc_bool),tc_bool)*.
% 299.64/300.39 62381[0:Obv:62269.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(v,c_Orderings_Obot__class_Obot(u)) equal(w,v) -> c_lessequals(w,v,u)*.
% 299.64/300.39 62382[0:Obv:62252.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(u),v) equal(v,w) -> c_lessequals(v,w,u)*.
% 299.64/300.39 62700[0:Obv:62604.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(w,v,u)* -> equal(w,v).
% 299.64/300.39 62701[0:Obv:62587.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(u),v) c_lessequals(v,w,u)* -> equal(v,w).
% 299.64/300.39 63507[0:Rew:140.1,63408.4] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(w,x,u)* -> c_lessequals(v,x,u)*.
% 299.64/300.39 63508[0:Rew:137.1,63407.4] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(w,x,u)* -> c_lessequals(v,x,u)*.
% 299.64/300.39 63557[0:Res:62367.1,17530.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),u)** equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 63588[0:SSi:63545.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),u) c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool)* -> c_lessequals(u,w,tc_bool).
% 299.64/300.39 63589[0:SSi:63544.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),u) c_lessequals(w,u,tc_bool) -> c_lessequals(w,c_HOL_Ominus__class_Ominus(u,v,tc_bool),tc_bool)*.
% 299.64/300.39 63769[0:Obv:63696.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x)* -> c_lessequals(w,x,u)*.
% 299.64/300.39 63770[0:Obv:63695.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x)* -> c_lessequals(v,x,u)*.
% 299.64/300.39 63775[0:SSi:63655.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),v)** -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.64/300.39 63776[0:SSi:63651.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(hAPP(c_Set_Oinsert(v,u),w),x)* -> c_lessequals(w,x,tc_fun(u,tc_bool))*.
% 299.64/300.39 63937[0:Rew:140.1,63811.4] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(x,w,u)* -> c_lessequals(x,v,u)*.
% 299.64/300.39 63938[0:Rew:137.1,63810.4] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(x,w,u)* -> c_lessequals(x,v,u)*.
% 299.64/300.39 64104[0:Res:679.1,18625.0] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v),hAPP(v_Procs,v),tc_bool)*.
% 299.64/300.39 64518[0:SpL:414.0,24257.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(v,c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.39 64544[0:SpL:9924.0,24257.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_in(tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.39 65955[0:SpR:65404.1,3279.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.39 65959[0:SpR:65404.1,3285.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.39 65960[0:SpR:65404.1,3291.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),v_Procs))*.
% 299.64/300.39 65961[4:SpR:65404.1,39023.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),x))*.
% 299.64/300.39 65962[4:SpR:65404.1,39064.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),v_x),x,t_a)*.
% 299.64/300.39 65965[0:SpR:65404.1,8376.2] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.39 65968[0:SpR:65404.1,15262.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.39 65973[0:SpR:65404.1,21267.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_x,tc_Com_Opname,v)),v_x)**.
% 299.64/300.39 65974[0:SpR:65404.1,21143.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.39 65975[0:SpR:65404.1,21131.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.39 65979[0:SpR:65404.1,21893.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v)),v_x)**.
% 299.64/300.39 65982[0:SpR:65404.1,31533.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x)),v_Procs))*.
% 299.64/300.39 65984[0:SpR:65404.1,32668.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 65989[0:SpR:65404.1,51231.0] class_Lattices_Olattice(u) || -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 65998[0:SpR:65404.1,3305.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.39 65999[0:SpR:65404.1,3317.1] class_Lattices_Olattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,v),w)))*.
% 299.64/300.39 66000[0:SpR:65404.1,21126.1] class_Lattices_Olattice(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,w),v),v_x))*.
% 299.64/300.39 66001[0:SpR:65404.1,28704.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,w)))*.
% 299.64/300.39 66002[0:SpR:65404.1,28859.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_x,tc_Com_Opname,w)))*.
% 299.64/300.39 66003[0:SpR:65404.1,28053.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v,tc_Com_Opname,w)))*.
% 299.64/300.39 66004[0:SpR:65404.1,28356.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,v_x,tc_Com_Opname,w)))*.
% 299.64/300.39 66005[0:SpR:65404.1,3346.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x))*.
% 299.64/300.39 66023[0:SpR:65404.1,9568.0] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),x),v),tc_bool)*.
% 299.64/300.39 66024[0:SpR:65404.1,9569.0] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),v),tc_bool)*.
% 299.64/300.39 66050[0:SpR:65404.1,20881.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(v,w),y)),v))*.
% 299.64/300.39 66169[0:SpR:8415.2,65404.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* -> equal(hAPP(v_x,v_x),v_x)**.
% 299.64/300.39 66185[0:SpL:65404.1,55992.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v) -> .
% 299.64/300.39 66191[0:SpL:65404.1,3484.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,v),v_x)** -> equal(v_x,v).
% 299.64/300.39 66198[0:SpL:65404.1,24254.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 66202[0:SpL:65404.1,58170.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),v)* -> .
% 299.64/300.39 66204[0:SpL:65404.1,3499.1] class_Lattices_Olattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* hBOOL(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.39 66209[0:SpL:65404.1,55910.1] class_Lattices_Olattice(u) || equal(c_COMBK(v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),v_x) -> .
% 299.64/300.39 66474[0:Rew:25.1,66326.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),v_Procs) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),v_x))*.
% 299.64/300.39 66819[0:Rew:13790.1,66818.3,66691.3,66818.3] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ozero__class_Ozero(u)),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.39 66821[0:Rew:14090.1,66820.3,66692.3,66820.3] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ozero__class_Ozero(u)),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.39 66828[0:Rew:66691.3,66827.3] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.39 66830[0:Rew:66692.3,66829.3] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.39 67124[0:Rew:66691.3,67123.3] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ozero__class_Ozero(u),v_Procs) -> hBOOL(hAPP(c_HOL_Ozero__class_Ozero(u),v_x))*.
% 299.64/300.39 67425[0:Rew:66692.3,67424.3] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ozero__class_Ozero(u),v_Procs) -> hBOOL(hAPP(c_HOL_Ozero__class_Ozero(u),v_x))*.
% 299.64/300.39 67438[0:Obv:67370.2] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)* -> c_lessequals(w,v,u)*.
% 299.64/300.39 67583[0:Rew:13790.1,67582.3,67446.3,67582.3] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ozero__class_Ozero(u)),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.39 67585[0:Rew:14090.1,67584.3,67447.3,67584.3] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ozero__class_Ozero(u)),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.39 67592[0:Rew:67446.3,67591.3] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.39 67594[0:Rew:67447.3,67593.3] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.39 67887[0:MRR:67886.5,67118.3] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || -> equal(v,c_HOL_Ozero__class_Ozero(u))*.
% 299.64/300.39 67888[0:MRR:67812.5,67118.3] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || -> c_lessequals(v,w,u)*.
% 299.64/300.39 68174[0:MRR:68173.5,67418.3] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || -> equal(v,c_HOL_Ozero__class_Ozero(u))*.
% 299.64/300.39 68176[0:MRR:68100.5,67418.3] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || -> c_lessequals(v,w,u)*.
% 299.64/300.39 68178[0:Rew:66692.3,68177.3] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ozero__class_Ozero(u),v) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.39 68754[0:Rew:67446.3,68753.3] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ozero__class_Ozero(u),v_Procs) -> hBOOL(hAPP(c_HOL_Ozero__class_Ozero(u),v_x))*.
% 299.64/300.39 69057[0:Rew:67447.3,69056.3] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ozero__class_Ozero(u),v_Procs) -> hBOOL(hAPP(c_HOL_Ozero__class_Ozero(u),v_x))*.
% 299.64/300.39 69070[0:Obv:69002.2] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)* -> c_lessequals(w,v,u)*.
% 299.64/300.39 69364[0:MRR:69363.5,67577.3] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || -> equal(v,c_HOL_Ozero__class_Ozero(u))*.
% 299.64/300.39 69366[0:MRR:69289.5,67577.3] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || -> c_lessequals(v,w,u)*.
% 299.64/300.39 69368[0:Rew:67447.3,69367.3] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ozero__class_Ozero(u),v) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.39 69658[0:MRR:69657.5,68748.3] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || -> equal(v,c_HOL_Ozero__class_Ozero(u))*.
% 299.64/300.39 69659[0:MRR:69582.5,68748.3] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || -> c_lessequals(v,w,u)*.
% 299.64/300.39 69723[0:SSi:69708.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),v)** -> equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v).
% 299.64/300.39 69953[0:Obv:69909.2] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)* -> equal(c_HOL_Ozero__class_Ozero(u),v).
% 299.64/300.39 70043[0:Obv:69998.2] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)* -> equal(c_HOL_Ozero__class_Ozero(u),v).
% 299.64/300.39 70347[0:SpL:3229.1,65954.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),v)* equal(hAPP(v,v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs))*.
% 299.64/300.39 70376[0:SpL:3229.1,70070.1] || equal(c_in(t_a),u) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool)) hBOOL(hAPP(hAPP(u,v_x),v))* -> .
% 299.64/300.39 70391[0:Res:254.1,70070.1] || hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(v,t_a),u),v_x),tc_bool))* -> .
% 299.64/300.39 70434[0:Res:1103.1,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(t_a),v_x)),v_x),tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(t_a),v_x),t_a).
% 299.64/300.39 70980[0:Res:23320.1,70856.2] || equal(c_in(tc_Com_Opname),c_in(t_a)) equal(u,hAPP(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_x))* hBOOL(u)* -> .
% 299.64/300.39 70981[0:Res:9267.0,70856.2] || equal(u,hAPP(hAPP(c_Set_Oinsert(v,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x))* hBOOL(u)* -> equal(v_x,v).
% 299.64/300.39 71075[0:SpR:3294.1,7568.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) -> c_lessequals(v_x,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_bool)),tc_fun(u,tc_bool))*.
% 299.64/300.39 71083[0:SpR:10090.1,7568.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(c_Set_Oinsert(v,u),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(u,tc_bool))*.
% 299.64/300.39 71303[0:Res:7538.0,18625.0] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(y,w),u)),v),tc_bool)*.
% 299.64/300.39 71317[0:Res:7538.0,1937.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.39 71321[0:Res:7538.0,32232.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))),v_x))*.
% 299.64/300.39 71322[0:Res:7538.0,44639.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),u)),v_x))*.
% 299.64/300.39 71329[0:Res:7538.0,18768.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),c_Set_Oinsert(v_x,tc_Com_Opname))),v_Procs),tc_bool)*.
% 299.64/300.39 71331[0:Res:7538.0,44750.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(v_x,t_a),x))),v_x))*.
% 299.64/300.39 71371[7:SpL:445.1,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)) equal(c_Fun_Ofun__upd(u,v,w,x,y),v_x)** -> equal(v_x,v).
% 299.64/300.39 71433[7:SpL:585.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool))* equal(hAPP(c_COMBC(u,w,x,y),v),v_x)** -> .
% 299.64/300.39 71434[7:SpL:586.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool))* equal(hAPP(c_COMBB(u,w,x,y),v),v_x)** -> .
% 299.64/300.39 71589[7:SpR:71455.1,9568.0] || equal(u,v_x) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a)),w),u),tc_bool)*.
% 299.64/300.39 71590[7:SpR:71455.1,9569.0] || equal(u,v_x) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_x,t_a)),u),tc_bool)*.
% 299.64/300.39 71616[7:SpR:71455.1,353.0] || equal(u,v_x) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(v,t_a),u)),hAPP(c_Set_Oinsert(v,t_a),u))**.
% 299.64/300.39 71624[7:SpR:71455.1,20881.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,v),x)),u))*.
% 299.64/300.39 72025[7:MRR:72011.1,6340.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname)).
% 299.64/300.39 72100[0:SpR:23902.1,7830.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Set_Oinsert(v,u),v_x),tc_fun(u,tc_bool))*.
% 299.64/300.39 72773[0:Res:448.2,4219.2] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* equal(v,c_Orderings_Otop__class_Otop(u)).
% 299.64/300.39 72775[0:Res:47.2,4219.2] class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)* -> equal(v,c_Orderings_Otop__class_Otop(u)).
% 299.64/300.39 72820[0:Obv:72785.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),v)** -> equal(v,c_Orderings_Otop__class_Otop(u)).
% 299.64/300.39 72945[7:SpR:8415.2,72313.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(u,t_a),v_x)))*.
% 299.64/300.39 73024[7:SpR:8415.2,71608.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(t_a)) equal(u,v_x) -> hBOOL(hAPP(v_x,u))*.
% 299.64/300.39 73064[7:Res:71608.1,464.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_x) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,t_a)),v_x)**.
% 299.64/300.39 73065[7:Res:71608.1,469.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_x) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,t_a)),v_x)**.
% 299.64/300.39 73234[7:SpR:71835.1,21126.1] || equal(c_Set_Oimage(u,tc_Com_Opname,v),c_Set_Oinsert(v_x,t_a))** equal(v_Procs,v_x) -> hBOOL(hAPP(v_x,hAPP(u,v_x)))*.
% 299.64/300.39 73243[7:SpR:71835.1,9568.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(hAPP(v_x,v),hAPP(hAPP(v_x,w),v),tc_bool)*.
% 299.64/300.39 73248[7:SpR:71835.1,10697.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(v,w),v_x),v_x),tc_bool)*.
% 299.64/300.39 73251[7:SpR:71835.1,9936.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* -> equal(hAPP(v_x,u),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.39 73265[7:SpR:71835.1,23882.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(v_x,u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),v_x,tc_bool)*.
% 299.64/300.39 73268[7:SpR:71835.1,23881.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,u,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x))*.
% 299.64/300.39 73280[7:SpR:71835.1,445.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Set_Oinsert(v_x,t_a))** -> equal(v_x,v) equal(hAPP(u,v_x),v_x).
% 299.64/300.39 73287[7:SpR:71835.1,31323.0] || equal(c_Set_Oinsert(v_x,t_a),v_Procs) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v_x),v_x,tc_bool)*.
% 299.64/300.39 73312[7:SpR:71835.1,7599.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),v_Procs))*.
% 299.64/300.39 73315[7:SpR:71835.1,19441.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))))*.
% 299.64/300.39 73316[7:SpR:71835.1,19436.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) equal(u,v_Procs) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),u)))*.
% 299.64/300.39 73321[7:SpR:71835.1,23934.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_Procs),u,v),v_x),v_Procs))*.
% 299.64/300.39 73333[7:SpR:71835.1,19452.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(t_a)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))))*.
% 299.64/300.39 73366[7:SpR:71835.1,3279.1] || equal(c_Set_Oinsert(v_x,t_a),u) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u)* -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.39 73371[7:SpR:71835.1,3285.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.39 73372[7:SpR:71835.1,3291.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),v_Procs))*.
% 299.64/300.39 73373[7:SpR:71835.1,39023.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),x))*.
% 299.64/300.39 73374[7:SpR:71835.1,39064.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),v_x),x,t_a)*.
% 299.64/300.39 73378[7:SpR:71835.1,8376.2] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_in(tc_Com_Opname),u) equal(v,v_Procs) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.39 73381[7:SpR:71835.1,15262.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_in(t_a),u) -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.39 73387[7:SpR:71835.1,21143.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.39 73388[7:SpR:71835.1,21131.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.39 73395[7:SpR:71835.1,31533.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),v_x)),v_Procs))*.
% 299.64/300.39 73397[7:SpR:71835.1,32668.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 73402[7:SpR:71835.1,51231.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(v,t_a),u),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 73411[7:SpR:71835.1,3305.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(v,u)* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.39 73412[7:SpR:71835.1,3317.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_in(v),u)* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,v),w)))*.
% 299.64/300.39 73413[7:SpR:71835.1,21126.1] || equal(c_Set_Oinsert(v_x,t_a),u) equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v),v_x))*.
% 299.64/300.39 73414[7:SpR:71835.1,28704.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,w)))*.
% 299.64/300.39 73415[7:SpR:71835.1,28859.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,w)))*.
% 299.64/300.39 73416[7:SpR:71835.1,28053.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(v,u)* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v,tc_Com_Opname,w)))*.
% 299.64/300.39 73417[7:SpR:71835.1,28356.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(v,u)* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,v_x,tc_Com_Opname,w)))*.
% 299.64/300.39 73421[7:SpR:71835.1,32691.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_x,tc_Com_Opname,v),v_x)))*.
% 299.64/300.39 73422[7:SpR:71835.1,1162.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.39 73423[7:SpR:71835.1,21704.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),v_x,tc_Com_Opname,v),v_x)**.
% 299.64/300.39 73424[7:SpR:71835.1,21689.1] class_Lattices_Obounded__lattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),v_x,tc_Com_Opname,v),v_x)**.
% 299.64/300.39 73425[7:SpR:71835.1,22333.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),v_x)**.
% 299.64/300.39 73426[7:SpR:71835.1,22318.1] class_Lattices_Obounded__lattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),v_x)**.
% 299.64/300.39 73427[7:SpR:71835.1,28058.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,v)))*.
% 299.64/300.39 73428[7:SpR:71835.1,28361.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,v)))*.
% 299.64/300.39 73432[7:SpR:71835.1,23961.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v_x,tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.39 73435[7:SpR:71835.1,26317.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,tc_bool),v_x)**.
% 299.64/300.39 73440[7:SpR:71835.1,28009.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u)),v_Procs))*.
% 299.64/300.39 73441[7:SpR:71835.1,28771.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 73444[7:SpR:71835.1,28312.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u)),v_Procs))*.
% 299.64/300.39 73445[7:SpR:71835.1,28926.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 73447[7:SpR:71835.1,23936.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.64/300.39 73448[7:SpR:71835.1,23954.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,t_a,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x))*.
% 299.64/300.39 73467[7:SpR:71835.1,40606.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),hAPP(v_x,y)))*.
% 299.64/300.39 73468[7:SpR:71835.1,43372.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),x))*.
% 299.64/300.39 73469[7:SpR:71835.1,43608.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),x,t_a)*.
% 299.64/300.39 73479[7:SpR:71835.1,3346.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_Set_Oinsert(v,w),u)* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x))*.
% 299.64/300.39 73500[7:SpR:71835.1,1157.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(c_COMBK(v_x,v,w),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.39 73503[7:SpR:71835.1,9246.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) -> hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))))* hBOOL(hAPP(v,v_x)).
% 299.64/300.39 73505[7:SpR:71835.1,9071.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) -> hBOOL(hAPP(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_x,u),tc_Com_Opname,tc_fun(u,tc_bool))))*.
% 299.64/300.39 73511[7:SpR:71835.1,9067.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v_x,u),w))))*.
% 299.64/300.39 73520[7:SpR:71835.1,18763.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(v_Procs,hAPP(hAPP(v_x,c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.39 73523[7:SpR:71835.1,26119.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> hBOOL(hAPP(hAPP(v_x,hAPP(c_Set_Oinsert(v,u),w)),v))*.
% 299.64/300.39 73546[7:SpR:71835.1,543.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* -> equal(hAPP(v_x,hAPP(v_x,v)),hAPP(v_x,v))**.
% 299.64/300.39 73547[7:SpR:71835.1,544.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* -> equal(hAPP(v_x,hAPP(v_x,v)),hAPP(v_x,v))**.
% 299.64/300.39 73555[7:SpR:71835.1,9935.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* -> equal(hAPP(v_x,u),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 73582[7:SpR:71835.1,9568.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x),tc_bool)*.
% 299.64/300.39 73583[7:SpR:71835.1,9569.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x),tc_bool)*.
% 299.64/300.39 73683[7:SpR:71835.1,9569.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(hAPP(v,w),hAPP(hAPP(v_x,v),w),tc_bool)*.
% 299.64/300.39 73702[7:SpR:71835.1,20881.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(v_x,v),x)),v_x))*.
% 299.64/300.39 73730[7:SpR:71835.1,9569.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(hAPP(w,v_x),v_x,tc_bool).
% 299.64/300.39 73732[7:SpR:71835.1,9568.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(hAPP(v,v_x),v_x,tc_bool).
% 299.64/300.39 73765[7:SpR:71835.1,18644.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(v_Procs,hAPP(v_x,v_Procs),tc_bool).
% 299.64/300.39 73784[7:SpR:71835.1,9568.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(hAPP(v,w),hAPP(v_x,w),tc_bool)*.
% 299.64/300.39 73807[7:SpR:71835.1,9936.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Set_Oinsert(v_x,t_a)) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.39 73855[7:SpR:71835.1,51231.0] || equal(hAPP(c_Set_Oinsert(u,t_a),v),c_Set_Oinsert(v_x,t_a))** -> equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),v_x,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 73873[7:SpR:71835.1,31323.0] || equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(v_x,hAPP(v_Procs,v_x),tc_bool).
% 299.64/300.39 73886[7:SpR:71835.1,585.0] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(hAPP(u,v_x),y),v_x).
% 299.64/300.39 73887[7:SpR:71835.1,586.0] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(u,hAPP(y,v_x)),v_x).
% 299.64/300.39 73888[7:SpR:71835.1,5877.0] || equal(hAPP(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Com_Ocom_OBODY,v,w,x),y),c_Set_Oinsert(v_x,t_a))** -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),v_x,u).
% 299.64/300.39 73900[7:SpR:71835.1,585.0] || equal(c_COMBC(u,v,w,x),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(hAPP(u,y),v_x),hAPP(v_x,y))**.
% 299.64/300.39 73901[7:SpR:71835.1,586.0] || equal(c_COMBB(u,v,w,x),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(u,hAPP(v_x,y)),hAPP(v_x,y))**.
% 299.64/300.39 73904[7:SpR:71835.1,10705.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,v_x,x,y,z)),c_Set_Oinsert(v_x,t_a))** -> c_lessequals(x,v_x,tc_bool).
% 299.64/300.39 73908[7:SpR:71835.1,5877.0] || equal(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Com_Ocom_OBODY,v,w,x),c_Set_Oinsert(v_x,t_a))** -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(v_x,y),u)*.
% 299.64/300.39 73918[7:SpR:71835.1,20881.0] || equal(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(u,v)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,v,x),v_x),hAPP(w,u)))*.
% 299.64/300.39 73919[7:SpR:71835.1,9067.0] || equal(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(u,v)) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oinsert(w,v),v_x)))*.
% 299.64/300.39 73933[7:SpR:71835.1,26119.0] || equal(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(u,v)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),u))*.
% 299.64/300.39 73938[7:SpR:71835.1,21035.0] || equal(c_Set_Oinsert(v_Procs,u),c_Set_Oinsert(v_x,t_a)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),v_x),v_Procs))*.
% 299.64/300.39 73942[7:SpR:71835.1,23961.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.39 73983[7:SpL:71835.1,1944.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,t_a)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v_x,v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.39 73984[7:SpL:71835.1,3303.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,t_a))** equal(hAPP(v_x,v_Procs),u) -> hBOOL(hAPP(u,v_x))*.
% 299.64/300.39 73993[7:SpL:71835.1,62081.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_Com_Ocom_OBODY,v_x) -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 74016[7:SpL:71835.1,12979.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,v_x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_Procs,t_a).
% 299.64/300.39 74019[7:SpL:71835.1,70070.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(t_a)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* hBOOL(hAPP(v_x,u)) -> .
% 299.64/300.39 74032[7:SpL:71835.1,55992.1] || equal(c_Set_Oinsert(v_x,t_a),u) equal(u,c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v) -> .
% 299.64/300.39 74038[7:SpL:71835.1,3484.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_Com_Ocom_OBODY,u) equal(hAPP(c_Com_Ocom_OBODY,v),v_x)** -> equal(v_x,v).
% 299.64/300.39 74045[7:SpL:71835.1,24254.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 74049[7:SpL:71835.1,58170.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(v,u)* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),v)* -> .
% 299.64/300.39 74051[7:SpL:71835.1,3499.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_in(v),u)* hBOOL(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.39 74055[7:SpL:71835.1,3945.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** equal(c_Com_Ocom_OBODY,v_x) equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.39 74067[7:SpL:71835.1,65954.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(c_in(tc_Com_Opname),v_x) -> hBOOL(hAPP(v_x,v_Procs))*.
% 299.64/300.39 74068[7:SpL:71835.1,3727.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(c_in(tc_Com_Opname),v_x) -> hBOOL(hAPP(v_x,v_Procs))*.
% 299.64/300.39 74069[7:SpL:71835.1,3331.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(v_x,v) -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.39 74071[7:SpL:71835.1,38888.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.39 74072[7:SpL:71835.1,38699.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.39 74073[7:SpL:71835.1,58179.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v,w),v_x)** -> .
% 299.64/300.39 74088[7:SpL:71835.1,23941.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.39 74093[7:SpL:71835.1,24034.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(u,v_x) equal(c_Com_Ocom_OBODY,u)* equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 74105[7:SpL:71835.1,57560.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),v_x),v_x),c_HOL_Ouminus__class_Ouminus(v_x,tc_bool))** -> .
% 299.64/300.39 74107[7:SpL:71835.1,55910.1] || equal(c_Set_Oinsert(v_x,t_a),u) equal(c_COMBK(v,w,x),u)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),v_x) -> .
% 299.64/300.39 74123[7:SpL:71835.1,279.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,v)) -> equal(hAPP(c_Set_Oinsert(v_x,u),v),v)**.
% 299.64/300.39 74198[7:SpL:71835.1,35720.0] || equal(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(u,v))* c_lessequals(v_x,w,tc_fun(v,tc_bool))* -> hBOOL(hAPP(w,u))*.
% 299.64/300.39 74219[7:SpL:71835.1,11894.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))* hBOOL(hAPP(v_x,v))* -> .
% 299.64/300.39 74467[7:Rew:71835.1,73504.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) -> hBOOL(hAPP(v_x,v)) hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))))*.
% 299.64/300.39 74485[7:MRR:73666.2,27297.0] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)).
% 299.64/300.39 74605[7:SpR:8415.2,71906.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(hAPP(v_x,v),v_x))*.
% 299.64/300.39 74773[7:SpL:2771.1,72021.1] || equal(u,v)* equal(hAPP(v_x,v_x),hAPP(u,v_x))* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))* -> .
% 299.64/300.39 74829[7:SpR:445.1,72297.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_in(t_a))** -> equal(v_x,v) hBOOL(hAPP(hAPP(u,v_x),v_x)).
% 299.64/300.39 74882[7:SpR:9935.1,72297.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x))*.
% 299.64/300.39 74886[7:SpR:9936.1,72297.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x))*.
% 299.64/300.39 74892[7:SpR:585.0,72297.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),y),v_x))*.
% 299.64/300.39 74893[7:SpR:586.0,72297.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_in(t_a))** -> hBOOL(hAPP(hAPP(u,hAPP(y,v_x)),v_x))*.
% 299.64/300.39 74898[7:SpR:15172.0,72297.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_x)).
% 299.64/300.39 74996[7:SpL:2771.1,74770.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),hAPP(v_x,v_x))** hBOOL(hAPP(u,v_x))* -> .
% 299.64/300.39 75237[7:SpR:8415.2,72312.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,t_a,v),v_x),v_x))*.
% 299.64/300.39 75305[7:SpR:8415.2,72312.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,t_a,v),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(u,v_x)))*.
% 299.64/300.39 75400[0:SpR:23902.1,7820.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),u)*.
% 299.64/300.39 75691[7:SpR:71883.1,3339.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(u,v_x) -> equal(c_Fun_Ofun__upd(u,v_x,v_x,v,w),u)**.
% 299.64/300.39 75852[0:SpR:3294.1,7823.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(tc_bool)),u)*.
% 299.64/300.39 75862[0:SpR:10090.1,7823.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_bool)),u)*.
% 299.64/300.39 76531[0:SpR:23902.1,29199.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),u)*.
% 299.64/300.39 76884[0:SpR:3294.1,30321.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(tc_bool)),u)*.
% 299.64/300.39 76894[0:SpR:10090.1,30321.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_bool)),u)*.
% 299.64/300.39 77179[7:SpL:88.1,74788.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_x)** equal(c_Orderings_Otop__class_Otop(u),v)* -> hBOOL(v)*.
% 299.64/300.39 77200[7:SpL:9.0,74788.1] || equal(c_Fun_Ocomp(u,v,w,x,y),v_x)** equal(hAPP(u,hAPP(v,v_x)),z)* -> hBOOL(z)*.
% 299.64/300.39 77340[0:SpR:2807.0,2399.2] class_Orderings_Olinorder(tc_bool) class_OrderedGroup_Olordered__ab__group__add(tc_bool) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_bool),u,tc_bool)* c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_bool),tc_bool)*.
% 299.64/300.39 77365[0:Res:2399.2,1048.0] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(tc_Com_Opname,tc_bool)) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(tc_Com_Opname,tc_bool)),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.39 77502[7:Res:9268.0,72390.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname))**.
% 299.64/300.39 77755[0:SpL:23682.0,5892.0] || hBOOL(hAPP(u,u))* -> hBOOL(hAPP(c_COMBS(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,x,y),u))*.
% 299.64/300.39 77837[0:SpL:300.1,5892.0] class_Lattices_Obounded__lattice(u) || hBOOL(c_Orderings_Obot__class_Obot(u)) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.39 77843[0:SpL:302.1,5892.0] class_Lattices_Obounded__lattice(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 77914[0:Res:36412.1,5892.0] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(c_COMBS(c_in(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x),hAPP(v_Procs,v_x)))*.
% 299.64/300.39 77935[4:Res:47158.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool)))*.
% 299.64/300.39 77938[0:Res:37923.1,5892.0] || hBOOL(u) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),u)))*.
% 299.64/300.39 77939[0:Res:37989.1,5892.0] || hBOOL(u) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),z)))*.
% 299.64/300.39 77966[4:Res:40792.1,5892.0] || c_lessequals(v_x,hAPP(u,u),tc_bool)* -> hBOOL(hAPP(c_COMBS(c_in(v),c_Set_Oinsert(w,x),y,z,x1),u))*.
% 299.64/300.39 77981[4:Res:39023.1,5892.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Set_Oinsert(w,x),y,z,x1),hAPP(u,v_x)))*.
% 299.64/300.39 77982[4:Res:43372.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oinsert(v,w),x,y,z),hAPP(c_Set_Oinsert(x1,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))))*.
% 299.64/300.39 77983[0:Res:20881.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(c_Set_Oinsert(v,w),w,x),y,z,x1),hAPP(c_Set_Oinsert(v,w),v)))*.
% 299.64/300.39 78175[7:Res:77996.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v)),u))* c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.64/300.39 78286[7:SpR:78167.0,645.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,u),tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.39 78292[7:SpR:78167.0,646.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Set_Oinsert(v_x,u),tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.39 78356[7:SpR:78167.0,317.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v_x),v),hAPP(c_Set_Oimage(u,w,v),v_x)),hAPP(c_Set_Oimage(u,w,v),v_x))**.
% 299.64/300.39 78505[4:Res:77988.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),u)*.
% 299.64/300.39 78506[4:Res:77988.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),v_x,u)*.
% 299.64/300.39 78516[4:Res:77988.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),t_a)* c_Hoare__Mirabelle_Otriple__valid(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.64/300.39 78549[4:MRR:15794.3,78524.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.39 78566[7:MRR:27841.3,78524.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.39 78574[4:MRR:29854.1,78524.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(v_Procs,u)),c_Set_Oinsert(v_Procs,u))**.
% 299.64/300.39 78579[4:MRR:36093.2,78524.0] || equal(v_Procs,v_x) equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> .
% 299.64/300.39 78584[4:MRR:54041.2,78524.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_Procs,u),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.39 78585[7:MRR:54040.2,78524.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_Procs,u),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.39 78678[4:Res:78665.1,355.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))),v_x)** -> equal(v,w).
% 299.64/300.39 79071[0:Res:78077.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u) -> c_lessequals(v_Procs,c_Finite__Set_Olinorder__class_OMax(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u),u)*.
% 299.64/300.39 79072[0:Res:78077.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u),v_Procs,u)*.
% 299.64/300.39 79080[0:Res:78077.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,v_Procs,t_a).
% 299.64/300.39 79099[7:Res:78199.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_in(v),v_x),u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_in(v),v_x),u),u)*.
% 299.64/300.39 79100[7:Res:78199.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_in(v),v_x),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_in(v),v_x),u),v_x,u)*.
% 299.64/300.39 79110[7:Res:78199.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),v_x),t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.64/300.39 79928[0:SpR:23912.0,21268.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),u,v,w)),u)**.
% 299.64/300.39 80347[0:Rew:331.0,79873.0] || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w,u,x),w)**.
% 299.64/300.39 80348[0:Rew:330.0,79464.0] || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,x),w)**.
% 299.64/300.39 81122[0:SpR:23912.0,21894.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w)),u)**.
% 299.64/300.39 81542[0:Rew:331.0,81067.0] || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),u,x),v)**.
% 299.64/300.39 81543[0:Rew:330.0,80657.0] || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u,x),w)**.
% 299.64/300.39 82129[7:SpR:78597.0,9568.0] || -> c_lessequals(c_Set_Oinsert(v_x,u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a)),w),c_Set_Oinsert(v_x,u)),tc_bool)*.
% 299.64/300.39 82130[7:SpR:78597.0,9569.0] || -> c_lessequals(c_Set_Oinsert(v_x,u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_x,t_a)),c_Set_Oinsert(v_x,u)),tc_bool)*.
% 299.64/300.39 82154[7:SpR:78597.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Set_Oinsert(v_x,v)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.39 82160[7:SpR:78597.0,353.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v))),hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v)))**.
% 299.64/300.39 82168[7:SpR:78597.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,v),hAPP(c_Set_Oinsert(c_Set_Oinsert(v_x,w),u),x)),c_Set_Oinsert(v_x,w)))*.
% 299.64/300.39 82571[7:Res:82148.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(v_x,w),u,t_a,tc_fun(x,tc_bool)),v))*.
% 299.64/300.39 82663[0:Res:448.2,7671.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* -> c_lessequals(x,w,u)* c_lessequals(v,x,u)*.
% 299.64/300.39 82795[0:Obv:82679.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || equal(v,w)* c_lessequals(x,v,u)* -> c_lessequals(x,w,u)*.
% 299.64/300.39 83204[7:SpR:445.1,78357.0] || -> equal(v_x,u) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(v,u,w,x,y),z,x1),v_x),hAPP(v,v_x)))*.
% 299.64/300.39 83254[7:SpR:9935.1,78357.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),v_x),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.39 83258[7:SpR:9936.1,78357.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),v_x),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.39 83264[7:SpR:585.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBC(u,v,w,x),y),z,x1),v_x),hAPP(hAPP(u,v_x),y)))*.
% 299.64/300.39 83265[7:SpR:586.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),z,x1),v_x),hAPP(u,hAPP(y,v_x))))*.
% 299.64/300.39 83270[7:SpR:15172.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y,z),v_x),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.39 83272[7:SpR:27043.1,78357.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),v_x),v_x))*.
% 299.64/300.39 84193[7:SpL:88.1,78767.0] class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_x)** -> .
% 299.64/300.39 84214[7:SpL:9.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),v_x)** equal(c_Fun_Ocomp(u,v,w,x,y),v_x)** -> .
% 299.64/300.39 84286[0:SpL:9961.0,10287.0] || equal(c_Fun_Ofun__upd(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** -> equal(w,c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 84287[0:SpL:10540.0,10287.0] || equal(c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w,x,y),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> equal(w,c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.39 84294[0:SpL:23864.0,10287.0] || equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Obot__class_Obot(tc_bool),v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))** -> equal(v,u).
% 299.64/300.39 84295[0:SpL:23965.1,10287.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) equal(c_Fun_Ofun__upd(u,v_x,v,w,x),u)** -> equal(v,v_x).
% 299.64/300.39 84893[4:SpL:30928.2,78744.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(u),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.39 84894[4:SpL:30368.2,78744.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_Orderings_Otop__class_Otop(u),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.39 84907[4:SpL:337.0,78744.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,t_a)*.
% 299.64/300.39 85016[0:SpR:644.0,11064.1] || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w,tc_fun(v,tc_bool)),v)*.
% 299.64/300.39 85020[0:SpR:644.0,22513.1] || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),w)*.
% 299.64/300.39 85126[0:Rew:64216.1,85042.1,20920.0,85042.1] || c_Fun_Oinj__on(c_COMBK(u,v,tc_Com_Opname),v_Procs,tc_Com_Opname,v)* -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v_Procs)**.
% 299.64/300.39 85152[0:SpL:353.0,85001.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),w),v),w)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> .
% 299.64/300.39 85296[0:SpL:2097.1,26240.0] || hBOOL(hAPP(u,v))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.39 85467[4:SpR:78507.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,u),v,tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_bool)*.
% 299.64/300.39 85726[0:SpR:2097.1,9066.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u)))*.
% 299.64/300.39 85891[4:SSi:85883.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_Procs) -> .
% 299.64/300.39 85903[7:SSi:85895.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) -> .
% 299.64/300.39 85957[4:Res:78665.1,13582.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),v_x)** hBOOL(hAPP(hAPP(c_in(w),x),v)) -> .
% 299.64/300.39 86021[0:SpL:445.1,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)) equal(c_Fun_Ofun__upd(u,v,w,x,y),v_Procs)** -> equal(v_x,v).
% 299.64/300.39 86081[0:SpL:585.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool))* equal(hAPP(c_COMBC(u,w,x,y),v),v_Procs)** -> .
% 299.64/300.39 86082[0:SpL:586.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool))* equal(hAPP(c_COMBB(u,w,x,y),v),v_Procs)** -> .
% 299.64/300.39 86242[0:SpR:86109.1,9568.0] || equal(u,v_Procs) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a)),w),u),tc_bool)*.
% 299.64/300.39 86243[0:SpR:86109.1,9569.0] || equal(u,v_Procs) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_x,t_a)),u),tc_bool)*.
% 299.64/300.39 86274[0:SpR:86109.1,353.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(v,t_a),u)),hAPP(c_Set_Oinsert(v,t_a),u))**.
% 299.64/300.39 86282[0:SpR:86109.1,20881.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,v),x)),u))*.
% 299.64/300.39 86414[0:SpL:86109.1,55992.1] || equal(v_Procs,v_x) equal(c_COMBK(u,v,w),c_Set_Oinsert(v_x,t_a))** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u) -> .
% 299.64/300.39 86658[0:Res:86261.1,464.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_Procs) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,t_a)),v_x)**.
% 299.64/300.39 86659[0:Res:86261.1,469.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_Procs) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,t_a)),v_x)**.
% 299.64/300.39 86738[4:SpL:88.1,86106.0] class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_Procs)** -> .
% 299.64/300.39 86759[4:SpL:9.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),v_x)** equal(c_Fun_Ocomp(u,v,w,x,y),v_Procs)** -> .
% 299.64/300.39 87089[0:MRR:87052.1,379.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool))* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),w).
% 299.64/300.39 87162[7:Res:82177.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(w,t_a),c_Set_Oinsert(v_x,x)),u,t_a)))*.
% 299.64/300.39 87163[7:Res:82177.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,t_a),c_Set_Oinsert(v_x,w)),x,u,t_a)))*.
% 299.64/300.39 87280[7:SpR:15476.0,71492.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)),v))*.
% 299.64/300.39 87297[7:SpR:302.1,71492.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v))*.
% 299.64/300.39 87428[7:SpR:15476.0,71493.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)),v,t_a)*.
% 299.64/300.39 87445[7:SpR:302.1,71493.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.39 87518[0:SpR:3229.1,769.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)* -> equal(c_Fun_Ofun__upd(hAPP(v,v_x),v_x,v_x,w,x),hAPP(v,v_x))**.
% 299.64/300.39 87558[7:SpR:15476.0,71679.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)))*.
% 299.64/300.39 87575[7:SpR:302.1,71679.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 88430[0:Res:8176.1,437.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(v,w) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),w)*.
% 299.64/300.39 88601[7:SpL:8498.1,88086.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(w,v_x,tc_bool))* -> .
% 299.64/300.39 88616[7:SpL:27278.1,88086.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),v_x) hBOOL(c_HOL_Ominus__class_Ominus(w,v_x,tc_bool))* -> .
% 299.64/300.39 88617[7:SpL:3586.1,88086.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),v_x) hBOOL(c_HOL_Ominus__class_Ominus(w,v_x,tc_bool))* -> .
% 299.64/300.39 88631[7:SpL:2098.1,88086.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,v_x,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a).
% 299.64/300.39 88645[7:SpL:88.1,88086.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,c_Orderings_Otop__class_Otop(u),tc_bool))* -> .
% 299.64/300.39 88666[7:SpL:9.0,88086.1] || equal(c_Fun_Ocomp(u,v,w,x,y),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(z,hAPP(u,hAPP(v,v_x)),tc_bool))* -> .
% 299.64/300.39 88887[0:SpR:456.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Option_Othe(u),v,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_Option_Ooption_OSome(x,u)))*.
% 299.64/300.39 88889[0:SpR:351.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_COMBK(u,v,w),x,y),hAPP(c_Set_Oinsert(u,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),z))*.
% 299.64/300.39 88931[0:SpR:23912.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),u))*.
% 299.64/300.39 89062[0:Res:78099.0,277.1] || hBOOL(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,y)))*.
% 299.64/300.39 89063[0:Res:78099.0,278.1] || hBOOL(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,u,y)))*.
% 299.64/300.39 89115[7:SSi:89106.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Set_Oinsert(v_x,u),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)))* equal(c_COMBK(v_x,v,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 89323[7:SpR:78590.1,5875.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,t_a),w,x,y),u))*.
% 299.64/300.39 89356[7:SpR:78590.1,15630.1] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,w,v,t_a)))*.
% 299.64/300.39 89361[7:SpR:78590.1,9567.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,t_a),v,tc_fun(w,tc_bool)),u),u,tc_bool)*.
% 299.64/300.39 89425[7:SpR:78590.1,15858.1] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,u,v,t_a)))*.
% 299.64/300.39 89699[7:Res:89344.1,169.1] class_Orderings_Olinorder(t_a) || equal(c_Set_Oinsert(v_x,t_a),u) c_Finite__Set_Ofinite(u,t_a) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(u,t_a),t_a)*.
% 299.64/300.39 89700[7:Res:89344.1,170.1] class_Orderings_Olinorder(t_a) || equal(c_Set_Oinsert(v_x,t_a),u) c_Finite__Set_Ofinite(u,t_a) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(u,t_a),v_x,t_a)*.
% 299.64/300.39 89705[7:Res:89344.1,147.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(hAPP(c_in(t_a),v_x),v))* -> .
% 299.64/300.39 90113[4:SpR:78660.1,5875.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,t_a),w,x,y),u))*.
% 299.64/300.39 90146[4:SpR:78660.1,15630.1] || equal(hAPP(u,v_x),v_x) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,w,v,t_a)))*.
% 299.64/300.39 90151[4:SpR:78660.1,9567.0] || equal(hAPP(u,v_x),v_x) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,t_a),v,tc_fun(w,tc_bool)),u),u,tc_bool)*.
% 299.64/300.39 90215[4:SpR:78660.1,15858.1] || equal(hAPP(u,v_x),v_x) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,u,v,t_a)))*.
% 299.64/300.39 90474[4:SpR:539.1,90130.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))*.
% 299.64/300.39 90475[4:SpR:540.1,90130.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))*.
% 299.64/300.39 90843[4:Res:90134.1,169.1] class_Orderings_Olinorder(t_a) || equal(hAPP(u,v_x),v_x) c_Finite__Set_Ofinite(u,t_a) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(u,t_a),t_a)*.
% 299.64/300.39 90844[4:Res:90134.1,170.1] class_Orderings_Olinorder(t_a) || equal(hAPP(u,v_x),v_x) c_Finite__Set_Ofinite(u,t_a) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(u,t_a),v_x,t_a)*.
% 299.64/300.39 91326[0:Rew:91288.1,91251.2,91288.1,91251.1] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(c_Orderings_Obot__class_Obot(u)) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.39 91412[0:Res:91291.2,426.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(v,w,u)*.
% 299.64/300.39 91414[0:Res:91291.2,405.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> equal(v,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.39 91944[0:SpR:79073.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_Procs,u),v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),tc_bool)*.
% 299.64/300.39 92058[7:SpR:79101.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_in(u),v_x),v),c_Set_Oinsert(v_x,w),x,y,z),hAPP(c_in(u),v_x)))*.
% 299.64/300.39 92097[7:SpR:79101.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,u),v,tc_fun(w,tc_bool)),hAPP(c_in(x),v_x)),hAPP(c_in(x),v_x),tc_bool)*.
% 299.64/300.39 92604[7:SpR:15476.0,82151.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_in(t_a)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Set_Oinsert(v_x,v)))*.
% 299.64/300.39 92611[7:SpR:34428.0,82151.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,v)))*.
% 299.64/300.39 92621[7:SpR:302.1,82151.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Set_Oinsert(v_x,v)))*.
% 299.64/300.39 92622[7:SpR:331.0,82151.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,v)))*.
% 299.64/300.39 92651[7:SpR:11177.1,82151.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,v)))*.
% 299.64/300.39 92655[7:SpR:11176.1,82151.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a)) -> hBOOL(hAPP(u,c_Set_Oinsert(v_x,v)))*.
% 299.64/300.39 92657[7:SpR:14216.0,82151.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Set_Oinsert(v_x,x)))*.
% 299.64/300.39 92864[0:SpR:456.0,5876.0] || -> c_lessequals(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Option_Othe(w),x,y,z),c_Option_Ooption_OSome(u,w)),tc_fun(v,tc_bool))*.
% 299.64/300.39 93264[4:SpR:15476.0,85556.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v),tc_bool)*.
% 299.64/300.39 93271[4:SpR:34428.0,85556.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v_x,v),tc_bool)*.
% 299.64/300.39 93281[4:SpR:302.1,85556.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(c_Orderings_Otop__class_Otop(u),v),tc_bool)*.
% 299.64/300.39 93282[4:SpR:331.0,85556.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v_x,v),tc_bool)*.
% 299.64/300.39 93311[4:SpR:11177.1,85556.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v_x,v),tc_bool)*.
% 299.64/300.39 93315[4:SpR:11176.1,85556.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(u,v),tc_bool)*.
% 299.64/300.39 93317[4:SpR:14216.0,85556.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(c_Orderings_Otop__class_Otop(tc_bool),x),tc_bool)*.
% 299.64/300.39 93354[4:SpR:538.0,85556.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_bool)*.
% 299.64/300.39 93356[4:SpR:542.0,85556.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool)*.
% 299.64/300.39 93362[4:SpR:329.1,85556.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,u,tc_bool).
% 299.64/300.39 93452[0:SpR:15476.0,86147.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)),v))*.
% 299.64/300.39 93469[0:SpR:302.1,86147.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v))*.
% 299.64/300.39 93603[0:SpR:15476.0,86148.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)),v,t_a)*.
% 299.64/300.39 93620[0:SpR:302.1,86148.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.39 93747[0:SpR:15476.0,86342.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)))*.
% 299.64/300.39 93764[0:SpR:302.1,86342.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 94178[0:Res:14364.3,10429.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,c_Orderings_Obot__class_Obot(tc_bool)))* c_Finite__Set_Ofinite(u,tc_bool) -> equal(c_Finite__Set_Olinorder__class_OMin(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.39 94185[0:Res:14364.3,37920.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) hBOOL(c_Finite__Set_Olinorder__class_OMin(u,tc_bool)) -> hBOOL(v).
% 299.64/300.39 94200[0:MRR:94199.2,1088.0] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),w))* -> c_lessequals(v,w,u).
% 299.64/300.39 94311[0:Res:14491.3,37920.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) hBOOL(v) -> hBOOL(c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.64/300.39 94318[0:Res:14491.3,9857.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,c_Orderings_Otop__class_Otop(tc_bool)))* c_Finite__Set_Ofinite(u,tc_bool) -> equal(c_Finite__Set_Olinorder__class_OMax(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 94343[0:MRR:94342.2,1088.0] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),w))* -> c_lessequals(w,v,u).
% 299.64/300.39 689[0:Res:522.1,590.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(c_Suc(v_na)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(v_Q,v_x)),t_a)* -> .
% 299.64/300.39 945[0:SpR:302.1,415.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,c_Orderings_Otop__class_Otop(u),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))**.
% 299.64/300.39 1112[0:SpR:321.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oimage(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x,y),c_Set_Oimage(u,v,w))**.
% 299.64/300.39 1135[0:SpR:105.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Ovimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x,y),c_Set_Ovimage(u,v,w))**.
% 299.64/300.39 1143[0:SpR:331.0,651.0] || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.39 1142[0:SpR:302.1,651.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.39 1147[0:SpR:38.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Ovimage(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),x,y),c_Set_Ovimage(u,v,w))**.
% 299.64/300.39 1155[0:SpR:331.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.39 1154[0:SpR:302.1,648.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.39 1174[0:SpR:88.1,683.1] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,v),v)*.
% 299.64/300.39 1207[0:SpR:87.1,415.0] class_Lattices_Oboolean__algebra(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.64/300.39 1467[0:SpL:1409.2,134.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) equal(c_Orderings_Obot__class_Obot(u),v)* -> equal(v,c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.39 1690[0:SpL:1605.2,134.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,w) equal(c_HOL_Ouminus__class_Ouminus(v,u),w)* -> equal(w,c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.39 1786[0:SpL:1628.2,134.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,w) equal(c_HOL_Ouminus__class_Ouminus(v,u),w)* -> equal(w,c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.39 1891[0:SpR:9.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(v,hAPP(w,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Fun_Ocomp(v,w,x,y,z),tc_Com_Opname,u),u)*.
% 299.64/300.39 2154[0:SpR:140.1,47.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 2153[0:SpR:137.1,47.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 2203[0:SpR:2098.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,u),u)*.
% 299.64/300.39 2229[0:SpR:140.1,43.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 2228[0:SpR:137.1,43.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 2242[0:SpR:2089.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),v,w),c_Set_Oinsert(v_x,tc_Com_Opname))**.
% 299.64/300.39 2389[0:SpL:140.1,48.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 2388[0:SpL:137.1,48.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 2419[0:SpL:140.1,44.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 2418[0:SpL:137.1,44.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 2449[0:SpR:140.1,49.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)*.
% 299.64/300.39 2448[0:SpR:137.1,49.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)*.
% 299.64/300.39 2477[0:SpR:140.1,45.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)*.
% 299.64/300.39 2476[0:SpR:137.1,45.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)*.
% 299.64/300.39 2505[0:SpL:140.1,50.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 2504[0:SpL:137.1,50.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 2531[0:SpL:140.1,46.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 2530[0:SpL:137.1,46.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 2552[0:SpR:369.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(u,v),w),x,y),c_Set_Oinsert(u,v))**.
% 299.64/300.39 2633[0:SpL:2267.1,1815.1] || equal(u,v)* equal(u,v_Procs)* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.39 2641[0:SpR:337.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_Com_Opname,v),v_Procs),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.39 2679[0:Res:1103.1,2629.1] || equal(c_HOL_Ouminus__class_Ouminus(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(tc_Com_Opname),v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(tc_Com_Opname),v_x),t_a).
% 299.64/300.39 2704[0:SpL:2267.1,2675.0] || equal(hAPP(c_Set_Oimage(c_COMBK(v_x,u,v),tc_Com_Opname,tc_Com_Opname),v_Procs),w)* equal(c_HOL_Ouminus__class_Ouminus(w,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.39 2742[0:SpR:25.1,1158.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_Com_Opname,w),v_Procs),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)))*.
% 299.64/300.39 3093[0:Res:503.1,401.0] || c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,u),v,w)* c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u)),v,x)* -> equal(x,w)*.
% 299.64/300.39 3185[0:SpR:365.1,2771.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v)* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool))*.
% 299.64/300.39 3183[0:SpR:397.1,2771.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool))*.
% 299.64/300.39 3528[0:SpL:3229.1,1815.1] || equal(u,c_in(tc_Com_Opname)) equal(v,v_Procs) hBOOL(hAPP(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.39 3525[0:SpL:3229.1,2629.1] || equal(u,c_in(tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) hBOOL(hAPP(hAPP(u,v_x),v))* -> .
% 299.64/300.39 3520[0:SpL:3229.1,502.0] || equal(u,c_Com_Obody) c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(u,v_x)),v,w)* -> c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,v_x),v,w).
% 299.64/300.39 3474[0:SpR:3229.1,517.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(w,x))* -> hBOOL(hAPP(hAPP(u,v_x),x))*.
% 299.64/300.39 3473[0:SpR:3229.1,518.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(v_x,x)) -> hBOOL(hAPP(hAPP(u,v_x),x))*.
% 299.64/300.39 3472[0:SpR:3229.1,337.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* -> equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))*.
% 299.64/300.39 3470[0:SpR:3229.1,517.1] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))* hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(u,v_x))*.
% 299.64/300.39 3469[0:SpR:3229.1,518.1] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))* hBOOL(hAPP(x,v_x)) -> hBOOL(hAPP(u,v_x))*.
% 299.64/300.39 3464[0:SpR:3229.1,518.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)))* hBOOL(hAPP(w,x)) -> hBOOL(hAPP(hAPP(hAPP(u,v_x),w),x))*.
% 299.64/300.39 3433[0:SpR:3229.1,336.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) -> equal(hAPP(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.64/300.39 3409[0:SpR:3229.1,25.1] class_HOL_Ouminus(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u))) -> equal(hAPP(v,v_x),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u))*.
% 299.64/300.39 3403[0:SpR:3229.1,1588.0] || equal(u,c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(u,v_x),v,w),tc_Com_Opname,tc_fun(x,tc_bool)),v_Procs))*.
% 299.64/300.39 3390[0:SpR:3229.1,517.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)))* hBOOL(hAPP(v_x,w)) -> hBOOL(hAPP(hAPP(hAPP(u,v_x),x),w))*.
% 299.64/300.39 3381[0:SpR:3229.1,503.1] || equal(u,c_Com_Obody) c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,v_x),v,w) -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(u,v_x)),v,w)*.
% 299.64/300.39 3678[0:SpR:3229.1,540.1] class_Lattices_Olattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x),hAPP(hAPP(v,v_x),w))*.
% 299.64/300.39 3651[0:SpR:540.1,3229.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> equal(hAPP(v,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w))*.
% 299.64/300.39 3645[0:SpR:540.1,1158.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.39 3734[0:SpR:540.1,3283.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_Procs))*.
% 299.64/300.39 3723[0:SpR:25.1,3283.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),v_Procs))*.
% 299.64/300.39 3832[0:SpR:3229.1,539.1] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x),hAPP(hAPP(v,v_x),w))*.
% 299.64/300.39 3803[0:SpR:539.1,3229.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> equal(hAPP(v,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w))*.
% 299.64/300.39 3799[0:SpR:539.1,3283.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_Procs))*.
% 299.64/300.39 3796[0:SpR:539.1,1158.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.39 3881[0:Res:448.1,436.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,w))* -> c_lessequals(x,v,tc_fun(u,tc_bool))* hBOOL(hAPP(x,w))*.
% 299.64/300.39 3961[0:SpL:586.0,3506.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(z,x1),hAPP(u,hAPP(y,v_x)))* -> .
% 299.64/300.39 3960[0:SpL:585.0,3506.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(z,x1),hAPP(hAPP(u,v_x),y))* -> .
% 299.64/300.39 3937[0:SpL:445.1,3506.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(z,x1),hAPP(u,v_x))* -> equal(v_x,v).
% 299.64/300.39 4100[0:SpL:3229.1,298.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* equal(hAPP(v,v_x),v_x)** -> c_lessequals(w,v_x,u).
% 299.64/300.39 4098[0:SpL:3229.1,298.1] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u))* equal(hAPP(hAPP(v,v_x),w),w)** -> c_lessequals(v_x,w,u)*.
% 299.64/300.39 4154[0:SpL:9.0,3929.0] || hBOOL(hAPP(u,hAPP(v,v_x))) equal(c_Fun_Ocomp(u,v,w,x,y),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.64/300.39 4152[0:SpL:88.1,3929.0] class_Lattices_Oboolean__algebra(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.39 4234[0:SpR:3229.1,299.2] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u))* c_lessequals(w,v_x,u)* -> equal(hAPP(hAPP(v,v_x),w),v_x)**.
% 299.64/300.39 4200[0:SpR:299.2,3229.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> equal(hAPP(w,v_x),v)*.
% 299.64/300.39 4196[0:SpR:299.2,3283.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v,v_Procs)).
% 299.64/300.39 4193[0:SpR:299.2,1158.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v_Procs),v))*.
% 299.64/300.39 4329[0:SpR:3229.1,297.2] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u))* c_lessequals(v_x,w,u)* -> equal(hAPP(hAPP(v,v_x),w),w)**.
% 299.64/300.39 4294[0:SpR:297.2,3229.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> equal(hAPP(w,v_x),v_x)**.
% 299.64/300.39 4289[0:SpR:297.2,3283.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.39 4286[0:SpR:297.2,1158.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.39 4377[0:SpL:3229.1,371.0] || equal(u,hAPP(c_Set_Oinsert(v,w),x))* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(x,v_x)) equal(v,v_x).
% 299.64/300.39 4373[0:SpL:3229.1,371.0] || equal(u,c_Set_Oinsert(v,w))* hBOOL(hAPP(hAPP(u,v_x),x))* -> hBOOL(hAPP(v_x,x)) equal(v,x)*.
% 299.64/300.39 4398[0:Res:34.1,3929.0] || hBOOL(hAPP(u,hAPP(v,v_x))) equal(hAPP(c_Set_Ovimage(v,w,x),u),y)* -> hBOOL(hAPP(y,v_x))*.
% 299.64/300.39 4393[0:SpR:3229.1,34.1] || equal(u,c_Set_Ovimage(v,w,x))* hBOOL(hAPP(v_x,hAPP(v,y)))* -> hBOOL(hAPP(hAPP(u,v_x),y))*.
% 299.64/300.39 4415[0:SpR:331.0,3284.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),v_x))*.
% 299.64/300.39 4414[0:SpR:302.1,3284.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 4436[0:SpL:3229.1,33.0] || equal(u,hAPP(c_Set_Ovimage(v,w,x),y))* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(y,hAPP(v,v_x))).
% 299.64/300.39 4432[0:SpL:3229.1,33.0] || equal(u,c_Set_Ovimage(v,w,x))* hBOOL(hAPP(hAPP(u,v_x),y))* -> hBOOL(hAPP(v_x,hAPP(v,y)))*.
% 299.64/300.39 4462[0:SpL:302.1,3493.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.39 4485[0:SpR:5.2,52.2] class_Int_Onumber__ring(u) class_Ring__and__Field_Oidom(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,v,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 4533[0:Res:3316.1,371.0] || equal(c_in(u),c_Set_Oinsert(v,w))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))* equal(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))*.
% 299.64/300.39 4512[0:SpR:331.0,3316.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.39 4511[0:SpR:302.1,3316.1] class_Lattices_Obounded__lattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.39 4547[0:SpR:3586.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(hAPP(c_in(v),w),v_Procs) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(w,v),tc_Com_Opname,u),u)*.
% 299.64/300.39 4628[0:Res:111.2,50.1] class_OrderedGroup_Opordered__ab__group__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 4627[0:Res:111.2,46.1] class_OrderedGroup_Opordered__ab__group__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 4626[0:Res:111.2,48.1] class_OrderedGroup_Opordered__ab__group__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 4625[0:Res:111.2,44.1] class_OrderedGroup_Opordered__ab__group__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 4648[0:SpL:331.0,3698.2] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* equal(c_Com_Ocom_OBODY,u) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 4647[0:SpL:302.1,3698.2] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_Com_Ocom_OBODY,v) equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 4729[0:SpR:1605.2,4703.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.39 4727[0:SpR:1259.2,4703.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.39 4724[0:SpR:1421.2,4703.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)*.
% 299.64/300.39 4812[0:SpR:1605.2,4790.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 4810[0:SpR:1259.2,4790.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 4806[0:SpR:1409.2,4790.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u)) -> c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.39 4856[0:SpL:5.2,51.1] class_Int_Onumber__ring(u) class_Ring__and__Field_Oidom(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(v,v,u)*.
% 299.64/300.39 4943[0:Res:49.2,112.1] class_OrderedGroup_Olordered__ab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)*.
% 299.64/300.39 4942[0:Res:45.2,112.1] class_OrderedGroup_Oordered__ab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)*.
% 299.64/300.39 4939[0:Res:47.2,112.1] class_OrderedGroup_Olordered__ab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 4938[0:Res:43.2,112.1] class_OrderedGroup_Oordered__ab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 4967[0:Res:1103.1,3863.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),t_a) hBOOL(hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)))))*.
% 299.64/300.39 5023[0:SSi:4987.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),u).
% 299.64/300.39 5070[0:SpR:3229.1,83.0] || equal(u,c_Set_Ovimage(v,w,x)) -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),hAPP(u,v_x)),v_x,tc_fun(x,tc_bool))*.
% 299.64/300.39 5104[0:SpR:331.0,3339.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> equal(c_Fun_Ofun__upd(u,v_x,v_x,w,x),u)**.
% 299.64/300.39 5103[0:SpR:302.1,3339.1] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> equal(c_Fun_Ofun__upd(v,v_x,c_Orderings_Otop__class_Otop(u),w,x),v)**.
% 299.64/300.39 5226[0:SpL:3229.1,348.0] || equal(u,c_Com_Ocom_OBODY) c_Natural_Oevaln(hAPP(u,v_x),v,w,x)* -> equal(c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_x,w,v,x)),w).
% 299.64/300.39 5948[0:SpR:525.1,584.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y,z),v),hAPP(v,hAPP(w,v)))**.
% 299.64/300.39 5911[0:SpR:525.1,584.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),w),hAPP(hAPP(v,w),w))**.
% 299.64/300.39 5904[0:SpR:584.0,586.0] || -> equal(hAPP(c_COMBS(c_COMBB(u,v,w,x),y,z,x1,x2),x3),hAPP(u,hAPP(x3,hAPP(y,x3))))*.
% 299.64/300.39 5903[0:SpR:584.0,585.0] || -> equal(hAPP(c_COMBS(c_COMBC(u,v,w,x),y,z,x1,x2),x3),hAPP(hAPP(u,hAPP(y,x3)),x3))*.
% 299.64/300.39 5868[0:SpR:584.0,3229.1] || equal(u,c_COMBS(v,w,x,y,z))* -> equal(hAPP(u,v_x),hAPP(hAPP(v,v_x),hAPP(w,v_x)))*.
% 299.64/300.39 5862[0:SpR:584.0,3283.1] || equal(c_COMBS(u,v,w,x,y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),hAPP(v,v_x)),v_Procs))*.
% 299.64/300.39 5859[0:SpR:584.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,v,w,x,y),tc_Com_Opname,z),v_Procs),hAPP(hAPP(u,v_x),hAPP(v,v_x))))*.
% 299.64/300.39 6041[0:SpR:9.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(u,hAPP(v,w)),x),c_Fun_Ocomp(u,v,y,z,x1),x2,x3,x4),w))*.
% 299.64/300.39 6315[0:SpR:300.1,3279.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.39 6307[0:SpR:365.1,3279.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(u),v_Procs),v_x))*.
% 299.64/300.39 6305[0:SpR:397.1,3279.1] class_Orderings_Otop(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(t_a,u))) -> hBOOL(hAPP(hAPP(c_Orderings_Otop__class_Otop(u),v_Procs),v_x))*.
% 299.64/300.39 6303[0:SpR:2097.1,3279.1] || hBOOL(hAPP(v_x,u))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(u,v))* -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.39 6473[0:SpL:538.0,3483.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.39 6496[0:SpR:300.1,3285.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.39 6488[0:SpR:365.1,3285.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.39 6486[0:SpR:397.1,3285.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.39 6484[0:SpR:2097.1,3285.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.39 6674[0:SpL:329.1,3483.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 6734[0:SpR:300.1,3291.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),v_Procs))*.
% 299.64/300.39 6726[0:SpR:365.1,3291.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(u)),v_Procs))*.
% 299.64/300.39 6724[0:SpR:397.1,3291.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(u)),v_Procs))*.
% 299.64/300.39 6722[0:SpR:2097.1,3291.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),v_x),v_Procs))*.
% 299.64/300.39 6837[0:SpL:328.1,3483.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Com_Ocom_OBODY)** equal(u,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 6864[0:SpL:300.1,3484.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,v),v_x)** -> equal(v_x,v).
% 299.64/300.39 6856[0:SpL:365.1,3484.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(u),hAPP(c_Com_Ocom_OBODY,v))* -> equal(v_x,v).
% 299.64/300.39 6854[0:SpL:397.1,3484.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(u),hAPP(c_Com_Ocom_OBODY,v))* -> equal(v_x,v).
% 299.64/300.39 6852[0:SpL:2097.1,3484.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,w),v_x)** -> equal(v_x,w).
% 299.64/300.39 6900[0:SpL:300.1,3499.1] class_Lattices_Obounded__lattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))* hBOOL(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.39 6892[0:SpL:365.1,3499.1] class_Orderings_Obot(u) || equal(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(t_a,u))) hBOOL(hAPP(c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.39 6890[0:SpL:397.1,3499.1] class_Orderings_Otop(u) || equal(c_in(v),c_Orderings_Otop__class_Otop(tc_fun(t_a,u))) hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.39 6949[0:SpL:299.2,312.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_lessequals(v,w,u)* equal(w,c_Orderings_Obot__class_Obot(u)) -> equal(v,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.39 6976[0:SSi:6963.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* equal(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.64/300.39 7013[0:SpL:584.0,311.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),c_Orderings_Obot__class_Obot(u))** -> equal(z,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.39 7025[0:Rew:6945.3,6993.3] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(u))* -> equal(w,v_x).
% 299.64/300.39 7027[0:Rew:6991.3,6943.3] class_Lattices_Obounded__lattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) equal(hAPP(hAPP(v,v_x),w),c_Orderings_Obot__class_Obot(u))* -> equal(w,v_x).
% 299.64/300.39 7121[0:SpR:300.1,3305.1] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.39 7113[0:SpR:365.1,3305.1] class_Orderings_Obot(u) || equal(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,u))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.39 7111[0:SpR:397.1,3305.1] class_Orderings_Otop(u) || equal(v,c_Orderings_Otop__class_Otop(tc_fun(t_a,u))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 7109[0:SpR:2097.1,3305.1] || hBOOL(hAPP(v_x,u))* equal(v,c_Set_Oinsert(u,w))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,x),v_Procs),v_x))*.
% 299.64/300.39 7164[0:SpR:300.1,3317.1] class_Lattices_Obounded__lattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,v),w)))*.
% 299.64/300.39 7156[0:SpR:365.1,3317.1] class_Orderings_Obot(u) || equal(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(t_a,u))) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(u),hAPP(c_Set_Oinsert(v_x,v),w)))*.
% 299.64/300.39 7154[0:SpR:397.1,3317.1] class_Orderings_Otop(u) || equal(c_in(v),c_Orderings_Otop__class_Otop(tc_fun(t_a,u))) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),hAPP(c_Set_Oinsert(v_x,v),w)))*.
% 299.64/300.39 7152[0:SpR:2097.1,3317.1] || hBOOL(hAPP(v_x,u))* equal(c_in(v),c_Set_Oinsert(u,w))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,v),x)))*.
% 299.64/300.39 7246[0:SpR:2095.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(w,v),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.39 7239[0:SpR:330.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.39 7221[0:SpR:414.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,x,v,y,z),x1,u),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.64/300.39 7202[0:SpR:2093.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.39 7304[0:SpR:336.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.39 7277[0:SpR:331.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),x))*.
% 299.64/300.39 7257[0:SpR:3744.1,7253.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_Procs))*.
% 299.64/300.39 7318[0:SpL:365.1,3507.1] class_Orderings_Obot(u) || equal(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)))* equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.39 7316[0:SpL:397.1,3507.1] class_Orderings_Otop(u) || equal(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)))* equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.39 7456[0:Res:364.1,436.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(u,x))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,w),v),x))*.
% 299.64/300.39 7497[0:SpR:300.1,3346.1] class_Lattices_Obounded__lattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x))*.
% 299.64/300.39 7489[0:SpR:365.1,3346.1] class_Orderings_Obot(u) || equal(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,u))) -> hBOOL(hAPP(hAPP(c_in(w),v),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.39 7487[0:SpR:397.1,3346.1] class_Orderings_Otop(u) || equal(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(t_a,u))) -> hBOOL(hAPP(hAPP(c_in(w),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 7485[0:SpR:2097.1,3346.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(v,w),c_Set_Oinsert(u,x))* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x))*.
% 299.64/300.39 7713[0:SpR:584.0,293.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),w),u)*.
% 299.64/300.39 8019[0:SpL:584.0,295.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),x1,u)* -> c_lessequals(z,x1,u).
% 299.64/300.39 8147[0:Res:309.1,427.1] class_Lattices_Olattice(u) class_Orderings_Opreorder(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,u)* -> c_lessequals(w,x,u).
% 299.64/300.39 8144[0:Res:310.1,427.1] class_Lattices_Olattice(u) class_Orderings_Opreorder(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,u)* -> c_lessequals(v,x,u).
% 299.64/300.39 8201[0:Obv:8199.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),v)),u)*.
% 299.64/300.39 8202[0:Obv:8198.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x1)),u)*.
% 299.64/300.39 8205[0:SSi:8194.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),hAPP(c_Set_Oinsert(x1,v),u)),tc_fun(v,tc_bool))*.
% 299.64/300.39 8272[0:Res:309.1,426.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(v,w,u) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w),u)*.
% 299.64/300.39 8269[0:Res:310.1,426.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(v,w,u) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),u)*.
% 299.64/300.39 8307[0:SSi:8232.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v),tc_fun(w,tc_bool))*.
% 299.64/300.39 8308[0:SSi:8231.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),tc_fun(w,tc_bool))*.
% 299.64/300.39 8451[0:SpR:8385.1,584.0] || equal(u,v_Procs) -> equal(hAPP(c_COMBS(c_Set_Oinsert(v_x,tc_Com_Opname),v,w,x,y),u),hAPP(u,hAPP(v,u)))*.
% 299.64/300.39 8450[0:SpR:8385.1,584.0] || equal(u,v_Procs) -> equal(hAPP(c_COMBS(v,c_Set_Oinsert(v_x,tc_Com_Opname),w,x,y),u),hAPP(hAPP(v,u),u))*.
% 299.64/300.39 8449[0:SpR:8385.1,1103.1] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Oinsert(v_x,tc_Com_Opname),t_a)* hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oinsert(v_x,tc_Com_Opname))).
% 299.64/300.39 8591[0:SpR:8498.1,5875.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,w),c_Set_Oinsert(x,v),y,z,x1),u))*.
% 299.64/300.39 8579[0:SpR:8498.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v_x) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(w,v),tc_Com_Opname,u),u)*.
% 299.64/300.39 8957[0:SpL:8415.2,527.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u))* hBOOL(hAPP(v_x,v))* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.39 8940[0:SpL:8415.2,3506.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_Com_Ocom_OBODY,u) equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.39 8866[0:SpR:8415.2,309.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v,hAPP(v_x,v),u)*.
% 299.64/300.39 8865[0:SpR:8415.2,306.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v,hAPP(v_x,v),u)*.
% 299.64/300.39 8859[0:SpR:8415.2,310.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(v,v_x,u).
% 299.64/300.39 8858[0:SpR:8415.2,305.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(v,v_x,u).
% 299.64/300.39 8825[0:SpR:8415.2,310.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,hAPP(v_x,v),u)*.
% 299.64/300.39 8824[0:SpR:8415.2,305.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,hAPP(v_x,v),u)*.
% 299.64/300.39 8823[0:SpR:8415.2,301.1] class_Lattices_Obounded__lattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(u)),v_x)**.
% 299.64/300.39 8814[0:SpR:8415.2,526.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u))* hBOOL(hAPP(v,v_x))* -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.39 8775[0:SpR:8415.2,365.1] class_Orderings_Obot(u) || equal(v_Procs,v_x) equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(c_Orderings_Obot__class_Obot(u),v_x).
% 299.64/300.39 8773[0:SpR:8415.2,397.1] class_Orderings_Otop(u) || equal(v_Procs,v_x) equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(c_Orderings_Otop__class_Otop(u),v_x).
% 299.64/300.39 8748[0:SpR:8415.2,318.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname))** c_Finite__Set_Ofinite(v_x,v) -> c_Finite__Set_Ofinite(v_x,w).
% 299.64/300.39 9013[4:MRR:8991.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v,u),v_x),v_x)**.
% 299.64/300.39 9070[0:Res:1145.0,214.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_Set_Oinsert(v,u),w),x,y),tc_Com_Opname,tc_fun(u,tc_bool))))*.
% 299.64/300.39 9053[0:SpL:3744.1,214.0] || equal(c_in(tc_Com_Opname),c_in(u)) c_lessequals(v_Procs,v,tc_fun(u,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),v))*.
% 299.64/300.39 9198[0:SpR:336.0,8376.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(tc_Com_Opname)) equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_Procs) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))*.
% 299.64/300.39 9187[0:SpR:540.1,8376.2] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x))*.
% 299.64/300.39 9186[0:SpR:539.1,8376.2] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x))*.
% 299.64/300.39 9185[0:SpR:297.2,8376.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u)* equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) equal(v,v_Procs) -> hBOOL(v).
% 299.64/300.39 9155[0:SpR:300.1,8376.2] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.39 9146[0:SpR:365.1,8376.2] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_in(tc_Com_Opname)) equal(v,v_Procs) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(u),v))*.
% 299.64/300.39 9144[0:SpR:397.1,8376.2] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_in(tc_Com_Opname)) equal(v,v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v))*.
% 299.64/300.39 9140[0:SpR:2097.1,8376.2] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_in(tc_Com_Opname))** equal(w,v_Procs) -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.39 9304[0:SpR:538.0,9269.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool))* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)).
% 299.64/300.39 9839[0:SpR:98.1,59.1] || c_Fun_Oinj__on(u,v,w,x) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,w,x),v),x)* equal(c_Finite__Set_Ocard(v,w),c_HOL_Ozero__class_Ozero(tc_nat)).
% 299.64/300.39 9914[0:Rew:9911.0,6328.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x)).
% 299.64/300.39 9917[0:Rew:9911.0,6208.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y,z),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.39 10107[0:Res:1145.0,431.0] || c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v,w,x),tc_Com_Opname,tc_fun(y,tc_bool)),y,z)* -> c_Fun_Oinj__on(u,v,y,z).
% 299.64/300.39 10496[0:Res:267.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v),w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v),w),u,t_a)*.
% 299.64/300.39 10658[0:Res:288.1,505.0] || c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u)),v,w,x)* -> c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,c_Suc(c_Suc(w)),x).
% 299.64/300.39 10738[0:SpR:586.0,9566.0] || -> c_lessequals(hAPP(u,hAPP(v,w)),hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_COMBB(u,z,x1,x2),v)),w),tc_bool)*.
% 299.64/300.39 10737[0:SpR:585.0,9566.0] || -> c_lessequals(hAPP(hAPP(u,v),w),hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_COMBC(u,z,x1,x2),w)),v),tc_bool)*.
% 299.64/300.39 10693[0:SpR:8415.2,9566.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x),tc_bool)*.
% 299.64/300.39 10689[0:SpR:369.0,9566.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(c_Set_Oinsert(x,y),c_Set_Oinsert(u,v)),hAPP(c_Set_Oinsert(u,v),w)),tc_bool)*.
% 299.64/300.39 10688[0:SpR:2089.0,9566.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,tc_Com_Opname)),hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs)),tc_bool)*.
% 299.64/300.39 10683[0:SpR:445.1,9566.0] || -> equal(u,v) c_lessequals(hAPP(w,u),hAPP(hAPP(c_Set_Oinsert(x,y),c_Fun_Ofun__upd(w,v,z,x1,x2)),u),tc_bool)*.
% 299.64/300.39 10676[0:SpR:8415.2,9566.0] || equal(v_Procs,v_x) equal(hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(hAPP(w,v_x),v_x,tc_bool)*.
% 299.64/300.39 10768[0:Res:254.1,2629.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),u)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,tc_Com_Opname),u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.39 10900[0:SpL:353.0,2693.0] || equal(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),w)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.39 10871[0:SpR:2097.1,353.0] || hBOOL(hAPP(u,v)) -> equal(hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),u)),hAPP(c_Set_Oinsert(x,w),u))**.
% 299.64/300.39 10830[0:SpR:353.0,9566.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),w),x),hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(y,v),w)),x),tc_bool)*.
% 299.64/300.39 10927[0:SpR:8415.2,10813.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Set_Oinsert(u,v)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,v),v_x),u))*.
% 299.64/300.39 11032[0:SpR:9987.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.39 11268[0:SpL:11176.1,3698.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* equal(c_Com_Ocom_OBODY,v) equal(u,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 11266[0:SpL:11176.1,3493.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.39 11215[0:SpR:11176.1,3339.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)) -> equal(c_Fun_Ofun__upd(v,v_x,u,w,x),v)**.
% 299.64/300.39 11214[0:SpR:11176.1,3316.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)) -> hBOOL(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.39 11211[0:SpR:11176.1,648.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.39 11205[0:SpR:11176.1,3284.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),u))*.
% 299.64/300.39 11197[0:SpR:11176.1,651.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.39 11397[0:SpL:11177.1,3698.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* equal(c_Com_Ocom_OBODY,u) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 11372[0:SpR:11177.1,584.0] || equal(hAPP(u,v),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,w,x,y),v),hAPP(u,v))**.
% 299.64/300.39 11364[0:SpR:11177.1,7253.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u))*.
% 299.64/300.39 11343[0:SpR:11177.1,3339.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* -> equal(c_Fun_Ofun__upd(u,v_x,v_x,w,x),u)**.
% 299.64/300.39 11342[0:SpR:11177.1,3316.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.39 11339[0:SpR:11177.1,648.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.39 11333[0:SpR:11177.1,3284.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),v_x))*.
% 299.64/300.39 11325[0:SpR:11177.1,651.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.39 11637[0:SpR:9.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Fun_Ocomp(u,v,w,x,y),z,tc_fun(x1,tc_bool)),x2),hAPP(u,hAPP(v,x2)),tc_bool)*.
% 299.64/300.39 11632[0:SpR:105.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Ovimage(u,v,w),x,tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_bool)*.
% 299.64/300.39 11631[0:SpR:1196.1,9567.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.39 11628[0:SpR:38.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Ovimage(u,v,w),x,tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_bool)*.
% 299.64/300.39 11627[0:SpR:321.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oimage(u,v,w),x,tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_bool)*.
% 299.64/300.39 11625[0:SpR:1195.1,9567.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(u)),c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.39 11613[0:SpR:87.1,9567.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,u)),c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.39 11612[0:SpR:88.1,9567.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),w,tc_fun(x,tc_bool)),v),c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.39 11604[0:SpR:2098.1,9567.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,tc_fun(x,tc_bool)),v),v,tc_bool)*.
% 299.64/300.39 11594[0:SpR:3586.1,9567.0] || equal(hAPP(c_in(u),v),v_Procs) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v,u),w,tc_fun(x,tc_bool)),v_x),v_x,tc_bool)*.
% 299.64/300.39 11582[0:SpR:653.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),v,tc_fun(w,tc_bool)),v_Procs),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool)*.
% 299.64/300.39 11577[0:SpR:8498.1,9567.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(w,v),x,tc_fun(y,tc_bool)),u),u,tc_bool)*.
% 299.64/300.39 12049[0:Res:341.0,325.0] || -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),x)),tc_fun(v,tc_bool))*.
% 299.64/300.39 12400[0:Res:341.0,324.0] || -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),u)),tc_fun(v,tc_bool))*.
% 299.64/300.39 12970[0:Res:12960.1,123.0] || c_Natural_Oevalc(u,v,w)* c_Natural_Oevalc(x,w,y)* -> c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSemi(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSKIP),u),x),v,y)*.
% 299.64/300.39 12997[0:Res:3282.1,501.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Procs)** c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,v_x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a)*.
% 299.64/300.39 12991[0:Res:8375.1,501.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,w,t_a)*.
% 299.64/300.39 12980[0:Res:648.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oimage(v,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(v,v_x),t_a).
% 299.64/300.39 13107[0:SpL:10090.1,347.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_bool),u,w)* -> c_Fun_Oinj__on(v,v_x,u,w).
% 299.64/300.39 13082[0:SpR:11176.1,10090.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(u,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.39 13081[0:SpR:11177.1,10090.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 13065[0:SpR:331.0,10090.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 13064[0:SpR:302.1,10090.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 13032[0:SpR:10090.1,328.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_fun(u,tc_bool))* -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.39 13021[0:SpR:10090.1,7253.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.39 13246[0:SpR:9493.1,9567.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,t_a),v,tc_fun(w,tc_bool)),u),u,tc_bool)*.
% 299.64/300.39 13233[0:SpR:9493.1,5875.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,t_a),w,x,y),u))*.
% 299.64/300.39 13391[0:Res:13385.1,430.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) c_lessequals(u,w,tc_fun(v,tc_bool))* -> c_lessequals(x,w,tc_fun(v,tc_bool))*.
% 299.64/300.39 13438[0:Res:13387.1,325.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> c_lessequals(v,x,tc_fun(u,tc_bool))*.
% 299.64/300.39 13437[0:Res:13387.1,324.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> c_lessequals(w,x,tc_fun(u,tc_bool))*.
% 299.64/300.39 13473[0:SSi:13457.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) c_lessequals(w,u,tc_fun(v,tc_bool))* -> c_lessequals(w,x,tc_fun(v,tc_bool))*.
% 299.64/300.39 13559[0:Res:11030.1,371.0] || equal(c_Set_Oinsert(u,v),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))* equal(u,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))*.
% 299.64/300.39 13541[0:SpR:11176.1,11030.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a)) -> hBOOL(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.39 13540[0:SpR:11177.1,11030.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.39 13524[0:SpR:331.0,11030.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.39 13523[0:SpR:302.1,11030.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.39 13584[0:Res:13238.1,147.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)) -> .
% 299.64/300.39 13583[0:Res:8375.1,147.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** hBOOL(hAPP(hAPP(c_in(w),x),v))* -> .
% 299.64/300.39 13581[0:Res:652.1,147.1] || c_lessequals(v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v)) -> .
% 299.64/300.39 13616[0:SpR:11473.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_Com_Opname,u),u)*.
% 299.64/300.39 13676[0:SpR:11499.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.39 14287[0:SpL:14216.0,3698.2] || equal(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))* equal(c_Com_Ocom_OBODY,u) equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 14285[0:SpL:14216.0,3493.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_in(tc_Com_Opname))** equal(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.39 14264[0:SpR:14216.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.39 14253[0:SpR:14216.0,3339.1] || equal(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))* -> equal(c_Fun_Ofun__upd(u,v_x,c_Orderings_Otop__class_Otop(tc_bool),y,z),u)**.
% 299.64/300.39 14252[0:SpR:14216.0,3316.1] || equal(c_in(u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.39 14249[0:SpR:14216.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.39 14247[0:SpR:14216.0,11030.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.64/300.39 14246[0:SpR:14216.0,10090.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 14241[0:SpR:14216.0,3284.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.39 14233[0:SpR:14216.0,651.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_Com_Opname,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.39 14378[0:Res:3282.1,170.1] class_Orderings_Olinorder(u) || equal(hAPP(c_in(u),v),v_Procs) c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_x,u),v,u)*.
% 299.64/300.39 14373[0:Res:13238.1,170.1] class_Orderings_Olinorder(t_a) || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) c_Finite__Set_Ofinite(u,t_a) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(u,t_a),v_x,t_a)*.
% 299.64/300.39 14367[0:Res:8375.1,170.1] class_Orderings_Olinorder(u) || equal(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))) c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),w,u)*.
% 299.64/300.39 14353[0:Res:652.1,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) c_Finite__Set_Ofinite(u,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(u,tc_Com_Opname),v_x,tc_Com_Opname)*.
% 299.64/300.39 14413[0:SpR:12944.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)),tc_Com_Opname,u),u)*.
% 299.64/300.39 14505[0:Res:3282.1,169.1] class_Orderings_Olinorder(u) || equal(hAPP(c_in(u),v),v_Procs) c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(v_x,u),u)*.
% 299.64/300.39 14500[0:Res:13238.1,169.1] class_Orderings_Olinorder(t_a) || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) c_Finite__Set_Ofinite(u,t_a) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(u,t_a),t_a)*.
% 299.64/300.39 14494[0:Res:8375.1,169.1] class_Orderings_Olinorder(u) || equal(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))) c_Finite__Set_Ofinite(v,u) -> c_lessequals(w,c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.64/300.39 14480[0:Res:652.1,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool))* c_Finite__Set_Ofinite(u,tc_Com_Opname) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(u,tc_Com_Opname),tc_Com_Opname).
% 299.64/300.39 15255[0:SpR:10063.0,9566.0] || -> c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,t_a)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_bool)*.
% 299.64/300.39 15253[0:SpR:10063.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,v),c_Set_Oinsert(v_x,t_a))**.
% 299.64/300.39 15326[0:Res:63.1,103.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),w)* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(x,w),v),w)* -> c_Finite__Set_Ofinite(u,w).
% 299.64/300.39 15379[0:SpR:353.0,15367.0] || -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),hAPP(c_Set_Oinsert(u,v),x),tc_fun(v,tc_bool)),v)*.
% 299.64/300.39 15502[0:Rew:15475.0,15470.2] || equal(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)))* equal(c_Com_Ocom_OBODY,u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.39 15503[0:Rew:15475.0,15468.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_in(tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.39 15506[0:Rew:15475.0,15442.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)))*.
% 299.64/300.39 15507[0:Rew:15475.0,15435.0] || -> equal(c_Fun_Ofun__upd(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_x,c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v,w),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)))**.
% 299.64/300.39 15508[0:Rew:15475.0,15431.1] || equal(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool))) -> equal(c_Fun_Ofun__upd(u,v_x,c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),w,x),u)**.
% 299.64/300.39 15509[0:Rew:15475.0,15430.1] || equal(c_in(u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool))) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.39 15510[0:Rew:15475.0,15427.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.39 15511[0:Rew:15475.0,15425.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_in(t_a)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.39 15512[0:Rew:15475.0,15424.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.39 15513[0:Rew:15475.0,15419.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)))*.
% 299.64/300.39 15514[0:Rew:15475.0,15411.0] || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.39 15652[0:Res:168.0,278.1] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,w)))* -> c_Hoare__Mirabelle_Ohoare__valids(v,w,t_a) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,x,u,tc_Hoare__Mirabelle_Otriple(t_a))))*.
% 299.64/300.39 15651[0:Res:3282.1,278.1] || equal(hAPP(c_in(u),v),v_Procs)** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,x,w,u)))*.
% 299.64/300.39 15645[0:Res:13238.1,278.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,w,v,t_a)))*.
% 299.64/300.39 15639[0:Res:8375.1,278.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) hBOOL(hAPP(w,x))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,y,w,v)))*.
% 299.64/300.39 15637[0:Res:3284.1,278.1] || equal(c_in(tc_Com_Opname),u) hBOOL(hAPP(v,v_Procs)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(u,v_x),w,v,x)))*.
% 299.64/300.39 15627[0:Res:648.0,278.1] || hBOOL(hAPP(u,hAPP(v,v_x))) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),x,u,w)))*.
% 299.64/300.39 15625[0:Res:652.1,278.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,w,v,tc_Com_Opname)))*.
% 299.64/300.39 15623[0:Res:649.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs),w,u,tc_Com_Opname)))*.
% 299.64/300.39 15622[0:Res:650.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v),w,u,tc_Com_Opname)))*.
% 299.64/300.39 15788[0:SpR:302.1,15482.1] class_Lattices_Obounded__lattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)).
% 299.64/300.39 15880[0:Res:168.0,277.1] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,w)))* -> c_Hoare__Mirabelle_Ohoare__valids(v,w,t_a) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,w,u,tc_Hoare__Mirabelle_Otriple(t_a))))*.
% 299.64/300.39 15879[0:Res:3282.1,277.1] || equal(hAPP(c_in(u),v),v_Procs)** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_x,w,u)))*.
% 299.64/300.39 15873[0:Res:13238.1,277.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,u,v,t_a)))*.
% 299.64/300.39 15867[0:Res:8375.1,277.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) hBOOL(hAPP(w,x))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,u,w,v)))*.
% 299.64/300.39 15865[0:Res:3284.1,277.1] || equal(c_in(tc_Com_Opname),u) hBOOL(hAPP(v,v_Procs)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(u,v_x),v,x)))*.
% 299.64/300.39 15855[0:Res:648.0,277.1] || hBOOL(hAPP(u,hAPP(v,v_x))) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oimage(v,tc_Com_Opname,x),v_Procs),u,x)))*.
% 299.64/300.39 15853[0:Res:652.1,277.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,u,v,tc_Com_Opname)))*.
% 299.64/300.39 15851[0:Res:649.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs),u,tc_Com_Opname)))*.
% 299.64/300.39 15850[0:Res:650.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w),u,tc_Com_Opname)))*.
% 299.64/300.39 15929[2:SpR:331.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.39 15928[2:SpR:302.1,15483.1] class_Lattices_Obounded__lattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)).
% 299.64/300.39 16143[0:SpR:300.1,15262.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.39 16132[0:SpR:365.1,15262.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.39 16131[0:SpR:397.1,15262.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.39 16126[0:SpR:2097.1,15262.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.39 16266[0:SpL:9.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Fun_Ocomp(u,v,w,x,y),v_Procs)** -> .
% 299.64/300.39 16255[0:SpL:88.1,16217.0] class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_Procs)** -> .
% 299.64/300.39 16247[0:SpL:2098.1,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a).
% 299.64/300.39 16236[0:SpL:3586.1,16217.0] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(v,u),v_Procs) -> .
% 299.64/300.39 16224[0:SpL:8498.1,16217.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(v,u),v_Procs)** -> .
% 299.64/300.39 16362[0:SpL:584.0,16286.0] || equal(hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(c_COMBS(u,v,w,x,y),v_Procs)** -> .
% 299.64/300.39 16350[0:SpL:337.0,16286.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_Procs)** -> .
% 299.64/300.39 16345[0:SpL:540.1,16286.0] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> .
% 299.64/300.39 16344[0:SpL:539.1,16286.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> .
% 299.64/300.39 16334[0:SpL:299.2,16286.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(v,c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs)** -> .
% 299.64/300.39 16323[0:SpL:25.1,16286.0] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_Orderings_Obot__class_Obot(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_Procs) -> .
% 299.64/300.39 16464[0:SpL:9935.1,3506.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.39 16438[0:SpR:9935.1,584.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(u,v),tc_bool) -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,w,x,y),v),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.39 16488[2:Rew:3014.0,16383.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.39 16702[0:SpL:9936.1,3506.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(v,w),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.39 16725[2:Rew:3014.0,16619.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.39 17145[0:SpR:17045.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x,tc_fun(y,tc_bool)),z),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)*.
% 299.64/300.39 17127[0:SpR:17045.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)),tc_Com_Opname,u),u)*.
% 299.64/300.39 17270[0:SpL:365.1,13272.0] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.39 17269[0:SpL:397.1,13272.0] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.39 17421[0:SpL:365.1,16327.1] class_Orderings_Obot(u) || equal(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)))* equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(v,v_Procs) -> .
% 299.64/300.39 17420[0:SpL:397.1,16327.1] class_Orderings_Otop(u) || equal(v,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)))* equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(v,v_Procs) -> .
% 299.64/300.39 17745[0:Res:9258.0,255.0] || c_lessequals(u,v,tc_fun(t_a,tc_bool))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* hBOOL(hAPP(hAPP(c_in(t_a),v_x),v))*.
% 299.64/300.39 17933[0:SpL:584.0,11894.1] || equal(hAPP(u,v),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) hBOOL(hAPP(c_COMBS(c_in(w),u,x,y,z),v))* -> .
% 299.64/300.39 18018[0:Res:9258.0,263.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(u,t_a),v),v_x),tc_bool))* hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)) equal(v_x,u).
% 299.64/300.39 18292[0:SpL:15172.0,3506.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(y,z),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.39 18309[2:Rew:2990.0,18242.1] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 18423[0:Res:545.1,11894.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(hAPP(c_Set_Oimage(x,u,y),w),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))** -> .
% 299.64/300.39 18456[0:Res:9258.0,156.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Ovimage(u,t_a,v),w),v_x),tc_bool))* hBOOL(hAPP(hAPP(c_in(v),hAPP(u,v_x)),w)).
% 299.64/300.39 18488[4:MRR:18468.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(v_x,u).
% 299.64/300.39 18732[0:Res:9568.0,17530.1] || equal(hAPP(u,v),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.39 18703[0:SpR:301.1,9568.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),x),c_Orderings_Obot__class_Obot(u)),tc_bool)*.
% 299.64/300.39 18664[0:SpR:300.1,9568.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u))),x),v),tc_bool)*.
% 299.64/300.39 18653[0:SpR:365.1,9568.0] class_Orderings_Obot(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,u))),w),v_x),tc_bool)*.
% 299.64/300.39 18652[0:SpR:397.1,9568.0] class_Orderings_Otop(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(t_a,u))),w),v_x),tc_bool)*.
% 299.64/300.39 18639[0:SpR:2097.1,9568.0] || hBOOL(hAPP(u,v)) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Set_Oinsert(v,x)),y),u),tc_bool)*.
% 299.64/300.39 18637[0:SpR:584.0,9568.0] || -> c_lessequals(hAPP(u,hAPP(v,w)),hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),v,y,z,x1),w),tc_bool)*.
% 299.64/300.39 18745[0:SSi:18728.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),y,tc_bool)* -> c_lessequals(hAPP(v,x),y,tc_bool).
% 299.64/300.39 18746[0:SSi:18727.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(v,w),tc_bool) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),y),w),tc_bool)*.
% 299.64/300.39 18791[0:SSi:18775.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),v),v_Procs),w,tc_bool)* -> c_lessequals(v_Procs,w,tc_bool).
% 299.64/300.39 18792[0:SSi:18774.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v_Procs,tc_bool) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),w),v_Procs),tc_bool)*.
% 299.64/300.39 18831[0:SSi:18816.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),w,tc_bool)* -> c_lessequals(v_Procs,w,tc_bool).
% 299.64/300.39 18832[0:SSi:18815.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v_Procs,tc_bool) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.39 19043[0:Res:9569.0,17530.1] || equal(hAPP(u,v),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),v),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.39 19014[0:SpR:301.1,9569.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),c_Orderings_Obot__class_Obot(u)),tc_bool)*.
% 299.64/300.39 18975[0:SpR:300.1,9569.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u))),v),tc_bool)*.
% 299.64/300.39 18964[0:SpR:365.1,9569.0] class_Orderings_Obot(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Orderings_Obot__class_Obot(tc_fun(t_a,u))),v_x),tc_bool)*.
% 299.64/300.39 18963[0:SpR:397.1,9569.0] class_Orderings_Otop(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Orderings_Otop__class_Otop(tc_fun(t_a,u))),v_x),tc_bool)*.
% 299.64/300.39 18950[0:SpR:2097.1,9569.0] || hBOOL(hAPP(u,v)) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Set_Oinsert(v,y)),u),tc_bool)*.
% 299.64/300.39 18948[0:SpR:584.0,9569.0] || -> c_lessequals(hAPP(u,hAPP(v,u)),hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v,y,z,x1),u),tc_bool)*.
% 299.64/300.39 18937[0:SpR:584.0,9569.0] || -> c_lessequals(hAPP(hAPP(u,v),w),hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u,y,z,x1),v),w),tc_bool)*.
% 299.64/300.39 18932[0:SpR:600.0,9569.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v),x),tc_bool)*.
% 299.64/300.39 19056[0:SSi:19039.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),y,tc_bool)* -> c_lessequals(hAPP(w,x),y,tc_bool).
% 299.64/300.39 19057[0:SSi:19038.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(v,w),tc_bool) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),v),w),tc_bool)*.
% 299.64/300.39 19087[0:SSi:19071.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x)),x),y,tc_bool)* -> c_lessequals(x,y,tc_bool).
% 299.64/300.39 19088[0:SSi:19070.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v)),v),tc_bool)*.
% 299.64/300.39 19192[0:Res:11611.0,12626.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,y),z,tc_fun(x1,tc_bool)),x2),u,tc_bool)*.
% 299.64/300.39 19191[0:Res:11610.0,12626.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Option_Ooption_OSome(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(x,y,tc_bool),z,tc_bool),u)),x,tc_bool)*.
% 299.64/300.39 19245[0:Res:12627.1,17530.1] || c_lessequals(u,v,tc_bool)* equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v).
% 299.64/300.39 19255[0:SSi:19236.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(v,w,tc_bool)* -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,x,tc_bool),y,tc_bool),w,tc_bool)*.
% 299.64/300.39 19256[0:SSi:19235.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(w,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,x,tc_bool),y,tc_bool),tc_bool)* -> c_lessequals(w,v,tc_bool)*.
% 299.64/300.39 19260[0:Rew:19259.1,12927.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,tc_bool),tc_bool)* -> equal(c_HOL_Ominus__class_Ominus(u,x,tc_bool),u).
% 299.64/300.39 19405[0:Res:11611.0,12719.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,x),y,tc_fun(z,tc_bool)),x1),x2,tc_bool),u,tc_bool)*.
% 299.64/300.39 19404[0:Res:11610.0,12719.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Option_Ooption_OSome(c_HOL_Ominus__class_Ominus(x,y,tc_bool),u)),z,tc_bool),x,tc_bool)*.
% 299.64/300.39 19497[0:Res:19451.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,t_a),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,u,t_a)))*.
% 299.64/300.39 19496[0:Res:19451.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(w,t_a),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),u,t_a)))*.
% 299.64/300.39 19519[0:Res:19440.0,278.1] || hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,w),hAPP(c_in(tc_Com_Opname),v_x)),x,u,w)))*.
% 299.64/300.39 19518[0:Res:19440.0,277.1] || hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(w,x),hAPP(c_in(tc_Com_Opname),v_x)),u,x)))*.
% 299.64/300.39 19516[0:Res:19440.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Com_Opname),v_x))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_Procs,t_a).
% 299.64/300.39 19679[0:Res:168.0,496.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,v)),v))* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),t_a)*.
% 299.64/300.39 19650[0:Res:678.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_in(tc_Com_Opname),v_x))),hAPP(c_in(tc_Com_Opname),v_x)))* c_Hoare__Mirabelle_Otriple__valid(u,v_Procs,t_a).
% 299.64/300.39 19693[0:SpL:300.1,19641.0] class_Lattices_Obounded__lattice(u) || hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,t_a)*.
% 299.64/300.39 19891[0:SpL:104.0,346.0] || c_Fun_Oinj__on(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),x,y)* -> c_Fun_Oinj__on(u,w,x,y).
% 299.64/300.39 19884[0:SpL:104.0,333.0] || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),w).
% 299.64/300.39 20150[0:Res:19747.0,214.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))*.
% 299.64/300.39 20203[0:Res:20152.0,431.0] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(y,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),w,x)*.
% 299.64/300.39 20257[0:Res:20186.0,431.0] || c_Fun_Oinj__on(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),w,x) -> c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(y,v,tc_fun(w,tc_bool)),w,x)*.
% 299.64/300.39 20388[0:Rew:20312.1,20356.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.64/300.39 20713[0:SSi:20700.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Fun_Ofun__upd(x,y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),u),x1,x2)),y),tc_bool)*.
% 299.64/300.39 20714[0:SSi:20699.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Fun_Ofun__upd(x,y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),z),x1,x2)),y),tc_bool)*.
% 299.64/300.39 20715[0:SSi:20696.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,y,z,x1)),x),x2,tc_bool)* -> c_lessequals(y,x2,tc_bool).
% 299.64/300.39 20716[0:SSi:20695.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(w,x),c_Fun_Ofun__upd(y,z,v,x1,x2)),z),tc_bool)*.
% 299.64/300.39 20751[0:SpL:2267.1,9223.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)),u)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.39 20788[0:SpL:3229.1,16237.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(u,v_x),v_Procs)** -> .
% 299.64/300.39 20789[0:Obv:20786.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(v_Procs,v_x) -> .
% 299.64/300.39 20792[2:SpL:3229.1,16387.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(hAPP(u,v_x),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 20813[0:SpR:3229.1,19748.0] || equal(u,c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.64/300.39 20810[0:SpR:2267.1,19748.0] || equal(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v)* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.64/300.39 20902[0:SpR:317.0,19744.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oimage(u,v,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(w,v),x)),hAPP(c_Set_Oimage(u,v,tc_Hoare__Mirabelle_Otriple(t_a)),x),t_a)*.
% 299.64/300.39 20857[0:SpR:317.0,376.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(y,v),x)),tc_fun(w,tc_bool))*.
% 299.64/300.39 21103[0:SpR:2935.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_in(t_a),v_x),u,v),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),u),w)),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.39 21098[0:SpR:301.1,20881.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),w),y)),v))*.
% 299.64/300.39 21059[0:SpR:300.1,20881.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w),hAPP(c_Set_Oinsert(x,v),y)),x))*.
% 299.64/300.39 21048[0:SpR:365.1,20881.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.39 21047[0:SpR:397.1,20881.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 21030[0:SpR:2097.1,20881.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,w),x,y),hAPP(c_Set_Oinsert(u,x),z)),u))*.
% 299.64/300.39 21187[0:SpR:14216.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,y),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.39 21186[0:SpR:11176.1,21130.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_in(tc_Com_Opname),v_x)),u))*.
% 299.64/300.39 21184[0:SpR:11177.1,21130.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.39 21163[0:SpR:331.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,w),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.39 21162[0:SpR:302.1,21130.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 21153[0:SpR:3744.1,21130.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.39 21248[0:SpR:14216.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),t_a,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.39 21247[0:SpR:11176.1,21141.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u))*.
% 299.64/300.39 21245[0:SpR:11177.1,21141.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.39 21224[0:SpR:331.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.39 21223[0:SpR:302.1,21141.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 21210[0:SpR:15476.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)))*.
% 299.64/300.39 21270[0:Res:526.1,469.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),y))* -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,u,y,v,w)),y)**.
% 299.64/300.39 21587[0:SpL:21267.0,3587.0] || equal(hAPP(c_in(u),v_x),v_Procs) -> hBOOL(hAPP(v_x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,v)))*.
% 299.64/300.39 21527[0:SpR:414.0,21267.0] || -> equal(hAPP(c_Fun_Ofun__upd(u,v_x,v,w,x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ofun__upd(u,v_x,v,w,x),v,tc_Com_Opname,y)),v)**.
% 299.64/300.39 21518[0:SpR:524.0,21267.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v_x,tc_Com_Opname,v)),v_x)**.
% 299.64/300.39 21514[0:SpR:8415.2,21267.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,v)),v_x)**.
% 299.64/300.39 21439[0:SpR:21267.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,x)),hAPP(u,v_x),tc_bool)*.
% 299.64/300.39 21326[0:SpR:21267.0,267.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,v),u),w)))*.
% 299.64/300.39 21767[0:SpR:300.1,21143.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.39 21756[0:SpR:365.1,21143.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.39 21755[0:SpR:397.1,21143.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 21750[0:SpR:2097.1,21143.0] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.39 21836[0:SpR:300.1,21131.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.39 21825[0:SpR:365.1,21131.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.39 21824[0:SpR:397.1,21131.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 21819[0:SpR:2097.1,21131.0] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.39 21896[0:Res:526.1,464.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),y))* -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(x,y,u,v,w)),y)**.
% 299.64/300.39 22214[0:SpL:21893.0,3587.0] || equal(hAPP(c_in(u),v_x),v_Procs) -> hBOOL(hAPP(v_x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,v)))*.
% 299.64/300.39 22154[0:SpR:414.0,21893.0] || -> equal(hAPP(c_Fun_Ofun__upd(u,v_x,v,w,x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_Fun_Ofun__upd(u,v_x,v,w,x),tc_Com_Opname,y)),v)**.
% 299.64/300.39 22145[0:SpR:524.0,21893.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,v)),v_x)**.
% 299.64/300.39 22141[0:SpR:8415.2,21893.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,v)),v_x)**.
% 299.64/300.39 22065[0:SpR:21893.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,x)),hAPP(u,v_x),tc_bool)*.
% 299.64/300.39 21952[0:SpR:21893.0,267.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,v),u),w)))*.
% 299.64/300.39 22468[0:SpR:300.1,21126.1] class_Lattices_Obounded__lattice(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_Com_Opname,w),v),v_x))*.
% 299.64/300.39 22457[0:SpR:365.1,21126.1] class_Orderings_Obot(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,w),v),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.39 22456[0:SpR:397.1,21126.1] class_Orderings_Otop(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,w),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 22451[0:SpR:2097.1,21126.1] || hBOOL(hAPP(v_x,u)) equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(u,w),tc_Com_Opname,x),v),v_x))*.
% 299.64/300.39 22658[0:SpL:158.0,17944.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.39 22716[0:SpL:2267.1,19863.0] || equal(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Com_Opname,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))** -> .
% 299.64/300.39 22877[0:SpL:3294.1,347.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_Fun_Oinj__on(v,c_Orderings_Obot__class_Obot(tc_bool),u,w)* -> c_Fun_Oinj__on(v,v_x,u,w).
% 299.64/300.39 22804[0:SpR:525.1,3294.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(t_a))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 22800[0:SpR:3229.1,3294.1] || equal(u,v)* equal(c_in(t_a),v)* -> equal(hAPP(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 22786[0:SpR:3294.1,586.0] || equal(c_COMBB(u,v,w,x),c_in(t_a))** -> equal(hAPP(u,hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 22785[0:SpR:3294.1,585.0] || equal(c_COMBC(u,v,w,x),c_in(t_a))** -> equal(hAPP(hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 22758[0:SpR:3294.1,9568.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(t_a))** -> c_lessequals(hAPP(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)*.
% 299.64/300.39 22756[0:SpR:3294.1,9569.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(t_a))** -> c_lessequals(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)*.
% 299.64/300.39 22745[0:SpR:3294.1,7253.0] || equal(c_in(t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.39 23180[0:SpL:3229.1,3487.1] || equal(u,v)* equal(c_Set_Oinsert(v_x,tc_Com_Opname),v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.39 23310[0:SpL:586.0,3489.1] || equal(c_COMBB(u,v,w,x),c_in(tc_Com_Opname))** hBOOL(hAPP(u,hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)))))* -> .
% 299.64/300.39 23309[0:SpL:585.0,3489.1] || equal(c_COMBC(u,v,w,x),c_in(tc_Com_Opname))** hBOOL(hAPP(hAPP(u,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))),v_x))* -> .
% 299.64/300.39 23261[0:SpL:525.1,3489.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(tc_Com_Opname))** hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.39 23257[0:SpL:3229.1,3489.1] || equal(u,v)* equal(c_in(tc_Com_Opname),v)* hBOOL(hAPP(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.39 23594[0:SSi:23586.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),hAPP(v,v_x)))* -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(v,v_x)).
% 299.64/300.39 24215[0:SpR:3294.1,542.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 24392[0:MRR:24273.1,3591.0] || equal(c_COMBK(u,v,tc_Com_Opname),w) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(w,v_x)))*.
% 299.64/300.39 24415[0:SpR:8415.2,23916.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x,tc_Com_Opname,u),v_x)**.
% 299.64/300.39 24422[0:SpR:8415.2,23923.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v_x)**.
% 299.64/300.39 24485[0:SpR:8415.2,23937.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,tc_Com_Opname,u),v_Procs),v_x))*.
% 299.64/300.39 24493[0:SpL:8415.2,23942.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(v_x,u) -> equal(hAPP(u,v_x),v_x)**.
% 299.64/300.39 24685[0:SpL:24020.1,3499.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_in(v),hAPP(u,v_x))* hBOOL(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.39 24678[0:SpL:24020.1,3484.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,v),v_x)** -> equal(v_x,v).
% 299.64/300.39 24672[0:SpR:15172.0,24020.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_x),v_x).
% 299.64/300.39 24667[0:SpR:586.0,24020.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(u,hAPP(y,v_x)),v_x),v_x)**.
% 299.64/300.39 24666[0:SpR:585.0,24020.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(hAPP(u,v_x),y),v_x),v_x)**.
% 299.64/300.39 24661[0:SpR:9936.1,24020.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x),v_x).
% 299.64/300.39 24657[0:SpR:9935.1,24020.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x),v_x).
% 299.64/300.39 24623[0:SpR:8415.2,24020.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(v_x,v_x),v_x)**.
% 299.64/300.39 24617[0:SpR:445.1,24020.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(v_x,v) equal(hAPP(hAPP(u,v_x),v_x),v_x).
% 299.64/300.39 24569[0:SpR:24020.1,20881.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),v_x))*.
% 299.64/300.39 24549[0:SpR:24020.1,9569.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(u,v_x)),v_x),tc_bool)*.
% 299.64/300.39 24548[0:SpR:24020.1,9568.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(u,v_x)),w),v_x),tc_bool)*.
% 299.64/300.39 24534[0:SpR:24020.1,3346.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_Set_Oinsert(v,w),hAPP(u,v_x))* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x))*.
% 299.64/300.39 24533[0:SpR:24020.1,21126.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(u,v_x),tc_Com_Opname,w),v),v_x))*.
% 299.64/300.39 24532[0:SpR:24020.1,3317.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_in(v),hAPP(u,v_x))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,v),w)))*.
% 299.64/300.39 24531[0:SpR:24020.1,3305.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(v,hAPP(u,v_x))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.39 24522[0:SpR:24020.1,21131.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(u,v_x),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.39 24521[0:SpR:24020.1,21143.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(u,v_x),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.39 24518[0:SpR:24020.1,15262.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.39 24515[0:SpR:24020.1,8376.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.39 24513[0:SpR:24020.1,3291.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),v_Procs))*.
% 299.64/300.39 24512[0:SpR:24020.1,3285.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.39 24508[0:SpR:24020.1,3279.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),hAPP(u,v_x))* -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.39 24919[0:Res:3346.1,467.0] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(w,x,v)) -> equal(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(v_x,w,x,v),u)),u)**.
% 299.64/300.39 24912[0:Res:8366.1,467.0] || equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),v_Procs) -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,tc_Com_Opname),v_x)),v_x)**.
% 299.64/300.39 25098[0:SpL:23902.1,346.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Fun_Oinj__on(v,v_x,u,w) -> c_Fun_Oinj__on(v,c_Orderings_Obot__class_Obot(tc_bool),u,w)*.
% 299.64/300.39 25064[0:SpR:12944.0,23902.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.39 25058[0:SpR:9.0,23902.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(u,hAPP(v,v_x)),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.39 25057[0:SpR:11473.0,23902.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.39 25041[0:SpR:88.1,23902.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.39 25038[0:SpR:17045.0,23902.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.39 25029[0:SpR:2098.1,23902.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.39 25018[0:SpR:3586.1,23902.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.39 25005[0:SpR:8498.1,23902.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.39 25702[0:Res:264.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)* c_Hoare__Mirabelle_Otriple__valid(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,w,t_a)*.
% 299.64/300.39 25916[0:SpR:339.0,518.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u)),v))*.
% 299.64/300.39 26084[0:SpR:338.0,517.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),y)),v))*.
% 299.64/300.39 26323[0:SSi:26306.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(v,tc_bool)),v,w)* -> c_Fun_Oinj__on(u,v_x,v,w).
% 299.64/300.39 26706[0:MRR:26674.3,290.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(c_Finite__Set_Ocard(w,u),c_HOL_Ozero__class_Ozero(tc_nat)) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),w),u)*.
% 299.64/300.39 26786[0:Res:23997.0,12532.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ominus__class_Ominus(u,v,tc_bool)),w,tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_bool)),u,tc_bool)*.
% 299.64/300.39 27049[0:Res:23946.1,501.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,v_x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_Procs,t_a).
% 299.64/300.39 27104[0:Res:11029.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,t_a,tc_fun(x,tc_bool)),v))*.
% 299.64/300.39 27078[0:Res:264.0,280.1] || hBOOL(hAPP(hAPP(u,v),w))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,x,tc_fun(y,tc_bool)),w))*.
% 299.64/300.39 27075[0:Res:678.0,280.1] || hBOOL(hAPP(hAPP(u,v_Procs),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_in(tc_Com_Opname),v_x),u,w,tc_fun(x,tc_bool)),v))*.
% 299.64/300.39 27295[7:Res:27207.1,278.1] || equal(hAPP(c_in(u),v),v_x)** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,x,w,u)))*.
% 299.64/300.39 27294[7:Res:27207.1,277.1] || equal(hAPP(c_in(u),v),v_x)** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_x,w,u)))*.
% 299.64/300.39 27291[7:Res:27207.1,501.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)** c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,v_x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a)*.
% 299.64/300.39 27277[7:Res:27207.1,170.1] class_Orderings_Olinorder(u) || equal(hAPP(c_in(u),v),v_x) c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_x,u),v,u)*.
% 299.64/300.39 27276[7:Res:27207.1,169.1] class_Orderings_Olinorder(u) || equal(hAPP(c_in(u),v),v_x) c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(v_x,u),u)*.
% 299.64/300.39 27333[7:MRR:17364.3,27297.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v_x,u) equal(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMax(v_x,u)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.39 27334[7:MRR:17482.3,27297.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v_x,u) equal(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMin(v_x,u)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.39 27385[0:Res:3284.1,470.0] || equal(c_Set_Oimage(u,v,w),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_x,v_Procs,u,v,w)),v_x))*.
% 299.64/300.39 27420[7:SpL:21893.0,27279.0] || equal(hAPP(c_in(u),v_x),v_x) -> hBOOL(hAPP(v_x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,v)))*.
% 299.64/300.39 27419[7:SpL:21267.0,27279.0] || equal(hAPP(c_in(u),v_x),v_x) -> hBOOL(hAPP(v_x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,v)))*.
% 299.64/300.39 27445[0:Res:3284.1,466.0] || equal(c_Set_Oimage(u,v,w),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_x,u,v_Procs,v,w)),v_x))*.
% 299.64/300.39 27835[7:SpR:302.1,27219.1] class_Lattices_Obounded__lattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)).
% 299.64/300.39 27942[0:Res:468.0,11894.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) -> equal(hAPP(c_Set_Oimage(w,v,x),u),hAPP(c_Set_Oimage(y,v,x),u))*.
% 299.64/300.39 28036[0:Res:27381.0,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,u,tc_Com_Opname)))*.
% 299.64/300.39 28035[0:Res:27381.0,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.39 28030[0:Res:27381.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname)*.
% 299.64/300.39 28029[0:Res:27381.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.39 28013[0:SpR:14216.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_Com_Opname,x)),v_Procs))*.
% 299.64/300.39 28011[0:SpR:11176.1,27381.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.39 28007[0:SpR:11177.1,27381.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.39 27982[0:SpR:302.1,27381.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.39 27969[0:SpR:15476.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.39 28099[0:SpR:584.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_COMBS(u,v,w,x,y),tc_Com_Opname,z)))*.
% 299.64/300.39 28080[0:SpR:337.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_Com_Opname,v)))*.
% 299.64/300.39 28071[0:SpR:540.1,28032.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w)))*.
% 299.64/300.39 28070[0:SpR:539.1,28032.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w)))*.
% 299.64/300.39 28069[0:SpR:297.2,28032.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w)))*.
% 299.64/300.39 28060[0:SpR:299.2,28032.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w)))*.
% 299.64/300.39 28049[0:SpR:25.1,28032.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_Com_Opname,w)))*.
% 299.64/300.39 28113[0:SpR:8415.2,28090.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u)))*.
% 299.64/300.39 28339[0:Res:27441.0,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,u,tc_Com_Opname)))*.
% 299.64/300.39 28338[0:Res:27441.0,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.39 28333[0:Res:27441.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname)*.
% 299.64/300.39 28332[0:Res:27441.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.39 28316[0:SpR:14216.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x)),v_Procs))*.
% 299.64/300.39 28314[0:SpR:11176.1,27441.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),u,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.39 28310[0:SpR:11177.1,27441.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.39 28284[0:SpR:302.1,27441.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.39 28271[0:SpR:15476.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.39 28403[0:SpR:584.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(u,v,w,x,y),hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_Com_Opname,z)))*.
% 299.64/300.39 28384[0:SpR:337.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v)))*.
% 299.64/300.39 28374[0:SpR:540.1,28335.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_Com_Opname,w)))*.
% 299.64/300.39 28373[0:SpR:539.1,28335.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_Com_Opname,w)))*.
% 299.64/300.39 28372[0:SpR:297.2,28335.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x,tc_Com_Opname,w)))*.
% 299.64/300.39 28363[0:SpR:299.2,28335.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v,tc_Com_Opname,w)))*.
% 299.64/300.39 28352[0:SpR:25.1,28335.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_Com_Opname,w)))*.
% 299.64/300.39 28417[0:SpR:8415.2,28394.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u)))*.
% 299.64/300.39 28575[0:SpL:118.0,3706.0] || equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,v_x,w,x,y),y,z,x),c_Com_Ocom_OBODY)** equal(hAPP(u,w),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 28775[0:SpR:14216.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 28773[0:SpR:11176.1,28031.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 28769[0:SpR:11177.1,28031.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 28743[0:SpR:302.1,28031.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 28730[0:SpR:15476.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 28707[0:SpR:28031.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),w,tc_fun(x,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.39 28930[0:SpR:14216.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 28928[0:SpR:11176.1,28334.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),u,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 28924[0:SpR:11177.1,28334.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 28898[0:SpR:302.1,28334.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 28885[0:SpR:15476.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 28862[0:SpR:28334.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),w,tc_fun(x,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.39 29291[0:Rew:29289.0,20141.0] || -> c_lessequals(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.39 29419[7:SpL:27278.1,16217.0] || equal(hAPP(c_in(u),v),v_x)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(v,u),v_Procs) -> .
% 299.64/300.39 29400[7:SpR:27278.1,9567.0] || equal(hAPP(c_in(u),v),v_x) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v,u),w,tc_fun(x,tc_bool)),v_x),v_x,tc_bool)*.
% 299.64/300.39 29357[7:SpR:27278.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(hAPP(c_in(v),w),v_x) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(w,v),tc_Com_Opname,u),u)*.
% 299.64/300.39 29356[7:SpR:27278.1,23902.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.39 29943[0:SpL:27043.1,3506.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.39 29898[0:SpR:27043.1,9566.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_Procs,w)),v_x),tc_bool)*.
% 299.64/300.39 29896[0:SpR:27043.1,415.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_Procs,u),v_x,v_x,v,w),c_Set_Oinsert(v_Procs,u))**.
% 299.64/300.39 29861[0:SpR:27043.1,24020.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.39 31069[0:SpR:28771.0,9566.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.39 31155[0:SpR:28926.0,9566.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.39 31324[0:Res:31315.0,430.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.39 31335[0:SSi:31332.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),tc_fun(tc_Com_Opname,tc_bool))* -> c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)).
% 299.64/300.39 31498[0:SpL:24020.1,24254.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 31461[0:SpL:300.1,24254.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 31449[0:SpL:365.1,24254.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(u),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 31448[0:SpL:397.1,24254.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 31442[0:SpL:2097.1,24254.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 31843[7:SpL:9.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Fun_Ocomp(u,v,w,x,y),v_x)** -> .
% 299.64/300.39 31823[7:SpL:88.1,31778.0] class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_x)** -> .
% 299.64/300.39 31810[7:SpL:2098.1,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a).
% 299.64/300.39 31799[7:SpL:3586.1,31778.0] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(v,u),v_x) -> .
% 299.64/300.39 31798[7:SpL:27278.1,31778.0] || equal(hAPP(c_in(u),v),v_x)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(v,u),v_x) -> .
% 299.64/300.39 31785[7:SpL:8498.1,31778.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(v,u),v_x)** -> .
% 299.64/300.39 31936[7:SpL:584.0,31868.0] || equal(hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(c_COMBS(u,v,w,x,y),v_x)** -> .
% 299.64/300.39 31917[7:SpL:337.0,31868.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x)** -> .
% 299.64/300.39 31905[7:SpL:540.1,31868.0] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> .
% 299.64/300.39 31904[7:SpL:539.1,31868.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> .
% 299.64/300.39 31894[7:SpL:299.2,31868.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(v,c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)** -> .
% 299.64/300.39 31882[7:SpL:25.1,31868.0] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_Orderings_Obot__class_Obot(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_x) -> .
% 299.64/300.39 32189[0:Res:31323.0,17530.1] || equal(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(v_Procs,u),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 32193[0:SSi:32187.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(v_Procs,u),v,tc_bool) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u),v,tc_bool)*.
% 299.64/300.39 32194[0:SSi:32186.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v),tc_bool)* -> c_lessequals(u,hAPP(v_Procs,v),tc_bool).
% 299.64/300.39 32323[0:SpL:330.0,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),v))* -> hBOOL(hAPP(u,x))*.
% 299.64/300.39 32650[0:SpR:24020.1,31533.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(u,v_x),tc_Com_Opname,v),v_x)),v_Procs))*.
% 299.64/300.39 32601[0:SpR:365.1,31533.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,v),c_Orderings_Obot__class_Obot(u))),v_Procs))*.
% 299.64/300.39 32600[0:SpR:397.1,31533.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u))),v_Procs))*.
% 299.64/300.39 32594[0:SpR:2097.1,31533.0] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),v_x)),v_Procs))*.
% 299.64/300.39 32743[0:SpR:27043.1,32669.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),v_x)))*.
% 299.64/300.39 32741[0:SpR:15172.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),tc_Com_Opname,y),c_Orderings_Obot__class_Obot(tc_bool))))*.
% 299.64/300.39 32736[0:SpR:586.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_COMBB(u,v,w,x),y),tc_Com_Opname,z),hAPP(u,hAPP(y,v_x)))))*.
% 299.64/300.39 32735[0:SpR:585.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_COMBC(u,v,w,x),y),tc_Com_Opname,z),hAPP(hAPP(u,v_x),y))))*.
% 299.64/300.39 32729[0:SpR:9936.1,32669.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.39 32725[0:SpR:9935.1,32669.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.39 32686[0:SpR:8415.2,32669.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),v_x)))*.
% 299.64/300.39 32680[0:SpR:445.1,32669.0] || -> equal(v_x,u) hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ofun__upd(v,u,w,x,y),tc_Com_Opname,z),hAPP(v,v_x))))*.
% 299.64/300.39 32816[0:Rew:6.0,32793.2] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(v,u).
% 299.64/300.39 33085[0:Res:16776.0,94.1] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(v,u,w,x),u,x,w,w),v,w,w)*.
% 299.64/300.39 33087[0:Obv:33084.0] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(c_Fun_Ocomp(c_Fun_Othe__inv__into(v,u,w,x),u,x,w,w),v,w,w)*.
% 299.64/300.39 33112[0:Res:362.1,32232.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(w,tc_Com_Opname),u,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.39 33306[0:SpR:24020.1,32668.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(u,v_x),tc_Com_Opname,v),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 33257[0:SpR:365.1,32668.0] class_Orderings_Obot(u) || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,v),c_Orderings_Obot__class_Obot(u)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 33256[0:SpR:397.1,32668.0] class_Orderings_Otop(u) || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 33250[0:SpR:2097.1,32668.0] || hBOOL(hAPP(v_x,u)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 33210[0:SpR:32668.0,9566.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,w,tc_Com_Opname,x),hAPP(w,v_x)),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.39 33366[0:Res:23789.0,17530.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),w).
% 299.64/300.39 33379[0:SSi:33360.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,tc_fun(x,tc_bool)),u),v,tc_bool)*.
% 299.64/300.39 33380[0:SSi:33359.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,tc_fun(w,tc_bool)),x),tc_bool)* -> c_lessequals(u,x,tc_bool).
% 299.64/300.39 33464[0:Res:23882.0,17530.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),u).
% 299.64/300.39 33476[0:SSi:33458.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),v,tc_bool)*.
% 299.64/300.39 33477[0:SSi:33457.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool)* -> c_lessequals(u,v,tc_bool).
% 299.64/300.39 33592[0:SpR:24020.1,28704.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(u,v_x),tc_Com_Opname,w)))*.
% 299.64/300.39 33543[0:SpR:365.1,28704.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,w)))*.
% 299.64/300.39 33542[0:SpR:397.1,28704.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,w)))*.
% 299.64/300.39 33536[0:SpR:2097.1,28704.0] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(u,w),tc_Com_Opname,x)))*.
% 299.64/300.39 33683[0:SpR:24020.1,28859.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(u,v_x),v_x,tc_Com_Opname,w)))*.
% 299.64/300.39 33634[0:SpR:365.1,28859.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Orderings_Obot__class_Obot(u),tc_Com_Opname,w)))*.
% 299.64/300.39 33633[0:SpR:397.1,28859.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,w)))*.
% 299.64/300.39 33627[0:SpR:2097.1,28859.0] || hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,w),v_x,tc_Com_Opname,x)))*.
% 299.64/300.39 33725[7:SpL:365.1,31886.1] class_Orderings_Obot(u) || equal(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)))* equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(v,v_x) -> .
% 299.64/300.39 33724[7:SpL:397.1,31886.1] class_Orderings_Otop(u) || equal(v,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)))* equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(v,v_x) -> .
% 299.64/300.39 33822[0:SpR:8415.2,23864.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_Fun_Ofun__upd(v_x,c_Orderings_Obot__class_Obot(tc_bool),v_x,u,v),v_x)**.
% 299.64/300.39 34246[0:SpR:24020.1,24914.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(hAPP(u,v_x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(u,v_x),tc_Com_Opname,v),v_x)),v_x)**.
% 299.64/300.39 34208[0:SpR:525.1,24914.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x)),v_x)**.
% 299.64/300.39 34190[0:SpR:2097.1,24914.0] || hBOOL(hAPP(v_x,u)) -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),v_x)),v_x)**.
% 299.64/300.39 34017[0:SpR:24914.0,9566.0] || -> c_lessequals(hAPP(u,v_x),hAPP(hAPP(c_Set_Oinsert(v,w),u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,x),hAPP(u,v_x))),tc_bool)*.
% 299.64/300.39 33958[0:SpR:24914.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.39 34474[0:Rew:99.1,34100.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,x),hAPP(u,v_x)),v_x)**.
% 299.64/300.39 34558[0:SpR:34427.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.39 34602[0:SpR:55.1,423.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),v))*.
% 299.64/300.39 34763[0:SpL:34428.0,3698.2] || equal(u,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v))* equal(c_Com_Ocom_OBODY,u) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 34743[0:SpR:34428.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x))*.
% 299.64/300.39 34722[0:SpR:34428.0,3339.1] || equal(u,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v))* -> equal(c_Fun_Ofun__upd(u,v_x,v_x,w,x),u)**.
% 299.64/300.39 34721[0:SpR:34428.0,3316.1] || equal(c_in(u),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.39 34718[0:SpR:34428.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.39 34709[0:SpR:34428.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 34707[0:SpR:34428.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.39 34703[0:SpR:34428.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 34701[0:SpR:34428.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.39 34700[0:SpR:34428.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.39 34698[0:SpR:34428.0,11030.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.39 34697[0:SpR:34428.0,10090.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 34691[0:SpR:34428.0,3284.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),v_x))*.
% 299.64/300.39 34686[2:SpR:34428.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.39 34680[0:SpR:34428.0,651.0] || -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.39 34901[0:SpR:24020.1,28053.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(v,hAPP(u,v_x))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v,tc_Com_Opname,w)))*.
% 299.64/300.39 34864[0:SpR:300.1,28053.1] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v,tc_Com_Opname,w)))*.
% 299.64/300.39 34851[0:SpR:365.1,28053.1] class_Orderings_Obot(u) || equal(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,u))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(u),v,tc_Com_Opname,w)))*.
% 299.64/300.39 34850[0:SpR:397.1,28053.1] class_Orderings_Otop(u) || equal(v,c_Orderings_Otop__class_Otop(tc_fun(t_a,u))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),v,tc_Com_Opname,w)))*.
% 299.64/300.39 34844[0:SpR:2097.1,28053.1] || hBOOL(hAPP(v_x,u))* equal(v,c_Set_Oinsert(u,w))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v,tc_Com_Opname,x)))*.
% 299.64/300.39 34980[0:SpR:24020.1,28356.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(v,hAPP(u,v_x))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,v_x,tc_Com_Opname,w)))*.
% 299.64/300.39 34943[0:SpR:300.1,28356.1] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,v_x,tc_Com_Opname,w)))*.
% 299.64/300.39 34930[0:SpR:365.1,28356.1] class_Orderings_Obot(u) || equal(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,u))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,c_Orderings_Obot__class_Obot(u),tc_Com_Opname,w)))*.
% 299.64/300.39 34929[0:SpR:397.1,28356.1] class_Orderings_Otop(u) || equal(v,c_Orderings_Otop__class_Otop(tc_fun(t_a,u))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,c_Orderings_Otop__class_Otop(u),tc_Com_Opname,w)))*.
% 299.64/300.39 34923[0:SpR:2097.1,28356.1] || hBOOL(hAPP(v_x,u))* equal(v,c_Set_Oinsert(u,w))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,v_x,tc_Com_Opname,x)))*.
% 299.64/300.39 35026[0:SpR:28755.0,9566.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,w,c_COMBK(w,x,y),tc_Com_Opname,z),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.39 35115[0:SpR:28910.0,9566.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(w,x,y),w,tc_Com_Opname,z),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.39 35244[0:SpR:410.0,9568.0] || -> c_lessequals(hAPP(hAPP(u,v),w),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,x),y),u,x,tc_fun(z,tc_bool)),w),tc_bool)*.
% 299.64/300.39 36723[0:SpR:67.0,19748.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.64/300.39 36845[0:SpR:66.0,124.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.39 37569[0:SpR:11176.1,36690.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Set_Oinsert(v_x,t_a)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool))*.
% 299.64/300.39 37914[0:Res:37799.1,449.0] || hBOOL(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w)) -> c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)),t_a)*.
% 299.64/300.39 37924[0:SSi:37887.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v)))*.
% 299.64/300.39 37978[0:Res:37921.1,449.0] || hBOOL(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w)) -> c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)),t_a)*.
% 299.64/300.39 37993[0:SSi:37953.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)))*.
% 299.64/300.39 38192[0:SSi:38109.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(w,v,tc_bool)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w))* -> hBOOL(v).
% 299.64/300.39 38743[4:SpR:584.0,37987.1] || equal(c_COMBS(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),hAPP(v,v_x)),z))*.
% 299.64/300.39 38712[4:SpR:540.1,37987.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),w))*.
% 299.64/300.39 38711[4:SpR:539.1,37987.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),w))*.
% 299.64/300.39 38710[4:SpR:297.2,37987.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.39 38701[4:SpR:299.2,37987.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v,w))*.
% 299.64/300.39 38688[4:SpR:25.1,37987.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),w))*.
% 299.64/300.39 38932[4:SpR:584.0,38042.1] || equal(c_COMBS(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(u,v_x),hAPP(v,v_x)),z,t_a)*.
% 299.64/300.39 38901[4:SpR:540.1,38042.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),w,t_a)*.
% 299.64/300.39 38900[4:SpR:539.1,38042.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),w,t_a)*.
% 299.64/300.39 38899[4:SpR:297.2,38042.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,w,t_a)*.
% 299.64/300.39 38890[4:SpR:299.2,38042.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(v,w,t_a)*.
% 299.64/300.39 38877[4:SpR:25.1,38042.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),w,t_a)*.
% 299.64/300.39 39371[0:SSi:39370.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.64/300.39 40025[4:SpR:8415.2,38566.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(v_x,v)))*.
% 299.64/300.39 40394[4:SSi:40359.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),u),v))* c_Finite__Set_Ofinite(v,tc_bool) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x,v,tc_bool,tc_bool))*.
% 299.64/300.39 40465[4:SpL:8415.2,40434.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(v_x,u),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(v)*.
% 299.64/300.39 40507[4:SpL:8415.2,40105.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(hAPP(v_x,u),v,tc_bool)* -> hBOOL(v).
% 299.64/300.39 40611[4:SSi:40578.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),v_x),u)) c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,u,tc_bool,tc_bool))*.
% 299.64/300.39 41507[4:SpR:12944.0,38236.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,tc_bool)).
% 299.64/300.39 41501[4:SpR:9.0,38236.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(u,hAPP(v,v_x)),tc_Com_Opname,tc_bool))*.
% 299.64/300.39 41500[4:SpR:11473.0,38236.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,tc_bool)).
% 299.64/300.39 41480[4:SpR:88.1,38236.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(u),tc_Com_Opname,tc_bool))*.
% 299.64/300.39 41477[4:SpR:17045.0,38236.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,tc_bool)).
% 299.64/300.39 42747[0:Rew:331.0,42714.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(w,v,tc_fun(u,tc_bool)))**.
% 299.64/300.39 42749[0:Rew:330.0,42699.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)))**.
% 299.64/300.39 44232[0:SSi:44224.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(v_Procs,v_x))))*.
% 299.64/300.39 44273[0:SSi:44253.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v_Procs,v_x)),v)))*.
% 299.64/300.39 44526[0:SSi:44505.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v))* equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_Procs,u,tc_bool)).
% 299.64/300.39 44527[0:SSi:44492.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(v_Procs,v_x),u,tc_bool) equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v))*.
% 299.64/300.39 44528[0:SSi:44489.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(v_Procs,v_x),u,tc_bool) equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u))*.
% 299.64/300.39 44643[0:SpR:584.0,35656.1] || equal(hAPP(u,v),v_Procs) -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u,w,x,y),v),v_x))*.
% 299.64/300.39 44626[0:SpR:600.0,35656.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_x))*.
% 299.64/300.39 44752[0:SpR:486.1,36599.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),u,tc_fun(x,tc_bool)),v_x))*.
% 299.64/300.39 45360[0:Con:45344.3] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)))*.
% 299.64/300.39 45714[0:SpR:410.0,44625.1] || equal(hAPP(u,v),v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),u,w,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.39 45976[0:Res:212.1,45899.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Set_Oinsert(v,w),u),tc_Com_Opname)))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x)).
% 299.64/300.39 45962[0:Res:8375.1,45899.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)).
% 299.64/300.39 46252[0:SpR:584.0,37923.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,x,y,z),v)))*.
% 299.64/300.39 46314[0:SSi:46290.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u))))*.
% 299.64/300.39 46418[0:SSi:46393.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x))))*.
% 299.64/300.39 46663[4:SpL:14216.0,46565.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.39 46661[4:SpL:11176.1,46565.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),u)* -> .
% 299.64/300.39 46628[4:SpL:302.1,46565.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(u))* -> .
% 299.64/300.39 46613[4:SpL:15476.0,46565.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* -> .
% 299.64/300.39 47119[0:Res:23997.0,38189.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),u))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u))*.
% 299.64/300.39 47118[0:Res:11611.0,38189.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),z))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x1),u))*.
% 299.64/300.39 47117[0:Res:11610.0,38189.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Option_Ooption_OSome(x,u)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),x))*.
% 299.64/300.39 47164[0:SSi:47050.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),x)))*.
% 299.64/300.39 47165[0:SSi:47047.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v)))*.
% 299.64/300.39 47511[4:Res:10705.0,47318.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool),y,z)),x))*.
% 299.64/300.39 47551[4:SSi:47540.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool))))*.
% 299.64/300.39 47685[4:SSi:47664.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool)),v)))*.
% 299.64/300.39 47735[4:SSi:47706.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool),u,tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v))*.
% 299.64/300.39 47736[4:SSi:47703.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool),u,tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u))*.
% 299.64/300.39 47839[0:Res:23997.0,38190.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),u))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x))*.
% 299.64/300.39 47838[0:Res:11611.0,38190.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),z))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x1))*.
% 299.64/300.39 47837[0:Res:11610.0,38190.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Option_Ooption_OSome(x,u)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),y))*.
% 299.64/300.39 48156[4:SpR:24020.1,39023.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),x))*.
% 299.64/300.39 48118[4:SpR:300.1,39023.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),x))*.
% 299.64/300.39 48105[4:SpR:365.1,39023.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(u)),x))*.
% 299.64/300.39 48104[4:SpR:397.1,39023.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(u)),x))*.
% 299.64/300.39 48098[4:SpR:2097.1,39023.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),v_x),y))*.
% 299.64/300.39 48271[4:SpR:24020.1,39064.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),v_x),x,t_a)*.
% 299.64/300.39 48233[4:SpR:300.1,39064.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),v_x),x,t_a)*.
% 299.64/300.39 48220[4:SpR:365.1,39064.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(u)),x,t_a)*.
% 299.64/300.39 48219[4:SpR:397.1,39064.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(u)),x,t_a)*.
% 299.64/300.39 48213[4:SpR:2097.1,39064.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),v_x),y,t_a)*.
% 299.64/300.39 48524[4:SSi:48497.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),v_x))))*.
% 299.64/300.39 48586[4:SSi:48548.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),z))))*.
% 299.64/300.39 48721[4:SpR:317.0,42357.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,tc_fun(z,tc_bool)),v_x))*.
% 299.64/300.39 49024[0:Res:48989.1,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,v,tc_Com_Opname)))* -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,u,tc_Com_Opname)))*.
% 299.64/300.39 49023[0:Res:48989.1,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,v,tc_Com_Opname)))* -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.39 49016[0:Res:48989.1,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> hBOOL(hAPP(u,v_x)) c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.39 49015[0:Res:48989.1,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> hBOOL(hAPP(u,v_x)) c_lessequals(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.39 49082[0:SpR:49017.1,9567.0] || -> hBOOL(hAPP(u,v_x)) c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,tc_fun(w,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.39 49378[0:SpR:49342.1,9566.0] || hBOOL(hAPP(u,v_x)) -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.39 50299[0:SpL:584.0,46309.0] || c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),y),z,tc_bool)* hBOOL(hAPP(u,y)) -> hBOOL(z).
% 299.64/300.39 50377[0:SSi:50345.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(v) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u,tc_bool))*.
% 299.64/300.39 50378[0:SSi:50332.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool)* hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x))*.
% 299.64/300.39 50379[0:SSi:50329.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool)* hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),w))*.
% 299.64/300.39 50380[0:SSi:50290.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),x,tc_bool)* hBOOL(w) -> hBOOL(x).
% 299.64/300.39 50580[0:SSi:50548.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(w) -> hBOOL(x)*.
% 299.64/300.39 50641[0:SSi:50609.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(v) -> hBOOL(x)*.
% 299.64/300.39 50759[0:SSi:50728.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(x) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u,tc_bool))*.
% 299.64/300.39 50760[0:SSi:50715.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool)* hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x))*.
% 299.64/300.39 50761[0:SSi:50712.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool)* hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),w))*.
% 299.64/300.39 50762[0:SSi:50670.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),x,tc_bool)* hBOOL(v) -> hBOOL(x).
% 299.64/300.39 51083[0:SSi:50956.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(u) -> hBOOL(x)*.
% 299.64/300.39 51084[0:SSi:50953.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(u) -> hBOOL(x)*.
% 299.64/300.39 51369[0:SpR:24020.1,51231.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(v,t_a),hAPP(u,v_x)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 51330[0:SpR:300.1,51231.0] class_Lattices_Obounded__lattice(u) || -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 51316[0:SpR:365.1,51231.0] class_Orderings_Obot(u) || -> equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(u),hAPP(hAPP(c_Set_Oinsert(v,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,u))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 51315[0:SpR:397.1,51231.0] class_Orderings_Otop(u) || -> equal(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,t_a),c_Orderings_Otop__class_Otop(tc_fun(t_a,u))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 51309[0:SpR:2097.1,51231.0] || hBOOL(hAPP(v_x,u)) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(v,t_a),c_Set_Oinsert(u,w)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 51424[0:Rew:15569.0,51378.0] || -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 51425[0:Rew:15569.0,51371.0] || -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 51837[4:SpR:584.0,40792.1] || c_lessequals(v_x,hAPP(u,hAPP(v,u)),tc_bool)* -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(w,x),v,y,z,x1),u))*.
% 299.64/300.39 52133[0:Res:23997.0,50366.0] || c_lessequals(u,v,tc_bool)* hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,tc_fun(x,tc_bool)),u))* -> hBOOL(v).
% 299.64/300.39 52132[0:Res:11611.0,50366.0] || c_lessequals(u,v,tc_bool)* hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(u,w,x),y,tc_fun(z,tc_bool)),x1))* -> hBOOL(v).
% 299.64/300.39 52131[0:Res:11610.0,50366.0] || c_lessequals(u,v,tc_bool)* hBOOL(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(w),x,tc_fun(y,tc_bool)),c_Option_Ooption_OSome(u,w)))* -> hBOOL(v).
% 299.64/300.39 52157[0:SSi:52065.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),x,tc_bool)* hBOOL(u) -> hBOOL(x).
% 299.64/300.39 52158[0:SSi:52062.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v),x,tc_bool)* hBOOL(u) -> hBOOL(x).
% 299.64/300.39 52301[0:Res:362.1,35720.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(x,y),u,tc_fun(y,tc_bool)),x))*.
% 299.64/300.39 52515[4:MRR:52497.2,6340.0] || equal(v_Procs,v_x) equal(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(u).
% 299.64/300.39 52624[0:SpR:2771.1,23320.1] || equal(u,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))) equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.39 52612[0:SpR:2267.1,23320.1] || equal(v_Procs,u) equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_x),tc_bool))*.
% 299.64/300.39 52625[0:SSi:52621.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_x))* equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))*.
% 299.64/300.39 52707[2:SpL:2267.1,23734.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.39 52713[0:Res:23944.1,3929.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** equal(hAPP(v_x,v_Procs),u) -> hBOOL(hAPP(u,v_x))*.
% 299.64/300.39 52881[0:SpL:2267.1,31349.0] || equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_Com_Opname),v_Procs),u)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.39 52872[0:SpL:3229.1,31349.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(hAPP(u,v_x),tc_Com_Opname,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.39 53001[0:Res:23739.1,3929.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(hAPP(c_in(u),v_Procs),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.39 53136[0:SpR:8415.2,53111.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u),v_x,tc_bool)*.
% 299.64/300.39 53158[0:Res:23956.0,3929.0] || equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),t_a,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.39 53254[0:SpR:8415.2,53243.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u),v_x,tc_bool)*.
% 299.64/300.39 53347[0:SpL:3229.1,25019.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)))* equal(hAPP(u,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.39 53353[0:SpR:3229.1,31543.0] || equal(u,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(u,v_x)),v_Procs))*.
% 299.64/300.39 53374[7:SpL:3229.1,31800.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(u,v_x),v_x)** -> .
% 299.64/300.39 53480[0:SpL:33303.0,35720.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x)))*.
% 299.64/300.39 53464[0:SpR:3229.1,33303.0] || equal(u,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v))* -> equal(hAPP(c_Set_Oinsert(hAPP(u,v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 53455[0:SpR:33303.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x)))*.
% 299.64/300.39 53451[0:SpR:33303.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.39 53449[0:SpR:33303.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),v_x))))*.
% 299.64/300.39 53514[0:SpL:3229.1,36115.0] || equal(u,c_HOL_Ominus__class_Ominus(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)))* equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.39 53527[0:Res:364.1,4247.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* -> equal(hAPP(c_Set_Oinsert(w,u),v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.39 53748[0:SpR:3229.1,7226.0] || equal(u,c_in(v)) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(c_Option_Othe(w),x,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.39 53791[0:SpR:53771.0,9566.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),u,c_Option_Othe(x),y,z)),tc_bool)*.
% 299.64/300.39 53822[0:SpR:53772.0,9566.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Option_Othe(x),u,y,z)),tc_bool)*.
% 299.64/300.39 53918[0:SpR:3229.1,51366.0] || equal(u,hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))* -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(u,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 54179[0:SpL:52997.1,35720.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) c_lessequals(v_x,u,tc_fun(v,tc_bool))* -> hBOOL(hAPP(u,v_Procs)).
% 299.64/300.39 54151[0:SpR:52997.1,21035.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),v_x),v_Procs))*.
% 299.64/300.39 54147[0:SpR:52997.1,26119.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),v_Procs))*.
% 299.64/300.39 54139[0:SpR:52997.1,9067.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oinsert(v,u),v_x)))*.
% 299.64/300.39 54138[0:SpR:52997.1,20881.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),v_x),hAPP(u,v_Procs)))*.
% 299.64/300.39 54100[4:SpR:52997.1,48288.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.39 54099[4:SpR:52997.1,48173.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.39 54083[0:SpR:52997.1,3229.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(u,c_Set_Oinsert(v_Procs,v))* -> equal(hAPP(u,v_x),v_x)**.
% 299.64/300.39 54068[0:SpR:52997.1,28032.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v)))*.
% 299.64/300.39 54062[0:SpR:52997.1,28335.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_Procs,u),v_x,tc_Com_Opname,v)))*.
% 299.64/300.39 54038[0:SpR:52997.1,1158.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.39 54256[0:SpR:2267.1,8667.0] || equal(u,v) -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),u,tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)))**.
% 299.64/300.39 54832[0:SpR:3229.1,13749.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(v,v_x),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 54815[0:SpR:13749.2,8376.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) equal(c_Orderings_Otop__class_Otop(u),v_Procs) -> hBOOL(c_Orderings_Otop__class_Otop(u))*.
% 299.64/300.39 54967[0:SpR:2771.1,54650.0] || equal(u,v) -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(v,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))**.
% 299.64/300.39 55040[0:SpR:2771.1,54699.1] || equal(u,v)* equal(w,hAPP(v,v_x))* -> equal(c_HOL_Ominus__class_Ominus(w,c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),tc_bool),w)**.
% 299.64/300.39 55307[0:SpR:3229.1,14043.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(v,v_x),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 55289[0:SpR:14043.2,8376.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) equal(c_Orderings_Otop__class_Otop(u),v_Procs) -> hBOOL(c_Orderings_Otop__class_Otop(u))*.
% 299.64/300.39 55439[0:SpR:55036.1,51231.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(u,t_a),v),v_x),tc_bool),hAPP(v,v_x))** -> equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.39 55629[0:Rew:25.1,55487.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool)*.
% 299.64/300.39 55980[0:SpL:302.1,55174.1] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Otop__class_Otop(u))* -> .
% 299.64/300.39 55964[0:SpL:15476.0,55174.1] || equal(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool))) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))* -> .
% 299.64/300.39 55898[0:SpL:302.1,55174.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v)* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),hAPP(v,v_x))* -> .
% 299.64/300.39 56342[0:SpL:30368.2,16286.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> .
% 299.64/300.39 56341[7:SpL:30368.2,31868.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> .
% 299.64/300.39 56174[0:SpR:30368.2,3229.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> equal(hAPP(v,v_x),c_Orderings_Otop__class_Otop(u))*.
% 299.64/300.39 56168[4:SpR:30368.2,38042.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Otop__class_Otop(u),v,t_a)*.
% 299.64/300.39 56158[0:SpR:30368.2,28032.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v)))*.
% 299.64/300.39 56152[0:SpR:30368.2,28335.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v)))*.
% 299.64/300.39 56145[4:SpR:30368.2,37987.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v))*.
% 299.64/300.39 56135[0:SpR:30368.2,3283.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_Procs)).
% 299.64/300.39 56128[0:SpR:30368.2,1158.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),v_Procs),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 56526[0:Res:55596.2,50366.0] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(c_Orderings_Obot__class_Obot(u),v,tc_bool)* hBOOL(w)* -> hBOOL(v).
% 299.64/300.39 56784[0:SpL:30928.2,16286.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> .
% 299.64/300.39 56783[7:SpL:30928.2,31868.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> .
% 299.64/300.39 56615[0:SpR:30928.2,3229.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> equal(hAPP(v,v_x),c_Orderings_Otop__class_Otop(u))*.
% 299.64/300.39 56609[4:SpR:30928.2,38042.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(c_Orderings_Otop__class_Otop(u),v,t_a)*.
% 299.64/300.39 56599[0:SpR:30928.2,28032.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v)))*.
% 299.64/300.39 56593[0:SpR:30928.2,28335.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v)))*.
% 299.64/300.39 56586[4:SpR:30928.2,37987.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v))*.
% 299.64/300.39 56576[0:SpR:30928.2,3283.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_Procs)).
% 299.64/300.39 56569[0:SpR:30928.2,1158.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),v_Procs),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 57054[0:Rew:56980.1,11212.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 57211[0:Rew:57162.1,16257.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),v_Procs)** -> .
% 299.64/300.39 57212[7:Rew:57162.1,31827.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),v_x)** -> .
% 299.64/300.39 57498[0:SpR:57008.1,51231.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),v),v_x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))** -> equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.39 57788[0:Res:55625.1,16481.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_bool)* -> equal(c_Orderings_Otop__class_Otop(tc_bool),v).
% 299.64/300.39 57807[0:SSi:57773.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_bool)* -> c_lessequals(w,v,tc_bool)*.
% 299.64/300.39 57962[0:SpL:24020.1,55910.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_COMBK(v,w,x),hAPP(u,v_x))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),v_x) -> .
% 299.64/300.39 57921[0:SpL:300.1,55910.1] class_Lattices_Obounded__lattice(u) || equal(c_COMBK(v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),v_x) -> .
% 299.64/300.39 57906[0:SpL:365.1,55910.1] class_Orderings_Obot(u) || equal(c_COMBK(v,w,x),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_Orderings_Obot__class_Obot(u)) -> .
% 299.64/300.39 57905[0:SpL:397.1,55910.1] class_Orderings_Otop(u) || equal(c_COMBK(v,w,x),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_Orderings_Otop__class_Otop(u)) -> .
% 299.64/300.39 57899[0:SpL:2097.1,55910.1] || hBOOL(hAPP(v_x,u))* equal(c_COMBK(v,w,x),c_Set_Oinsert(u,y))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),v_x) -> .
% 299.64/300.39 58119[0:SpL:24020.1,55992.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v) -> .
% 299.64/300.39 58078[0:SpL:300.1,55992.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v) -> .
% 299.64/300.39 58063[0:SpL:365.1,55992.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool),v) -> .
% 299.64/300.39 58062[0:SpL:397.1,55992.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v)* -> .
% 299.64/300.39 58056[0:SpL:2097.1,55992.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w) -> .
% 299.64/300.39 58147[0:Rew:56980.1,58118.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_COMBK(v,w,x))* equal(c_Orderings_Obot__class_Obot(tc_bool),v) -> .
% 299.64/300.39 58148[0:Rew:56980.1,58114.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_COMBK(v,w,x))* equal(c_Orderings_Obot__class_Obot(tc_bool),v) -> .
% 299.64/300.39 58151[0:Rew:3014.0,58128.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_COMBK(y,z,x1))* equal(c_Orderings_Obot__class_Obot(tc_bool),y) -> .
% 299.64/300.39 58152[0:Rew:3014.0,58121.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_COMBK(w,x,y))* equal(c_Orderings_Obot__class_Obot(tc_bool),w) -> .
% 299.64/300.39 58153[0:Rew:2990.0,58097.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_COMBK(x,y,z))* equal(c_Orderings_Otop__class_Otop(tc_bool),x) -> .
% 299.64/300.39 58232[0:SpL:52997.1,58055.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u,v),c_Set_Oinsert(v_Procs,w))* -> .
% 299.64/300.39 58227[0:SpL:584.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_bool),w,x),c_COMBS(u,v,y,z,x1))* -> .
% 299.64/300.39 58207[0:SpL:337.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))* -> .
% 299.64/300.39 58194[0:SpL:540.1,58055.0] class_Lattices_Olattice(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))** -> .
% 299.64/300.39 58193[0:SpL:539.1,58055.0] class_Lattices_Oupper__semilattice(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))** -> .
% 299.64/300.39 58192[0:SpL:297.2,58055.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> .
% 299.64/300.39 58185[0:SpL:30368.2,58055.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> .
% 299.64/300.39 58184[0:SpL:30928.2,58055.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> .
% 299.64/300.39 58181[0:SpL:299.2,58055.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v,tc_bool),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> .
% 299.64/300.39 58175[0:SpL:24019.2,58055.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u,v),v_x)** -> .
% 299.64/300.39 58166[0:SpL:25.1,58055.0] class_HOL_Ouminus(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool),w,x),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)))** -> .
% 299.64/300.39 58354[0:SpL:2771.1,58198.0] || equal(u,v) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),w,x),c_COMBK(hAPP(v,v_x),y,z))* -> .
% 299.64/300.39 58505[0:SpL:12944.0,58248.0] || equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),u,v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(w,x),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),y,z)),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 58499[0:SpL:9.0,58248.0] || equal(c_COMBK(hAPP(u,hAPP(v,v_x)),w,x),c_HOL_Ouminus__class_Ouminus(c_Fun_Ocomp(u,v,y,z,x1),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 58498[0:SpL:11473.0,58248.0] || equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),u,v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 58478[0:SpL:88.1,58248.0] class_Lattices_Oboolean__algebra(u) || equal(c_COMBK(c_Orderings_Otop__class_Otop(u),v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 58474[0:SpL:17045.0,58248.0] || equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x,tc_fun(y,tc_bool)),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 58464[0:SpL:2098.1,58248.0] || equal(c_COMBK(v_x,u,v),c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(t_a,tc_bool)))* -> c_Hoare__Mirabelle_Ohoare__valids(w,v_x,t_a).
% 299.64/300.39 58449[0:SpL:3586.1,58248.0] || equal(hAPP(c_in(u),v),v_Procs) equal(c_COMBK(v_x,w,x),c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v,u),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 58448[7:SpL:27278.1,58248.0] || equal(hAPP(c_in(u),v),v_x) equal(c_COMBK(v_x,w,x),c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v,u),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 58434[0:SpL:8498.1,58248.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) equal(c_COMBK(v_x,v,w),c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(x,u),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 58523[0:SSi:58515.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** equal(c_COMBK(v_x,u,v),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)))** -> .
% 299.64/300.39 58524[0:SSi:58514.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)))** equal(c_COMBK(v_x,u,v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.39 58599[0:Res:10771.1,3929.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v))* equal(hAPP(c_Set_Oinsert(w,u),v),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.39 58551[0:SpR:3229.1,10771.1] || equal(u,c_Set_Oinsert(v,w))* hBOOL(hAPP(hAPP(c_in(w),x),v_x))* -> hBOOL(hAPP(hAPP(u,v_x),x))*.
% 299.64/300.39 58617[0:SSi:58608.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_COMBK(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))* equal(c_COMBK(u,x,y),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)))** -> .
% 299.64/300.39 58889[0:Res:3317.1,15629.0] || equal(c_in(u),v)* -> hBOOL(hAPP(hAPP(v,v_x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(v,v_x),w)))*.
% 299.64/300.39 58698[0:SpL:3229.1,15629.0] || equal(u,v)* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,v,w)))*.
% 299.64/300.39 59124[0:Rew:331.0,58714.1] || hBOOL(u)* -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),v))*.
% 299.64/300.39 59397[0:Res:3317.1,15857.0] || equal(c_in(u),v)* -> hBOOL(hAPP(hAPP(v,v_x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(v,v_x),x)))*.
% 299.64/300.39 59206[0:SpL:3229.1,15857.0] || equal(u,v)* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),v,x)))*.
% 299.64/300.39 59634[0:Rew:331.0,59222.1] || hBOOL(u)* -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),w))*.
% 299.64/300.39 59697[0:SpL:2267.1,19883.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)* c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(v,w).
% 299.64/300.39 59744[0:SpL:3229.1,21018.0] || equal(u,c_Set_Oinsert(v,w))* equal(hAPP(c_Set_Oimage(x,w,y),hAPP(u,v_x)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))** -> .
% 299.64/300.39 59780[0:SpL:158.0,59737.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),hAPP(c_in(tc_Com_Opname),v_x))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.39 59783[0:SpL:158.0,59750.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,t_a,v),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.39 59824[0:SpL:3229.1,4126.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* equal(hAPP(v,v_x),w)* -> c_lessequals(v_x,w,u).
% 299.64/300.39 59818[0:SpL:3229.1,4126.1] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u))* equal(hAPP(hAPP(v,v_x),w),v_x)** -> c_lessequals(w,v_x,u)*.
% 299.64/300.39 60119[0:Obv:60091.0] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),u),u)*.
% 299.64/300.39 60231[0:SpL:24020.1,58170.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(v,hAPP(u,v_x))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),v)* -> .
% 299.64/300.39 60190[0:SpL:300.1,58170.1] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),v)* -> .
% 299.64/300.39 60175[0:SpL:365.1,58170.1] class_Orderings_Obot(u) || equal(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,u))) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool),w,x),v)* -> .
% 299.64/300.39 60174[0:SpL:397.1,58170.1] class_Orderings_Otop(u) || equal(v,c_Orderings_Otop__class_Otop(tc_fun(t_a,u))) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),w,x),v)* -> .
% 299.64/300.39 60168[0:SpL:2097.1,58170.1] || hBOOL(hAPP(v_x,u))* equal(v,c_Set_Oinsert(u,w))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),x,y),v)* -> .
% 299.64/300.39 60259[0:Rew:56980.1,60230.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),v)* -> .
% 299.64/300.39 60260[0:Rew:56980.1,60226.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),u)* -> .
% 299.64/300.39 60263[0:Rew:3014.0,60240.1] || equal(u,hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)))* equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),z,x1),u)* -> .
% 299.64/300.39 60264[0:Rew:3014.0,60233.1] || equal(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),x,y),u)* -> .
% 299.64/300.39 60265[0:Rew:2990.0,60209.1] || equal(u,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)))* equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),y,z),u)* -> .
% 299.64/300.39 60363[0:Obv:60333.0] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),u),v,u)*.
% 299.64/300.39 60730[0:SpR:3229.1,5890.0] || equal(u,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z))* -> c_lessequals(v_x,hAPP(u,v_x),tc_fun(v,tc_bool))*.
% 299.64/300.39 60978[7:SpL:2267.1,57078.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.39 61140[0:Res:61046.3,112.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u)) -> c_lessequals(w,v,u)*.
% 299.64/300.39 61138[0:Res:61046.3,42.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 61132[0:Res:61046.3,144.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 61194[0:Obv:61142.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_Orderings_Obot__class_Obot(u))** -> c_lessequals(w,x,u)*.
% 299.64/300.39 61195[0:Obv:61141.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_Orderings_Obot__class_Obot(u))** -> c_lessequals(v,x,u)*.
% 299.64/300.39 61214[0:SpL:2267.1,57079.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)* equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.39 61249[0:SpL:2267.1,7597.0] || equal(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),w)* equal(c_HOL_Ouminus__class_Ouminus(w,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.39 61434[0:Res:61338.3,112.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)) -> c_lessequals(v,w,u)*.
% 299.64/300.39 61433[0:Res:61338.3,146.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Otop__class_Otop(u),v) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.39 61508[0:SpR:2771.1,9267.0] || equal(u,hAPP(c_Set_Oinsert(v,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* equal(v_x,v).
% 299.64/300.39 61511[0:SSi:61503.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(hAPP(c_Set_Oinsert(v,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool))* equal(v_x,v).
% 299.64/300.39 61620[0:SpR:3229.1,10492.1] || equal(u,c_in(tc_Com_Opname)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_in(tc_Com_Opname),v_x),v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(u,v_x),v),v_Procs,t_a)*.
% 299.64/300.39 61715[0:SpL:353.0,10885.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),w))),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.39 61980[0:SpL:2771.1,15487.1] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.39 61978[0:SpL:57059.1,15487.1] || equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 61977[0:SpL:56980.1,15487.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 61915[0:SpL:525.1,15487.1] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 61984[0:Rew:3014.0,61958.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 61988[0:SSi:61975.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,hAPP(v,v_x))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.39 62006[0:SpL:2267.1,61981.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 62017[0:SpL:2267.1,61982.0] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 62033[0:SpL:2267.1,15838.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w)* equal(c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.39 62084[2:Res:55596.2,16623.0] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 62116[0:SpR:3229.1,19719.1] || equal(u,c_in(tc_Com_Opname)) equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_in(tc_Com_Opname),v_x),v),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(u,v_x),v,t_a)*.
% 299.64/300.39 62126[0:SpL:2267.1,23321.0] || equal(v_Procs,u) hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool))))* equal(c_Set_Oinsert(v,w),c_in(tc_Com_Opname))** -> .
% 299.64/300.39 62130[0:SpR:3229.1,23727.0] || equal(u,c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,w),hAPP(u,v_x)),v_Procs))*.
% 299.64/300.39 62151[0:Res:23747.0,3929.0] || equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),t_a,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.39 62156[0:SpR:3229.1,23754.0] || equal(u,c_in(v)) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.39 62386[0:SSi:62339.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),u) -> c_lessequals(u,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),tc_bool)*.
% 299.64/300.39 62400[0:SSi:62216.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),u) -> c_lessequals(u,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.39 63505[0:Obv:63470.0] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,u),u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),u)*.
% 299.64/300.39 63553[0:Res:62367.1,38189.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),u) hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),c_HOL_Ominus__class_Ominus(u,v,tc_bool)))*.
% 299.64/300.39 63552[0:Res:62367.1,38190.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),u) hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ominus__class_Ominus(u,v,tc_bool)),w))*.
% 299.64/300.39 63550[0:Res:62367.1,50366.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),u) c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool)* hBOOL(u) -> hBOOL(w).
% 299.64/300.39 63684[0:Res:62368.3,50.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),v) -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 63683[0:Res:62368.3,46.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),v) -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 63672[0:Res:62368.3,48.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),v) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.39 63671[0:Res:62368.3,44.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),v) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.39 63777[0:SSi:63650.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(hAPP(c_Set_Oinsert(v,u),w),x)* -> hBOOL(hAPP(hAPP(c_in(u),v),x))*.
% 299.64/300.39 63778[0:SSi:63623.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(v,w)* c_Fun_Oinj__on(x,w,u,y)* -> c_Fun_Oinj__on(x,v,u,y)*.
% 299.64/300.39 63932[0:Obv:63897.0] class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(w,u),u),u),v,u)*.
% 299.64/300.39 64016[0:SpL:647.0,103.1] || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),tc_Com_Opname).
% 299.64/300.39 63968[0:SpR:647.0,114.1] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),tc_Com_Opname,w) -> c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,w)*.
% 299.64/300.39 64108[0:Res:679.1,436.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) hBOOL(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v))* -> hBOOL(hAPP(v_Procs,v)).
% 299.64/300.39 64301[0:SpR:3229.1,23948.1] || equal(u,c_Set_Oinsert(v,w))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(u,v_x),v_Procs))*.
% 299.64/300.39 64455[0:Res:23957.0,3929.0] || equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.39 64501[0:SpL:3229.1,24257.1] || equal(u,v)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v)* equal(hAPP(u,v_x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs))*.
% 299.64/300.39 64577[0:SpL:3229.1,24629.1] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u))* equal(hAPP(v,v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x)**.
% 299.64/300.39 64662[7:SpL:2267.1,27900.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w)* equal(c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.39 64868[0:SpL:28747.0,35720.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w)))*.
% 299.64/300.39 64846[0:SpR:28747.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w)))*.
% 299.64/300.39 64842[0:SpR:28747.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.39 64840[0:SpR:28747.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x))))*.
% 299.64/300.39 64988[0:SpL:28748.0,35720.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w)))*.
% 299.64/300.39 64966[0:SpR:28748.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w)))*.
% 299.64/300.39 64962[0:SpR:28748.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.39 64960[0:SpR:28748.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x))))*.
% 299.64/300.39 65108[0:SpL:28902.0,35720.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))*.
% 299.64/300.39 65086[0:SpR:28902.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))*.
% 299.64/300.39 65082[0:SpR:28902.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.39 65080[0:SpR:28902.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x))))*.
% 299.64/300.39 65228[0:SpL:28903.0,35720.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w)))*.
% 299.64/300.39 65206[0:SpR:28903.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w)))*.
% 299.64/300.39 65202[0:SpR:28903.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.39 65200[0:SpR:28903.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,x))))*.
% 299.64/300.39 66197[0:SpL:65404.1,3489.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(tc_Com_Opname))** hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.39 66187[0:SpL:65404.1,15487.1] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 66165[0:SpR:65404.1,584.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y,z),v),hAPP(v,hAPP(w,v)))**.
% 299.64/300.39 66164[0:SpR:65404.1,584.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),w),hAPP(hAPP(v,w),w))**.
% 299.64/300.39 65986[0:SpR:65404.1,24914.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x)),v_x)**.
% 299.64/300.39 65980[0:SpR:65404.1,3294.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_in(t_a))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 68234[0:SpR:1250.3,367.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Ogroup__add(u) class_Orderings_Obot(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.39 70926[0:SpL:10090.1,6582.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_fun(u,tc_bool))*.
% 299.64/300.39 70974[0:SpL:2771.1,70856.2] || equal(u,v)* equal(w,hAPP(v,v_x))* hBOOL(w)* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* -> .
% 299.64/300.39 71011[0:SpL:2771.1,70970.0] || equal(u,v)* equal(w,c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* hBOOL(w)* hBOOL(hAPP(v,v_x))* -> .
% 299.64/300.39 71070[0:SpR:584.0,7568.0] || -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,y,z,x1),u)),tc_fun(w,tc_bool))*.
% 299.64/300.39 71307[0:Res:7538.0,436.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(y,w),u)),v))*.
% 299.64/300.39 71435[7:SpL:584.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_bool))* equal(c_COMBS(u,v,w,x,y),v_x)** -> .
% 299.64/300.39 71415[7:SpL:337.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x)** -> .
% 299.64/300.39 71402[7:SpL:540.1,71221.0] class_Lattices_Olattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> .
% 299.64/300.39 71401[7:SpL:539.1,71221.0] class_Lattices_Oupper__semilattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> .
% 299.64/300.39 71393[7:SpL:30368.2,71221.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> .
% 299.64/300.39 71392[7:SpL:30928.2,71221.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> .
% 299.64/300.39 71389[7:SpL:299.2,71221.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)** -> .
% 299.64/300.39 71374[7:SpL:25.1,71221.0] class_HOL_Ouminus(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_x) -> .
% 299.64/300.39 71645[7:SpR:71455.1,584.0] || equal(u,v_x) -> equal(hAPP(c_COMBS(c_Set_Oinsert(v_x,t_a),v,w,x,y),u),hAPP(u,hAPP(v,u)))*.
% 299.64/300.39 71644[7:SpR:71455.1,584.0] || equal(u,v_x) -> equal(hAPP(c_COMBS(v,c_Set_Oinsert(v_x,t_a),w,x,y),u),hAPP(hAPP(v,u),u))*.
% 299.64/300.39 72393[7:MRR:70388.1,72294.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(t_a),v_x),v_x),hAPP(c_in(t_a),v_x),tc_Com_Opname,u),v_x),tc_bool))* -> .
% 299.64/300.39 72394[7:MRR:70387.1,72294.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(t_a),v_x),hAPP(hAPP(c_in(t_a),v_x),v_x),tc_Com_Opname,u),v_x),tc_bool))* -> .
% 299.64/300.39 73063[7:Res:71608.1,467.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_x) -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,t_a),v_x)),v_x)**.
% 299.64/300.39 74240[7:SpL:71835.1,33.0] || equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(v_x,x)) -> hBOOL(hAPP(v_x,hAPP(u,x)))*.
% 299.64/300.39 74208[7:SpL:71835.1,4126.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a))** equal(v_x,v) -> c_lessequals(v_x,v,u).
% 299.64/300.39 74172[7:SpL:71835.1,4126.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) equal(hAPP(v_x,v),v_x) -> c_lessequals(v,v_x,u)*.
% 299.64/300.39 74167[7:SpL:71835.1,298.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) equal(hAPP(v_x,v),v) -> c_lessequals(v_x,v,u)*.
% 299.64/300.39 74103[7:SpL:71835.1,31349.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(v_x,tc_Com_Opname,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.39 74074[7:SpL:71835.1,24029.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Com_Ocom_OBODY,v_x) equal(hAPP(c_Com_Ocom_OBODY,u),v_x)** -> equal(v_x,u).
% 299.64/300.39 74060[7:SpL:71835.1,25019.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.39 74044[7:SpL:71835.1,3489.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_in(tc_Com_Opname),u) hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.39 74034[7:SpL:71835.1,15487.1] || equal(c_Set_Oinsert(v_x,t_a),u) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 73994[7:SpL:71835.1,16387.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(c_Com_Ocom_OBODY,v_x) -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.39 73965[7:SpL:71835.1,502.0] || equal(c_Set_Oinsert(v_x,t_a),c_Com_Obody) c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),v_x),u,v)* -> c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,v_x),u,v).
% 299.64/300.39 73961[7:SpL:71835.1,348.0] || equal(c_Set_Oinsert(v_x,t_a),c_Com_Ocom_OBODY) c_Natural_Oevaln(v_x,u,v,w) -> equal(c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_x,v,u,w)),v)**.
% 299.64/300.39 73943[7:SpR:71835.1,23754.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.39 73891[7:SpR:71835.1,584.0] || equal(c_COMBS(u,v,w,x,y),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(hAPP(u,v_x),hAPP(v,v_x)),v_x)**.
% 299.64/300.39 73783[7:SpR:71835.1,517.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(v,w))* -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.39 73763[7:SpR:71835.1,337.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Set_Oinsert(v_x,t_a))** -> equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x).
% 299.64/300.39 73690[7:SpR:71835.1,83.0] || equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,t_a)) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),v_x),v_x,tc_fun(w,tc_bool))*.
% 299.64/300.39 73682[7:SpR:71835.1,518.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(v,w)) -> hBOOL(hAPP(hAPP(v_x,v),w))*.
% 299.64/300.39 73647[7:SpR:71835.1,299.2] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v,v_x,u)* -> equal(hAPP(v_x,v),v_x).
% 299.64/300.39 73646[7:SpR:71835.1,540.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(v_x,v))**.
% 299.64/300.39 73645[7:SpR:71835.1,539.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(v_x,v))**.
% 299.64/300.39 73635[7:SpR:71835.1,540.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_x)**.
% 299.64/300.39 73634[7:SpR:71835.1,539.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_x)**.
% 299.64/300.39 73572[7:SpR:71835.1,30368.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Set_Oinsert(v_x,t_a))** -> equal(c_Orderings_Otop__class_Otop(u),v_x).
% 299.64/300.39 73571[7:SpR:71835.1,30928.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Set_Oinsert(v_x,t_a))** -> equal(c_Orderings_Otop__class_Otop(u),v_x).
% 299.64/300.39 73570[7:SpR:71835.1,299.2] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a))** c_lessequals(v_x,v,u) -> equal(v_x,v).
% 299.64/300.39 73543[7:SpR:71835.1,13749.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 73542[7:SpR:71835.1,14043.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 73541[7:SpR:71835.1,297.2] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v_x,v,u)* -> equal(hAPP(v_x,v),v).
% 299.64/300.39 73518[7:SpR:71835.1,336.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.39 73512[7:SpR:71835.1,7226.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(c_Option_Othe(v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.39 73472[7:SpR:71835.1,51366.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(u,t_a),v_x),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 73452[7:SpR:71835.1,33303.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_x,tc_Com_Opname,u),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.39 73451[7:SpR:71835.1,31543.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_x,tc_Com_Opname,u),v_x)),v_Procs))*.
% 299.64/300.39 73449[7:SpR:71835.1,23956.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,t_a,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.39 73433[7:SpR:71835.1,23957.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,tc_Com_Opname,u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.39 73393[7:SpR:71835.1,3294.1] || equal(c_Set_Oinsert(v_x,t_a),u)* equal(c_in(t_a),u) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.39 73346[7:SpR:71835.1,25.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Set_Oinsert(v_x,t_a)) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),v_x)**.
% 299.64/300.39 73325[7:SpR:71835.1,23727.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v),v_x),v_Procs))*.
% 299.64/300.39 73317[7:SpR:71835.1,19748.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.64/300.39 73311[7:SpR:71835.1,1588.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_x,u,v),tc_Com_Opname,tc_fun(w,tc_bool)),v_Procs))*.
% 299.64/300.39 73281[7:SpR:71835.1,34.1] || equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(v_x,hAPP(u,x)))* -> hBOOL(hAPP(v_x,x)).
% 299.64/300.39 73242[7:SpR:71835.1,517.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(hAPP(v_x,w),v))*.
% 299.64/300.39 73200[7:SpR:71835.1,503.1] || equal(c_Set_Oinsert(v_x,t_a),c_Com_Obody) c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,v_x),u,v) -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),v_x),u,v)*.
% 299.64/300.39 74464[7:Rew:74168.3,74169.3] class_Lattices_Obounded__lattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) equal(hAPP(v_x,v),c_Orderings_Obot__class_Obot(u))* -> equal(v,v_x).
% 299.64/300.39 74468[7:MRR:74270.1,6340.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_Set_Oinsert(v_x,t_a)) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v_x,v),u,t_a)*.
% 299.64/300.39 74469[7:Rew:71835.1,73506.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(w,u),v)))*.
% 299.64/300.39 74894[7:SpR:584.0,72297.1] || equal(c_COMBS(u,v,w,x,y),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),hAPP(v,v_x)),v_x))*.
% 299.64/300.39 74861[7:SpR:540.1,72297.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_x))*.
% 299.64/300.39 74860[7:SpR:539.1,72297.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_x))*.
% 299.64/300.39 74852[7:SpR:30368.2,72297.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_x)).
% 299.64/300.39 74851[7:SpR:30928.2,72297.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_x)).
% 299.64/300.39 74848[7:SpR:299.2,72297.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a))** -> hBOOL(hAPP(v,v_x)).
% 299.64/300.39 74832[7:SpR:25.1,72297.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),v_x))*.
% 299.64/300.39 75243[7:SpR:24019.2,72312.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,t_a,u),v_x),v_x))*.
% 299.64/300.39 75747[7:SpL:71883.1,58170.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(u,v_x) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v,w),u)* -> .
% 299.64/300.39 75733[7:SpL:71883.1,55992.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_COMBK(u,v,w),v_x)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u) -> .
% 299.64/300.39 75726[7:SpR:71883.1,20881.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,u,v),hAPP(c_Set_Oinsert(v_x,u),w)),v_x))*.
% 299.64/300.39 75711[7:SpR:71883.1,9569.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),v_x),tc_bool)*.
% 299.64/300.39 75710[7:SpR:71883.1,9568.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),v_x),tc_bool)*.
% 299.64/300.39 75699[7:SpR:71883.1,3346.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Set_Oinsert(u,v),v_x) -> hBOOL(hAPP(hAPP(c_in(v),u),v_x))*.
% 299.64/300.39 75698[7:SpR:71883.1,28356.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(u,v_x) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,v)))*.
% 299.64/300.39 75697[7:SpR:71883.1,28053.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(u,v_x) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,v)))*.
% 299.64/300.39 75696[7:SpR:71883.1,28859.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,v)))*.
% 299.64/300.39 75695[7:SpR:71883.1,28704.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,v)))*.
% 299.64/300.39 75694[7:SpR:71883.1,21126.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,tc_Com_Opname,v),u),v_x))*.
% 299.64/300.39 75692[7:SpR:71883.1,3305.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(u,v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.39 75847[0:SpR:584.0,7823.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v)),u)*.
% 299.64/300.39 76748[7:SpR:353.0,71682.1] || equal(hAPP(c_Set_Oinsert(u,v),w),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(x,v),w)),v_x))*.
% 299.64/300.39 76879[0:SpR:584.0,30321.1] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v)),u)*.
% 299.64/300.39 77202[7:SpL:586.0,74788.1] || equal(hAPP(c_COMBB(u,v,w,x),y),v_x)** equal(hAPP(u,hAPP(y,v_x)),z)* -> hBOOL(z)*.
% 299.64/300.39 77201[7:SpL:585.0,74788.1] || equal(hAPP(c_COMBC(u,v,w,x),y),v_x)** equal(hAPP(hAPP(u,v_x),y),z)* -> hBOOL(z)*.
% 299.64/300.39 77137[7:SpL:445.1,74788.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),v_x)** equal(hAPP(u,v_x),z)* -> equal(v_x,v) hBOOL(z)*.
% 299.64/300.39 77235[0:SpR:3229.1,801.1] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u))* -> equal(c_Fun_Ofun__upd(hAPP(v,v_x),v_x,v_x,w,x),hAPP(v,v_x))**.
% 299.64/300.39 77293[7:SpR:8415.2,75266.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(c_COMBK(u,v,w),t_a,x),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(v_x,u)).
% 299.64/300.39 77978[0:Res:10771.1,5892.0] || hBOOL(hAPP(hAPP(c_in(u),v),v))* -> hBOOL(hAPP(c_COMBS(c_in(w),c_Set_Oinsert(x,u),y,z,x1),v))*.
% 299.64/300.39 77972[0:Res:517.1,5892.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(c_COMBS(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),y,z,x1),v))*.
% 299.64/300.39 77968[0:Res:518.1,5892.0] || hBOOL(hAPP(u,u))* -> hBOOL(hAPP(c_COMBS(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y,z,x1),u))*.
% 299.64/300.39 77937[0:Res:7226.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_in(v),w,x,y),hAPP(c_Set_Oimage(c_Option_Othe(z),x1,v),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.64/300.39 77922[0:Res:34.1,5892.0] || hBOOL(hAPP(u,hAPP(v,u)))* -> hBOOL(hAPP(c_COMBS(c_in(w),c_Set_Ovimage(v,x,y),z,x1,x2),u))*.
% 299.64/300.39 77712[0:SpL:456.0,5892.0] || hBOOL(hAPP(u,c_Option_Ooption_OSome(u,v)))* -> hBOOL(hAPP(c_COMBS(c_in(w),c_Option_Othe(v),x,y,z),c_Option_Ooption_OSome(u,v)))*.
% 299.64/300.39 78048[0:Rew:584.0,77833.2] || equal(u,hAPP(v,v_x))* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(v,v_x)))*.
% 299.64/300.39 78055[0:Rew:584.0,77684.2] || equal(u,v)* hBOOL(hAPP(hAPP(u,v_x),v_x))* -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(v,v_x)))*.
% 299.64/300.39 78190[7:Rew:78167.0,64020.0] || -> equal(c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,tc_Com_Opname),v_x,tc_Com_Opname,u),v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_HOL_Ominus__class_Ominus(v_x,v_Procs,tc_fun(tc_Com_Opname,tc_bool)))**.
% 299.64/300.39 78193[7:Rew:78167.0,64019.0] || -> equal(c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname,u),v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_HOL_Ominus__class_Ominus(v_x,v_Procs,tc_fun(tc_Com_Opname,tc_bool)))**.
% 299.64/300.39 78208[7:Rew:78167.0,78191.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,tc_Com_Opname),v_x,tc_Com_Opname,u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))* -> c_lessequals(v_x,v_Procs,tc_fun(tc_Com_Opname,tc_bool)).
% 299.64/300.39 78209[7:Rew:78167.0,78194.1] || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname,u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))* -> c_lessequals(v_x,v_Procs,tc_fun(tc_Com_Opname,tc_bool)).
% 299.64/300.39 78517[4:Res:77988.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))* c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.39 78510[4:Res:77988.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,w,tc_fun(x,tc_bool)),v))*.
% 299.64/300.39 78550[4:MRR:15804.2,78524.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.64/300.39 78567[7:MRR:27857.2,78524.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.64/300.39 78586[4:MRR:54042.1,78524.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(v_Procs,u)),c_Set_Oinsert(v_Procs,u))**.
% 299.64/300.39 78740[4:Res:78665.1,454.0] || equal(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(v,w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v,w),u,t_a)*.
% 299.64/300.39 79051[0:Rew:300.1,78973.1] class_Lattices_Obounded__lattice(u) || hBOOL(v) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,w),x),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w))*.
% 299.64/300.39 79081[0:Res:78077.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* c_Hoare__Mirabelle_Otriple__valid(u,v_Procs,t_a).
% 299.64/300.39 79075[0:Res:78077.0,280.1] || hBOOL(hAPP(hAPP(u,v_Procs),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,x,tc_fun(y,tc_bool)),v))*.
% 299.64/300.39 79111[7:Res:78199.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_in(v),v_x))),hAPP(c_in(v),v_x)))* c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.39 79104[7:Res:78199.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_in(w),v_x),u,x,tc_fun(y,tc_bool)),v))*.
% 299.64/300.39 79271[0:Rew:300.1,79193.1] class_Lattices_Obounded__lattice(u) || hBOOL(v) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oinsert(v,x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x))*.
% 299.64/300.39 79527[0:SpR:21268.0,415.0] || -> equal(c_Fun_Ofun__upd(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,hAPP(u,w),v,x),hAPP(u,w),y,z),u)**.
% 299.64/300.39 79350[0:SpR:21268.0,451.0] || -> c_Com_OWT(hAPP(c_Com_Ocom_OBODY,u)) equal(hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,u),v,w)),c_Option_Ooption_ONone(tc_Com_Ocom))**.
% 299.64/300.39 80720[0:SpR:21894.0,415.0] || -> equal(c_Fun_Ofun__upd(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(u,w),u,v,x),hAPP(u,w),y,z),u)**.
% 299.64/300.39 80543[0:SpR:21894.0,451.0] || -> c_Com_OWT(hAPP(c_Com_Ocom_OBODY,u)) equal(hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Com_Ocom_OBODY,u),c_Com_Ocom_OBODY,v,w)),c_Option_Ooption_ONone(tc_Com_Ocom))**.
% 299.64/300.39 82022[0:Rew:584.0,81811.2] class_Lattices_Oupper__semilattice(u) || equal(v,w) -> c_lessequals(hAPP(v,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(w,v_x)),u)*.
% 299.64/300.39 82029[0:SSi:81988.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,w,x,y),v)),z))*.
% 299.64/300.39 82493[0:Rew:584.0,82283.2] class_Lattices_Olattice(u) || equal(v,w) -> c_lessequals(hAPP(v,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(w,v_x)),u)*.
% 299.64/300.39 82565[7:Res:82148.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,t_a),t_a,v),c_Set_Oinsert(v_x,w)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.64/300.39 82800[0:Obv:82713.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.39 82802[0:Obv:82680.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(w,v,u)* -> c_lessequals(w,x,u)*.
% 299.64/300.39 82850[7:Res:77991.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,w),v_x),t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,v_x,t_a).
% 299.64/300.39 83096[0:SpL:5924.0,3483.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Com_Ocom_OBODY)** equal(hAPP(hAPP(u,v_x),v),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 83271[7:SpR:52997.1,78357.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),v_x),v_x))*.
% 299.64/300.39 83266[7:SpR:584.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,v,w,x,y),z,x1),v_x),hAPP(hAPP(u,v_x),hAPP(v,v_x))))*.
% 299.64/300.39 83246[7:SpR:337.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,w),v_x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.39 83233[7:SpR:540.1,78357.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.39 83232[7:SpR:539.1,78357.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.39 83231[7:SpR:297.2,78357.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),v_x),v_x))*.
% 299.64/300.39 83224[7:SpR:30368.2,78357.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),v_x),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 83223[7:SpR:30928.2,78357.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),v_x),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 83220[7:SpR:299.2,78357.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),v_x),v))*.
% 299.64/300.39 83207[7:SpR:25.1,78357.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w,x),v_x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)))*.
% 299.64/300.39 83416[0:SpL:5961.0,3483.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Com_Ocom_OBODY)** equal(hAPP(u,hAPP(x,v_x)),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 84216[7:SpL:586.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),v_x) equal(hAPP(c_COMBB(u,w,x,y),v),v_x)** -> .
% 299.64/300.39 84215[7:SpL:585.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool),v_x) equal(hAPP(c_COMBC(u,w,x,y),v),v_x)** -> .
% 299.64/300.39 84155[7:SpL:445.1,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v_x) equal(c_Fun_Ofun__upd(u,v,w,x,y),v_x)** -> equal(v_x,v).
% 299.64/300.39 84278[7:SpL:2771.1,78774.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v_x)** equal(hAPP(v_x,v_x),hAPP(v,v_x))* -> .
% 299.64/300.39 84662[7:SpL:2771.1,84274.1] || equal(u,v)* equal(hAPP(v,v_x),v_x)** equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(v_x,v_x))** -> .
% 299.64/300.39 85006[0:Res:84957.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,w),v),t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,v,t_a)*.
% 299.64/300.39 85117[0:Rew:610.0,85077.1] || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) equal(c_Finite__Set_Ocard(v_Procs,tc_Com_Opname),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) -> c_Fun_Oinj__on(c_COMBK(u,v,tc_Com_Opname),v_Procs,tc_Com_Opname,v)*.
% 299.64/300.39 85372[0:SpL:104.0,26240.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.39 85312[0:SpL:2098.1,26240.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),u),v),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)))** -> c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a)*.
% 299.64/300.39 85302[0:SpL:3744.1,26240.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.39 85456[4:SpR:78507.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.39 85732[0:SpR:3744.1,9066.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs)))*.
% 299.64/300.39 86084[0:SpL:584.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_bool))* equal(c_COMBS(u,v,w,x,y),v_Procs)** -> .
% 299.64/300.39 86063[0:SpL:337.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_Procs)** -> .
% 299.64/300.39 86050[0:SpL:540.1,86011.0] class_Lattices_Olattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> .
% 299.64/300.39 86049[0:SpL:539.1,86011.0] class_Lattices_Oupper__semilattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> .
% 299.64/300.39 86041[0:SpL:30368.2,86011.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> .
% 299.64/300.39 86040[0:SpL:30928.2,86011.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> .
% 299.64/300.39 86037[0:SpL:299.2,86011.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs)** -> .
% 299.64/300.39 86024[0:SpL:25.1,86011.0] class_HOL_Ouminus(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_Procs) -> .
% 299.64/300.39 86303[0:SpR:86109.1,584.0] || equal(u,v_Procs) -> equal(hAPP(c_COMBS(c_Set_Oinsert(v_x,t_a),v,w,x,y),u),hAPP(u,hAPP(v,u)))*.
% 299.64/300.39 86302[0:SpR:86109.1,584.0] || equal(u,v_Procs) -> equal(hAPP(c_COMBS(v,c_Set_Oinsert(v_x,t_a),w,x,y),u),hAPP(hAPP(v,u),u))*.
% 299.64/300.39 86301[0:SpR:86109.1,1103.1] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oinsert(v_x,t_a)),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Oinsert(v_x,t_a),t_a)* hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oinsert(v_x,t_a))).
% 299.64/300.39 86657[0:Res:86261.1,467.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_Procs) -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,t_a),v_x)),v_x)**.
% 299.64/300.39 86761[4:SpL:586.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),v_x) equal(hAPP(c_COMBB(u,w,x,y),v),v_Procs)** -> .
% 299.64/300.39 86760[4:SpL:585.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool),v_x) equal(hAPP(c_COMBC(u,w,x,y),v),v_Procs)** -> .
% 299.64/300.39 86700[4:SpL:445.1,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v_x) equal(c_Fun_Ofun__upd(u,v,w,x,y),v_Procs)** -> equal(v_x,v).
% 299.64/300.39 86853[0:SpR:353.0,86345.1] || equal(hAPP(c_Set_Oinsert(u,v),w),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(x,v),w)),v_x))*.
% 299.64/300.39 86964[0:SpR:32817.1,10.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* -> equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.64/300.39 87149[7:Res:82177.0,255.0] || c_lessequals(hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v)),w,tc_fun(t_a,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),w)).
% 299.64/300.39 87224[0:SSi:87220.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),w)** -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.64/300.39 87335[7:SpR:9.0,71492.1] || equal(c_Fun_Ocomp(u,v,w,x,y),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,hAPP(v,v_x))),z))*.
% 299.64/300.39 87314[7:SpR:88.1,71492.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v))*.
% 299.64/300.39 87483[7:SpR:9.0,71493.1] || equal(c_Fun_Ocomp(u,v,w,x,y),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,hAPP(v,v_x))),z,t_a)*.
% 299.64/300.39 87462[7:SpR:88.1,71493.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.39 87613[7:SpR:9.0,71679.1] || equal(c_Fun_Ocomp(u,v,w,x,y),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(u,hAPP(v,v_x))))*.
% 299.64/300.39 87592[7:SpR:88.1,71679.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 88422[0:Res:8176.1,18625.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),y),hAPP(v,y),tc_bool)*.
% 299.64/300.39 88557[0:Res:20152.0,8306.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),v,tc_fun(x,tc_bool))*.
% 299.64/300.39 88589[0:SSi:88584.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(v,c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)))* -> c_lessequals(v,w,tc_fun(u,tc_bool))*.
% 299.64/300.39 88676[7:SpL:27043.1,88086.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(v_Procs,u),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,v_x,tc_bool))* -> .
% 299.64/300.39 88668[7:SpL:586.0,88086.1] || equal(hAPP(c_COMBB(u,v,w,x),y),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(z,hAPP(u,hAPP(y,v_x)),tc_bool))* -> .
% 299.64/300.39 88667[7:SpL:585.0,88086.1] || equal(hAPP(c_COMBC(u,v,w,x),y),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(z,hAPP(hAPP(u,v_x),y),tc_bool))* -> .
% 299.64/300.39 88607[7:SpL:445.1,88086.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(z,hAPP(u,v_x),tc_bool))* -> equal(v_x,v).
% 299.64/300.39 88949[0:SpR:23840.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.39 88930[0:SpR:23682.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),w))*.
% 299.64/300.39 88880[0:SpR:10463.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),x))*.
% 299.64/300.39 88879[0:SpR:9911.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),x))*.
% 299.64/300.39 89045[0:Res:78099.0,255.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),v))*.
% 299.64/300.39 89178[0:SpL:23902.1,25984.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),v_x),u)* -> c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_bool),u).
% 299.64/300.39 89203[0:Rew:26279.0,89160.0] || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(x,w).
% 299.64/300.39 89586[7:SpL:78590.1,26240.0] || equal(c_Set_Oinsert(v_x,t_a),u) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** -> .
% 299.64/300.39 89544[7:SpL:78590.1,214.0] || equal(c_Set_Oinsert(v_x,t_a),u) c_lessequals(u,v,tc_fun(t_a,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v))*.
% 299.64/300.39 89420[7:SpR:78590.1,9066.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u)))*.
% 299.64/300.39 89360[7:SpR:78590.1,7253.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),u))*.
% 299.64/300.39 89659[7:MRR:89658.1,6340.0] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname),c_Set_Oinsert(v_x,t_a)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname))*.
% 299.64/300.39 89661[7:MRR:89660.1,6340.0] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,c_Set_Oinsert(v_x,t_a),tc_Com_Opname),c_Set_Oinsert(v_x,t_a)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,c_Set_Oinsert(v_x,t_a),tc_Com_Opname))*.
% 299.64/300.39 89707[7:Res:89344.1,156.0] || equal(hAPP(c_Set_Ovimage(u,t_a,v),w),c_Set_Oinsert(v_x,t_a)) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(u,v_x)),w))*.
% 299.64/300.39 89690[7:Res:89344.1,263.0] || equal(hAPP(c_Set_Oinsert(u,t_a),v),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v))* equal(v_x,u).
% 299.64/300.39 89873[0:SpR:3229.1,26183.0] || equal(u,c_Set_Oinsert(v,w))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),hAPP(u,v_x)),hAPP(u,v_x))**.
% 299.64/300.39 90377[4:SpL:78660.1,26240.0] || equal(hAPP(u,v_x),v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** -> .
% 299.64/300.39 90335[4:SpL:78660.1,214.0] || equal(hAPP(u,v_x),v_x) c_lessequals(u,v,tc_fun(t_a,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v))*.
% 299.64/300.39 90210[4:SpR:78660.1,9066.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u)))*.
% 299.64/300.39 90150[4:SpR:78660.1,7253.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),u))*.
% 299.64/300.39 90433[7:MRR:90432.1,6340.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname),v_x),v_x)** -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname)).
% 299.64/300.39 90435[7:MRR:90434.1,6340.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,c_Set_Oinsert(v_x,t_a),tc_Com_Opname),v_x),v_x)** -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,c_Set_Oinsert(v_x,t_a),tc_Com_Opname)).
% 299.64/300.39 90500[4:SpR:538.0,90130.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))*.
% 299.64/300.39 90607[7:MRR:90606.1,27297.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x) -> hBOOL(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))*.
% 299.64/300.39 90685[0:SpL:10090.1,26231.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),c_Orderings_Otop__class_Otop(tc_bool)),u)* -> c_Finite__Set_Ofinite(v_x,u).
% 299.64/300.39 90677[0:SpL:3294.1,26231.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_bool)),u)* -> c_Finite__Set_Ofinite(v_x,u).
% 299.64/300.39 90761[0:SpL:10.0,26480.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),u,tc_fun(v,tc_bool))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,tc_fun(v,tc_bool)).
% 299.64/300.39 90803[0:SSi:90789.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),w)** -> c_lessequals(v,w,tc_fun(u,tc_bool)).
% 299.64/300.39 90851[4:Res:90134.1,156.0] || equal(hAPP(hAPP(c_Set_Ovimage(u,t_a,v),w),v_x),v_x) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(u,v_x)),w))*.
% 299.64/300.39 90834[4:Res:90134.1,263.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),v),v_x),v_x)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)) equal(v_x,u).
% 299.64/300.39 91029[4:Rew:25.1,90908.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool))* -> .
% 299.64/300.39 91305[0:Rew:91288.1,91103.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),w),y)),v))*.
% 299.64/300.39 91306[0:Rew:91288.1,91072.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),c_Orderings_Obot__class_Obot(u)),tc_bool)*.
% 299.64/300.39 91307[0:Rew:91288.1,91071.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),x),c_Orderings_Obot__class_Obot(u)),tc_bool)*.
% 299.64/300.39 91933[0:SpR:79073.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,w),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.39 92086[7:SpR:79101.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(v),v_x)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,w),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.39 92675[7:SpR:297.2,82151.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,c_Set_Oinsert(v_x,v),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> hBOOL(c_Set_Oinsert(v_x,v)).
% 299.64/300.39 92666[7:SpR:12944.0,82151.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Set_Oinsert(v_x,y)))*.
% 299.64/300.39 92659[7:SpR:9.0,82151.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_in(t_a))** -> hBOOL(hAPP(hAPP(u,hAPP(v,v_x)),c_Set_Oinsert(v_x,z)))*.
% 299.64/300.39 92658[7:SpR:11473.0,82151.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Set_Oinsert(v_x,w)))*.
% 299.64/300.39 92638[7:SpR:88.1,82151.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Set_Oinsert(v_x,v)))*.
% 299.64/300.39 92634[7:SpR:17045.0,82151.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Set_Oinsert(v_x,x)))*.
% 299.64/300.39 92624[7:SpR:2098.1,82151.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,v)))*.
% 299.64/300.39 92610[7:SpR:3586.1,82151.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_in(t_a)) -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,w)))*.
% 299.64/300.39 92609[7:SpR:27278.1,82151.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_in(t_a)) -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,w)))*.
% 299.64/300.39 92592[7:SpR:8498.1,82151.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,w)))*.
% 299.64/300.39 92743[7:SpR:532.0,82185.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,w)),x)),v_x))*.
% 299.64/300.39 93129[7:SpR:533.0,82187.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_Set_Oinsert(v_x,x))),v_x))*.
% 299.64/300.39 93326[4:SpR:12944.0,85556.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(c_Orderings_Otop__class_Otop(tc_bool),y),tc_bool)*.
% 299.64/300.39 93319[4:SpR:9.0,85556.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(hAPP(u,hAPP(v,v_x)),z),tc_bool)*.
% 299.64/300.39 93318[4:SpR:11473.0,85556.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(c_Orderings_Otop__class_Otop(tc_bool),w),tc_bool)*.
% 299.64/300.39 93298[4:SpR:88.1,85556.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(c_Orderings_Otop__class_Otop(u),v),tc_bool)*.
% 299.64/300.39 93294[4:SpR:17045.0,85556.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(c_Orderings_Obot__class_Obot(tc_bool),x),tc_bool)*.
% 299.64/300.39 93284[4:SpR:2098.1,85556.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) c_lessequals(v_x,hAPP(v_x,v),tc_bool)*.
% 299.64/300.39 93270[4:SpR:3586.1,85556.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(v_x,w),tc_bool)*.
% 299.64/300.39 93269[7:SpR:27278.1,85556.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(v_x,w),tc_bool)*.
% 299.64/300.39 93252[4:SpR:8498.1,85556.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v_x,w),tc_bool)*.
% 299.64/300.39 93507[0:SpR:9.0,86147.1] || equal(c_Fun_Ocomp(u,v,w,x,y),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,hAPP(v,v_x))),z))*.
% 299.64/300.39 93486[0:SpR:88.1,86147.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v))*.
% 299.64/300.39 93658[0:SpR:9.0,86148.1] || equal(c_Fun_Ocomp(u,v,w,x,y),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,hAPP(v,v_x))),z,t_a)*.
% 299.64/300.39 93637[0:SpR:88.1,86148.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.39 93802[0:SpR:9.0,86342.1] || equal(c_Fun_Ocomp(u,v,w,x,y),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(u,hAPP(v,v_x))))*.
% 299.64/300.39 93781[0:SpR:88.1,86342.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 698[0:Res:529.1,590.0] || c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),hAPP(v_Q,v_x)),t_a)* -> .
% 299.64/300.39 664[0:Res:589.0,372.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.64/300.39 638[0:Res:589.0,375.0] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(u,v_x),w,tc_fun(v,tc_bool)).
% 299.64/300.39 637[0:Res:589.0,471.0] || c_lessequals(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),w,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),hAPP(u,v_x)),w)).
% 299.64/300.39 919[0:SpR:330.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v))**.
% 299.64/300.39 1175[0:SpR:88.1,648.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.39 1172[0:SpR:88.1,651.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.39 1232[0:SpR:1195.1,415.0] class_Lattices_Oboolean__algebra(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))**.
% 299.64/300.39 1244[0:SpR:1196.1,415.0] class_Lattices_Oboolean__algebra(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(u),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))**.
% 299.64/300.39 1310[0:SpR:1259.2,87.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ozero__class_Ozero(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 1309[0:SpR:1259.2,88.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 1459[0:SpR:1409.2,1259.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Ogroup__add(u) || equal(v,c_Orderings_Otop__class_Otop(u))* equal(v,c_HOL_Ozero__class_Ozero(u)) -> equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.39 1499[0:SpR:1421.2,1259.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Ogroup__add(u) || equal(v,c_Orderings_Obot__class_Obot(u))* equal(v,c_HOL_Ozero__class_Ozero(u)) -> equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.39 1558[0:SpL:141.1,15.1] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Ogroup__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ominus__class_Ominus(w,x,u))* -> equal(v,c_HOL_Ominus__class_Ominus(x,w,u))*.
% 299.64/300.39 1557[0:SpL:141.1,14.1] class_OrderedGroup_Oab__group__add(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ominus__class_Ominus(w,x,u))* -> equal(v,c_HOL_Ominus__class_Ominus(x,w,u))*.
% 299.64/300.39 1556[0:SpL:141.1,1394.1] class_OrderedGroup_Oab__group__add(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_Orderings_Obot__class_Obot(u))** -> equal(c_HOL_Ominus__class_Ominus(w,v,u),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 1555[0:SpL:141.1,1393.1] class_OrderedGroup_Oab__group__add(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_Orderings_Otop__class_Otop(u))** -> equal(c_HOL_Ominus__class_Ominus(w,v,u),c_Orderings_Obot__class_Obot(u))**.
% 299.64/300.39 1552[0:SpL:141.1,116.1] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Ogroup__add(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u))** -> equal(c_HOL_Ominus__class_Ominus(w,v,u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.39 1536[0:SpR:141.1,87.1] class_OrderedGroup_Oab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ominus__class_Ominus(v,w,u)),c_HOL_Ominus__class_Ominus(w,v,u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 1600[0:SpL:141.1,1367.1] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Ogroup__add(u) || equal(v,c_HOL_Ominus__class_Ominus(w,x,u))* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ominus__class_Ominus(x,w,u))*.
% 299.64/300.39 1622[0:SpL:141.1,1395.1] class_OrderedGroup_Oab__group__add(u) class_Lattices_Oboolean__algebra(u) || equal(v,c_HOL_Ominus__class_Ominus(w,x,u))* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ominus__class_Ominus(x,w,u))*.
% 299.64/300.39 1892[0:SpR:9.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,v_x))),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.39 1889[0:SpR:9.0,651.0] || -> c_lessequals(hAPP(u,hAPP(v,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.64/300.39 2091[0:Res:649.0,279.0] || -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs))**.
% 299.64/300.39 2090[0:Res:650.0,279.0] || -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u))**.
% 299.64/300.39 2125[0:SpR:2097.1,1103.1] || hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oinsert(v,w)),v))* -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Oinsert(v,w),t_a) hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oinsert(v,w))).
% 299.64/300.39 2204[0:SpR:2098.1,648.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.39 2201[0:SpR:2098.1,651.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.39 2567[0:SpR:585.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(hAPP(v,v_x),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_COMBC(v,x,y,z),w),tc_Com_Opname,u),u)*.
% 299.64/300.39 2578[0:SpR:586.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(v,hAPP(w,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_COMBB(v,x,y,z),w),tc_Com_Opname,u),u)*.
% 299.64/300.39 2597[0:SpR:445.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(v_x,v) c_lessequals(hAPP(w,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Fun_Ofun__upd(w,v,x,y,z),tc_Com_Opname,u),u)*.
% 299.64/300.39 3191[0:SpR:302.1,2771.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v)* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool))*.
% 299.64/300.39 3560[1:MRR:3375.1,589.0] || equal(u,v_P) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(u,v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(v_Q,v_x)),t_a)*.
% 299.64/300.39 3561[1:MRR:3373.1,589.0] || equal(u,c_Com_Ocom_OBODY) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(u,v_x)),hAPP(v_Q,v_x)),t_a)*.
% 299.64/300.39 3562[1:MRR:3372.1,589.0] || equal(u,v_Q) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(u,v_x)),t_a)*.
% 299.64/300.39 3958[0:SpL:337.0,3506.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))* -> .
% 299.64/300.39 3955[0:SpL:540.1,3506.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))* -> .
% 299.64/300.39 3954[0:SpL:539.1,3506.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))* -> .
% 299.64/300.39 3942[0:SpL:25.1,3506.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(w,x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))* -> .
% 299.64/300.39 4156[0:SpL:586.0,3929.0] || hBOOL(hAPP(u,hAPP(v,v_x))) equal(hAPP(c_COMBB(u,w,x,y),v),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.64/300.39 4155[0:SpL:585.0,3929.0] || hBOOL(hAPP(hAPP(u,v_x),v)) equal(hAPP(c_COMBC(u,w,x,y),v),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.64/300.39 4132[0:SpL:445.1,3929.0] || hBOOL(hAPP(u,v_x)) equal(c_Fun_Ofun__upd(u,v,w,x,y),z)* -> equal(v_x,v) hBOOL(hAPP(z,v_x))*.
% 299.64/300.39 4239[0:SpL:299.2,3506.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(w,x),v)* -> .
% 299.64/300.39 4334[0:SpL:297.2,3506.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(w,x),v_x)** -> .
% 299.64/300.39 4424[0:SpR:9.0,3284.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(z),v_Procs),hAPP(u,hAPP(v,v_x))))*.
% 299.64/300.39 4422[0:SpR:88.1,3284.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 4417[0:SpR:2098.1,3284.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(hAPP(c_in(v),v_Procs),v_x))*.
% 299.64/300.39 4472[0:SpL:9.0,3493.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_in(tc_Com_Opname))** equal(hAPP(u,hAPP(v,v_x)),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))* -> .
% 299.64/300.39 4470[0:SpL:88.1,3493.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_in(tc_Com_Opname))** equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.39 4521[0:SpR:9.0,3316.1] || equal(c_in(u),c_Fun_Ocomp(v,w,x,y,z))* -> hBOOL(hAPP(hAPP(v,hAPP(w,v_x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.39 4519[0:SpR:88.1,3316.1] class_Lattices_Oboolean__algebra(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.39 4514[0:SpR:2098.1,3316.1] || equal(c_in(u),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,v_x),tc_Hoare__Mirabelle_Otriple(t_a)))* -> c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.39 4551[0:SpR:3586.1,3316.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_in(w),c_Set_Oinsert(v,u))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.39 4548[0:SpR:3586.1,648.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),tc_Com_Opname,w),v_Procs)))*.
% 299.64/300.39 4546[0:SpR:3586.1,3284.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),v_x))*.
% 299.64/300.39 4540[0:SpR:3586.1,651.0] || equal(hAPP(c_in(u),v),v_Procs) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.39 4657[0:SpL:9.0,3698.2] || equal(u,c_Fun_Ocomp(v,w,x,y,z))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(v,hAPP(w,v_x)),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 4655[0:SpL:88.1,3698.2] class_Lattices_Oboolean__algebra(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* equal(c_Com_Ocom_OBODY,v) equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 4650[0:SpL:2098.1,3698.2] || equal(u,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,v_x),tc_Hoare__Mirabelle_Otriple(t_a)))* equal(c_Com_Ocom_OBODY,u) equal(v_x,c_Com_Ocom_OSKIP) -> c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a).
% 299.64/300.39 4640[0:SpL:3586.1,3698.2] || equal(hAPP(c_in(u),v),v_Procs)** equal(w,c_Set_Oinsert(v,u))* equal(c_Com_Ocom_OBODY,w) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 4709[0:Res:989.1,146.1] class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(c_HOL_Ouminus__class_Ouminus(v,u),w,x),tc_Com_Opname,u),u),v,u)*.
% 299.64/300.39 5113[0:SpR:9.0,3339.1] || equal(u,c_Fun_Ocomp(v,w,x,y,z))* -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(v,hAPP(w,v_x)),x1,x2),u)**.
% 299.64/300.39 5111[0:SpR:88.1,3339.1] class_Lattices_Oboolean__algebra(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* -> equal(c_Fun_Ofun__upd(v,v_x,c_Orderings_Otop__class_Otop(u),w,x),v)**.
% 299.64/300.39 5106[0:SpR:2098.1,3339.1] || equal(u,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,v_x),tc_Hoare__Mirabelle_Otriple(t_a)))* -> c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) equal(c_Fun_Ofun__upd(u,v_x,v_x,w,x),u)**.
% 299.64/300.39 5096[0:SpR:3586.1,3339.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(w,c_Set_Oinsert(v,u))* -> equal(c_Fun_Ofun__upd(w,v_x,v_x,x,y),w)**.
% 299.64/300.39 5161[0:SpR:1605.2,4691.2] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.39 5157[0:SpR:1259.2,4691.2] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.39 5261[0:SpR:1605.2,4693.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.39 5260[0:SpR:1628.2,4693.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.39 5257[0:SpR:1259.2,4693.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.39 5254[0:SpR:1421.2,4693.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)*.
% 299.64/300.39 5253[0:SpR:1409.2,4693.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)) -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.39 5307[0:SpR:1628.2,5280.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 5303[0:SpR:1421.2,5280.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.39 5302[0:SpR:1409.2,5280.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.39 5356[0:SpR:1605.2,4694.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Oorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.39 5355[0:SpR:1628.2,4694.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Oorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.39 5352[0:SpR:1259.2,4694.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Oorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.39 5349[0:SpR:1421.2,4694.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Oorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)*.
% 299.64/300.39 5348[0:SpR:1409.2,4694.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Oorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)) -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.39 5458[0:SpL:5390.2,134.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),v)** -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.39 5530[0:SpR:1628.2,5375.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Oorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 5526[0:SpR:1421.2,5375.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Oorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.39 5525[0:SpR:1409.2,5375.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Oorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.39 5582[0:SpR:1605.2,4695.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.39 5581[0:SpR:1628.2,4695.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.39 5577[0:SpR:1259.2,4695.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.39 5574[0:SpR:1421.2,4695.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)*.
% 299.64/300.39 5573[0:SpR:1409.2,4695.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)) -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.39 5629[0:SpR:1628.2,5602.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 5625[0:SpR:1421.2,5602.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.39 5624[0:SpR:1409.2,5602.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.39 5680[0:SpR:1605.2,4783.2] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 5675[0:SpR:1259.2,4783.2] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 5788[0:SpR:1605.2,4785.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 5787[0:SpR:1628.2,4785.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 5783[0:SpR:1259.2,4785.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 5780[0:SpR:1421.2,4785.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u)) -> c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.39 5779[0:SpR:1409.2,4785.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)) -> c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.39 5840[0:SpR:1628.2,5810.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 5836[0:SpR:1421.2,5810.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 5835[0:SpR:1409.2,5810.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 5990[0:SpL:584.0,33.0] || hBOOL(hAPP(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2))* -> hBOOL(hAPP(x2,hAPP(u,hAPP(x,x2))))*.
% 299.64/300.39 5981[0:SpL:584.0,3506.1] || equal(c_COMBS(u,v,w,x,y),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(z,x1),hAPP(hAPP(u,v_x),hAPP(v,v_x)))* -> .
% 299.64/300.39 5949[0:SpR:300.1,584.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w,x,y),z),hAPP(z,hAPP(v,z)))*.
% 299.64/300.39 5942[0:SpR:2097.1,584.0] || hBOOL(hAPP(u,v)) -> equal(hAPP(c_COMBS(c_Set_Oinsert(v,w),x,y,z,x1),u),hAPP(u,hAPP(x,u)))*.
% 299.64/300.39 5912[0:SpR:300.1,584.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,x,y),z),hAPP(hAPP(v,z),z))*.
% 299.64/300.39 5905[0:SpR:2097.1,584.0] || hBOOL(hAPP(u,v)) -> equal(hAPP(c_COMBS(w,c_Set_Oinsert(v,x),y,z,x1),u),hAPP(hAPP(w,u),u))*.
% 299.64/300.39 5900[0:SpR:584.0,34.1] || hBOOL(hAPP(u,hAPP(v,hAPP(w,u))))* -> hBOOL(hAPP(c_COMBS(c_Set_Ovimage(v,x,y),w,z,x1,x2),u))*.
% 299.64/300.39 5897[0:SpR:584.0,518.1] || hBOOL(hAPP(hAPP(u,v),w)) -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u,y,z,x1),v),w))*.
% 299.64/300.39 5895[0:SpR:584.0,517.1] || hBOOL(hAPP(u,hAPP(v,w))) -> hBOOL(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),v,y,z,x1),w))*.
% 299.64/300.39 5894[0:SpR:584.0,518.1] || hBOOL(hAPP(u,hAPP(v,u)))* -> hBOOL(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v,y,z,x1),u))*.
% 299.64/300.39 5886[0:SpR:584.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(u,v),hAPP(w,v),hAPP(c_COMBS(u,w,x,y,z),v),x1,x2),hAPP(u,v))**.
% 299.64/300.39 5883[0:SpR:584.0,331.0] || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),hAPP(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))**.
% 299.64/300.39 5881[0:SpR:584.0,299.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(v,w),w,u)* -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),w),w)**.
% 299.64/300.39 6043[0:SpR:586.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(u,hAPP(v,w)),x),hAPP(c_COMBB(u,y,z,x1),v),x2,x3,x4),w))*.
% 299.64/300.39 6042[0:SpR:585.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(u,v),w),x),hAPP(c_COMBC(u,y,z,x1),w),x2,x3,x4),v))*.
% 299.64/300.39 6002[0:SpR:369.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),w),x),c_Set_Oinsert(u,v),y,z,x1),hAPP(c_Set_Oinsert(u,v),w)))*.
% 299.64/300.39 6001[0:SpR:2089.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),v),c_Set_Oinsert(v_x,tc_Com_Opname),w,x,y),hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs)))*.
% 299.64/300.39 5996[0:SpR:445.1,5875.0] || -> equal(u,v) hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(w,u),x),c_Fun_Ofun__upd(w,v,y,z,x1),x2,x3,x4),u))*.
% 299.64/300.39 6117[0:SpR:1605.2,4787.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 6116[0:SpR:1628.2,4787.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.39 6112[0:SpR:1259.2,4787.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 6109[0:SpR:1421.2,4787.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u)) -> c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.39 6108[0:SpR:1409.2,4787.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)) -> c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.39 6169[0:SpR:1628.2,6139.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 6165[0:SpR:1421.2,6139.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 6164[0:SpR:1409.2,6139.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Opreorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.39 6231[0:SpR:3229.1,599.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) -> equal(hAPP(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.64/300.39 6245[0:SSi:6200.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))).
% 299.64/300.39 6292[0:Res:49.2,70.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(v,c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.64/300.39 6282[0:SpL:2267.1,70.0] || equal(u,v) c_lessequals(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.64/300.39 6278[0:SpL:135.0,70.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),u,tc_fun(v,tc_bool))* -> equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.64/300.39 6320[0:SpR:331.0,3279.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x)).
% 299.64/300.39 6319[0:SpR:302.1,3279.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(c_Orderings_Otop__class_Otop(u),v_Procs),v_x))*.
% 299.64/300.39 6459[0:SpR:3229.1,538.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),hAPP(hAPP(u,v_x),w))*.
% 299.64/300.39 6421[0:SpR:538.0,3229.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) -> equal(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w))*.
% 299.64/300.39 6414[0:SpR:538.0,3283.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),v_Procs))*.
% 299.64/300.39 6411[0:SpR:538.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)))*.
% 299.64/300.39 6521[0:Res:3285.1,279.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))**.
% 299.64/300.39 6501[0:SpR:331.0,3285.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.39 6500[0:SpR:302.1,3285.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.39 6568[0:SpL:3229.1,327.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* equal(hAPP(u,v_x),v_x)** -> c_lessequals(w,v_x,tc_fun(v,tc_bool)).
% 299.64/300.39 6566[0:SpL:3229.1,327.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)))* equal(hAPP(hAPP(u,v_x),w),w)** -> c_lessequals(v_x,w,tc_fun(v,tc_bool))*.
% 299.64/300.39 6668[0:SpR:3229.1,329.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)))* c_lessequals(v_x,w,tc_fun(v,tc_bool))* -> equal(hAPP(hAPP(u,v_x),w),w)**.
% 299.64/300.39 6620[0:SpR:329.1,3229.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> equal(hAPP(w,v_x),v_x)**.
% 299.64/300.39 6612[0:SpR:329.1,3283.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.39 6609[0:SpR:329.1,1158.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.39 6739[0:SpR:331.0,3291.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),v_Procs))*.
% 299.64/300.39 6738[0:SpR:302.1,3291.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(u)),v_Procs))*.
% 299.64/300.39 6831[0:SpR:3229.1,328.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)))* c_lessequals(w,v_x,tc_fun(v,tc_bool))* -> equal(hAPP(hAPP(u,v_x),w),v_x)**.
% 299.64/300.39 6782[0:SpR:328.1,3229.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> equal(hAPP(w,v_x),u)*.
% 299.64/300.39 6773[0:SpR:328.1,3283.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(u,v_Procs)).
% 299.64/300.39 6770[0:SpR:328.1,1158.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),v_Procs),u))*.
% 299.64/300.39 6869[0:SpL:331.0,3484.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,v),v_x)** -> equal(v_x,v).
% 299.64/300.39 6868[0:SpL:302.1,3484.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(u),hAPP(c_Com_Ocom_OBODY,v))* -> equal(v_x,v).
% 299.64/300.39 6904[0:SpL:302.1,3499.1] class_Lattices_Obounded__lattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.39 6945[0:SpL:3229.1,312.1] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(u))* -> equal(c_Orderings_Obot__class_Obot(u),v_x).
% 299.64/300.39 6991[0:SpL:3229.1,311.1] class_Lattices_Obounded__lattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) equal(hAPP(hAPP(v,v_x),w),c_Orderings_Obot__class_Obot(u))* -> equal(c_Orderings_Obot__class_Obot(u),v_x).
% 299.64/300.39 7126[0:SpR:331.0,3305.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.39 7125[0:SpR:302.1,3305.1] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 7193[0:Res:3317.1,279.0] || equal(c_in(u),c_in(v)) -> equal(hAPP(c_Set_Oinsert(v_x,v),hAPP(c_Set_Oinsert(v_x,u),w)),hAPP(c_Set_Oinsert(v_x,u),w))**.
% 299.64/300.39 7169[0:SpR:331.0,3317.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,u),w)))*.
% 299.64/300.39 7168[0:SpR:302.1,3317.1] class_Lattices_Obounded__lattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),hAPP(c_Set_Oinsert(v_x,v),w)))*.
% 299.64/300.39 7245[0:SpR:105.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(w,v,x),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.64/300.39 7241[0:SpR:38.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(w,v,x),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.64/300.39 7240[0:SpR:321.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oimage(w,x,v),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.64/300.39 7237[0:SpR:301.1,474.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.39 7214[0:SpR:525.1,474.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.39 7211[0:SpR:3229.1,474.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),hAPP(c_Set_Oimage(v,x,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.39 7203[0:SpR:2089.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.39 7305[0:SpR:9.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),hAPP(u,hAPP(v,x2))))*.
% 299.64/300.39 7293[0:SpR:584.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(u,v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(c_COMBS(u,y,z,x1,x2),v)))*.
% 299.64/300.39 7279[0:SpR:2098.1,7253.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v))*.
% 299.64/300.39 7269[0:SpR:3586.1,7253.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.39 7330[0:SpL:302.1,3507.1] class_Lattices_Obounded__lattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.39 7451[0:SpR:3229.1,364.1] || equal(u,c_Set_Oinsert(v,w))* c_lessequals(x,v_x,tc_fun(w,tc_bool)) -> c_lessequals(x,hAPP(u,v_x),tc_fun(w,tc_bool))*.
% 299.64/300.39 7502[0:SpR:331.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(v),u),v_x))*.
% 299.64/300.39 7501[0:SpR:302.1,3346.1] class_Lattices_Obounded__lattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(hAPP(c_in(w),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.39 7555[0:Res:448.1,363.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,hAPP(c_Set_Oinsert(w,u),x),tc_fun(u,tc_bool))* c_lessequals(x,v,tc_fun(u,tc_bool)).
% 299.64/300.39 7540[0:Res:364.1,363.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* -> c_lessequals(w,hAPP(c_Set_Oinsert(y,v),x),tc_fun(v,tc_bool))*.
% 299.64/300.39 7531[0:SpL:3229.1,363.0] || equal(u,c_Set_Oinsert(v,w))* c_lessequals(hAPP(u,v_x),x,tc_fun(w,tc_bool))* -> c_lessequals(v_x,x,tc_fun(w,tc_bool)).
% 299.64/300.39 7629[0:SpR:3229.1,294.2] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* c_lessequals(x,v_x,u) -> c_lessequals(x,hAPP(v,v_x),u)*.
% 299.64/300.39 7627[0:SpR:3229.1,294.2] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(w,x,u) -> c_lessequals(w,hAPP(hAPP(v,v_x),x),u)*.
% 299.64/300.39 7674[0:SSi:7663.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v),w)* -> c_Finite__Set_Ofinite(u,w).
% 299.64/300.39 7675[0:SSi:7662.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_in(tc_Com_Opname),v_x),u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_Procs))*.
% 299.64/300.39 7693[0:SpR:3229.1,293.2] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* c_lessequals(x,w,u)* -> c_lessequals(x,hAPP(v,v_x),u)*.
% 299.64/300.39 7691[0:SpR:3229.1,293.2] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(w,v_x,u) -> c_lessequals(w,hAPP(hAPP(v,v_x),x),u)*.
% 299.64/300.39 7737[0:SSi:7727.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),w)* -> c_Finite__Set_Ofinite(u,w).
% 299.64/300.39 7738[0:SSi:7726.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_in(tc_Com_Opname),v_x),u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_Procs))*.
% 299.64/300.39 7754[0:SpL:3229.1,296.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* c_lessequals(hAPP(v,v_x),x,u)* -> c_lessequals(v_x,x,u).
% 299.64/300.39 7752[0:SpL:3229.1,296.1] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(hAPP(hAPP(v,v_x),w),x,u)* -> c_lessequals(w,x,u).
% 299.64/300.39 7834[0:SSi:7786.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),u))),tc_fun(w,tc_bool))*.
% 299.64/300.39 7999[0:SpL:3229.1,295.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* c_lessequals(hAPP(v,v_x),x,u)* -> c_lessequals(w,x,u)*.
% 299.64/300.39 7997[0:SpL:3229.1,295.1] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(hAPP(hAPP(v,v_x),w),x,u)* -> c_lessequals(v_x,x,u).
% 299.64/300.39 8078[0:SSi:8031.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y))),tc_fun(w,tc_bool))*.
% 299.64/300.39 8153[0:Res:683.1,427.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Opreorder(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,u),w,u)* -> c_lessequals(hAPP(v,v_x),w,u).
% 299.64/300.39 8152[0:Res:4790.2,427.1] class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),v,u)* -> c_lessequals(w,v,u)*.
% 299.64/300.39 8177[0:SSi:8115.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> c_lessequals(v_x,w,tc_fun(v,tc_bool)).
% 299.64/300.39 8178[0:SSi:8109.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),y,tc_fun(v,tc_bool))* -> c_lessequals(x,y,tc_fun(v,tc_bool)).
% 299.64/300.39 8280[0:Res:683.1,426.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Oorder(u) || c_lessequals(v,hAPP(w,v_x),u) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,w,tc_Com_Opname,u),u)*.
% 299.64/300.39 8256[0:Res:4703.2,426.1] class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),u)* -> c_lessequals(v,w,u)*.
% 299.64/300.39 8309[0:SSi:8240.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(w,v),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.39 8310[0:SSi:8239.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(v,v_x),tc_fun(w,tc_bool)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.39 8311[0:SSi:8234.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oinsert(y,w),v)),tc_fun(w,tc_bool))*.
% 299.64/300.39 8440[0:SpR:8385.1,474.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.39 8620[0:SpL:8498.1,3698.2] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(v,c_Set_Oinsert(w,u))* equal(c_Com_Ocom_OBODY,v) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 8599[0:SpR:8498.1,7253.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(w,v),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),u))*.
% 299.64/300.39 8584[0:SpR:8498.1,3339.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(v,c_Set_Oinsert(w,u))* -> equal(c_Fun_Ofun__upd(v,v_x,v_x,x,y),v)**.
% 299.64/300.39 8583[0:SpR:8498.1,3316.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_in(v),c_Set_Oinsert(w,u))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.39 8580[0:SpR:8498.1,648.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(w,u),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.39 8576[0:SpR:8498.1,3284.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),v_x))*.
% 299.64/300.39 8569[0:SpR:8498.1,651.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.39 8947[0:SpL:8415.2,3700.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.39 8928[0:SpL:8415.2,656.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) hBOOL(hAPP(v_x,c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.39 8871[0:SpR:8415.2,341.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> c_lessequals(v,hAPP(v_x,v),tc_fun(u,tc_bool))*.
% 299.64/300.39 8863[0:SpR:8415.2,342.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(v,v_x,tc_fun(u,tc_bool)).
% 299.64/300.39 8839[0:SpR:8415.2,302.1] class_Lattices_Obounded__lattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(c_Orderings_Otop__class_Otop(u),v_x).
% 299.64/300.39 8829[0:SpR:8415.2,303.1] class_Lattices_Obounded__lattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.39 8816[0:SpR:8415.2,330.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_x)**.
% 299.64/300.39 8794[0:SpR:8415.2,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),v) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,u),u)*.
% 299.64/300.39 8749[0:SpR:8415.2,342.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> c_lessequals(v_x,hAPP(v_x,v),tc_fun(u,tc_bool))*.
% 299.64/300.39 9022[4:MRR:8998.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_Set_Ovimage(u,v,w),x),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(x,hAPP(u,v_x))).
% 299.64/300.39 9023[4:MRR:8997.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(w,v_x)) equal(u,v_x).
% 299.64/300.39 9060[0:SpL:3586.1,214.0] || equal(hAPP(c_in(u),v),v_Procs) c_lessequals(v_x,w,tc_fun(u,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),v),w))*.
% 299.64/300.39 9050[0:SpL:8498.1,214.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) c_lessequals(u,w,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),x),w))*.
% 299.64/300.39 9106[0:SSi:9092.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w,x,y,z),hAPP(c_Set_Oinsert(v,u),x1))))*.
% 299.64/300.40 9193[0:SpR:329.1,8376.2] || c_lessequals(v_x,u,tc_fun(v,tc_bool))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_in(tc_Com_Opname)) equal(u,v_Procs) -> hBOOL(u).
% 299.64/300.40 9191[0:SpR:538.0,8376.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(tc_Com_Opname)) equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x))*.
% 299.64/300.40 9160[0:SpR:331.0,8376.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.40 9159[0:SpR:302.1,8376.2] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v))*.
% 299.64/300.40 9259[0:SpR:8415.2,9258.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(v_x,u)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.40 9376[0:SpL:584.0,347.0] || c_Fun_Oinj__on(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),x1),v,x2)* -> c_Fun_Oinj__on(u,x1,v,x2).
% 299.64/300.40 9465[0:SpR:414.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Fun_Ofun__upd(v,v_x,u,w,x)),c_Fun_Ofun__upd(v,v_x,u,w,x))**.
% 299.64/300.40 9450[0:SpR:365.1,9268.0] class_Orderings_Obot(u) || -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,u))),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)))**.
% 299.64/300.40 9448[0:SpR:397.1,9268.0] class_Orderings_Otop(u) || -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(t_a,u))),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)))**.
% 299.64/300.40 10112[0:Res:83.0,431.0] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(y,z,w),hAPP(c_Set_Ovimage(y,z,w),v)),w,x)*.
% 299.64/300.40 10511[0:Res:8376.2,454.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) equal(u,v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(u,v),v_x,t_a)*.
% 299.64/300.40 10502[0:Res:3346.1,454.0] || equal(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(v,v_x),w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(v,v_x),w),u,t_a)*.
% 299.64/300.40 10590[0:SpL:2807.0,57.1] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_bool)),u),c_HOL_Ozero__class_Ozero(tc_bool))** -> equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_HOL_Ozero__class_Ozero(tc_bool)).
% 299.64/300.40 10739[0:SpR:584.0,9566.0] || -> c_lessequals(hAPP(hAPP(u,v),hAPP(w,v)),hAPP(hAPP(c_Set_Oinsert(x,y),c_COMBS(u,w,z,x1,x2)),v),tc_bool)*.
% 299.64/300.40 10734[0:SpR:336.0,9566.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_bool)*.
% 299.64/300.40 10723[0:SpR:584.0,9566.0] || -> c_lessequals(hAPP(c_COMBS(u,v,w,x,y),z),hAPP(hAPP(c_Set_Oinsert(x1,x2),hAPP(u,z)),hAPP(v,z)),tc_bool)*.
% 299.64/300.40 10718[0:SpR:337.0,9566.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))),x),tc_bool)*.
% 299.64/300.40 10711[0:SpR:540.1,9566.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),v),tc_bool)*.
% 299.64/300.40 10710[0:SpR:539.1,9566.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),v),tc_bool)*.
% 299.64/300.40 10709[0:SpR:297.2,9566.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(w,hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),w),tc_bool)*.
% 299.64/300.40 10700[0:SpR:299.2,9566.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(w,hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),v),tc_bool)*.
% 299.64/300.40 10692[0:SpR:25.1,9566.0] class_HOL_Ouminus(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),hAPP(hAPP(c_Set_Oinsert(w,x),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u))),v_x),tc_bool)*.
% 299.64/300.40 10876[0:SpR:2093.0,353.0] || -> equal(hAPP(c_Set_Oinsert(v_Procs,u),hAPP(c_Set_Oinsert(v,u),hAPP(c_in(tc_Com_Opname),v_x))),hAPP(c_Set_Oinsert(v,u),hAPP(c_in(tc_Com_Opname),v_x)))**.
% 299.64/300.40 10875[0:SpR:3744.1,353.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(c_Set_Oinsert(v,u),v_Procs)),hAPP(c_Set_Oinsert(v,u),v_Procs))**.
% 299.64/300.40 10829[0:SpR:353.0,212.1] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),x)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(y,v),w)),x))*.
% 299.64/300.40 11109[0:Res:288.1,121.0] || c_Natural_Oevaln(u,v,w,x)* c_Natural_Oevaln(y,x,c_Suc(w),z)* -> c_Natural_Oevaln(c_Com_Ocom_OSemi(u,y),v,c_Suc(w),z)*.
% 299.64/300.40 11271[0:SpL:11176.1,3507.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* equal(u,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.40 11270[0:SpL:11176.1,3499.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)) hBOOL(hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.40 11267[0:SpL:11176.1,3484.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY)** equal(u,hAPP(c_Com_Ocom_OBODY,v))* -> equal(v_x,v).
% 299.64/300.40 11260[0:SpR:8415.2,11176.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(hAPP(v_x,u),v_x)**.
% 299.64/300.40 11218[0:SpR:11176.1,3346.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)) -> hBOOL(hAPP(hAPP(c_in(w),v),u))*.
% 299.64/300.40 11217[0:SpR:11176.1,3317.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)) -> hBOOL(hAPP(u,hAPP(c_Set_Oinsert(v_x,v),w)))*.
% 299.64/300.40 11216[0:SpR:11176.1,3305.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),u))*.
% 299.64/300.40 11209[0:SpR:11176.1,8376.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(u,v))*.
% 299.64/300.40 11208[0:SpR:11176.1,8415.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(u,v_x).
% 299.64/300.40 11207[0:SpR:11176.1,3291.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),v_Procs))*.
% 299.64/300.40 11206[0:SpR:11176.1,3285.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.40 11203[0:SpR:11176.1,3279.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(u,v_Procs),v_x))*.
% 299.64/300.40 11406[0:SpL:11177.1,57.1] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_HOL_Ozero__class_Ozero(tc_bool)) -> equal(u,c_HOL_Ozero__class_Ozero(tc_bool)).
% 299.64/300.40 11399[0:SpL:11177.1,3499.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* hBOOL(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.40 11396[0:SpL:11177.1,3484.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,v),v_x)** -> equal(v_x,v).
% 299.64/300.40 11389[0:SpR:8415.2,11177.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(v_x,u),u)**.
% 299.64/300.40 11346[0:SpR:11177.1,3346.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w))* -> hBOOL(hAPP(hAPP(c_in(v),u),v_x))*.
% 299.64/300.40 11345[0:SpR:11177.1,3317.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,u),w)))*.
% 299.64/300.40 11344[0:SpR:11177.1,3305.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.40 11337[0:SpR:11177.1,8376.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.40 11335[0:SpR:11177.1,3291.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),v_Procs))*.
% 299.64/300.40 11334[0:SpR:11177.1,3285.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.40 11331[0:SpR:11177.1,3279.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.40 11461[0:SpR:8415.2,10745.0] || equal(v_Procs,v_x) equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(w,v_x,tc_bool).
% 299.64/300.40 11454[0:SpR:8415.2,10745.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(u,v),v_x),w),tc_bool)*.
% 299.64/300.40 11490[0:SpR:584.0,10746.0] || -> c_lessequals(hAPP(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v)),hAPP(c_COMBS(c_Set_Oinsert(w,x),u,y,z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v)),tc_bool)*.
% 299.64/300.40 11480[0:SpR:8415.2,10746.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),v_x),u),tc_bool)*.
% 299.64/300.40 11652[0:SpR:8415.2,9567.0] || equal(v_Procs,v_x) equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(v_x,hAPP(u,v_x),tc_bool).
% 299.64/300.40 11639[0:SpR:586.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_COMBB(u,v,w,x),y),z,tc_fun(x1,tc_bool)),x2),hAPP(u,hAPP(y,x2)),tc_bool)*.
% 299.64/300.40 11638[0:SpR:585.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_COMBC(u,v,w,x),y),z,tc_fun(x1,tc_bool)),x2),hAPP(hAPP(u,x2),y),tc_bool)*.
% 299.64/300.40 11591[0:SpR:8415.2,9567.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x),v_x,tc_bool)*.
% 299.64/300.40 11585[0:SpR:369.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(u,v),w,tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),y)),hAPP(c_Set_Oinsert(u,v),y),tc_bool)*.
% 299.64/300.40 11584[0:SpR:2089.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),tc_bool)*.
% 299.64/300.40 11579[0:SpR:445.1,9567.0] || -> equal(u,v) c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Fun_Ofun__upd(w,v,x,y,z),x1,tc_fun(x2,tc_bool)),u),hAPP(w,u),tc_bool)*.
% 299.64/300.40 11715[2:SpR:130.1,4250.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))*.
% 299.64/300.40 11707[0:SpR:130.1,3282.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_Procs) -> hBOOL(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))*.
% 299.64/300.40 12583[0:Res:47.2,12532.0] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),c_HOL_Ominus__class_Ominus(u,v,tc_bool),tc_bool) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),tc_bool),u,tc_bool)*.
% 299.64/300.40 12713[0:Res:12533.1,50.1] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),tc_bool),tc_bool)* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_bool),c_HOL_Ozero__class_Ozero(tc_bool),tc_bool).
% 299.64/300.40 12932[0:SpR:8415.2,10713.0] || equal(v_Procs,v_x) equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(w,x,y)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(w,v_x,tc_bool).
% 299.64/300.40 12955[0:Res:11108.1,121.0] || c_Natural_Oevaln(u,v,w,x)* c_Natural_Oevaln(y,x,w,z)* -> c_Natural_Oevaln(c_Com_Ocom_OSemi(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,u),y),v,w,z)*.
% 299.64/300.40 12990[0:Res:3346.1,501.0] || equal(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v)* c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,hAPP(v,v_x)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.64/300.40 12985[0:Res:1157.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oimage(c_COMBK(v,w,x),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v,t_a).
% 299.64/300.40 13083[0:SpR:9.0,10090.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(u,hAPP(v,v_x)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.40 13074[0:SpR:88.1,10090.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.40 13067[0:SpR:2098.1,10090.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.40 13057[0:SpR:3586.1,10090.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.40 13158[0:SpR:135.0,108.1] || c_lessequals(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.40 13137[0:SpR:135.0,108.1] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)),u,tc_fun(v,tc_bool))*.
% 299.64/300.40 13277[0:SpL:9493.1,214.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(u,v,tc_fun(t_a,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v))*.
% 299.64/300.40 13245[0:SpR:9493.1,7253.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),u))*.
% 299.64/300.40 13542[0:SpR:9.0,11030.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_in(t_a))** -> hBOOL(hAPP(hAPP(u,hAPP(v,v_x)),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))*.
% 299.64/300.40 13533[0:SpR:88.1,11030.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.40 13526[0:SpR:2098.1,11030.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.40 13516[0:SpR:3586.1,11030.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_in(t_a)) -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.40 13505[0:SpR:8498.1,11030.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.40 13654[0:SpL:11473.0,3698.2] || equal(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* equal(c_Com_Ocom_OBODY,u) equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 13652[0:SpL:11473.0,3493.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_in(tc_Com_Opname))** equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.40 13621[0:SpR:11473.0,3339.1] || equal(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* -> equal(c_Fun_Ofun__upd(u,v_x,c_Orderings_Otop__class_Otop(tc_bool),x,y),u)**.
% 299.64/300.40 13620[0:SpR:11473.0,3316.1] || equal(c_in(u),hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.40 13617[0:SpR:11473.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.40 13615[0:SpR:11473.0,11030.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.40 13614[0:SpR:11473.0,10090.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.40 13609[0:SpR:11473.0,3284.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 13601[0:SpR:11473.0,651.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.40 13790[0:Obv:13747.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v))**.
% 299.64/300.40 14090[0:Obv:14040.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v))**.
% 299.64/300.40 14093[0:Obv:13992.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v).
% 299.64/300.40 14122[0:SpR:659.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),hAPP(c_Set_Oinsert(v_Procs,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))))*.
% 299.64/300.40 14290[0:SpL:14216.0,3507.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))))* equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.40 14289[0:SpL:14216.0,3499.1] || equal(c_in(u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))* hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.40 14286[0:SpL:14216.0,3484.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(v_x,x).
% 299.64/300.40 14256[0:SpR:14216.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(v),u),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 14255[0:SpR:14216.0,3317.1] || equal(c_in(u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(v_x,u),y)))*.
% 299.64/300.40 14254[0:SpR:14216.0,3305.1] || equal(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,y),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 14245[0:SpR:14216.0,8376.2] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_in(tc_Com_Opname))** equal(x,v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),x))*.
% 299.64/300.40 14244[0:SpR:14216.0,8415.2] || equal(v_Procs,v_x) equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.40 14243[0:SpR:14216.0,3291.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),c_Orderings_Otop__class_Otop(tc_bool)),v_Procs))*.
% 299.64/300.40 14242[0:SpR:14216.0,3285.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)))*.
% 299.64/300.40 14239[0:SpR:14216.0,3279.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_Procs),v_x)).
% 299.64/300.40 14308[0:MRR:14307.0,826.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))),hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))**.
% 299.64/300.40 14323[0:SpR:11695.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.64/300.40 14358[0:Res:267.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),w),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(v,u),w),u),v,u)*.
% 299.64/300.40 14349[0:Res:658.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),tc_Com_Opname),v_x,tc_Com_Opname)*.
% 299.64/300.40 14451[0:SpL:12944.0,3698.2] || equal(u,hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)))* equal(c_Com_Ocom_OBODY,u) equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 14449[0:SpL:12944.0,3493.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_in(tc_Com_Opname))** equal(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.40 14429[0:SpR:12944.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 14418[0:SpR:12944.0,3339.1] || equal(u,hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)))* -> equal(c_Fun_Ofun__upd(u,v_x,c_Orderings_Otop__class_Otop(tc_bool),z,x1),u)**.
% 299.64/300.40 14417[0:SpR:12944.0,3316.1] || equal(c_in(u),hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.40 14414[0:SpR:12944.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.40 14412[0:SpR:12944.0,11030.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))))*.
% 299.64/300.40 14411[0:SpR:12944.0,10090.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.40 14406[0:SpR:12944.0,3284.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(y),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 14398[0:SpR:12944.0,651.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),tc_Com_Opname,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.64/300.40 14485[0:Res:267.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),w),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(v,u),w),u),u)*.
% 299.64/300.40 14476[0:Res:658.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),tc_Com_Opname) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.40 14752[0:SpR:135.0,128.0] || -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x))**.
% 299.64/300.40 14856[0:SpR:1605.2,11007.2] class_OrderedGroup_Ogroup__add(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.40 14855[0:SpR:1628.2,11007.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.40 14851[0:SpR:1259.2,11007.2] class_OrderedGroup_Ogroup__add(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.40 14848[0:SpR:1421.2,11007.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u)) -> c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.40 14847[0:SpR:1409.2,11007.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)) -> c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.40 14930[0:SpR:1628.2,14899.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.40 14926[0:SpR:1421.2,14899.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.40 14925[0:SpR:1409.2,14899.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.40 14991[0:SpR:1605.2,11008.2] class_OrderedGroup_Ogroup__add(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.40 14990[0:SpR:1628.2,11008.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.40 14986[0:SpR:1259.2,11008.2] class_OrderedGroup_Ogroup__add(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.40 14983[0:SpR:1421.2,11008.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)*.
% 299.64/300.40 14982[0:SpR:1409.2,11008.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)) -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.40 15054[0:SpR:1628.2,15023.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.40 15050[0:SpR:1421.2,15023.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.40 15049[0:SpR:1409.2,15023.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.40 15195[0:SpR:8385.1,446.1] || equal(u,v_Procs) c_lessequals(v,u,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),u,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.40 15269[0:SpR:10063.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,t_a),u,tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_bool)*.
% 299.64/300.40 15264[0:SpR:10063.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))))*.
% 299.64/300.40 15295[0:Res:15261.0,170.1] class_Orderings_Olinorder(t_a) || c_Finite__Set_Ofinite(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),t_a) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),t_a),v_x,t_a)*.
% 299.64/300.40 15294[0:Res:15261.0,169.1] class_Orderings_Olinorder(t_a) || c_Finite__Set_Ofinite(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),t_a) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),t_a),t_a)*.
% 299.64/300.40 15515[0:Rew:15475.0,15473.1] || equal(c_Set_Oinsert(u,v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.40 15516[0:Rew:15475.0,15472.1] || equal(c_in(u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool))) hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.40 15518[0:Rew:15475.0,15469.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(c_Com_Ocom_OBODY,v))* -> equal(v_x,v).
% 299.64/300.40 15519[0:Rew:15475.0,15434.1] || equal(c_Set_Oinsert(u,v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,tc_bool))) -> hBOOL(hAPP(hAPP(c_in(v),u),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool)))*.
% 299.64/300.40 15520[0:Rew:15475.0,15433.1] || equal(c_in(u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool))) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),hAPP(c_Set_Oinsert(v_x,u),w)))*.
% 299.64/300.40 15521[0:Rew:15475.0,15432.1] || equal(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v_Procs),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool)))*.
% 299.64/300.40 15524[0:Rew:15475.0,15423.2] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_in(tc_Com_Opname)) equal(v,v_Procs) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v))*.
% 299.64/300.40 15525[0:Rew:15475.0,15422.2] || equal(v_Procs,v_x) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v_x)**.
% 299.64/300.40 15526[0:Rew:15475.0,15421.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)),v_Procs))*.
% 299.64/300.40 15527[0:Rew:15475.0,15420.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.40 15528[0:Rew:15475.0,15417.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v_Procs),v_x))*.
% 299.64/300.40 15638[0:Res:3346.1,278.1] || equal(c_Set_Oinsert(u,v),w)* hBOOL(hAPP(x,u))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(w,v_x),y,x,v)))*.
% 299.64/300.40 15635[0:Res:9071.0,278.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,tc_fun(w,tc_bool)),x,u,w)))*.
% 299.64/300.40 15632[0:Res:1157.0,278.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(c_COMBK(v,w,x),tc_Com_Opname,y),v_Procs),z,u,y)))*.
% 299.64/300.40 15810[0:SpR:9.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Fun_Ocomp(u,v,w,x,y),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool)).
% 299.64/300.40 15799[0:SpR:88.1,15482.1] class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)).
% 299.64/300.40 15866[0:Res:3346.1,277.1] || equal(c_Set_Oinsert(u,v),w)* hBOOL(hAPP(x,u))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(w,v_x),x,v)))*.
% 299.64/300.40 15863[0:Res:9071.0,277.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,x),tc_Com_Opname,tc_fun(x,tc_bool)),u,x)))*.
% 299.64/300.40 15860[0:Res:1157.0,277.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oimage(c_COMBK(v,x,y),tc_Com_Opname,z),v_Procs),u,z)))*.
% 299.64/300.40 15950[2:SpR:9.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Fun_Ocomp(u,v,w,x,y),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool)).
% 299.64/300.40 15939[2:SpR:88.1,15483.1] class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)).
% 299.64/300.40 15931[2:SpR:2098.1,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.40 15920[2:SpR:3586.1,15483.1] || equal(hAPP(c_in(u),v),v_Procs) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.40 15908[2:SpR:8498.1,15483.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.40 16185[0:Res:15262.1,279.0] || equal(c_in(t_a),c_in(u)) -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.64/300.40 16167[0:SpR:14216.0,15262.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.40 16166[0:SpR:11176.1,15262.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a)) -> hBOOL(hAPP(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.40 16165[0:SpR:11177.1,15262.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.40 16148[0:SpR:331.0,15262.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))).
% 299.64/300.40 16147[0:SpR:302.1,15262.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.40 16134[0:SpR:15476.0,15262.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_in(t_a)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.40 16268[0:SpL:586.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_COMBB(u,w,x,y),v),v_Procs)** -> .
% 299.64/300.40 16267[0:SpL:585.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_COMBC(u,w,x,y),v),v_Procs)** -> .
% 299.64/300.40 16233[0:SpL:8415.2,16217.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(u,v_Procs) -> .
% 299.64/300.40 16227[0:SpL:445.1,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Fun_Ofun__upd(u,v,w,x,y),v_Procs)** -> equal(v_x,v).
% 299.64/300.40 16352[0:SpL:328.1,16286.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_Procs)** -> .
% 299.64/300.40 16351[0:SpL:538.0,16286.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs) -> .
% 299.64/300.40 16477[0:SpL:9935.1,57.1] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_bool),tc_bool)* equal(c_Orderings_Otop__class_Otop(tc_bool),c_HOL_Ozero__class_Ozero(tc_bool)) -> equal(u,c_HOL_Ozero__class_Ozero(tc_bool)).
% 299.64/300.40 16414[0:SpR:9935.1,415.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,c_Orderings_Otop__class_Otop(tc_bool),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))**.
% 299.64/300.40 16396[0:SpR:9935.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),tc_Com_Opname,u),u)*.
% 299.64/300.40 16507[0:SpR:659.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,tc_Com_Opname),v,u),u)*.
% 299.64/300.40 16650[0:SpR:9936.1,415.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,c_Orderings_Otop__class_Otop(tc_bool),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))**.
% 299.64/300.40 16632[0:SpR:9936.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v,tc_bool) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),tc_Com_Opname,u),u)*.
% 299.64/300.40 16743[0:Res:13385.1,202.1] || equal(hAPP(c_Set_Oimage(u,v,v),w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** c_Finite__Set_Ofinite(w,v) -> c_Fun_Oinj__on(u,w,v,v).
% 299.64/300.40 16779[0:Res:13385.1,390.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(x,u,v,w),y,w,v)*.
% 299.64/300.40 16849[0:SSi:16841.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_Procs) -> .
% 299.64/300.40 16942[0:SpR:600.0,518.1] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v),x))*.
% 299.64/300.40 17006[0:SSi:16989.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,tc_fun(w,tc_bool)),w,x)* -> c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_bool),w,x).
% 299.64/300.40 17025[0:SSi:17014.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,tc_fun(w,tc_bool)),w,x)* -> c_Fun_Oinj__on(u,c_Orderings_Obot__class_Obot(tc_bool),w,x).
% 299.64/300.40 17167[0:SpL:17045.0,3698.2] || equal(u,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)))* equal(c_Com_Ocom_OBODY,u) equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 17164[0:SpL:17045.0,3493.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_in(tc_Com_Opname))** equal(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.40 17144[0:SpR:17045.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.40 17132[0:SpR:17045.0,3339.1] || equal(u,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)))* -> equal(c_Fun_Ofun__upd(u,v_x,c_Orderings_Obot__class_Obot(tc_bool),y,z),u)**.
% 299.64/300.40 17131[0:SpR:17045.0,3316.1] || equal(c_in(u),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)))* -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.40 17128[0:SpR:17045.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.40 17125[0:SpR:17045.0,11030.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.64/300.40 17124[0:SpR:17045.0,10090.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.40 17119[0:SpR:17045.0,3284.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.40 17109[0:SpR:17045.0,651.0] || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),tc_Com_Opname,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.40 17285[0:SpL:302.1,13272.0] class_Lattices_Obounded__lattice(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.40 17272[0:SpL:15476.0,13272.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.40 17369[0:Obv:17357.2] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.64/300.40 17382[0:SpR:14526.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),x,tc_fun(y,tc_bool)),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),u)),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)*.
% 299.64/300.40 17403[0:SSi:17395.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_COMBK(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))* equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)).
% 299.64/300.40 17413[2:SSi:17405.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_COMBK(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))* equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(u,tc_bool)).
% 299.64/300.40 17414[2:SSi:17404.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_COMBK(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(u,tc_bool)).
% 299.64/300.40 17436[0:SpL:302.1,16327.1] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(v,v_Procs) -> .
% 299.64/300.40 17423[0:SpL:15476.0,16327.1] || equal(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_Procs) -> .
% 299.64/300.40 17735[0:Res:3284.1,255.0] || equal(c_in(tc_Com_Opname),u) c_lessequals(hAPP(u,v_x),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),v)).
% 299.64/300.40 17721[0:Res:652.1,255.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool))* c_lessequals(u,v,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v))*.
% 299.64/300.40 17719[0:Res:649.0,255.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),v,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v)).
% 299.64/300.40 17718[0:Res:650.0,255.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u),v,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v)).
% 299.64/300.40 17949[0:Res:176.0,11894.1] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(u,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> .
% 299.64/300.40 18017[0:Res:13238.1,263.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)) equal(v_x,u).
% 299.64/300.40 18014[0:Res:8375.1,263.0] || equal(hAPP(c_Set_Oinsert(u,v),w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(v),x),w))* equal(x,u)*.
% 299.64/300.40 18008[0:Res:652.1,263.0] || c_lessequals(v_Procs,hAPP(c_Set_Oinsert(u,tc_Com_Opname),v),tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v)) equal(v_x,u).
% 299.64/300.40 18124[0:SSi:18104.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))** -> .
% 299.64/300.40 18125[0:SSi:18101.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))** -> .
% 299.64/300.40 18273[0:SpR:15172.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y,tc_fun(z,tc_bool)),x1),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)*.
% 299.64/300.40 18255[0:SpR:15172.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)),tc_Com_Opname,u),u)*.
% 299.64/300.40 18455[0:Res:13238.1,156.0] || equal(hAPP(hAPP(c_Set_Ovimage(u,t_a,v),w),v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(u,v_x)),w))*.
% 299.64/300.40 18454[0:Res:8375.1,156.0] || equal(hAPP(c_Set_Ovimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,y)),x))*.
% 299.64/300.40 18449[0:Res:652.1,156.0] || c_lessequals(v_Procs,hAPP(c_Set_Ovimage(u,tc_Com_Opname,v),w),tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),hAPP(u,v_x)),w)).
% 299.64/300.40 18533[0:Res:9246.0,278.1] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(w,v))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool)),y,u,x)))*.
% 299.64/300.40 18532[0:Res:9246.0,277.1] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(w,v))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_HOL_Ouminus__class_Ouminus(w,tc_fun(y,tc_bool)),u,y)))*.
% 299.64/300.40 18530[0:Res:9246.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)* -> hBOOL(hAPP(v,w))* c_Hoare__Mirabelle_Otriple__valid(u,w,t_a)*.
% 299.64/300.40 18714[0:SpR:9987.0,9568.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a)),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_bool)*.
% 299.64/300.40 18712[0:SpR:2095.0,9568.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(w,u)),x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_bool)*.
% 299.64/300.40 18709[0:SpR:303.1,9568.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),x),c_Orderings_Otop__class_Otop(u)),tc_bool)*.
% 299.64/300.40 18705[0:SpR:330.0,9568.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u)),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_bool)*.
% 299.64/300.40 18700[0:SpR:14216.0,9568.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))),y),z),tc_bool)*.
% 299.64/300.40 18669[0:SpR:331.0,9568.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),x),u),tc_bool)*.
% 299.64/300.40 18668[0:SpR:302.1,9568.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),w),x),tc_bool)*.
% 299.64/300.40 18655[0:SpR:15476.0,9568.0] || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool))),w),v_x),tc_bool)*.
% 299.64/300.40 18647[0:SpR:2093.0,9568.0] || -> c_lessequals(hAPP(c_in(tc_Com_Opname),v_x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_Procs,v)),w),hAPP(c_in(tc_Com_Opname),v_x)),tc_bool)*.
% 299.64/300.40 18645[0:SpR:3744.1,9568.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,u)),w),v_Procs),tc_bool)*.
% 299.64/300.40 18900[0:Res:463.1,12959.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x)* -> c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u)))),v,x)*.
% 299.64/300.40 19025[0:SpR:9987.0,9569.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_x,t_a)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_bool)*.
% 299.64/300.40 19023[0:SpR:2095.0,9569.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(x,u)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_bool)*.
% 299.64/300.40 19020[0:SpR:303.1,9569.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x)),c_Orderings_Otop__class_Otop(u)),tc_bool)*.
% 299.64/300.40 19016[0:SpR:330.0,9569.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_bool)*.
% 299.64/300.40 19011[0:SpR:14216.0,9569.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),z),tc_bool)*.
% 299.64/300.40 18980[0:SpR:331.0,9569.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),u),tc_bool)*.
% 299.64/300.40 18979[0:SpR:302.1,9569.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),x),tc_bool)*.
% 299.64/300.40 18966[0:SpR:15476.0,9569.0] || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool))),v_x),tc_bool)*.
% 299.64/300.40 18958[0:SpR:2093.0,9569.0] || -> c_lessequals(hAPP(c_in(tc_Com_Opname),v_x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_Procs,w)),hAPP(c_in(tc_Com_Opname),v_x)),tc_bool)*.
% 299.64/300.40 18956[0:SpR:3744.1,9569.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_x,u)),v_Procs),tc_bool)*.
% 299.64/300.40 19249[0:Res:12627.1,12626.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,w,tc_bool),x,tc_bool),tc_bool)* -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,y,tc_bool),z,tc_bool),v,tc_bool)*.
% 299.64/300.40 19334[0:SSi:19328.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) c_lessequals(v,c_Orderings_Obot__class_Obot(tc_bool),tc_bool) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 19403[0:Res:12627.1,12719.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_bool),tc_bool)* -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,x,tc_bool),y,tc_bool),z,tc_bool),v,tc_bool)*.
% 299.64/300.40 19477[0:Res:9067.0,278.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),hAPP(c_Set_Oinsert(v,x),y)),z,u,x)))*.
% 299.64/300.40 19476[0:Res:9067.0,277.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oinsert(v,y),z)),u,y)))*.
% 299.64/300.40 19490[0:Res:19451.0,255.0] || c_lessequals(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w,tc_fun(t_a,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),w)).
% 299.64/300.40 19510[0:Res:19440.0,255.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_in(tc_Com_Opname),v_x)),w,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)).
% 299.64/300.40 19536[0:Res:19452.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,u,t_a)))*.
% 299.64/300.40 19535[0:Res:19452.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u,t_a)))*.
% 299.64/300.40 19600[0:Res:19441.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),x,u,tc_Com_Opname)))*.
% 299.64/300.40 19599[0:Res:19441.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(w,tc_Com_Opname),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),u,tc_Com_Opname)))*.
% 299.64/300.40 19633[0:Res:19436.1,278.1] || equal(u,v_Procs) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,tc_Com_Opname),u),x,v,tc_Com_Opname)))*.
% 299.64/300.40 19632[0:Res:19436.1,277.1] || equal(u,v_Procs) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oinsert(x,tc_Com_Opname),u),v,tc_Com_Opname)))*.
% 299.64/300.40 19671[0:Res:3283.1,496.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,v_Procs)),v_Procs))* c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.40 19732[0:Res:8369.1,19641.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),w)),v))* c_Hoare__Mirabelle_Ohoare__valids(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),w,t_a).
% 299.64/300.40 19731[0:Res:10930.1,19641.0] || equal(hAPP(c_in(u),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Set_Oinsert(v,u),v_x),w)),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,u),v_x),w,t_a).
% 299.64/300.40 19690[0:SpL:8385.1,19641.0] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(v_x,tc_Com_Opname),u),v_Procs) hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(v_x,tc_Com_Opname),u)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oinsert(v_x,tc_Com_Opname),u,t_a)*.
% 299.64/300.40 19827[0:SpR:104.0,9568.0] || -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),w),tc_bool)*.
% 299.64/300.40 20024[0:Rew:2095.0,20008.0] || -> equal(hAPP(c_Set_Oinsert(u,v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.64/300.40 20071[0:SpL:2093.0,215.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_in(tc_Com_Opname),v_x),v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v_Procs,tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.64/300.40 20169[0:SSi:20126.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** -> c_lessequals(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.40 20208[0:Res:20152.0,357.1] || c_Finite__Set_Ofinite(u,v) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(x,v,y),u),tc_fun(y,tc_bool)),tc_fun(y,tc_bool)),y)*.
% 299.64/300.40 20270[0:SSi:20228.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> c_lessequals(c_HOL_Ominus__class_Ominus(w,u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.40 20395[0:Rew:20362.1,20296.1] || c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)),v_Procs).
% 299.64/300.40 20734[0:Res:313.1,390.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v,x,w,y),hAPP(c_Set_Oimage(x,w,y),u),y,w)*.
% 299.64/300.40 21019[0:SpL:317.0,377.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),y),w).
% 299.64/300.40 20869[0:SpR:317.0,3291.1] || equal(c_Set_Oimage(u,v,w),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),v_x)),v_Procs))*.
% 299.64/300.40 20861[0:SpR:317.0,378.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(y,v),x)),w)*.
% 299.64/300.40 21109[0:SpR:9987.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,v),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u),x)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.40 21107[0:SpR:2095.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w),y)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.40 21104[0:SpR:303.1,20881.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),y)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.40 21100[0:SpR:330.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),w),y)),v))*.
% 299.64/300.40 21095[0:SpR:14216.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,y),hAPP(c_Set_Oinsert(z,x),x1)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21093[0:SpR:11176.1,20881.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_Set_Oinsert(x,v),y)),u))*.
% 299.64/300.40 21091[0:SpR:11177.1,20881.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),hAPP(c_Set_Oinsert(u,w),y)),u))*.
% 299.64/300.40 21064[0:SpR:331.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,w),hAPP(c_Set_Oinsert(x,v),y)),x))*.
% 299.64/300.40 21063[0:SpR:302.1,20881.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_Set_Oinsert(x,v),y)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.40 21050[0:SpR:15476.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)))*.
% 299.64/300.40 21038[0:SpR:2093.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),hAPP(c_Set_Oinsert(hAPP(c_in(tc_Com_Opname),v_x),v),x)),hAPP(c_in(tc_Com_Opname),v_x)))*.
% 299.64/300.40 21036[0:SpR:3744.1,20881.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),hAPP(c_Set_Oinsert(v_Procs,v),x)),v_Procs))*.
% 299.64/300.40 21193[0:SpR:12944.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y,z),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21189[0:SpR:9.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),z,x1),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(u,hAPP(v,v_Procs))))*.
% 299.64/300.40 21188[0:SpR:11473.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,x),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21175[0:SpR:88.1,21130.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_Procs,u)),v,w),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.40 21174[0:SpR:17045.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x,y),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.40 21165[0:SpR:2098.1,21130.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_Procs,t_a) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_Procs),tc_Hoare__Mirabelle_Otriple(t_a)),v,w),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.40 21154[0:SpR:653.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),v,w),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.40 21148[0:SpR:8498.1,21130.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,x),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.40 21254[0:SpR:12944.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),t_a,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21250[0:SpR:9.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),t_a,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),hAPP(u,hAPP(v,v_x))))*.
% 299.64/300.40 21249[0:SpR:11473.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21236[0:SpR:88.1,21141.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.40 21235[0:SpR:17045.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),t_a,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.40 21226[0:SpR:2098.1,21141.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.40 21215[0:SpR:3586.1,21141.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),v_x))*.
% 299.64/300.40 21203[0:SpR:8498.1,21141.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),v_x))*.
% 299.64/300.40 21276[0:Res:9258.0,469.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),tc_bool))* equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,t_a)),v_x)**.
% 299.64/300.40 21585[0:SpL:21267.0,527.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,w)))*.
% 299.64/300.40 21547[0:SpR:11177.1,21267.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x,tc_Com_Opname,v)),v_x)**.
% 299.64/300.40 21517[0:SpR:3586.1,21267.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),v_x,tc_Com_Opname,w)),v_x)**.
% 299.64/300.40 21510[0:SpR:365.1,21267.0] class_Orderings_Obot(u) || -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Orderings_Obot__class_Obot(u),tc_Com_Opname,v)),c_Orderings_Obot__class_Obot(u))**.
% 299.64/300.40 21509[0:SpR:397.1,21267.0] class_Orderings_Otop(u) || -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.40 21505[0:SpR:8498.1,21267.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),v_x,tc_Com_Opname,w)),v_x)**.
% 299.64/300.40 21337[0:SpR:21267.0,526.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(v),hAPP(c_in(v),v_x),tc_Com_Opname,w)))* -> hBOOL(hAPP(hAPP(c_in(v),v_x),u)).
% 299.64/300.40 21291[0:SpR:21267.0,376.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x),tc_fun(v,tc_bool))*.
% 299.64/300.40 21796[0:SpR:14216.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),t_a,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21795[0:SpR:11176.1,21143.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u))*.
% 299.64/300.40 21793[0:SpR:11177.1,21143.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.40 21772[0:SpR:331.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.40 21771[0:SpR:302.1,21143.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.40 21758[0:SpR:15476.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)))*.
% 299.64/300.40 21862[0:SpR:11177.1,21131.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.40 21841[0:SpR:331.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.40 21827[0:SpR:15476.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)))*.
% 299.64/300.40 21902[0:Res:9258.0,464.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),tc_bool))* equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,t_a)),v_x)**.
% 299.64/300.40 22212[0:SpL:21893.0,527.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,w)))*.
% 299.64/300.40 22174[0:SpR:11177.1,21893.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v)),v_x)**.
% 299.64/300.40 22144[0:SpR:3586.1,21893.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v,u),tc_Com_Opname,w)),v_x)**.
% 299.64/300.40 22137[0:SpR:365.1,21893.0] class_Orderings_Obot(u) || -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,v)),c_Orderings_Obot__class_Obot(u))**.
% 299.64/300.40 22136[0:SpR:397.1,21893.0] class_Orderings_Otop(u) || -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,v)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.40 22132[0:SpR:8498.1,21893.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v,u),tc_Com_Opname,w)),v_x)**.
% 299.64/300.40 21963[0:SpR:21893.0,526.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(v),v_x),c_in(v),tc_Com_Opname,w)))* -> hBOOL(hAPP(hAPP(c_in(v),v_x),u)).
% 299.64/300.40 21917[0:SpR:21893.0,376.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x),tc_fun(v,tc_bool))*.
% 299.64/300.40 22497[0:SpR:14216.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),tc_Com_Opname,y),u),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 22496[0:SpR:11176.1,21126.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,w),v),u))*.
% 299.64/300.40 22494[0:SpR:11177.1,21126.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),tc_Com_Opname,w),u),v_x))*.
% 299.64/300.40 22473[0:SpR:331.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_Com_Opname,w),u),v_x))*.
% 299.64/300.40 22472[0:SpR:302.1,21126.1] class_Lattices_Obounded__lattice(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,w),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.40 22459[0:SpR:15476.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),tc_Com_Opname,w),u),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool)))*.
% 299.64/300.40 22673[0:Rew:9.0,22589.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,t_a,v),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),hAPP(u,hAPP(x,v_x))))*.
% 299.64/300.40 22674[0:Rew:9.0,22588.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),hAPP(u,hAPP(x,z))))*.
% 299.64/300.40 22675[0:Rew:9.0,22521.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),hAPP(c_in(tc_Com_Opname),v_x))),hAPP(u,hAPP(x,v_Procs))))*.
% 299.64/300.40 22676[0:Rew:9.0,22518.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,v_x))),hAPP(c_Set_Oimage(v,x,u),hAPP(c_Set_Oimage(w,tc_Com_Opname,x),v_Procs))))*.
% 299.64/300.40 22805[0:SpR:300.1,3294.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_in(t_a))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 22794[0:SpR:365.1,3294.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_in(t_a)) -> equal(hAPP(c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 22793[0:SpR:397.1,3294.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_in(t_a)) -> equal(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 22788[0:SpR:2097.1,3294.1] || hBOOL(hAPP(v_x,u))* equal(c_Set_Oinsert(u,v),c_in(t_a))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 22728[0:SpR:3294.1,415.0] || equal(c_in(t_a),u) -> equal(c_Fun_Ofun__upd(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),v,w),hAPP(u,v_x))**.
% 299.64/300.40 23174[0:SpL:365.1,3487.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.40 23173[0:SpL:397.1,3487.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.40 23262[0:SpL:300.1,3489.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_in(tc_Com_Opname))** hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.40 23251[0:SpL:365.1,3489.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_in(tc_Com_Opname)) hBOOL(hAPP(c_Orderings_Obot__class_Obot(u),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.40 23250[0:SpL:397.1,3489.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_in(tc_Com_Opname)) hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.40 23469[0:SSi:23454.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))* equal(c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)),v_Procs) equal(c_Set_Oinsert(u,v),c_in(tc_Com_Opname))** -> .
% 299.64/300.40 23597[0:SSi:23559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_fun(t_a,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),hAPP(v,v_x)),hAPP(v,v_x))**.
% 299.64/300.40 23598[0:SSi:23558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_fun(t_a,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v,v_x)),hAPP(u,v_x)),hAPP(v,v_x))**.
% 299.64/300.40 24682[0:SpL:24020.1,3489.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_in(tc_Com_Opname))** hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.40 24668[0:SpR:584.0,24020.1] || equal(c_COMBS(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(hAPP(u,v_x),hAPP(v,v_x)),v_x),v_x)**.
% 299.64/300.40 24642[0:SpR:540.1,24020.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_x),v_x)**.
% 299.64/300.40 24641[0:SpR:539.1,24020.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_x),v_x)**.
% 299.64/300.40 24640[0:SpR:297.2,24020.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.40 24631[0:SpR:299.2,24020.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v,v_x),v_x).
% 299.64/300.40 24620[0:SpR:25.1,24020.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),v_x),v_x)**.
% 299.64/300.40 24524[0:SpR:24020.1,3294.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(u,v_x),c_in(t_a))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 24917[0:Res:526.1,467.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),y)) -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(x,u,v,w),y)),y)**.
% 299.64/300.40 25065[0:SpR:15172.0,23902.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.40 25060[0:SpR:586.0,23902.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(u,hAPP(y,v_x)),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.40 25059[0:SpR:585.0,23902.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(hAPP(u,v_x),y),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.40 25053[0:SpR:9936.1,23902.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.40 25049[0:SpR:9935.1,23902.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.40 25015[0:SpR:8415.2,23902.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.40 25009[0:SpR:445.1,23902.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(v_x,v) equal(hAPP(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.40 24967[0:SpR:23902.1,20881.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),v),x)),v_x))*.
% 299.64/300.40 24949[0:SpR:23902.1,9569.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(u,v_x)),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool)*.
% 299.64/300.40 24948[0:SpR:23902.1,9568.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(u,v_x)),w),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool)*.
% 299.64/300.40 25138[0:SpL:8415.2,24027.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(c_Com_Ocom_OSemi(u,v),v_x)** -> .
% 299.64/300.40 25678[0:Rew:25636.1,25635.1] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(w,x),hAPP(v,x)).
% 299.64/300.40 25683[0:Rew:25636.1,25614.1] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),v),v_Procs),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(v,v_Procs),v_Procs).
% 299.64/300.40 25712[0:Res:526.1,455.0] || hBOOL(hAPP(u,v))* c_Hoare__Mirabelle_Ohoare__valids(w,u,t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,v,t_a)*.
% 299.64/300.40 25703[0:Res:267.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w),t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,v,t_a)*.
% 299.64/300.40 25740[0:SpL:8415.2,25662.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(v_x,u),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(u,v_x).
% 299.64/300.40 25797[0:Rew:25660.1,25782.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),c_Orderings_Obot__class_Obot(tc_bool)) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),u)**.
% 299.64/300.40 25798[0:Rew:25660.1,25781.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),c_Orderings_Obot__class_Obot(tc_bool)) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x,tc_Com_Opname,v),u)**.
% 299.64/300.40 25891[0:SpR:339.0,342.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),tc_fun(v,tc_bool))*.
% 299.64/300.40 26213[0:SpR:330.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))),hAPP(c_Set_Oinsert(w,u),v))**.
% 299.64/300.40 26026[0:SpR:338.0,341.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),w)),tc_fun(v,tc_bool))*.
% 299.64/300.40 26271[0:SSi:26270.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.40 26511[0:SpR:330.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> c_lessequals(u,v,tc_fun(w,tc_bool)).
% 299.64/300.40 26985[2:SSi:26975.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.40 27003[0:Res:8366.1,175.0] || equal(hAPP(c_Set_Ovimage(u,tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),v_Procs)** -> equal(hAPP(u,v_x),w).
% 299.64/300.40 27052[0:Res:23946.1,278.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,v,u,w)))*.
% 299.64/300.40 27051[0:Res:23946.1,277.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,v_x,u,w)))*.
% 299.64/300.40 27042[0:Res:23946.1,170.1] class_Orderings_Olinorder(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_x,u),v_Procs,u)*.
% 299.64/300.40 27041[0:Res:23946.1,169.1] class_Orderings_Olinorder(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(v_Procs,c_Finite__Set_Olinorder__class_OMax(v_x,u),u)*.
% 299.64/300.40 27105[0:Res:15261.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,t_a,tc_fun(w,tc_bool)),v))*.
% 299.64/300.40 27079[0:Res:267.0,280.1] || hBOOL(hAPP(hAPP(u,v),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,x),y),u,x,tc_fun(z,tc_bool)),w))*.
% 299.64/300.40 27073[0:Res:8366.1,280.1] || equal(u,v_Procs) hBOOL(hAPP(hAPP(v,v_x),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,tc_Com_Opname,tc_fun(x,tc_bool)),w))*.
% 299.64/300.40 27070[0:Res:658.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),u,tc_Com_Opname,tc_fun(x,tc_bool)),v))*.
% 299.64/300.40 27275[7:Res:27207.1,255.0] || equal(hAPP(c_in(u),v),v_x) c_lessequals(v_x,w,tc_fun(u,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),v),w))*.
% 299.64/300.40 27220[7:SpR:130.1,27207.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_x) -> hBOOL(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))*.
% 299.64/300.40 27306[7:MRR:24361.2,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Com_Ocom_OBODY)** equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.40 27386[0:Res:3346.1,470.0] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(w,x,v)) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_x,u,w,x,v)),v_x))*.
% 299.64/300.40 27379[0:Res:8366.1,470.0] || equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,tc_Com_Opname)),w))*.
% 299.64/300.40 27446[0:Res:3346.1,466.0] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(w,x,v)) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_x,w,u,x,v)),v_x))*.
% 299.64/300.40 27439[0:Res:8366.1,466.0] || equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,tc_Com_Opname)),w))*.
% 299.64/300.40 27868[7:SpR:9.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Fun_Ocomp(u,v,w,x,y),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool)).
% 299.64/300.40 27850[7:SpR:88.1,27219.1] class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)).
% 299.64/300.40 28028[0:Res:27381.0,255.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)),u))*.
% 299.64/300.40 28021[0:SpR:12944.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),tc_Com_Opname,y)),v_Procs))*.
% 299.64/300.40 28015[0:SpR:9.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,hAPP(v,v_x)),c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname,z)),v_Procs))*.
% 299.64/300.40 28014[0:SpR:11473.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.40 27997[0:SpR:88.1,27381.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.40 27994[0:SpR:17045.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),tc_Com_Opname,x)),v_Procs))*.
% 299.64/300.40 27985[0:SpR:2098.1,27381.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.40 27974[0:SpR:3586.1,27381.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v,u),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.40 27961[0:SpR:8498.1,27381.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v,u),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.40 28085[0:SpR:329.1,28032.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w)))*.
% 299.64/300.40 28084[0:SpR:328.1,28032.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w)))*.
% 299.64/300.40 28081[0:SpR:538.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w)))*.
% 299.64/300.40 28331[0:Res:27441.0,255.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)),u))*.
% 299.64/300.40 28324[0:SpR:12944.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,y)),v_Procs))*.
% 299.64/300.40 28318[0:SpR:9.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ocomp(u,v,w,x,y),hAPP(u,hAPP(v,v_x)),tc_Com_Opname,z)),v_Procs))*.
% 299.64/300.40 28317[0:SpR:11473.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.40 28300[0:SpR:88.1,27441.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.40 28297[0:SpR:17045.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,x)),v_Procs))*.
% 299.64/300.40 28287[0:SpR:2098.1,27441.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),v_x,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.40 28276[0:SpR:3586.1,27441.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),v_x,tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.40 28263[0:SpR:8498.1,27441.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),v_x,tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.40 28389[0:SpR:329.1,28335.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x,tc_Com_Opname,w)))*.
% 299.64/300.40 28388[0:SpR:328.1,28335.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),u,tc_Com_Opname,w)))*.
% 299.64/300.40 28385[0:SpR:538.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_Com_Opname,w)))*.
% 299.64/300.40 28579[0:SpL:118.0,16339.1] || equal(hAPP(u,v),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(w,v_x,v,x,y),y,z,x),v_Procs)** -> .
% 299.64/300.40 28577[0:SpL:118.0,3340.0] || equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,v_x,w,x,y),y,z,x),x1)* -> equal(hAPP(x1,v_x),hAPP(u,w))*.
% 299.64/300.40 28576[0:SpL:118.0,3732.0] || equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,v_x,w,x,y),y,z,x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(u,w),v_Procs)).
% 299.64/300.40 28430[0:SpR:118.0,1166.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,v_x,w,x,y),y,z,x),tc_Com_Opname,x1),v_Procs),hAPP(u,w)))*.
% 299.64/300.40 28783[0:SpR:12944.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),tc_Com_Opname,y),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28777[0:SpR:9.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,hAPP(v,v_x)),c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28776[0:SpR:11473.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28759[0:SpR:88.1,28031.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28756[0:SpR:17045.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28746[0:SpR:2098.1,28031.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28735[0:SpR:3586.1,28031.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v,u),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28722[0:SpR:8498.1,28031.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v,u),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28706[0:SpR:28031.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_Procs))*.
% 299.64/300.40 28679[0:SpR:28031.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.40 28938[0:SpR:12944.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,y),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28932[0:SpR:9.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ocomp(u,v,w,x,y),hAPP(u,hAPP(v,v_x)),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28931[0:SpR:11473.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28914[0:SpR:88.1,28334.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28911[0:SpR:17045.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28901[0:SpR:2098.1,28334.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),v_x,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28890[0:SpR:3586.1,28334.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),v_x,tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28877[0:SpR:8498.1,28334.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),v_x,tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 28861[0:SpR:28334.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_Procs))*.
% 299.64/300.40 28834[0:SpR:28334.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.40 29213[0:SSi:29183.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),u)* -> c_Finite__Set_Ofinite(x,u).
% 299.64/300.40 29214[0:SSi:29162.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))** -> .
% 299.64/300.40 29220[0:SSi:28975.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_in(tc_Com_Opname),v_x))),v_Procs))*.
% 299.64/300.40 29221[0:SSi:28972.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs))))*.
% 299.64/300.40 29428[7:SpL:27278.1,3698.2] || equal(hAPP(c_in(u),v),v_x)** equal(w,c_Set_Oinsert(v,u))* equal(c_Com_Ocom_OBODY,w) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 29399[7:SpR:27278.1,7253.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.40 29362[7:SpR:27278.1,3339.1] || equal(hAPP(c_in(u),v),v_x)** equal(w,c_Set_Oinsert(v,u))* -> equal(c_Fun_Ofun__upd(w,v_x,v_x,x,y),w)**.
% 299.64/300.40 29361[7:SpR:27278.1,3316.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_in(w),c_Set_Oinsert(v,u))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.40 29358[7:SpR:27278.1,648.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),tc_Com_Opname,w),v_Procs)))*.
% 299.64/300.40 29354[7:SpR:27278.1,21893.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v,u),tc_Com_Opname,w)),v_x)**.
% 299.64/300.40 29353[7:SpR:27278.1,28031.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v,u),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 29351[7:SpR:27278.1,27381.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v,u),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.40 29348[7:SpR:27278.1,21267.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),v_x,tc_Com_Opname,w)),v_x)**.
% 299.64/300.40 29347[7:SpR:27278.1,28334.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),v_x,tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 29345[7:SpR:27278.1,27441.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),v_x,tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.40 29344[7:SpR:27278.1,21141.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),v_x))*.
% 299.64/300.40 29342[7:SpR:27278.1,11030.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_in(t_a)) -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.40 29341[7:SpR:27278.1,10090.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.40 29335[7:SpR:27278.1,3284.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),v_x))*.
% 299.64/300.40 29330[7:SpR:27278.1,15483.1] || equal(hAPP(c_in(u),v),v_x) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.40 29324[7:SpR:27278.1,651.0] || equal(hAPP(c_in(u),v),v_x) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.40 29491[0:SpR:118.0,28065.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v),c_Fun_Ocomp(u,c_Fun_Ofun__upd(w,v_x,v,x,y),y,z,x),tc_Com_Opname,x1)))*.
% 299.64/300.40 29811[0:SpR:118.0,28368.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,v_x,w,x,y),y,z,x),hAPP(u,w),tc_Com_Opname,x1)))*.
% 299.64/300.40 29941[0:SpL:27043.1,16217.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(v_Procs,u),v_Procs)** -> .
% 299.64/300.40 29923[0:SpR:27043.1,9567.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_Procs,u),v,tc_fun(w,tc_bool)),v_x),v_x,tc_bool)*.
% 299.64/300.40 29882[0:SpR:27043.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_Procs,v),tc_Com_Opname,u),u)*.
% 299.64/300.40 29881[0:SpR:27043.1,23902.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.40 30348[0:SSi:30306.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),u)* -> c_Finite__Set_Ofinite(w,u).
% 299.64/300.40 30349[0:SSi:30299.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))** -> .
% 299.64/300.40 30359[0:SSi:30074.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),w)),v_Procs))*.
% 299.64/300.40 30360[0:SSi:30061.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v))))*.
% 299.64/300.40 30512[0:Res:28009.0,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,u,tc_Com_Opname)))*.
% 299.64/300.40 30511[0:Res:28009.0,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.40 30506[0:Res:28009.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname)*.
% 299.64/300.40 30505[0:Res:28009.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.40 30524[0:Res:28312.0,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,u,tc_Com_Opname)))*.
% 299.64/300.40 30523[0:Res:28312.0,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.40 30518[0:Res:28312.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname)*.
% 299.64/300.40 30517[0:Res:28312.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.40 31094[0:SpR:28771.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v,tc_fun(w,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.40 31180[0:SpR:28926.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v,tc_fun(w,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.40 31314[0:Rew:31262.0,17875.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),w,tc_fun(u,tc_bool))*.
% 299.64/300.40 31368[0:Res:23961.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_Procs),w,u,v)))*.
% 299.64/300.40 31367[0:Res:23961.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),v_Procs),u,w)))*.
% 299.64/300.40 31365[0:Res:23961.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.40 31499[0:SpL:14216.0,24254.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 31497[0:SpL:11176.1,24254.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(u,c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 31493[0:SpL:11177.1,24254.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 31466[0:SpL:331.0,24254.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 31465[0:SpL:302.1,24254.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 31451[0:SpL:15476.0,24254.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 31537[0:Res:3284.1,473.0] || equal(c_Set_Oimage(u,v,w),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(v_x,u,v,w),v_Procs)),v_x))*.
% 299.64/300.40 31852[7:SpL:27043.1,31778.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(v_Procs,u),v_x)** -> .
% 299.64/300.40 31845[7:SpL:586.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_COMBB(u,w,x,y),v),v_x)** -> .
% 299.64/300.40 31844[7:SpL:585.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_COMBC(u,w,x,y),v),v_x)** -> .
% 299.64/300.40 31795[7:SpL:8415.2,31778.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(u,v_x) -> .
% 299.64/300.40 31789[7:SpL:445.1,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Fun_Ofun__upd(u,v,w,x,y),v_x)** -> equal(v_x,v).
% 299.64/300.40 31921[7:SpL:328.1,31868.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)** -> .
% 299.64/300.40 31918[7:SpL:538.0,31868.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x) -> .
% 299.64/300.40 32014[0:SpL:383.1,3706.0] || equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v_x,v,w,x),y,z,w,x),c_Com_Ocom_OBODY)** equal(v,c_Com_Ocom_OSKIP) -> equal(v_x,y).
% 299.64/300.40 32082[7:SpL:118.0,31899.1] || equal(hAPP(u,v),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(w,v_x,v,x,y),y,z,x),v_x)** -> .
% 299.64/300.40 32191[0:Res:31323.0,24120.1] || equal(hAPP(v_Procs,u),c_Orderings_Obot__class_Obot(tc_bool)) -> equal(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u),hAPP(v_Procs,u))**.
% 299.64/300.40 32274[0:SSi:32258.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),v,w)* -> c_Fun_Oinj__on(u,v_x,v,w).
% 299.64/300.40 32430[7:SSi:32422.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) -> .
% 299.64/300.40 32673[0:Res:31533.0,278.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,u,tc_Com_Opname)))*.
% 299.64/300.40 32672[0:Res:31533.0,277.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.40 32667[0:Res:31533.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname)*.
% 299.64/300.40 32666[0:Res:31533.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.40 32651[0:SpR:14216.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_Com_Opname,x),c_Orderings_Otop__class_Otop(tc_bool))),v_Procs))*.
% 299.64/300.40 32649[0:SpR:11176.1,31533.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),u)),v_Procs))*.
% 299.64/300.40 32645[0:SpR:11177.1,31533.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),v_x)),v_Procs))*.
% 299.64/300.40 32617[0:SpR:302.1,31533.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u))),v_Procs))*.
% 299.64/300.40 32603[0:SpR:15476.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),tc_Com_Opname,v),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))),v_Procs))*.
% 299.64/300.40 32737[0:SpR:584.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(u,v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(u,v_x),hAPP(v,v_x)))))*.
% 299.64/300.40 32718[0:SpR:337.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))))*.
% 299.64/300.40 32706[0:SpR:540.1,32669.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))))*.
% 299.64/300.40 32705[0:SpR:539.1,32669.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))))*.
% 299.64/300.40 32704[0:SpR:297.2,32669.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v_x)))*.
% 299.64/300.40 32695[0:SpR:299.2,32669.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v)))*.
% 299.64/300.40 32683[0:SpR:25.1,32669.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_Com_Opname,w),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))))*.
% 299.64/300.40 32746[0:SpR:8415.2,32728.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_x,tc_Com_Opname,u),v_x)))*.
% 299.64/300.40 33307[0:SpR:14216.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_Com_Opname,x),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 33305[0:SpR:11176.1,32668.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),u),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 33301[0:SpR:11177.1,32668.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 33273[0:SpR:302.1,32668.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 33259[0:SpR:15476.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),tc_Com_Opname,v),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 33236[0:SpR:32668.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),w,tc_fun(x,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.40 33370[0:Res:23789.0,12626.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(w,x,tc_bool),y,tc_bool)),w,tc_bool)*.
% 299.64/300.40 33368[0:Res:23789.0,12719.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(w,x,tc_bool)),y,tc_bool),w,tc_bool)*.
% 299.64/300.40 33468[0:Res:23882.0,12626.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool)),x,tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_bool)*.
% 299.64/300.40 33466[0:Res:23882.0,12719.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ominus__class_Ominus(u,v,tc_bool)),w,tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),y,tc_bool),u,tc_bool)*.
% 299.64/300.40 33535[7:SSi:33527.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_COMBK(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))* equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)).
% 299.64/300.40 33593[0:SpR:14216.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),tc_Com_Opname,y)))*.
% 299.64/300.40 33591[0:SpR:11176.1,28704.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,w)))*.
% 299.64/300.40 33587[0:SpR:11177.1,28704.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),tc_Com_Opname,w)))*.
% 299.64/300.40 33559[0:SpR:302.1,28704.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,w)))*.
% 299.64/300.40 33545[0:SpR:15476.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),tc_Com_Opname,w)))*.
% 299.64/300.40 33684[0:SpR:14216.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,y)))*.
% 299.64/300.40 33682[0:SpR:11176.1,28859.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),u,tc_Com_Opname,w)))*.
% 299.64/300.40 33678[0:SpR:11177.1,28859.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),v_x,tc_Com_Opname,w)))*.
% 299.64/300.40 33650[0:SpR:302.1,28859.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,w)))*.
% 299.64/300.40 33636[0:SpR:15476.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),tc_Com_Opname,w)))*.
% 299.64/300.40 33741[7:SpL:302.1,31886.1] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(v,v_x) -> .
% 299.64/300.40 33727[7:SpL:15476.0,31886.1] || equal(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_x) -> .
% 299.64/300.40 34308[7:SpL:24914.0,27279.0] || equal(hAPP(c_in(u),v_x),v_x) -> hBOOL(hAPP(v_x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),hAPP(c_in(u),v_x))))*.
% 299.64/300.40 34294[0:SpL:24914.0,3587.0] || equal(hAPP(c_in(u),v_x),v_Procs) -> hBOOL(hAPP(v_x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),hAPP(c_in(u),v_x))))*.
% 299.64/300.40 34215[0:SpR:414.0,24914.0] || -> equal(hAPP(c_Fun_Ofun__upd(u,v_x,v,w,x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ofun__upd(u,v_x,v,w,x),tc_Com_Opname,y),v)),v)**.
% 299.64/300.40 34206[0:SpR:524.0,24914.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,v),v_x)),v_x)**.
% 299.64/300.40 34201[0:SpR:8415.2,24914.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),v_x)),v_x)**.
% 299.64/300.40 34098[0:SpR:24914.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,x),hAPP(u,v_x))),hAPP(u,v_x),tc_bool)*.
% 299.64/300.40 33962[0:SpR:24914.0,267.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),hAPP(c_in(u),v_x)),u),w)))*.
% 299.64/300.40 34569[0:SpR:8415.2,34427.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v_x),v_x)**.
% 299.64/300.40 34565[0:SpR:34427.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v,w),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v),x)),v_x))*.
% 299.64/300.40 34551[0:SpR:34427.0,9569.0] || -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,w)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),tc_bool)*.
% 299.64/300.40 34550[0:SpR:34427.0,9568.0] || -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,v)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),tc_bool)*.
% 299.64/300.40 34547[0:SpR:34427.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,v,w),c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u))**.
% 299.64/300.40 34764[0:SpL:34428.0,3499.1] || equal(c_in(u),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v))* hBOOL(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.40 34762[0:SpL:34428.0,24254.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 34756[0:SpL:34428.0,3484.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,v),v_x)** -> equal(v_x,v).
% 299.64/300.40 34748[0:SpR:34428.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),v_x))*.
% 299.64/300.40 34734[0:SpR:34428.0,9569.0] || -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,w)),v_x),tc_bool)*.
% 299.64/300.40 34733[0:SpR:34428.0,9568.0] || -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v)),w),v_x),tc_bool)*.
% 299.64/300.40 34728[0:SpR:34428.0,3346.1] || equal(c_Set_Oinsert(u,v),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,w))* -> hBOOL(hAPP(hAPP(c_in(v),u),v_x))*.
% 299.64/300.40 34727[0:SpR:34428.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),v_x,tc_Com_Opname,w)))*.
% 299.64/300.40 34726[0:SpR:34428.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),tc_Com_Opname,w)))*.
% 299.64/300.40 34725[0:SpR:34428.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),tc_Com_Opname,w),u),v_x))*.
% 299.64/300.40 34724[0:SpR:34428.0,3317.1] || equal(c_in(u),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,u),w)))*.
% 299.64/300.40 34723[0:SpR:34428.0,3305.1] || equal(u,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.40 34715[0:SpR:34428.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_Com_Opname,v),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.40 34713[0:SpR:34428.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_Com_Opname,v),v_x)),v_Procs))*.
% 299.64/300.40 34706[0:SpR:34428.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.40 34705[0:SpR:34428.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.40 34699[0:SpR:34428.0,15262.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))).
% 299.64/300.40 34696[0:SpR:34428.0,8376.2] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.40 34694[0:SpR:34428.0,3291.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),v_Procs))*.
% 299.64/300.40 34693[0:SpR:34428.0,3285.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.40 34689[0:SpR:34428.0,3279.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x)).
% 299.64/300.40 34828[0:Res:27383.0,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,z,u,tc_Com_Opname)))*.
% 299.64/300.40 34827[0:Res:27383.0,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.40 34822[0:Res:27383.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname)*.
% 299.64/300.40 34821[0:Res:27383.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.40 34838[0:Res:27443.0,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,z,u,tc_Com_Opname)))*.
% 299.64/300.40 34837[0:Res:27443.0,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.40 34832[0:Res:27443.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname)*.
% 299.64/300.40 34831[0:Res:27443.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.40 34842[0:Res:229.0,443.1] || c_Hoare__Mirabelle_Ohoare__derivs(u,v,w) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),x),c_Com_Ocom_OSKIP),x),tc_Hoare__Mirabelle_Otriple(w)),v),w)*.
% 299.64/300.40 34902[0:SpR:14216.0,28053.1] || equal(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),u,tc_Com_Opname,y)))*.
% 299.64/300.40 34900[0:SpR:11176.1,28053.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,v,tc_Com_Opname,w)))*.
% 299.64/300.40 34896[0:SpR:11177.1,28053.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,w)))*.
% 299.64/300.40 34869[0:SpR:331.0,28053.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,w)))*.
% 299.64/300.40 34868[0:SpR:302.1,28053.1] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),v,tc_Com_Opname,w)))*.
% 299.64/300.40 34860[0:SpR:34428.0,28053.1] || equal(u,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,w)))*.
% 299.64/300.40 34853[0:SpR:15476.0,28053.1] || equal(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),u,tc_Com_Opname,w)))*.
% 299.64/300.40 34981[0:SpR:14216.0,28356.1] || equal(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,y)))*.
% 299.64/300.40 34979[0:SpR:11176.1,28356.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,u,tc_Com_Opname,w)))*.
% 299.64/300.40 34975[0:SpR:11177.1,28356.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,w)))*.
% 299.64/300.40 34948[0:SpR:331.0,28356.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,w)))*.
% 299.64/300.40 34947[0:SpR:302.1,28356.1] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,c_Orderings_Otop__class_Otop(u),tc_Com_Opname,w)))*.
% 299.64/300.40 34939[0:SpR:34428.0,28356.1] || equal(u,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,w)))*.
% 299.64/300.40 34932[0:SpR:15476.0,28356.1] || equal(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),tc_Com_Opname,w)))*.
% 299.64/300.40 35052[0:SpR:28755.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),y,tc_fun(z,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.40 35141[0:SpR:28910.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),y,tc_fun(z,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.40 35481[0:SpR:113.0,124.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool))*.
% 299.64/300.40 35597[7:Res:29397.1,19641.0] || equal(hAPP(c_in(u),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Set_Oinsert(v,u),v_x),w)),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,u),v_x),w,t_a).
% 299.64/300.40 35645[0:Rew:586.0,35608.0] || -> c_lessequals(hAPP(u,hAPP(v,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),u,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.40 37438[0:SpR:205.1,318.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w)* -> c_Finite__Set_Ofinite(x,v).
% 299.64/300.40 38772[4:SpR:338.0,37987.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),w)))*.
% 299.64/300.40 38768[4:SpR:536.1,37987.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)))*.
% 299.64/300.40 38767[4:SpR:535.1,37987.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)))*.
% 299.64/300.40 38729[4:SpR:329.1,37987.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.40 38728[4:SpR:328.1,37987.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(u,w))*.
% 299.64/300.40 38725[4:SpR:538.0,37987.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),w))*.
% 299.64/300.40 38918[4:SpR:329.1,38042.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,w,t_a)*.
% 299.64/300.40 38917[4:SpR:328.1,38042.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(u,w,t_a)*.
% 299.64/300.40 38914[4:SpR:538.0,38042.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),w,t_a)*.
% 299.64/300.40 40198[0:Rew:585.0,40188.1,585.0,40188.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_in(w),x),u),hAPP(hAPP(c_in(w),x),v),tc_bool)*.
% 299.64/300.40 40846[4:SSi:40777.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(v_x,hAPP(x,v),tc_bool)* -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_bool))*.
% 299.64/300.40 41508[4:SpR:15172.0,38236.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,tc_bool)).
% 299.64/300.40 41503[4:SpR:586.0,38236.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(u,hAPP(y,v_x)),tc_Com_Opname,tc_bool))*.
% 299.64/300.40 41502[4:SpR:585.0,38236.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(u,v_x),y),tc_Com_Opname,tc_bool))*.
% 299.64/300.40 41496[4:SpR:9936.1,38236.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,tc_bool))*.
% 299.64/300.40 41492[4:SpR:9935.1,38236.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,tc_bool))*.
% 299.64/300.40 41445[4:SpR:445.1,38236.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(v_x,v) hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(u,v_x),tc_Com_Opname,tc_bool))*.
% 299.64/300.40 41772[4:SpR:8415.2,40094.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x,u,v,w),x))*.
% 299.64/300.40 41923[4:SpR:8415.2,41783.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x,u,v,w),x,t_a)*.
% 299.64/300.40 42015[0:Res:37962.1,19641.0] || hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),y)) -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),y,t_a)*.
% 299.64/300.40 42026[4:SpR:383.1,38616.0] || -> equal(u,v) hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),c_Fun_Ofun__upd(c_Fun_Ofun__upd(y,v,v_x,z,x1),u,x2,z,x1)),v))*.
% 299.64/300.40 42188[4:SSi:42183.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(v_x,tc_bool),u),tc_bool,tc_bool),w,tc_bool)* -> hBOOL(w).
% 299.64/300.40 42189[4:SSi:42182.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(v_x,tc_bool),u),tc_bool,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(w)*.
% 299.64/300.40 42190[4:SSi:42145.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,hAPP(c_Set_Oinsert(v_x,tc_bool),u),tc_bool,tc_bool)))*.
% 299.64/300.40 42191[4:SSi:42139.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v_x,v,tc_bool) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,hAPP(c_Set_Oinsert(v,tc_bool),u),tc_bool,tc_bool))*.
% 299.64/300.40 42192[0:Obv:42073.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> c_lessequals(w,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(w,u),v),u,u),u)*.
% 299.64/300.40 42354[4:SpR:532.0,40371.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x)),v_x))*.
% 299.64/300.40 42411[4:SpR:533.0,40372.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x))),v_x))*.
% 299.64/300.40 42580[4:SpR:532.0,40590.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w)),x))*.
% 299.64/300.40 42758[0:Rew:104.0,42717.0,10.0,42717.0,337.0,42717.0] || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)))**.
% 299.64/300.40 42784[4:SpL:8415.2,42604.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x))* -> .
% 299.64/300.40 42816[4:SpR:533.0,40591.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))),x))*.
% 299.64/300.40 43174[4:SpR:532.0,42609.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w)),x,t_a)*.
% 299.64/300.40 43217[4:SpR:533.0,42829.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))),x,t_a)*.
% 299.64/300.40 43321[4:SSi:43294.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),v_x))*.
% 299.64/300.40 43322[4:SSi:43291.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v),v_x))*.
% 299.64/300.40 43427[4:SSi:43400.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),x))*.
% 299.64/300.40 43428[4:SSi:43397.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),x))*.
% 299.64/300.40 43656[4:SSi:43636.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(v,tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),x,t_a)*.
% 299.64/300.40 43657[4:SSi:43633.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(v,tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),x,t_a)*.
% 299.64/300.40 43797[0:Rew:337.0,43749.0] || -> equal(hAPP(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.40 43798[0:Rew:336.0,43734.0] || -> equal(hAPP(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.40 44026[4:SpL:118.0,38706.0] || equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,v_x,w,x,y),y,z,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(u,w),x1))*.
% 299.64/300.40 44037[4:SpL:118.0,38895.0] || equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,v_x,w,x,y),y,z,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(u,w),x1,t_a)*.
% 299.64/300.40 44515[0:Res:10705.0,36528.1] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,hAPP(v_Procs,v_x),y,z)),x))*.
% 299.64/300.40 44831[0:SpR:532.0,44716.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)),v_x))*.
% 299.64/300.40 44893[0:SpR:533.0,44824.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))),v_x))*.
% 299.64/300.40 44986[0:SSi:44952.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),v_x))*.
% 299.64/300.40 44987[0:SSi:44949.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v),v_x))*.
% 299.64/300.40 45453[0:Res:45357.1,11894.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.40 45477[0:Rew:9.0,45437.0] || hBOOL(hAPP(u,hAPP(v,v_x))) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname))))*.
% 299.64/300.40 45704[0:SpR:104.0,44625.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.40 46001[0:Rew:9.0,45952.1] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname))))* -> hBOOL(hAPP(u,hAPP(v,v_x))).
% 299.64/300.40 46671[4:SpL:12944.0,46565.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.40 46665[4:SpL:9.0,46565.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)),hAPP(u,hAPP(v,v_x)))* -> .
% 299.64/300.40 46664[4:SpL:11473.0,46565.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.40 46644[4:SpL:88.1,46565.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(u))* -> .
% 299.64/300.40 46641[4:SpL:17045.0,46565.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.40 47123[0:Res:31323.0,38189.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(v_Procs,u)))*.
% 299.64/300.40 47122[0:Res:9569.0,38189.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u),v)))*.
% 299.64/300.40 47121[0:Res:9568.0,38189.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),y),v)))*.
% 299.64/300.40 47120[0:Res:23882.0,38189.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u))*.
% 299.64/300.40 47116[0:Res:23789.0,38189.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),w))*.
% 299.64/300.40 47114[0:Res:12627.1,38189.0] || c_lessequals(u,v,tc_bool)* hBOOL(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v))*.
% 299.64/300.40 47106[0:Res:10705.0,38189.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Set_Oinsert(w,x),c_Fun_Ofun__upd(y,z,u,x1,x2)),z)))*.
% 299.64/300.40 47103[0:Res:10697.0,38189.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u)),u)))*.
% 299.64/300.40 47097[0:Res:18763.0,38189.0] || hBOOL(v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs)))*.
% 299.64/300.40 47096[0:Res:18644.0,38189.0] || hBOOL(v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),w),v_Procs)))*.
% 299.64/300.40 47055[0:Res:49.2,38189.0] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(u,c_HOL_Ozero__class_Ozero(tc_bool),tc_bool) hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_HOL_Ouminus__class_Ouminus(u,tc_bool)))*.
% 299.64/300.40 47031[0:Res:47.2,38189.0] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),u,tc_bool) hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u))*.
% 299.64/300.40 47726[4:Res:10705.0,47549.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool),y,z)),x))*.
% 299.64/300.40 47843[0:Res:31323.0,38190.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v_Procs,u)),v))*.
% 299.64/300.40 47842[0:Res:9569.0,38190.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),v)),y))*.
% 299.64/300.40 47841[0:Res:9568.0,38190.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v)),y))*.
% 299.64/300.40 47840[0:Res:23882.0,38190.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x))*.
% 299.64/300.40 47836[0:Res:23789.0,38190.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x))*.
% 299.64/300.40 47834[0:Res:12627.1,38190.0] || c_lessequals(u,v,tc_bool)* hBOOL(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),y))*.
% 299.64/300.40 47826[0:Res:10705.0,38190.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(v,w),c_Fun_Ofun__upd(x,y,u,z,x1)),y)),x2))*.
% 299.64/300.40 47823[0:Res:10697.0,38190.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u)),u)),y))*.
% 299.64/300.40 47817[0:Res:18763.0,38190.0] || hBOOL(v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs)),w))*.
% 299.64/300.40 47816[0:Res:18644.0,38190.0] || hBOOL(v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),v),v_Procs)),w))*.
% 299.64/300.40 47775[0:Res:49.2,38190.0] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(u,c_HOL_Ozero__class_Ozero(tc_bool),tc_bool) hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_bool)),v))*.
% 299.64/300.40 47751[0:Res:47.2,38190.0] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),u,tc_bool) hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v))*.
% 299.64/300.40 48177[4:SpR:317.0,39023.1] || equal(c_Set_Oimage(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),v_x)),y))*.
% 299.64/300.40 48157[4:SpR:14216.0,39023.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),c_Orderings_Otop__class_Otop(tc_bool)),z))*.
% 299.64/300.40 48155[4:SpR:11176.1,39023.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),x))*.
% 299.64/300.40 48151[4:SpR:11177.1,39023.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),x))*.
% 299.64/300.40 48123[4:SpR:331.0,39023.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),x))*.
% 299.64/300.40 48122[4:SpR:302.1,39023.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(u)),x))*.
% 299.64/300.40 48114[4:SpR:34428.0,39023.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),x))*.
% 299.64/300.40 48107[4:SpR:15476.0,39023.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)),x))*.
% 299.64/300.40 48292[4:SpR:317.0,39064.1] || equal(c_Set_Oimage(u,v,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),v_x)),y,t_a)*.
% 299.64/300.40 48272[4:SpR:14216.0,39064.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(x,y),c_Orderings_Otop__class_Otop(tc_bool)),z,t_a)*.
% 299.64/300.40 48270[4:SpR:11176.1,39064.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),u),x,t_a)*.
% 299.64/300.40 48266[4:SpR:11177.1,39064.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),v_x),x,t_a)*.
% 299.64/300.40 48238[4:SpR:331.0,39064.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),v_x),x,t_a)*.
% 299.64/300.40 48237[4:SpR:302.1,39064.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(u)),x,t_a)*.
% 299.64/300.40 48229[4:SpR:34428.0,39064.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),v_x),x,t_a)*.
% 299.64/300.40 48222[4:SpR:15476.0,39064.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)),x,t_a)*.
% 299.64/300.40 49014[0:Res:48989.1,255.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,v,tc_Com_Opname)),u))*.
% 299.64/300.40 49081[0:SpR:49017.1,7253.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_Procs))*.
% 299.64/300.40 49052[0:SpR:49017.1,21130.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.40 49349[0:Res:49314.1,278.1] || hBOOL(hAPP(u,v_x)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,v,tc_Com_Opname)))*.
% 299.64/300.40 49348[0:Res:49314.1,277.1] || hBOOL(hAPP(u,v_x)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,v,tc_Com_Opname)))*.
% 299.64/300.40 49341[0:Res:49314.1,170.1] class_Orderings_Olinorder(tc_Com_Opname) || hBOOL(hAPP(u,v_x)) c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.40 49340[0:Res:49314.1,169.1] class_Orderings_Olinorder(tc_Com_Opname) || hBOOL(hAPP(u,v_x)) c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.40 49405[0:SpR:49342.1,9567.0] || hBOOL(hAPP(u,v_x)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,tc_fun(w,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.40 50050[0:Rew:585.0,49997.0] || -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),u),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool)*.
% 299.64/300.40 50051[0:Rew:585.0,49995.0] || -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),u),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u)),tc_bool)*.
% 299.64/300.40 50357[0:Res:10705.0,46309.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Fun_Ofun__upd(x,y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),u),x1,x2)),y))*.
% 299.64/300.40 50740[0:Res:10705.0,46413.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Fun_Ofun__upd(x,y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),z),x1,x2)),y))*.
% 299.64/300.40 51028[0:Res:9569.0,50575.0] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(hAPP(w,x)) -> hBOOL(y)*.
% 299.64/300.40 51027[0:Res:9568.0,50575.0] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(hAPP(v,x)) -> hBOOL(y)*.
% 299.64/300.40 51020[0:Res:12627.1,50575.0] || c_lessequals(u,v,tc_bool)* equal(v,c_Orderings_Obot__class_Obot(tc_bool)) hBOOL(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool))* -> hBOOL(y)*.
% 299.64/300.40 51012[0:Res:10705.0,50575.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,y,z,x1)),x),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(y) -> hBOOL(x2)*.
% 299.64/300.40 51009[0:Res:10697.0,50575.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x)),x),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(x) -> hBOOL(y)*.
% 299.64/300.40 51003[0:Res:18763.0,50575.0] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(v_Procs) -> hBOOL(w)*.
% 299.64/300.40 51002[0:Res:18644.0,50575.0] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),v),v_Procs),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(v_Procs) -> hBOOL(w)*.
% 299.64/300.40 51335[0:SpR:331.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 51334[0:SpR:302.1,51231.0] class_Lattices_Obounded__lattice(u) || -> equal(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 51326[0:SpR:34428.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(u,t_a),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 51318[0:SpR:15476.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(hAPP(c_Set_Oinsert(v,t_a),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 51426[0:Rew:15569.0,51367.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 51427[0:Rew:15569.0,51363.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 51857[4:Res:40792.1,19641.0] || c_lessequals(v_x,hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Set_Oinsert(v,w),u),x)),tc_bool)* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),u),x,t_a).
% 299.64/300.40 52137[0:Res:31323.0,50366.0] || c_lessequals(hAPP(v_Procs,u),v,tc_bool)* hBOOL(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u))* -> hBOOL(v).
% 299.64/300.40 52136[0:Res:9569.0,50366.0] || c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),y,tc_bool)* hBOOL(hAPP(w,x)) -> hBOOL(y).
% 299.64/300.40 52135[0:Res:9568.0,50366.0] || c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),y,tc_bool)* hBOOL(hAPP(v,x)) -> hBOOL(y).
% 299.64/300.40 52134[0:Res:23882.0,50366.0] || c_lessequals(u,v,tc_bool)* hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)))* -> hBOOL(v).
% 299.64/300.40 52130[0:Res:23789.0,50366.0] || c_lessequals(u,v,tc_bool)* hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,tc_fun(x,tc_bool)),u))* -> hBOOL(v).
% 299.64/300.40 52128[0:Res:12627.1,50366.0] || c_lessequals(u,v,tc_bool)* c_lessequals(v,w,tc_bool)* hBOOL(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,x,tc_bool),y,tc_bool))* -> hBOOL(w).
% 299.64/300.40 52121[0:Res:10705.0,50366.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,y,z,x1)),x),x2,tc_bool)* hBOOL(y) -> hBOOL(x2).
% 299.64/300.40 52118[0:Res:10697.0,50366.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x)),x),y,tc_bool)* hBOOL(x) -> hBOOL(y).
% 299.64/300.40 52112[0:Res:18763.0,50366.0] || c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),w,tc_bool)* hBOOL(v_Procs) -> hBOOL(w).
% 299.64/300.40 52111[0:Res:18644.0,50366.0] || c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),v),v_Procs),w,tc_bool)* hBOOL(v_Procs) -> hBOOL(w).
% 299.64/300.40 52070[0:Res:49.2,50366.0] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(u,c_HOL_Ozero__class_Ozero(tc_bool),tc_bool) c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v,tc_bool)* hBOOL(u) -> hBOOL(v).
% 299.64/300.40 52046[0:Res:47.2,50366.0] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),u,tc_bool)* c_lessequals(u,v,tc_bool)* hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)) -> hBOOL(v).
% 299.64/300.40 52782[0:SpR:24019.2,21893.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(v_x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u)),v_x)**.
% 299.64/300.40 52776[0:SpR:24019.2,21267.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(v_x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u)),v_x)**.
% 299.64/300.40 53005[0:Res:23739.1,501.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,v_x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_Procs,t_a).
% 299.64/300.40 53416[0:SpR:33303.0,9566.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),v_x),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.40 53776[0:Res:7226.0,237.0] || c_Fun_Oinj__on(c_Option_Othe(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(hAPP(c_Option_Othe(u),c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(x,c_Option_Othe(u),w,v)),x)**.
% 299.64/300.40 53804[0:SpR:53771.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Option_Othe(u),x,z)),y,tc_bool)*.
% 299.64/300.40 53790[0:SpR:53771.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),c_Option_Othe(w),x,y,z),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),u,c_Option_Othe(w),x1,x2)))*.
% 299.64/300.40 53835[0:SpR:53772.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Option_Othe(u),y,x,z)),y,tc_bool)*.
% 299.64/300.40 53821[0:SpR:53772.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),c_Option_Othe(w),x,y,z),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Option_Othe(w),u,x1,x2)))*.
% 299.64/300.40 54159[0:SpL:52997.1,3506.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.40 54103[0:SpR:52997.1,9566.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_Procs,w)),v_x),tc_bool)*.
% 299.64/300.40 54101[0:SpR:52997.1,415.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_Procs,u),v_x,v_x,v,w),c_Set_Oinsert(v_Procs,u))**.
% 299.64/300.40 54074[0:SpR:52997.1,32669.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),v_x)))*.
% 299.64/300.40 54049[0:SpR:52997.1,24020.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.40 54303[0:Rew:42758.0,54302.0] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),u,tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)))**.
% 299.64/300.40 54719[0:SpR:13749.2,9566.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x)),c_Orderings_Otop__class_Otop(u)),tc_bool)*.
% 299.64/300.40 55193[0:SpR:14043.2,9566.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x)),c_Orderings_Otop__class_Otop(u)),tc_bool)*.
% 299.64/300.40 55819[0:Rew:25.1,55733.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.40 56018[0:SpL:9.0,55174.1] || equal(u,c_Fun_Ocomp(v,w,x,y,z))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(v,hAPP(w,v_x)))* -> .
% 299.64/300.40 55997[0:SpL:88.1,55174.1] class_Lattices_Oboolean__algebra(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Otop__class_Otop(u))* -> .
% 299.64/300.40 55936[0:SpL:9.0,55174.1] || equal(c_Fun_Ocomp(u,v,w,x,y),z)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),hAPP(z,v_x))* -> .
% 299.64/300.40 55915[0:SpL:88.1,55174.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v)* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),hAPP(v,v_x))* -> .
% 299.64/300.40 56336[0:SpL:30368.2,3506.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),c_Orderings_Otop__class_Otop(u))* -> .
% 299.64/300.40 56197[0:SpR:30368.2,9566.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),x),tc_bool)*.
% 299.64/300.40 56164[0:SpR:30368.2,32669.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u))))*.
% 299.64/300.40 56139[0:SpR:30368.2,24020.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),v_x),v_x).
% 299.64/300.40 56778[0:SpL:30928.2,3506.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(v,w),c_Orderings_Otop__class_Otop(u))* -> .
% 299.64/300.40 56639[0:SpR:30928.2,9566.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),x),tc_bool)*.
% 299.64/300.40 56605[0:SpR:30928.2,32669.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u))))*.
% 299.64/300.40 56580[0:SpR:30928.2,24020.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),v_x),v_x).
% 299.64/300.40 57778[0:Res:55625.1,50366.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_bool)* hBOOL(w)* -> hBOOL(v).
% 299.64/300.40 57963[0:SpL:14216.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(c_Set_Oinsert(x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> .
% 299.64/300.40 57961[0:SpL:11176.1,55910.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_COMBK(v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),u) -> .
% 299.64/300.40 57957[0:SpL:11177.1,55910.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_COMBK(u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) -> .
% 299.64/300.40 57928[0:SpL:331.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) -> .
% 299.64/300.40 57927[0:SpL:302.1,55910.1] class_Lattices_Obounded__lattice(u) || equal(c_COMBK(v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_Orderings_Otop__class_Otop(u)) -> .
% 299.64/300.40 57917[0:SpL:34428.0,55910.1] || equal(c_COMBK(u,v,w),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) -> .
% 299.64/300.40 57908[0:SpL:15476.0,55910.1] || equal(c_COMBK(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(x,v_x),tc_bool))* -> .
% 299.64/300.40 58016[0:Res:989.1,4229.2] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(c_Orderings_Otop__class_Otop(u),v,w),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.40 58049[0:Obv:58013.0] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.40 58050[0:Obv:58010.0] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.40 58085[0:SpL:331.0,55992.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v) -> .
% 299.64/300.40 58084[0:SpL:302.1,55992.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v) -> .
% 299.64/300.40 58074[0:SpL:34428.0,55992.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v) -> .
% 299.64/300.40 58154[0:Rew:2990.0,58129.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_COMBK(y,z,x1))* equal(c_Orderings_Otop__class_Otop(tc_bool),y) -> .
% 299.64/300.40 58155[0:Rew:3014.0,58117.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_COMBK(v,w,x))* equal(c_Orderings_Obot__class_Obot(tc_bool),v) -> .
% 299.64/300.40 58156[0:Rew:3014.0,58113.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_COMBK(v,w,x))* equal(c_Orderings_Obot__class_Obot(tc_bool),v) -> .
% 299.64/300.40 58213[0:SpL:329.1,58055.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> .
% 299.64/300.40 58212[0:SpL:328.1,58055.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(u,tc_bool),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> .
% 299.64/300.40 58208[0:SpL:538.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v))** -> .
% 299.64/300.40 58391[0:Res:989.1,5005.2] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Otop(u) class_Orderings_Oorder(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(c_Orderings_Otop__class_Otop(u),v,w),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.40 58508[0:SpL:27043.1,58248.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_COMBK(v_x,u,v),c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_Procs,w),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.40 58506[0:SpL:15172.0,58248.0] || equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),y,tc_fun(z,tc_bool)),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.40 58501[0:SpL:586.0,58248.0] || equal(c_COMBK(hAPP(u,hAPP(v,v_x)),w,x),c_HOL_Ouminus__class_Ouminus(hAPP(c_COMBB(u,y,z,x1),v),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.40 58500[0:SpL:585.0,58248.0] || equal(c_COMBK(hAPP(hAPP(u,v_x),v),w,x),c_HOL_Ouminus__class_Ouminus(hAPP(c_COMBC(u,y,z,x1),v),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.40 58494[0:SpL:9936.1,58248.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.40 58490[0:SpL:9935.1,58248.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),u,v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.40 58438[0:SpL:445.1,58248.0] || equal(c_COMBK(hAPP(u,v_x),v,w),c_HOL_Ouminus__class_Ouminus(c_Fun_Ofun__upd(u,x,y,z,x1),tc_fun(t_a,tc_bool)))* -> equal(v_x,x).
% 299.64/300.40 58581[0:SpR:584.0,10771.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),w))* -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(x,u),v,y,z,x1),w))*.
% 299.64/300.40 58649[0:SpL:118.0,58188.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(u,v),tc_bool),w,x),c_Fun_Ocomp(u,c_Fun_Ofun__upd(y,v_x,v,z,x1),x1,x2,z))* -> .
% 299.64/300.40 58869[0:Res:1158.0,15629.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),w)))*.
% 299.64/300.40 58790[0:SpL:2095.0,15629.0] || hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))) -> hBOOL(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Oinsert(v,u),w)))*.
% 299.64/300.40 58674[0:SpL:2093.0,15629.0] || hBOOL(hAPP(c_in(tc_Com_Opname),v_x)) -> hBOOL(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Set_Oinsert(v_Procs,u),v)))*.
% 299.64/300.40 59113[4:MRR:58696.2,6340.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,u,v)))*.
% 299.64/300.40 59114[4:MRR:58675.0,6340.0] || -> hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v)))*.
% 299.64/300.40 59377[0:Res:1158.0,15857.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),x)))*.
% 299.64/300.40 59298[0:SpL:2095.0,15857.0] || hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))) -> hBOOL(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(v,u),x)))*.
% 299.64/300.40 59182[0:SpL:2093.0,15857.0] || hBOOL(hAPP(c_in(tc_Com_Opname),v_x)) -> hBOOL(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v_Procs,u),w)))*.
% 299.64/300.40 59623[4:MRR:59204.2,6340.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,w)))*.
% 299.64/300.40 59624[4:MRR:59183.0,6340.0] || -> hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),w)))*.
% 299.64/300.40 59656[0:SSi:59648.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** equal(c_COMBK(v_x,u,v),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)))** -> .
% 299.64/300.40 59657[0:SSi:59647.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)))** equal(c_COMBK(v_x,u,v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.40 59774[0:SpL:158.0,21018.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),hAPP(c_Set_Oinsert(z,y),x1))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.40 59877[0:SpL:584.0,4126.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),z)** -> c_lessequals(hAPP(v,z),z,u)*.
% 299.64/300.40 59920[0:Obv:59841.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v,u)*.
% 299.64/300.40 60197[0:SpL:331.0,58170.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),u)* -> .
% 299.64/300.40 60196[0:SpL:302.1,58170.1] class_Lattices_Obounded__lattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),w,x),v)* -> .
% 299.64/300.40 60186[0:SpL:34428.0,58170.1] || equal(u,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),u)* -> .
% 299.64/300.40 60266[0:Rew:2990.0,60241.1] || equal(u,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)))* equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),z,x1),u)* -> .
% 299.64/300.40 60267[0:Rew:3014.0,60229.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),v)* -> .
% 299.64/300.40 60268[0:Rew:3014.0,60225.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),u)* -> .
% 299.64/300.40 60427[7:Res:58968.1,527.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w),v))*.
% 299.64/300.40 60405[7:SpR:23682.0,58968.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u))*.
% 299.64/300.40 60452[0:SpR:5882.1,9566.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,w),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1)),c_Orderings_Otop__class_Otop(u)),tc_bool)*.
% 299.64/300.40 60540[0:Res:58969.1,527.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w),v))*.
% 299.64/300.40 60518[0:SpR:23682.0,58969.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u))*.
% 299.64/300.40 60613[7:Res:59476.1,527.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x),v))*.
% 299.64/300.40 60591[7:SpR:23682.0,59476.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v))*.
% 299.64/300.40 60686[0:Res:59477.1,527.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x),v))*.
% 299.64/300.40 60664[0:SpR:23682.0,59477.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v))*.
% 299.64/300.40 60871[0:Res:59017.1,527.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a)* hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(v),w),x),w))*.
% 299.64/300.40 60849[0:SpR:23682.0,59017.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v))*.
% 299.64/300.40 60944[0:Res:59525.1,527.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a)* hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(v),w),y),w))*.
% 299.64/300.40 60922[0:SpR:23682.0,59525.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w))*.
% 299.64/300.40 61137[0:Res:61046.3,51.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_Orderings_Obot__class_Obot(u))** -> c_lessequals(v,w,u).
% 299.64/300.40 61124[0:Res:61046.3,48.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.40 61123[0:Res:61046.3,44.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.40 61425[0:Res:61338.3,50.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)) -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.40 61424[0:Res:61338.3,46.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)) -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.40 61549[0:Res:989.1,7766.2] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(c_Orderings_Otop__class_Otop(u),w,x),tc_Com_Opname,u),u)*.
% 299.64/300.40 61604[0:Rew:73.1,61551.4] class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.40 61607[0:Obv:61546.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u) -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),u)*.
% 299.64/300.40 61608[0:Obv:61543.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u) -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v),u)*.
% 299.64/300.40 61621[0:Rew:8415.2,61618.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,u,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v_x,u),v_Procs,t_a)*.
% 299.64/300.40 61659[0:Res:989.1,8141.2] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(c_Orderings_Otop__class_Otop(u),w,x),tc_Com_Opname,u),u)*.
% 299.64/300.40 61777[0:SpR:11167.1,9566.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,x),c_Set_Oinsert(v_x,tc_Com_Opname))),v_Procs),tc_bool)*.
% 299.64/300.40 61957[0:SpL:24020.1,15487.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 61916[0:SpL:300.1,15487.1] class_Lattices_Obounded__lattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 61901[0:SpL:365.1,15487.1] class_Orderings_Obot(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 61900[0:SpL:397.1,15487.1] class_Orderings_Otop(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 61894[0:SpL:2097.1,15487.1] || hBOOL(hAPP(v_x,u)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(u,v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 61985[0:Rew:56980.1,61956.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 61986[0:Rew:56980.1,61952.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 61989[0:Rew:3014.0,61966.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 61990[0:Rew:3014.0,61959.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 61991[0:Rew:2990.0,61935.1] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 62085[2:Res:55625.1,16623.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.40 62117[0:Rew:8415.2,62114.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v_x,u),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,u,t_a)*.
% 299.64/300.40 62389[0:Obv:62293.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.40 62391[0:Obv:62274.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),w) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),w,u)*.
% 299.64/300.40 62704[0:Obv:62628.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)* -> equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.40 62706[0:Obv:62609.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),w,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),w).
% 299.64/300.40 62708[0:Obv:62580.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(u),v) c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> equal(v,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.40 63021[0:SpL:62710.2,134.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),v)** -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.40 63694[0:Res:62368.3,112.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(w,v,u)*.
% 299.64/300.40 63693[0:Res:62368.3,146.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),w) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(w,u),v,u)*.
% 299.64/300.40 63692[0:Res:62368.3,42.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.40 63691[0:Res:62368.3,51.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u))** -> c_lessequals(v,w,u).
% 299.64/300.40 63690[0:Res:62368.3,54.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.40 63686[0:Res:62368.3,8252.2] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || equal(v,c_Orderings_Obot__class_Obot(u)) -> c_lessequals(v,w,u)*.
% 299.64/300.40 63685[0:Res:62368.3,144.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.40 63673[0:Res:62368.3,8141.2] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || equal(c_Orderings_Otop__class_Otop(u),v) -> c_lessequals(w,v,u)*.
% 299.64/300.40 63779[0:SSi:63666.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(v,hAPP(c_Set_Oimage(w,x,u),y))* c_Finite__Set_Ofinite(y,x) -> c_Finite__Set_Ofinite(v,u)*.
% 299.64/300.40 64236[0:SpR:23912.0,646.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_Procs,tc_Com_Opname,u) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),v_x)**.
% 299.64/300.40 64216[0:SpR:351.0,646.1] || c_Fun_Oinj__on(c_COMBK(u,v,w),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,x),u),v_x)**.
% 299.64/300.40 64189[0:SpR:3229.1,646.1] || equal(u,v) c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,v,tc_Com_Opname,w),hAPP(u,v_x)),v_x)**.
% 299.64/300.40 64403[0:SpR:23912.0,645.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_Procs,tc_Com_Opname,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),v_x)**.
% 299.64/300.40 64383[0:SpR:351.0,645.1] || c_Fun_Oinj__on(c_COMBK(u,v,w),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,x),u),v_x)**.
% 299.64/300.40 64356[0:SpR:3229.1,645.1] || equal(u,v) c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(u,v_x)),v_x)**.
% 299.64/300.40 64476[0:Res:662.1,3929.0] || hBOOL(hAPP(hAPP(u,v_x),v_x)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.40 64495[0:SpL:365.1,24257.1] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.40 64494[0:SpL:397.1,24257.1] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.40 64646[0:SpL:2267.1,2064.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** -> equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),u)*.
% 299.64/300.40 64688[0:SpL:2267.1,2065.0] || equal(u,v)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> equal(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u)*.
% 299.64/300.40 64806[0:SpR:28747.0,9566.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.40 64926[0:SpR:28748.0,9566.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.40 65046[0:SpR:28902.0,9566.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.40 65166[0:SpR:28903.0,9566.0] || -> c_lessequals(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,x),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.40 66043[0:SpR:65404.1,474.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.40 66436[0:Res:65575.1,15629.0] || equal(hAPP(u,v_x),v_Procs) -> hBOOL(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(u,v_x),v)))*.
% 299.64/300.40 66435[0:Res:65575.1,15857.0] || equal(hAPP(u,v_x),v_Procs) -> hBOOL(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(u,v_x),w)))*.
% 299.64/300.40 66354[0:SpR:540.1,65575.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_x))*.
% 299.64/300.40 66353[0:SpR:539.1,65575.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_x))*.
% 299.64/300.40 66510[0:Res:66452.2,15629.0] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(u),v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Orderings_Otop__class_Otop(u),v)))*.
% 299.64/300.40 66509[0:Res:66452.2,15857.0] class_Orderings_Otop(u) || equal(c_Orderings_Otop__class_Otop(u),v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(u),w)))*.
% 299.64/300.40 66518[0:Res:66453.2,15629.0] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),v_Procs) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Orderings_Obot__class_Obot(u),v)))*.
% 299.64/300.40 66517[0:Res:66453.2,15857.0] class_Orderings_Obot(u) || equal(c_Orderings_Obot__class_Obot(u),v_Procs) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(u),w)))*.
% 299.64/300.40 66526[0:Res:66455.2,15629.0] class_Lattices_Obounded__lattice(u) || equal(c_Orderings_Otop__class_Otop(u),v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Orderings_Otop__class_Otop(u),v)))*.
% 299.64/300.40 66525[0:Res:66455.2,15857.0] class_Lattices_Obounded__lattice(u) || equal(c_Orderings_Otop__class_Otop(u),v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(u),w)))*.
% 299.64/300.40 66534[0:Res:66459.2,15629.0] class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Otop__class_Otop(u),v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Orderings_Otop__class_Otop(u),v)))*.
% 299.64/300.40 66533[0:Res:66459.2,15857.0] class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Otop__class_Otop(u),v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(u),w)))*.
% 299.64/300.40 66579[0:SpR:1605.2,65888.2] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.40 66578[0:SpR:1628.2,65888.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.40 66573[0:SpR:1259.2,65888.2] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.40 66569[0:SpR:1409.2,65888.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)) -> c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.40 69710[0:Res:448.1,6239.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v).
% 299.64/300.40 69698[0:Res:47.2,6239.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* -> equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v).
% 299.64/300.40 69688[0:SpL:2267.1,6239.0] || equal(u,v) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),u,tc_fun(w,tc_bool))* -> equal(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u).
% 299.64/300.40 69738[0:SpR:1628.2,66670.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.40 69734[0:SpR:1421.2,66670.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.40 70073[0:SpL:3229.1,11883.0] || equal(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)))* hBOOL(hAPP(u,v_x))* hBOOL(hAPP(hAPP(c_in(w),v_x),v))* -> .
% 299.64/300.40 70068[0:SpL:2267.1,11883.0] || equal(u,v)* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),x))* hBOOL(hAPP(hAPP(c_in(w),x),u))* -> .
% 299.64/300.40 70221[0:SpR:1605.2,65893.2] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.40 70220[0:SpR:1628.2,65893.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.40 70215[0:SpR:1259.2,65893.2] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.40 70212[0:SpR:1421.2,65893.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)*.
% 299.64/300.40 70305[0:SpR:1628.2,70279.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.40 70300[0:SpR:1409.2,70279.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.40 70393[0:Res:176.0,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Ovimage(u,t_a,v),hAPP(c_Set_Oinsert(hAPP(u,v_x),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),v_x),tc_bool))* -> .
% 299.64/300.40 70582[0:Obv:70563.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || equal(v,w)* equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u))** -> equal(c_HOL_Ozero__class_Ozero(u),w)*.
% 299.64/300.40 70683[0:SpL:540.1,70400.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))* -> .
% 299.64/300.40 70682[0:SpL:539.1,70400.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))* -> .
% 299.64/300.40 70865[0:SpL:3229.1,6582.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* equal(hAPP(u,v_x),w)* -> c_lessequals(v_x,w,tc_fun(v,tc_bool)).
% 299.64/300.40 70859[0:SpL:3229.1,6582.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)))* equal(hAPP(hAPP(u,v_x),w),v_x)** -> c_lessequals(w,v_x,tc_fun(v,tc_bool))*.
% 299.64/300.40 71022[0:SpR:3229.1,7568.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) -> c_lessequals(w,hAPP(c_Set_Oinsert(x,v),hAPP(u,v_x)),tc_fun(v,tc_bool))*.
% 299.64/300.40 71016[0:SpR:3229.1,7568.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) -> c_lessequals(v_x,hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(u,v_x),x)),tc_fun(v,tc_bool))*.
% 299.64/300.40 71325[0:Res:7538.0,363.0] || -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(y,v),u))),tc_fun(v,tc_bool))*.
% 299.64/300.40 71297[0:SpR:339.0,7538.0] || -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(y,w),u))),tc_fun(w,tc_bool))*.
% 299.64/300.40 71271[0:SpR:3229.1,7538.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) -> c_lessequals(w,hAPP(hAPP(u,v_x),hAPP(c_Set_Oinsert(x,v),w)),tc_fun(v,tc_bool))*.
% 299.64/300.40 71238[0:SpR:3229.1,7538.0] || equal(u,c_Set_Oinsert(v,w))* -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(u,v_x)),tc_fun(w,tc_bool))*.
% 299.64/300.40 71420[7:SpL:328.1,71221.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)** -> .
% 299.64/300.40 71416[7:SpL:538.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x) -> .
% 299.64/300.40 71614[7:SpR:71455.1,474.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.40 71596[7:SpR:71455.1,446.1] || equal(u,v_x) c_lessequals(v,u,tc_fun(t_a,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),v),u,tc_fun(t_a,tc_bool))*.
% 299.64/300.40 72026[7:MRR:72012.1,6340.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,c_Set_Oinsert(v_x,t_a),tc_Com_Opname),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,c_Set_Oinsert(v_x,t_a),tc_Com_Opname)).
% 299.64/300.40 72027[7:MRR:72013.1,6340.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname)).
% 299.64/300.40 72046[0:SpR:3229.1,7830.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* -> c_lessequals(v_x,hAPP(c_Set_Oinsert(x,v),hAPP(u,v_x)),tc_fun(v,tc_bool))*.
% 299.64/300.40 72040[0:SpR:3229.1,7830.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) -> c_lessequals(w,hAPP(c_Set_Oinsert(x,v),hAPP(hAPP(u,v_x),w)),tc_fun(v,tc_bool))*.
% 299.64/300.40 72395[7:MRR:70385.1,72294.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname,u),hAPP(hAPP(c_in(t_a),v_x),v_x)),v_x),tc_bool))* -> .
% 299.64/300.40 72476[0:SpL:3229.1,12554.0] || equal(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)))* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(hAPP(c_in(x),v_x),v))*.
% 299.64/300.40 72472[0:SpL:647.0,12554.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u)))*.
% 299.64/300.40 72692[0:SpL:3229.1,18903.0] || equal(u,c_Com_Ocom_OBODY) c_Natural_Oevaln(hAPP(u,v_x),v,w,x)* -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x)),v,x)*.
% 299.64/300.40 72824[0:Obv:72750.0] class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || equal(v,w) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)* -> equal(w,c_Orderings_Otop__class_Otop(u)).
% 299.64/300.40 72830[0:SSi:72765.1,72765.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(u,v) c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(v,v_x),tc_bool)* -> equal(hAPP(v,v_x),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.40 73070[7:Res:71608.1,280.1] || equal(u,v_x) hBOOL(hAPP(hAPP(v,v_x),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,t_a,tc_fun(x,tc_bool)),w))*.
% 299.64/300.40 73066[7:Res:71608.1,175.0] || equal(hAPP(c_Set_Ovimage(u,t_a,v),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),v_x)** -> equal(hAPP(u,v_x),w).
% 299.64/300.40 73062[7:Res:71608.1,470.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_x) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,t_a)),w))*.
% 299.64/300.40 73061[7:Res:71608.1,466.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_x) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,t_a)),w))*.
% 299.64/300.40 73182[0:Obv:73154.0] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.40 73184[0:Obv:73152.0] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),v,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.40 74362[7:SpL:71835.1,12983.0] || equal(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(v_x,t_a))** c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,v_x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a)*.
% 299.64/300.40 74289[7:SpL:71835.1,6582.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a))** equal(v_x,v) -> c_lessequals(v_x,v,tc_fun(u,tc_bool)).
% 299.64/300.40 74206[7:SpL:71835.1,295.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a))** c_lessequals(v_x,w,u)* -> c_lessequals(v,w,u)*.
% 299.64/300.40 74204[7:SpL:71835.1,311.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a))** equal(c_Orderings_Obot__class_Obot(u),v_x) -> equal(v,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.40 74171[7:SpL:71835.1,296.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(hAPP(v_x,v),w,u)* -> c_lessequals(v,w,u).
% 299.64/300.40 74170[7:SpL:71835.1,295.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(hAPP(v_x,v),w,u)* -> c_lessequals(v_x,w,u).
% 299.64/300.40 74168[7:SpL:71835.1,311.1] class_Lattices_Obounded__lattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) equal(hAPP(v_x,v),c_Orderings_Obot__class_Obot(u))* -> equal(c_Orderings_Obot__class_Obot(u),v_x).
% 299.64/300.40 74163[7:SpL:71835.1,6582.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) equal(hAPP(v_x,v),v_x) -> c_lessequals(v,v_x,tc_fun(u,tc_bool))*.
% 299.64/300.40 74157[7:SpL:71835.1,327.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) equal(hAPP(v_x,v),v) -> c_lessequals(v_x,v,tc_fun(u,tc_bool))*.
% 299.64/300.40 73960[7:SpL:71835.1,18903.0] || equal(c_Set_Oinsert(v_x,t_a),c_Com_Ocom_OBODY) c_Natural_Oevaln(v_x,u,v,w)* -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x)),u,w)*.
% 299.64/300.40 73787[7:SpR:71835.1,7568.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a)) -> c_lessequals(v,hAPP(c_Set_Oinsert(w,u),v_x),tc_fun(u,tc_bool))*.
% 299.64/300.40 73782[7:SpR:71835.1,328.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a))** c_lessequals(v_x,v,tc_fun(u,tc_bool)) -> equal(v_x,v).
% 299.64/300.40 73764[7:SpR:71835.1,538.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),v_x)**.
% 299.64/300.40 73755[7:SpR:71835.1,293.2] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a))** c_lessequals(w,v,u)* -> c_lessequals(w,v_x,u)*.
% 299.64/300.40 73686[7:SpR:71835.1,294.2] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v,w,u) -> c_lessequals(v,hAPP(v_x,w),u)*.
% 299.64/300.40 73661[7:SpR:71835.1,474.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(u,w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.40 73654[7:SpR:71835.1,538.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(v_x,v))**.
% 299.64/300.40 73653[7:SpR:71835.1,7538.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> c_lessequals(v,hAPP(v_x,hAPP(c_Set_Oinsert(w,u),v)),tc_fun(u,tc_bool))*.
% 299.64/300.40 73648[7:SpR:71835.1,293.2] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v,v_x,u) -> c_lessequals(v,hAPP(v_x,w),u)*.
% 299.64/300.40 73531[7:SpR:71835.1,328.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) c_lessequals(v,v_x,tc_fun(u,tc_bool))* -> equal(hAPP(v_x,v),v_x).
% 299.64/300.40 73404[7:SpR:71835.1,646.1] || equal(c_Set_Oinsert(v_x,t_a),u) c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.40 73398[7:SpR:71835.1,645.1] || equal(c_Set_Oinsert(v_x,t_a),u) c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.40 73247[7:SpR:71835.1,329.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) c_lessequals(v_x,v,tc_fun(u,tc_bool))* -> equal(hAPP(v_x,v),v).
% 299.64/300.40 74470[7:MRR:74280.1,6340.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(w,v_x)).
% 299.64/300.40 74472[7:Rew:71835.1,74128.2] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))))* -> hBOOL(hAPP(v_x,v)).
% 299.64/300.40 74473[7:Rew:71835.1,74126.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,v)) hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))))* -> .
% 299.64/300.40 74490[7:Rew:73654.1,73519.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(v_x,c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool))),hAPP(v_x,v))**.
% 299.64/300.40 74505[7:MRR:73194.1,589.0] || equal(c_Set_Oinsert(v_x,t_a),v_P) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_x),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(v_Q,v_x)),t_a)*.
% 299.64/300.40 74506[7:MRR:73192.1,589.0] || equal(c_Set_Oinsert(v_x,t_a),c_Com_Ocom_OBODY) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),v_x),hAPP(v_Q,v_x)),t_a)*.
% 299.64/300.40 74507[7:MRR:73191.1,589.0] || equal(c_Set_Oinsert(v_x,t_a),v_Q) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_x),t_a)*.
% 299.64/300.40 74816[0:SpR:3229.1,5893.0] || equal(u,c_Hoare__Mirabelle_Otriple_Otriple(v)) -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_COMBS(hAPP(u,v_x),w,x,y,z),hAPP(c_Com_Ocom_OBODY,x1)),v)*.
% 299.64/300.40 74813[7:SpR:71835.1,5893.0] || equal(c_Set_Oinsert(v_x,t_a),c_Hoare__Mirabelle_Otriple_Otriple(u)) -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_COMBS(v_x,v,w,x,y),hAPP(c_Com_Ocom_OBODY,z)),u)*.
% 299.64/300.40 74809[0:SpR:3229.1,5893.0] || equal(u,c_Com_Ocom_OBODY) -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_COMBS(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x,y,z,x1),hAPP(u,v_x)),v)*.
% 299.64/300.40 75416[0:SpR:3229.1,7820.1] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(w,hAPP(hAPP(v,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w)),u)*.
% 299.64/300.40 75413[7:SpR:71835.1,7820.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v,hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v)),u)*.
% 299.64/300.40 75338[0:SpR:3229.1,7820.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(v,v_x)),u)*.
% 299.64/300.40 75331[0:SpR:3229.1,7820.1] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(v,v_x),w)),u)*.
% 299.64/300.40 75735[7:SpL:71883.1,15487.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 75870[0:SpR:3229.1,7823.1] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(w,hAPP(hAPP(v,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),u)*.
% 299.64/300.40 75867[7:SpR:71835.1,7823.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v,hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),u)*.
% 299.64/300.40 75792[0:SpR:3229.1,7823.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(v,v_x)),u)*.
% 299.64/300.40 75789[7:SpR:71835.1,7823.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a)) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x),u)*.
% 299.64/300.40 75785[0:SpR:3229.1,7823.1] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(v,v_x),x)),u)*.
% 299.64/300.40 76155[0:SpR:9915.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 76275[0:SpR:10469.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),x2,x3),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.40 76405[0:SpR:10470.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.40 76547[0:SpR:3229.1,29199.1] class_Lattices_Olattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(w,hAPP(hAPP(v,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w)),u)*.
% 299.64/300.40 76544[7:SpR:71835.1,29199.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v,hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v)),u)*.
% 299.64/300.40 76469[0:SpR:3229.1,29199.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(v,v_x)),u)*.
% 299.64/300.40 76462[0:SpR:3229.1,29199.1] class_Lattices_Olattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(v,v_x),w)),u)*.
% 299.64/300.40 76902[0:SpR:3229.1,30321.1] class_Lattices_Olattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(w,hAPP(hAPP(v,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),u)*.
% 299.64/300.40 76899[7:SpR:71835.1,30321.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v,hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),u)*.
% 299.64/300.40 76824[0:SpR:3229.1,30321.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(v,v_x)),u)*.
% 299.64/300.40 76821[7:SpR:71835.1,30321.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a)) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x),u)*.
% 299.64/300.40 76817[0:SpR:3229.1,30321.1] class_Lattices_Olattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(v,v_x),x)),u)*.
% 299.64/300.40 77203[7:SpL:584.0,74788.1] || equal(c_COMBS(u,v,w,x,y),v_x)** equal(hAPP(hAPP(u,v_x),hAPP(v,v_x)),z)* -> hBOOL(z)*.
% 299.64/300.40 77183[7:SpL:337.0,74788.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x)** equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v)* -> hBOOL(v)*.
% 299.64/300.40 77170[7:SpL:540.1,74788.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),w)* -> hBOOL(w)*.
% 299.64/300.40 77169[7:SpL:539.1,74788.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),w)* -> hBOOL(w)*.
% 299.64/300.40 77161[7:SpL:30368.2,74788.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** equal(c_Orderings_Otop__class_Otop(u),v)* -> hBOOL(v)*.
% 299.64/300.40 77160[7:SpL:30928.2,74788.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** equal(c_Orderings_Otop__class_Otop(u),v)* -> hBOOL(v)*.
% 299.64/300.40 77157[7:SpL:299.2,74788.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)** equal(v,w)* -> hBOOL(w)*.
% 299.64/300.40 77140[7:SpL:25.1,74788.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_x) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),w)* -> hBOOL(w)*.
% 299.64/300.40 77315[0:SpR:73.1,2399.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u).
% 299.64/300.40 77314[0:SpR:74.1,2399.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u).
% 299.64/300.40 77464[7:SpR:71894.1,20881.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,u,v),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),u),w)),v_x))*.
% 299.64/300.40 77449[7:SpR:71894.1,9569.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool)*.
% 299.64/300.40 77448[7:SpR:71894.1,9568.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool)*.
% 299.64/300.40 77482[7:SpL:8415.2,72390.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(t_a)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,v_x,tc_Com_Opname),v_x),tc_bool))* -> .
% 299.64/300.40 77507[0:SpR:73.1,2429.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u).
% 299.64/300.40 77506[0:SpR:74.1,2429.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) || -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_Orderings_Otop__class_Otop(u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u).
% 299.64/300.40 77640[7:SpL:8415.2,77504.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(t_a)) equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,v_x,tc_Com_Opname),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.40 77920[0:Res:38131.1,5892.0] || hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Set_Oinsert(w,x),y,z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)))*.
% 299.64/300.40 77917[0:Res:21126.1,5892.0] || equal(hAPP(u,v_x),v_Procs) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Set_Oimage(u,tc_Com_Opname,w),x,y,z),hAPP(u,v_x)))*.
% 299.64/300.40 77904[0:Res:3346.1,5892.0] || equal(c_Set_Oinsert(hAPP(u,v_x),v),u) -> hBOOL(hAPP(c_COMBS(c_in(w),c_in(v),x,y,z),hAPP(u,v_x)))*.
% 299.64/300.40 77892[0:SpL:586.0,5892.0] || hBOOL(hAPP(u,hAPP(v,v)))* -> hBOOL(hAPP(c_COMBS(c_in(w),c_COMBB(u,x,y,z),x1,x2,x3),v))*.
% 299.64/300.40 77891[0:SpL:585.0,5892.0] || hBOOL(hAPP(hAPP(u,v),v))* -> hBOOL(hAPP(c_COMBS(c_in(w),c_COMBC(u,x,y,z),x1,x2,x3),v))*.
% 299.64/300.40 77999[7:MRR:21650.1,77996.0] || equal(c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(tc_Com_Opname),v_x),hAPP(hAPP(c_in(tc_Com_Opname),v_x),v_x),tc_Com_Opname,u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.40 78000[7:MRR:22278.1,77996.0] || equal(c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(tc_Com_Opname),v_x),v_x),hAPP(c_in(tc_Com_Opname),v_x),tc_Com_Opname,u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.40 78079[4:MRR:78078.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(u,v_x),c_Set_Oinsert(v_x,tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(u,v_x)))*.
% 299.64/300.40 78196[7:Rew:78167.0,64021.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname,u),v_x),v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_HOL_Ominus__class_Ominus(v_x,v_Procs,tc_fun(tc_Com_Opname,tc_bool)))**.
% 299.64/300.40 78210[7:Rew:78167.0,78197.1] || c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname,u),v_x),v_Procs,tc_fun(tc_Com_Opname,tc_bool))* -> c_lessequals(v_x,v_Procs,tc_fun(tc_Com_Opname,tc_bool)).
% 299.64/300.40 78211[7:Rew:78167.0,78189.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,tc_Com_Opname),v_x,tc_Com_Opname,u),v_Procs)** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,tc_Com_Opname),v_x,tc_Com_Opname,u),v_x).
% 299.64/300.40 78212[7:Rew:78167.0,78192.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname,u),v_Procs)** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname,u),v_x).
% 299.64/300.40 78370[7:SpR:78167.0,338.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x))**.
% 299.64/300.40 78345[7:SpR:78167.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,x),v,u),u)*.
% 299.64/300.40 78339[7:SpR:78167.0,339.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))**.
% 299.64/300.40 78320[7:SpR:78167.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,v),u,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.64/300.40 78503[4:Res:77988.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.64/300.40 78536[4:MRR:9467.2,78524.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.64/300.40 78537[4:MRR:9466.1,78524.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a))),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)))**.
% 299.64/300.40 78599[0:SpL:3229.1,5986.0] || equal(u,c_COMBS(c_in(v),w,x,y,z))* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(hAPP(w,v_x),v_x)).
% 299.64/300.40 78757[4:Res:78665.1,519.0] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),v_x)** -> hBOOL(hAPP(v,x)) hBOOL(hAPP(w,x)).
% 299.64/300.40 78693[4:Res:78665.1,148.0] || equal(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))),v_x)** -> hBOOL(hAPP(hAPP(c_in(u),v),w)).
% 299.64/300.40 78692[4:Res:78665.1,150.1] || equal(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))),v_x)** hBOOL(hAPP(hAPP(c_in(u),v),w)) -> .
% 299.64/300.40 78785[0:SpL:3229.1,5988.0] || equal(u,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z))* c_Finite__Set_Ofinite(hAPP(u,v_x),v)* -> c_Finite__Set_Ofinite(v_x,v).
% 299.64/300.40 78868[0:SpR:3229.1,11064.1] || equal(u,c_Set_Oimage(v,w,x))* c_Finite__Set_Ofinite(v_x,w) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),y,tc_fun(x,tc_bool)),x)*.
% 299.64/300.40 79055[0:Rew:331.0,78978.0] || hBOOL(u) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),v))*.
% 299.64/300.40 79069[0:Res:78077.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.64/300.40 79097[7:Res:78199.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(c_in(x),v_x)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.64/300.40 79275[0:Rew:331.0,79198.0] || hBOOL(u) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(u,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),w))*.
% 299.64/300.40 80124[0:SpL:21268.0,541.0] || equal(hAPP(c_Com_Ocom_OBODY,u),hAPP(c_Com_Ocom_OBODY,v))* -> equal(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,v),w,x))*.
% 299.64/300.40 79960[0:SpR:9925.0,21268.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_bool),v,w)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.40 79944[0:SpR:2935.0,21268.0] || -> equal(hAPP(hAPP(c_in(t_a),v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_in(t_a),v_x),c_Orderings_Obot__class_Obot(tc_bool),u,v)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 79858[0:SpR:3229.1,21268.0] || equal(u,v) -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,hAPP(u,v_x),w,x)),hAPP(u,v_x))**.
% 299.64/300.40 79826[7:SpR:71455.1,21268.0] || equal(u,v_x) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),u,v,w)),u)**.
% 299.64/300.40 79825[0:SpR:8385.1,21268.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),u,v,w)),u)**.
% 299.64/300.40 81319[0:SpL:21894.0,541.0] || equal(hAPP(c_Com_Ocom_OBODY,u),hAPP(c_Com_Ocom_OBODY,v))* -> equal(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Com_Ocom_OBODY,v),c_Com_Ocom_OBODY,w,x))*.
% 299.64/300.40 81154[0:SpR:9925.0,21894.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.40 81138[0:SpR:2935.0,21894.0] || -> equal(hAPP(hAPP(c_in(t_a),v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_in(t_a),v_x),u,v)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 81052[0:SpR:3229.1,21894.0] || equal(u,v) -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(u,v_x),v,w,x)),hAPP(u,v_x))**.
% 299.64/300.40 81020[7:SpR:71455.1,21894.0] || equal(u,v_x) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,c_Set_Oinsert(v_x,t_a),v,w)),u)**.
% 299.64/300.40 81019[0:SpR:8385.1,21894.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,c_Set_Oinsert(v_x,tc_Com_Opname),v,w)),u)**.
% 299.64/300.40 81742[0:SpR:3229.1,5075.1] || equal(u,c_Set_Ovimage(v,w,x)) c_Finite__Set_Ofinite(v_x,x) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,x),hAPP(u,v_x)),x)*.
% 299.64/300.40 81768[0:SpR:3229.1,5879.1] class_Lattices_Oupper__semilattice(u) || equal(v,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z))* -> c_lessequals(hAPP(w,v_x),hAPP(v,v_x),u)*.
% 299.64/300.40 82157[7:SpR:78597.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,v),c_Set_Oinsert(v_x,t_a),u,w)),c_Set_Oinsert(v_x,v))**.
% 299.64/300.40 82156[7:SpR:78597.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(v_x,v),u,w)),c_Set_Oinsert(v_x,v))**.
% 299.64/300.40 82136[7:SpR:78597.0,446.1] || c_lessequals(u,c_Set_Oinsert(v_x,v),tc_fun(t_a,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),u),c_Set_Oinsert(v_x,v),tc_fun(t_a,tc_bool))*.
% 299.64/300.40 82240[0:SpR:3229.1,5880.1] class_Lattices_Olattice(u) || equal(v,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z))* -> c_lessequals(hAPP(w,v_x),hAPP(v,v_x),u)*.
% 299.64/300.40 82704[0:Res:683.1,7671.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,hAPP(w,v_x),u) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,w,tc_Com_Opname,u),u)*.
% 299.64/300.40 82666[0:Res:4703.2,7671.1] class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),u)* -> c_lessequals(v,w,u)*.
% 299.64/300.40 82809[0:Obv:82656.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(u),v) c_lessequals(w,c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(w,v,u)*.
% 299.64/300.40 82844[7:Res:77991.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),v_x),u,y,tc_fun(z,tc_bool)),v))*.
% 299.64/300.40 82840[7:Res:77991.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,w),v_x),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(v,w),v_x),u),v_x,u)*.
% 299.64/300.40 82839[7:Res:77991.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,w),v_x),u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(v,w),v_x),u),u)*.
% 299.64/300.40 82921[0:SpR:3229.1,22513.1] || equal(u,c_Set_Oimage(v,w,x))* c_Finite__Set_Ofinite(v_x,w) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(y,x,z),hAPP(u,v_x)),z)*.
% 299.64/300.40 83102[0:SpL:5924.0,16286.0] || equal(hAPP(hAPP(u,v_x),v),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_Procs)** -> .
% 299.64/300.40 83101[7:SpL:5924.0,31868.0] || equal(hAPP(hAPP(u,v_x),v),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_x)** -> .
% 299.64/300.40 83094[0:SpL:5924.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool),w,x),c_COMBS(u,c_COMBK(v,y,z),x1,x2,x3))* -> .
% 299.64/300.40 83089[7:SpL:5924.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool)) equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_x)** -> .
% 299.64/300.40 83018[0:SpR:5924.0,3229.1] || equal(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2))* -> equal(hAPP(u,v_x),hAPP(hAPP(v,v_x),w))*.
% 299.64/300.40 83011[4:SpR:5924.0,38042.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(u,v_x),v),x2,t_a)*.
% 299.64/300.40 83000[0:SpR:5924.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(u,v_x),v),c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname,x2)))*.
% 299.64/300.40 82994[0:SpR:5924.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),hAPP(hAPP(u,v_x),v),tc_Com_Opname,x2)))*.
% 299.64/300.40 82987[4:SpR:5924.0,37987.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),v),x2))*.
% 299.64/300.40 82978[0:SpR:5924.0,3283.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),v),v_Procs)).
% 299.64/300.40 82971[0:SpR:5924.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname,x2),v_Procs),hAPP(hAPP(u,v_x),v)))*.
% 299.64/300.40 83281[7:Res:78357.0,15629.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),v_x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Set_Oimage(u,v,w),v_x),x)))*.
% 299.64/300.40 83280[7:Res:78357.0,15857.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),v_x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(u,v,w),v_x),y)))*.
% 299.64/300.40 83274[7:SpR:5924.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,x3),v_x),hAPP(hAPP(u,v_x),v)))*.
% 299.64/300.40 83252[7:SpR:329.1,78357.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w,x),v_x),v_x))*.
% 299.64/300.40 83251[7:SpR:328.1,78357.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w,x),v_x),u))*.
% 299.64/300.40 83247[7:SpR:538.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)))*.
% 299.64/300.40 83422[0:SpL:5961.0,16286.0] || equal(hAPP(u,hAPP(v,v_x)),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),v_Procs)** -> .
% 299.64/300.40 83421[7:SpL:5961.0,31868.0] || equal(hAPP(u,hAPP(v,v_x)),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),v_x)** -> .
% 299.64/300.40 83414[0:SpL:5961.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),w,x),c_COMBS(c_COMBK(u,y,z),v,x1,x2,x3))* -> .
% 299.64/300.40 83409[7:SpL:5961.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool)) equal(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),v_x)** -> .
% 299.64/300.40 83349[0:SpR:5961.0,3229.1] || equal(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2))* -> equal(hAPP(u,v_x),hAPP(v,hAPP(y,v_x)))*.
% 299.64/300.40 83345[7:SpR:5961.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2,x3),v_x),hAPP(u,hAPP(x,v_x))))*.
% 299.64/300.40 83341[4:SpR:5961.0,38042.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(u,hAPP(x,v_x)),x2,t_a)*.
% 299.64/300.40 83330[0:SpR:5961.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,hAPP(v,v_x)),c_COMBS(c_COMBK(u,w,x),v,y,z,x1),tc_Com_Opname,x2)))*.
% 299.64/300.40 83324[0:SpR:5961.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(c_COMBK(u,v,w),x,y,z,x1),hAPP(u,hAPP(x,v_x)),tc_Com_Opname,x2)))*.
% 299.64/300.40 83317[4:SpR:5961.0,37987.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(u,hAPP(x,v_x)),x2))*.
% 299.64/300.40 83308[0:SpR:5961.0,3283.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(u,hAPP(x,v_x)),v_Procs)).
% 299.64/300.40 83301[0:SpR:5961.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),tc_Com_Opname,x2),v_Procs),hAPP(u,hAPP(x,v_x))))*.
% 299.64/300.40 84218[7:SpL:584.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_bool),v_x)** equal(c_COMBS(u,v,w,x,y),v_x)** -> .
% 299.64/300.40 84197[7:SpL:337.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x)** -> .
% 299.64/300.40 84184[7:SpL:540.1,78767.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> .
% 299.64/300.40 84183[7:SpL:539.1,78767.0] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> .
% 299.64/300.40 84175[7:SpL:30368.2,78767.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> .
% 299.64/300.40 84174[7:SpL:30928.2,78767.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> .
% 299.64/300.40 84171[7:SpL:299.2,78767.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)** -> .
% 299.64/300.40 84158[7:SpL:25.1,78767.0] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool),v_x)** equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_x) -> .
% 299.64/300.40 84303[0:SpL:801.1,10287.0] class_Lattices_Oupper__semilattice(u) || equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v,w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))** -> equal(v,w).
% 299.64/300.40 84513[4:SSi:84467.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v_x),tc_bool),u),tc_bool,tc_bool))*.
% 299.64/300.40 84622[4:SSi:84573.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w),tc_bool),u),tc_bool,tc_bool))*.
% 299.64/300.40 84746[4:SSi:84719.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(v_x,tc_bool),u),tc_bool,tc_bool)),w,t_a)*.
% 299.64/300.40 84891[4:SpL:300.1,78744.0] class_Lattices_Obounded__lattice(u) || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,t_a)*.
% 299.64/300.40 85000[0:Res:84957.0,280.1] || hBOOL(hAPP(hAPP(u,v),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,x),v),u,y,tc_fun(z,tc_bool)),w))*.
% 299.64/300.40 84996[0:Res:84957.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,w),v),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(v,w),v),u),v,u)*.
% 299.64/300.40 84995[0:Res:84957.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,w),v),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(v,w),v),u),u)*.
% 299.64/300.40 85080[0:SpL:644.0,357.1] || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) c_lessequals(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))* -> c_Finite__Set_Ofinite(u,w).
% 299.64/300.40 85300[0:SpL:9493.1,26240.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** -> .
% 299.64/300.40 85297[0:SpL:8498.1,26240.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> .
% 299.64/300.40 85532[4:SpL:78507.0,215.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.64/300.40 85471[4:SpR:78507.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v),x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))*.
% 299.64/300.40 85465[4:SpR:78507.0,353.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(c_Set_Oinsert(v,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))),hAPP(c_Set_Oinsert(v,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))**.
% 299.64/300.40 85431[4:SpR:78507.0,9569.0] || -> c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,w)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),tc_bool)*.
% 299.64/300.40 85430[4:SpR:78507.0,9568.0] || -> c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,v)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),tc_bool)*.
% 299.64/300.40 85768[0:SpR:49017.1,9066.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)))*.
% 299.64/300.40 85761[0:SpR:28334.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.64/300.40 85756[0:SpR:28031.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.64/300.40 85741[0:SpR:3586.1,9066.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))*.
% 299.64/300.40 85740[7:SpR:27278.1,9066.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))*.
% 299.64/300.40 85730[0:SpR:9493.1,9066.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u)))*.
% 299.64/300.40 85727[0:SpR:8498.1,9066.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),u)))*.
% 299.64/300.40 86093[0:SpL:5961.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool)) equal(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),v_Procs)** -> .
% 299.64/300.40 86092[0:SpL:5924.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool)) equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_Procs)** -> .
% 299.64/300.40 86068[0:SpL:328.1,86011.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_Procs)** -> .
% 299.64/300.40 86064[0:SpL:538.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs) -> .
% 299.64/300.40 86480[0:SpL:86109.1,19641.0] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(v_x,t_a),u),v_Procs) hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(v_x,t_a),u)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oinsert(v_x,t_a),u,t_a)*.
% 299.64/300.40 86271[0:SpR:86109.1,21894.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,c_Set_Oinsert(v_x,t_a),v,w)),u)**.
% 299.64/300.40 86270[0:SpR:86109.1,21268.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),u,v,w)),u)**.
% 299.64/300.40 86267[0:SpR:86109.1,474.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.40 86249[0:SpR:86109.1,446.1] || equal(u,v_Procs) c_lessequals(v,u,tc_fun(t_a,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),v),u,tc_fun(t_a,tc_bool))*.
% 299.64/300.40 86548[7:Rew:78167.0,86392.1,78167.0,86392.0] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),v_Procs)** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),v_x).
% 299.64/300.40 86549[7:Rew:78167.0,86390.1,78167.0,86390.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,t_a),v_x,tc_Com_Opname,u),v_Procs)** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,t_a),v_x,tc_Com_Opname,u),v_x).
% 299.64/300.40 86664[0:Res:86261.1,280.1] || equal(u,v_Procs) hBOOL(hAPP(hAPP(v,v_x),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,t_a,tc_fun(x,tc_bool)),w))*.
% 299.64/300.40 86660[0:Res:86261.1,175.0] || equal(hAPP(c_Set_Ovimage(u,t_a,v),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),v_Procs)** -> equal(hAPP(u,v_x),w).
% 299.64/300.40 86656[0:Res:86261.1,470.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,t_a)),w))*.
% 299.64/300.40 86655[0:Res:86261.1,466.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,t_a)),w))*.
% 299.64/300.40 86763[4:SpL:584.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_bool),v_x)** equal(c_COMBS(u,v,w,x,y),v_Procs)** -> .
% 299.64/300.40 86742[4:SpL:337.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_Procs)** -> .
% 299.64/300.40 86729[4:SpL:540.1,86106.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> .
% 299.64/300.40 86728[4:SpL:539.1,86106.0] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> .
% 299.64/300.40 86720[4:SpL:30368.2,86106.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> .
% 299.64/300.40 86719[4:SpL:30928.2,86106.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> .
% 299.64/300.40 86716[4:SpL:299.2,86106.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs)** -> .
% 299.64/300.40 86703[4:SpL:25.1,86106.0] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool),v_x)** equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_Procs) -> .
% 299.64/300.40 87337[7:SpR:586.0,71492.1] || equal(hAPP(c_COMBB(u,v,w,x),y),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,hAPP(y,v_x))),z))*.
% 299.64/300.40 87336[7:SpR:585.0,71492.1] || equal(hAPP(c_COMBC(u,v,w,x),y),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(u,v_x),y)),z))*.
% 299.64/300.40 87276[7:SpR:445.1,71492.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),v_x)** -> equal(v_x,v) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),z))*.
% 299.64/300.40 87485[7:SpR:586.0,71493.1] || equal(hAPP(c_COMBB(u,v,w,x),y),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,hAPP(y,v_x))),z,t_a)*.
% 299.64/300.40 87484[7:SpR:585.0,71493.1] || equal(hAPP(c_COMBC(u,v,w,x),y),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(u,v_x),y)),z,t_a)*.
% 299.64/300.40 87424[7:SpR:445.1,71493.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),v_x)** -> equal(v_x,v) c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),z,t_a)*.
% 299.64/300.40 87615[7:SpR:586.0,71679.1] || equal(hAPP(c_COMBB(u,v,w,x),y),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(u,hAPP(y,v_x))))*.
% 299.64/300.40 87614[7:SpR:585.0,71679.1] || equal(hAPP(c_COMBC(u,v,w,x),y),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(hAPP(u,v_x),y)))*.
% 299.64/300.40 87554[7:SpR:445.1,71679.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),v_x)** -> equal(v_x,v) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(u,v_x)))*.
% 299.64/300.40 87793[0:Rew:1528.3,87792.4] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u))* equal(c_Orderings_Otop__class_Otop(u),v) -> equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.40 88426[0:Res:8176.1,436.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),y))* -> hBOOL(hAPP(v,y))*.
% 299.64/300.40 88419[0:Res:8176.1,416.0] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.64/300.40 88556[0:Res:83.0,8306.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)))),x,tc_fun(w,tc_bool))*.
% 299.64/300.40 88675[7:SpL:52997.1,88086.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,v_x,tc_bool))* -> .
% 299.64/300.40 88670[7:SpL:584.0,88086.1] || equal(c_COMBS(u,v,w,x,y),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(z,hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_bool))* -> .
% 299.64/300.40 88649[7:SpL:337.0,88086.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool))* -> .
% 299.64/300.40 88636[7:SpL:540.1,88086.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) hBOOL(c_HOL_Ominus__class_Ominus(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))* -> .
% 299.64/300.40 88635[7:SpL:539.1,88086.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) hBOOL(c_HOL_Ominus__class_Ominus(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))* -> .
% 299.64/300.40 88634[7:SpL:297.2,88086.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(w,v_x,tc_bool))* -> .
% 299.64/300.40 88627[7:SpL:30368.2,88086.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,c_Orderings_Otop__class_Otop(u),tc_bool))* -> .
% 299.64/300.40 88626[7:SpL:30928.2,88086.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(v,c_Orderings_Otop__class_Otop(u),tc_bool))* -> .
% 299.64/300.40 88623[7:SpL:299.2,88086.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(w,v,tc_bool))* -> .
% 299.64/300.40 88610[7:SpL:25.1,88086.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_x) hBOOL(c_HOL_Ominus__class_Ominus(w,c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool))* -> .
% 299.64/300.40 88963[0:SpR:9925.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 88927[0:SpR:9924.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,v),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),w))*.
% 299.64/300.40 88877[0:SpR:414.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Fun_Ofun__upd(u,v,w,x,y),z,x1),hAPP(c_Set_Oinsert(w,x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),v))*.
% 299.64/300.40 88866[0:SpR:524.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v))*.
% 299.64/300.40 89501[7:SpL:78590.1,55992.1] || equal(c_Set_Oinsert(v_x,t_a),v_x) equal(c_COMBK(u,v,w),c_Set_Oinsert(v_x,t_a))** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u) -> .
% 299.64/300.40 89366[7:SpR:78590.1,20881.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,v),x)),u))*.
% 299.64/300.40 89359[7:SpR:78590.1,353.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(v,t_a),u)),hAPP(c_Set_Oinsert(v,t_a),u))**.
% 299.64/300.40 89326[7:SpR:78590.1,9569.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_x,t_a)),u),tc_bool)*.
% 299.64/300.40 89325[7:SpR:78590.1,9568.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a)),w),u),tc_bool)*.
% 299.64/300.40 89715[7:Res:89344.1,469.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,t_a)),v_x)**.
% 299.64/300.40 89714[7:Res:89344.1,464.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,t_a)),v_x)**.
% 299.64/300.40 89791[0:SpR:26183.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(c_Set_Oinsert(y,u),v)))*.
% 299.64/300.40 90292[4:SpL:78660.1,55992.1] || equal(hAPP(v_x,v_x),v_x) equal(c_COMBK(u,v,w),c_Set_Oinsert(v_x,t_a))** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u) -> .
% 299.64/300.40 90156[4:SpR:78660.1,20881.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,v),x)),u))*.
% 299.64/300.40 90149[4:SpR:78660.1,353.0] || equal(hAPP(u,v_x),v_x) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(v,t_a),u)),hAPP(c_Set_Oinsert(v,t_a),u))**.
% 299.64/300.40 90116[4:SpR:78660.1,9569.0] || equal(hAPP(u,v_x),v_x) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_x,t_a)),u),tc_bool)*.
% 299.64/300.40 90115[4:SpR:78660.1,9568.0] || equal(hAPP(u,v_x),v_x) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a)),w),u),tc_bool)*.
% 299.64/300.40 90672[0:SpL:584.0,26231.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),x1)),v)* -> c_Finite__Set_Ofinite(x1,v).
% 299.64/300.40 90859[4:Res:90134.1,469.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),v_x)** -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,t_a)),v_x)**.
% 299.64/300.40 90858[4:Res:90134.1,464.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),v_x)** -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,t_a)),v_x)**.
% 299.64/300.40 91091[0:SpR:44588.1,474.0] class_Complete__Lattice_Ocomplete__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.40 91795[0:SpR:3229.1,834.1] class_Lattices_Obounded__lattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(c_Fun_Ofun__upd(hAPP(v,v_x),c_Orderings_Obot__class_Obot(u),v_x,w,x),hAPP(v,v_x))**.
% 299.64/300.40 91996[0:SpL:79073.0,215.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v_Procs,tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.64/300.40 91982[0:SpL:79073.0,15629.0] || hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))* -> hBOOL(hAPP(c_Set_Oinsert(v_Procs,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Oinsert(v_Procs,v),w)))*.
% 299.64/300.40 91981[0:SpL:79073.0,15857.0] || hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))* -> hBOOL(hAPP(c_Set_Oinsert(v_Procs,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(v_Procs,v),x)))*.
% 299.64/300.40 91949[0:SpR:79073.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),v),y)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.64/300.40 91942[0:SpR:79073.0,353.0] || -> equal(hAPP(c_Set_Oinsert(v_Procs,u),hAPP(c_Set_Oinsert(v,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))),hAPP(c_Set_Oinsert(v,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))**.
% 299.64/300.40 91912[0:SpR:79073.0,9569.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_Procs,x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_bool)*.
% 299.64/300.40 91911[0:SpR:79073.0,9568.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_Procs,w)),x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_bool)*.
% 299.64/300.40 92158[7:SpL:79101.0,215.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_in(v),v_x),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.64/300.40 92102[7:SpR:79101.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),hAPP(c_Set_Oinsert(hAPP(c_in(x),v_x),v),y)),hAPP(c_in(x),v_x)))*.
% 299.64/300.40 92095[7:SpR:79101.0,353.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(c_Set_Oinsert(v,u),hAPP(c_in(w),v_x))),hAPP(c_Set_Oinsert(v,u),hAPP(c_in(w),v_x)))**.
% 299.64/300.40 92061[7:SpR:79101.0,9569.0] || -> c_lessequals(hAPP(c_in(u),v_x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_x,x)),hAPP(c_in(u),v_x)),tc_bool)*.
% 299.64/300.40 92060[7:SpR:79101.0,9568.0] || -> c_lessequals(hAPP(c_in(u),v_x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,w)),x),hAPP(c_in(u),v_x)),tc_bool)*.
% 299.64/300.40 92173[0:SpR:73.1,4019.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u).
% 299.64/300.40 92325[7:SSi:92296.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(hAPP(hAPP(c_in(w),v_x),v_x),tc_bool),u),tc_bool,tc_bool))*.
% 299.64/300.40 92709[7:Res:82151.1,278.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Set_Oinsert(v_x,w),x,v,u)))*.
% 299.64/300.40 92708[7:Res:82151.1,277.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Set_Oinsert(v_x,x),v,u)))*.
% 299.64/300.40 92705[7:Res:82151.1,454.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oinsert(v_x,u),v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_Set_Oinsert(v_x,u),v),v_x,t_a)*.
% 299.64/300.40 92704[7:Res:82151.1,501.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_Set_Oinsert(v_x,v)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.40 92677[7:SpR:329.1,82151.1] || c_lessequals(v_x,c_Set_Oinsert(v_x,u),tc_fun(v,tc_bool))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_in(t_a)) -> hBOOL(c_Set_Oinsert(v_x,u)).
% 299.64/300.40 92669[7:SpR:27043.1,82151.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(v_Procs,u),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,v)))*.
% 299.64/300.40 92667[7:SpR:15172.0,82151.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Set_Oinsert(v_x,y)))*.
% 299.64/300.40 92661[7:SpR:586.0,82151.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_in(t_a))** -> hBOOL(hAPP(hAPP(u,hAPP(y,v_x)),c_Set_Oinsert(v_x,z)))*.
% 299.64/300.40 92660[7:SpR:585.0,82151.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),y),c_Set_Oinsert(v_x,z)))*.
% 299.64/300.40 92654[7:SpR:9936.1,82151.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Set_Oinsert(v_x,v)))*.
% 299.64/300.40 92650[7:SpR:9935.1,82151.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Set_Oinsert(v_x,v)))*.
% 299.64/300.40 92600[7:SpR:445.1,82151.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_in(t_a))** -> equal(v_x,v) hBOOL(hAPP(hAPP(u,v_x),c_Set_Oinsert(v_x,z)))*.
% 299.64/300.40 93037[0:Rew:584.0,92838.1] || equal(u,v) -> c_lessequals(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),hAPP(v,v_x)),tc_fun(w,tc_bool))*.
% 299.64/300.40 93407[4:Res:85556.1,24120.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(hAPP(u,v_x),v),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(hAPP(u,v_x),v),v_x).
% 299.64/300.40 93329[4:SpR:27043.1,85556.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v_x,v),tc_bool)*.
% 299.64/300.40 93327[4:SpR:15172.0,85556.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(c_Orderings_Obot__class_Obot(tc_bool),y),tc_bool)*.
% 299.64/300.40 93321[4:SpR:586.0,85556.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(hAPP(u,hAPP(y,v_x)),z),tc_bool)*.
% 299.64/300.40 93320[4:SpR:585.0,85556.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(hAPP(hAPP(u,v_x),y),z),tc_bool)*.
% 299.64/300.40 93314[4:SpR:9936.1,85556.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(c_Orderings_Otop__class_Otop(tc_bool),v),tc_bool)*.
% 299.64/300.40 93310[4:SpR:9935.1,85556.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(c_Orderings_Otop__class_Otop(tc_bool),v),tc_bool)*.
% 299.64/300.40 93260[4:SpR:445.1,85556.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(v_x,v) c_lessequals(v_x,hAPP(hAPP(u,v_x),z),tc_bool)*.
% 299.64/300.40 93434[4:SSi:93397.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) c_lessequals(hAPP(hAPP(u,v_x),v),v_x,tc_bool)* -> equal(hAPP(hAPP(u,v_x),v),v_x).
% 299.64/300.40 93435[4:SSi:93394.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(hAPP(hAPP(u,v_x),v),v_x) -> c_lessequals(hAPP(hAPP(u,v_x),v),v_x,tc_bool)*.
% 299.64/300.40 93509[0:SpR:586.0,86147.1] || equal(hAPP(c_COMBB(u,v,w,x),y),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,hAPP(y,v_x))),z))*.
% 299.64/300.40 93508[0:SpR:585.0,86147.1] || equal(hAPP(c_COMBC(u,v,w,x),y),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(u,v_x),y)),z))*.
% 299.64/300.40 93448[0:SpR:445.1,86147.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),v_Procs)** -> equal(v_x,v) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),z))*.
% 299.64/300.40 93660[0:SpR:586.0,86148.1] || equal(hAPP(c_COMBB(u,v,w,x),y),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,hAPP(y,v_x))),z,t_a)*.
% 299.64/300.40 93659[0:SpR:585.0,86148.1] || equal(hAPP(c_COMBC(u,v,w,x),y),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(u,v_x),y)),z,t_a)*.
% 299.64/300.40 93599[0:SpR:445.1,86148.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),v_Procs)** -> equal(v_x,v) c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),z,t_a)*.
% 299.64/300.40 93804[0:SpR:586.0,86342.1] || equal(hAPP(c_COMBB(u,v,w,x),y),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(u,hAPP(y,v_x))))*.
% 299.64/300.40 93803[0:SpR:585.0,86342.1] || equal(hAPP(c_COMBC(u,v,w,x),y),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(hAPP(u,v_x),y)))*.
% 299.64/300.40 93743[0:SpR:445.1,86342.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),v_Procs)** -> equal(v_x,v) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(u,v_x)))*.
% 299.64/300.40 94189[0:Res:14364.3,12532.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,c_HOL_Ominus__class_Ominus(v,w,tc_bool)))* c_Finite__Set_Ofinite(u,tc_bool) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(u,tc_bool),v,tc_bool).
% 299.64/300.40 94184[4:Res:14364.3,40171.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMin(u,tc_bool),tc_bool)* -> hBOOL(v).
% 299.64/300.40 94183[4:Res:14364.3,40323.1] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) equal(c_Finite__Set_Olinorder__class_OMin(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(v).
% 299.64/300.40 94327[7:Res:14491.3,92132.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,hAPP(hAPP(c_in(v),v_x),v_x)))* c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.64/300.40 94326[4:Res:14491.3,40105.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v)))* c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.64/300.40 94325[4:Res:14491.3,40016.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),v_x)))* c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.64/300.40 94320[4:Res:14491.3,40433.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v_x))* c_Finite__Set_Ofinite(u,tc_bool) equal(c_Finite__Set_Olinorder__class_OMax(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) -> hBOOL(v)*.
% 299.64/300.40 94310[4:Res:14491.3,40171.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v_x,v,tc_bool) -> hBOOL(c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.64/300.40 699[0:Res:589.0,595.0] || c_Hoare__Mirabelle_Otriple__valid(v_na,v_xa,t_a) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(v_Q,v_x)),t_a)*.
% 299.64/300.40 636[0:Res:589.0,201.1] class_Lattices_Oupper__semilattice(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),v_x),u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_Com_Opname),u,v_Procs,tc_Com_Opname,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.40 1178[0:SpR:88.1,415.0] class_Lattices_Oboolean__algebra(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),v,c_Orderings_Otop__class_Otop(u),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)))**.
% 299.64/300.40 1896[0:SpR:9.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Fun_Ocomp(v,w,x,y,z),t_a) hBOOL(hAPP(v,hAPP(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Fun_Ocomp(v,w,x,y,z)))))*.
% 299.64/300.40 1893[0:SpR:9.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,w,x,y),z,hAPP(u,hAPP(v,z)),x1,x2),c_Fun_Ocomp(u,v,w,x,y))**.
% 299.64/300.40 1898[0:Rew:9.0,1895.0] || hBOOL(hAPP(u,hAPP(v,v_x))) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,c_Fun_Ocomp(u,v,x,y,z),tc_Com_Opname))))*.
% 299.64/300.40 1899[0:Rew:9.0,1894.0] || hBOOL(hAPP(u,hAPP(v,v_x))) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,c_Fun_Ocomp(u,v,x,y,z),tc_Com_Opname))))*.
% 299.64/300.40 2156[0:SpR:1605.2,47.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,w) c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.40 2155[0:SpR:1628.2,47.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,w) c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.40 2149[0:SpR:1421.2,47.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) -> c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)*.
% 299.64/300.40 2148[0:SpR:1409.2,47.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.40 2205[0:SpR:2098.1,415.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) equal(c_Fun_Ofun__upd(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),v,v,w,x),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)))**.
% 299.64/300.40 2231[0:SpR:1605.2,43.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,w) c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.40 2230[0:SpR:1628.2,43.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,w) c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.40 2224[0:SpR:1421.2,43.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) -> c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)*.
% 299.64/300.40 2223[0:SpR:1409.2,43.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.40 2391[0:SpL:1605.2,48.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,w) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u).
% 299.64/300.40 2390[0:SpL:1628.2,48.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,w) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u).
% 299.64/300.40 2384[0:SpL:1421.2,48.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u).
% 299.64/300.40 2383[0:SpL:1409.2,48.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u).
% 299.64/300.40 2421[0:SpL:1605.2,44.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,w) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u).
% 299.64/300.40 2420[0:SpL:1628.2,44.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,w) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u).
% 299.64/300.40 2414[0:SpL:1421.2,44.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u).
% 299.64/300.40 2413[0:SpL:1409.2,44.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u).
% 299.64/300.40 2451[0:SpR:1605.2,49.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,w) c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.40 2450[0:SpR:1628.2,49.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,w) c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.40 2444[0:SpR:1421.2,49.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.40 2443[0:SpR:1409.2,49.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.40 2479[0:SpR:1605.2,45.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,w) c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.40 2478[0:SpR:1628.2,45.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,w) c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.40 2472[0:SpR:1421.2,45.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.40 2471[0:SpR:1409.2,45.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.40 2507[0:SpL:1605.2,50.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,w) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.40 2506[0:SpL:1628.2,50.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,w) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.40 2500[0:SpL:1421.2,50.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)* -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.40 2499[0:SpL:1409.2,50.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.40 2533[0:SpL:1605.2,46.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,w) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.40 2532[0:SpL:1628.2,46.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,w) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.40 2526[0:SpL:1421.2,46.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)* -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.40 2525[0:SpL:1409.2,46.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.40 2568[0:SpR:585.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(v,v_x),w)),hAPP(c_Set_Oimage(hAPP(c_COMBC(v,x,y,z),w),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.40 2565[0:SpR:585.0,651.0] || -> c_lessequals(hAPP(hAPP(u,v_x),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_COMBC(u,w,x,y),v),tc_Com_Opname,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.64/300.40 2579[0:SpR:586.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,v_x))),hAPP(c_Set_Oimage(hAPP(c_COMBB(v,x,y,z),w),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.40 2576[0:SpR:586.0,651.0] || -> c_lessequals(hAPP(u,hAPP(v,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_COMBB(u,w,x,y),v),tc_Com_Opname,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.64/300.40 2598[0:SpR:445.1,648.0] || -> equal(v_x,u) hBOOL(hAPP(hAPP(c_in(v),hAPP(w,v_x)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,u,x,y,z),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.40 2595[0:SpR:445.1,651.0] || -> equal(v_x,u) c_lessequals(hAPP(v,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Fun_Ofun__upd(v,u,w,x,y),tc_Com_Opname,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.64/300.40 2642[0:SpR:337.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),tc_Com_Opname,u),u)*.
% 299.64/300.40 2743[0:SpR:25.1,683.1] class_HOL_Ouminus(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u)),tc_Com_Opname,v),v)*.
% 299.64/300.40 3198[0:SpR:9.0,2771.1] || equal(c_Fun_Ocomp(u,v,w,x,y),z)* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(z,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool))*.
% 299.64/300.40 3196[0:SpR:88.1,2771.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v)* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool))*.
% 299.64/300.40 3661[0:SpR:540.1,415.0] class_Lattices_Olattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v),x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.64/300.40 3648[0:SpR:540.1,683.1] class_Lattices_Olattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),tc_Com_Opname,v),v)*.
% 299.64/300.40 3814[0:SpR:539.1,415.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v),x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.64/300.40 3800[0:SpR:539.1,683.1] class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),tc_Com_Opname,v),v)*.
% 299.64/300.40 4153[0:SpL:337.0,3929.0] || hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.40 4150[0:SpL:540.1,3929.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.40 4149[0:SpL:539.1,3929.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.40 4137[0:SpL:25.1,3929.0] class_HOL_Ouminus(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.40 4237[0:SpL:299.2,3929.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) hBOOL(v) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.40 4232[0:SpR:299.2,1103.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),w,u)* -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),t_a) hBOOL(w).
% 299.64/300.40 4212[0:SpR:299.2,415.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))**.
% 299.64/300.40 4197[0:SpR:299.2,683.1] class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || c_lessequals(v_x,w,u) -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),tc_Com_Opname,v),v)*.
% 299.64/300.40 4306[0:SpR:297.2,415.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.64/300.40 4291[0:SpR:297.2,683.1] class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || c_lessequals(w,v_x,u) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),tc_Com_Opname,v),v)*.
% 299.64/300.40 4426[0:SpR:586.0,3284.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(z),v_Procs),hAPP(u,hAPP(y,v_x))))*.
% 299.64/300.40 4425[0:SpR:585.0,3284.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(z),v_Procs),hAPP(hAPP(u,v_x),y)))*.
% 299.64/300.40 4400[0:SpR:445.1,3284.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_in(tc_Com_Opname))** -> equal(v_x,v) hBOOL(hAPP(hAPP(c_in(z),v_Procs),hAPP(u,v_x)))*.
% 299.64/300.40 4442[0:Res:1103.1,33.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Ovimage(v,w,x),y),t_a) hBOOL(hAPP(y,hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Ovimage(v,w,x),y)))))*.
% 299.64/300.40 4474[0:SpL:586.0,3493.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_in(tc_Com_Opname))** equal(hAPP(u,hAPP(y,v_x)),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))* -> .
% 299.64/300.40 4473[0:SpL:585.0,3493.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_in(tc_Com_Opname))** equal(hAPP(hAPP(u,v_x),y),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))* -> .
% 299.64/300.40 4448[0:SpL:445.1,3493.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_in(tc_Com_Opname))** equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))* -> equal(v_x,v).
% 299.64/300.40 4525[0:SpR:297.2,3316.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u)* equal(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(u)) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))).
% 299.64/300.40 4523[0:SpR:586.0,3316.1] || equal(c_in(u),hAPP(c_COMBB(v,w,x,y),z))* -> hBOOL(hAPP(hAPP(v,hAPP(z,v_x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.40 4522[0:SpR:585.0,3316.1] || equal(c_in(u),hAPP(c_COMBC(v,w,x,y),z))* -> hBOOL(hAPP(hAPP(hAPP(v,v_x),z),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.40 4497[0:SpR:445.1,3316.1] || equal(c_in(u),c_Fun_Ofun__upd(v,w,x,y,z))* -> equal(v_x,w) hBOOL(hAPP(hAPP(v,v_x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.40 4659[0:SpL:586.0,3698.2] || equal(u,hAPP(c_COMBB(v,w,x,y),z))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(v,hAPP(z,v_x)),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 4658[0:SpL:585.0,3698.2] || equal(u,hAPP(c_COMBC(v,w,x,y),z))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(hAPP(v,v_x),z),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 4632[0:SpL:445.1,3698.2] || equal(u,c_Fun_Ofun__upd(v,w,x,y,z))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(v,v_x),c_Com_Ocom_OSKIP) -> equal(v_x,w).
% 299.64/300.40 5031[0:Res:4714.3,405.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> equal(v,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.40 5049[0:Res:4722.3,405.1] class_Lattices_Oboolean__algebra(u) class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> equal(v,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.40 5063[0:Res:4805.3,405.1] class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> equal(c_Orderings_Otop__class_Otop(u),v).
% 299.64/300.40 5115[0:SpR:586.0,3339.1] || equal(u,hAPP(c_COMBB(v,w,x,y),z))* -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(v,hAPP(z,v_x)),x1,x2),u)**.
% 299.64/300.40 5114[0:SpR:585.0,3339.1] || equal(u,hAPP(c_COMBC(v,w,x,y),z))* -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(hAPP(v,v_x),z),x1,x2),u)**.
% 299.64/300.40 5088[0:SpR:445.1,3339.1] || equal(u,c_Fun_Ofun__upd(v,w,x,y,z))* -> equal(v_x,w) equal(c_Fun_Ofun__upd(u,v_x,hAPP(v,v_x),x1,x2),u)**.
% 299.64/300.40 5546[0:Obv:5536.0] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.40 5985[0:SpL:584.0,279.0] || hBOOL(hAPP(c_COMBS(c_in(u),v,w,x,y),z))* -> equal(hAPP(c_Set_Oinsert(z,u),hAPP(v,z)),hAPP(v,z))**.
% 299.64/300.40 5979[0:SpL:584.0,3929.0] || hBOOL(hAPP(hAPP(u,v_x),hAPP(v,v_x)))* equal(c_COMBS(u,v,w,x,y),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.64/300.40 5965[0:SpR:301.1,584.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y,z),c_Orderings_Obot__class_Obot(u)),hAPP(v,hAPP(w,c_Orderings_Obot__class_Obot(u))))**.
% 299.64/300.40 5954[0:SpR:331.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,w,x,y),z),hAPP(z,hAPP(v,z)))*.
% 299.64/300.40 5953[0:SpR:302.1,584.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w,x,y),z),hAPP(c_Orderings_Otop__class_Otop(u),hAPP(v,z)))**.
% 299.64/300.40 5928[0:SpR:301.1,584.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),c_Orderings_Obot__class_Obot(u)),hAPP(hAPP(v,c_Orderings_Obot__class_Obot(u)),w))**.
% 299.64/300.40 5917[0:SpR:331.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w,x,y),z),hAPP(hAPP(u,z),z))*.
% 299.64/300.40 5916[0:SpR:302.1,584.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,x,y),z),hAPP(hAPP(v,z),c_Orderings_Otop__class_Otop(u)))**.
% 299.64/300.40 5865[0:SpR:584.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(hAPP(v,v_x),hAPP(w,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBS(v,w,x,y,z),tc_Com_Opname,u),u)*.
% 299.64/300.40 6044[0:SpR:584.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(u,v),hAPP(w,v)),x),c_COMBS(u,w,y,z,x1),x2,x3,x4),v))*.
% 299.64/300.40 6029[0:SpR:584.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_COMBS(u,v,w,x,y),z),x1),hAPP(u,z),x2,x3,x4),hAPP(v,z)))*.
% 299.64/300.40 6023[0:SpR:540.1,5875.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,z,x1),v))*.
% 299.64/300.40 6022[0:SpR:539.1,5875.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,z,x1),v))*.
% 299.64/300.40 6021[0:SpR:297.2,5875.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,z,x1),w))*.
% 299.64/300.40 6329[0:SpR:9.0,3279.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(hAPP(u,hAPP(v,v_x)),v_Procs),v_x))*.
% 299.64/300.40 6327[0:SpR:88.1,3279.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(c_Orderings_Otop__class_Otop(u),v_Procs),v_x))*.
% 299.64/300.40 6322[0:SpR:2098.1,3279.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(hAPP(v_x,v_Procs),v_x)).
% 299.64/300.40 6312[0:SpR:3586.1,3279.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v,u)) -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.40 6474[0:SpL:538.0,3506.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))* -> .
% 299.64/300.40 6523[0:Res:3285.1,371.0] || equal(c_Set_Oinsert(u,v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))* equal(u,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))*.
% 299.64/300.40 6512[0:SpR:9.0,3285.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(u,hAPP(v,v_x)),hAPP(c_Set_Oinsert(z,tc_Com_Opname),v_Procs)))*.
% 299.64/300.40 6508[0:SpR:88.1,3285.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.40 6503[0:SpR:2098.1,3285.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.40 6493[0:SpR:3586.1,3285.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.40 6675[0:SpL:329.1,3506.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(w,x),v_x)** -> .
% 299.64/300.40 6751[0:SpR:9.0,3291.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(u,hAPP(v,v_x))),v_Procs))*.
% 299.64/300.40 6746[0:SpR:88.1,3291.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(u)),v_Procs))*.
% 299.64/300.40 6741[0:SpR:2098.1,3291.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),v_Procs))*.
% 299.64/300.40 6731[0:SpR:3586.1,3291.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),v_x),v_Procs))*.
% 299.64/300.40 6838[0:SpL:328.1,3506.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(w,x),u)* -> .
% 299.64/300.40 6814[0:SpR:328.1,584.0] || c_lessequals(hAPP(u,v),v,tc_fun(w,tc_bool))* -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u,x,y,z),v),v)**.
% 299.64/300.40 6882[0:SpL:9.0,3484.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Com_Ocom_OBODY)** equal(hAPP(u,hAPP(v,v_x)),hAPP(c_Com_Ocom_OBODY,z))* -> equal(v_x,z).
% 299.64/300.40 6876[0:SpL:88.1,3484.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(u),hAPP(c_Com_Ocom_OBODY,v))* -> equal(v_x,v).
% 299.64/300.40 6871[0:SpL:2098.1,3484.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,v),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(v_x,v).
% 299.64/300.40 6861[0:SpL:3586.1,3484.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_Com_Ocom_OBODY) equal(hAPP(c_Com_Ocom_OBODY,w),v_x)** -> equal(v_x,w).
% 299.64/300.40 6918[0:SpL:9.0,3499.1] || equal(c_in(u),c_Fun_Ocomp(v,w,x,y,z))* hBOOL(hAPP(hAPP(v,hAPP(w,v_x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.40 6912[0:SpL:88.1,3499.1] class_Lattices_Oboolean__algebra(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.40 6965[0:SpL:584.0,312.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),c_Orderings_Obot__class_Obot(u))** -> equal(hAPP(v,z),c_Orderings_Obot__class_Obot(u)).
% 299.64/300.40 6981[0:SpL:1259.2,3580.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ozero__class_Ozero(u),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v_Procs)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.40 7033[2:SpL:1259.2,4273.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ozero__class_Ozero(u),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.40 7139[0:SpR:9.0,3305.1] || equal(u,c_Fun_Ocomp(v,w,x,y,z))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x1),v_Procs),hAPP(v,hAPP(w,v_x))))*.
% 299.64/300.40 7133[0:SpR:88.1,3305.1] class_Lattices_Oboolean__algebra(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.40 7128[0:SpR:2098.1,3305.1] || equal(u,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,v_x),tc_Hoare__Mirabelle_Otriple(t_a)))* -> c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.40 7118[0:SpR:3586.1,3305.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(w,c_Set_Oinsert(v,u))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,tc_Com_Opname,x),v_Procs),v_x))*.
% 299.64/300.40 7195[0:Res:3317.1,371.0] || equal(c_in(u),c_Set_Oinsert(v,w))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,u),x)))* equal(v,hAPP(c_Set_Oinsert(v_x,u),x))*.
% 299.64/300.40 7182[0:SpR:9.0,3317.1] || equal(c_in(u),c_Fun_Ocomp(v,w,x,y,z))* -> hBOOL(hAPP(hAPP(v,hAPP(w,v_x)),hAPP(c_Set_Oinsert(v_x,u),x1)))*.
% 299.64/300.40 7176[0:SpR:88.1,3317.1] class_Lattices_Oboolean__algebra(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),hAPP(c_Set_Oinsert(v_x,v),w)))*.
% 299.64/300.40 7171[0:SpR:2098.1,3317.1] || equal(c_in(u),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,v_x),tc_Hoare__Mirabelle_Otriple(t_a)))* -> c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,u),w)))*.
% 299.64/300.40 7161[0:SpR:3586.1,3317.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_in(w),c_Set_Oinsert(v,u))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,w),x)))*.
% 299.64/300.40 7243[0:SpR:303.1,474.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.40 7229[0:SpR:87.1,474.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.40 7215[0:SpR:300.1,474.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.40 7207[0:SpR:365.1,474.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.40 7205[0:SpR:397.1,474.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.40 7197[0:SpR:2097.1,474.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v,x),y,w),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.64/300.40 7307[0:SpR:586.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),hAPP(u,hAPP(y,x2))))*.
% 299.64/300.40 7306[0:SpR:585.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBC(u,v,w,x),y),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),hAPP(hAPP(u,x2),y)))*.
% 299.64/300.40 7255[0:SpR:445.1,7253.0] || -> equal(u,v) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,y,z),x1,x2),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),hAPP(w,u)))*.
% 299.64/300.40 7344[0:SpL:9.0,3507.1] || equal(c_Set_Oinsert(u,v),c_Fun_Ocomp(w,x,y,z,x1))* equal(hAPP(w,hAPP(x,v_x)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.40 7338[0:SpL:88.1,3507.1] class_Lattices_Oboolean__algebra(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.40 7458[0:Res:364.1,2092.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),u)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),u))**.
% 299.64/300.40 7515[0:SpR:9.0,3346.1] || equal(c_Set_Oinsert(u,v),c_Fun_Ocomp(w,x,y,z,x1))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(w,hAPP(x,v_x))))*.
% 299.64/300.40 7509[0:SpR:88.1,3346.1] class_Lattices_Oboolean__algebra(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* -> hBOOL(hAPP(hAPP(c_in(w),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.40 7504[0:SpR:2098.1,3346.1] || equal(c_Set_Oinsert(u,v),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,v_x),tc_Hoare__Mirabelle_Otriple(t_a)))* -> c_Hoare__Mirabelle_Ohoare__valids(w,v_x,t_a) hBOOL(hAPP(hAPP(c_in(v),u),v_x))*.
% 299.64/300.40 7494[0:SpR:3586.1,3346.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(w,x),c_Set_Oinsert(v,u))* -> hBOOL(hAPP(hAPP(c_in(x),w),v_x))*.
% 299.64/300.40 7649[0:SpR:584.0,294.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,hAPP(w,x),u) -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,y,z,x1),x),u)*.
% 299.64/300.40 7676[0:SSi:7660.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.40 7677[0:SSi:7658.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.40 7739[0:SSi:7724.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.40 7740[0:SSi:7722.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.40 7809[0:Res:989.1,296.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v),x,y),tc_Com_Opname,u),u)*.
% 299.64/300.40 7774[0:SpL:584.0,296.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),x1,u)* -> c_lessequals(hAPP(v,z),x1,u).
% 299.64/300.40 7831[0:Obv:7808.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,u)* -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y),u)*.
% 299.64/300.40 7832[0:Obv:7805.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,u)* -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),x),u)*.
% 299.64/300.40 7835[0:SSi:7788.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),x,y),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.40 7858[0:SpR:1605.2,4801.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.40 7853[0:SpR:1259.2,4801.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.40 7941[0:SpR:1605.2,4834.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.40 7936[0:SpR:1259.2,4834.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.40 8054[0:Res:989.1,295.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,y),tc_Com_Opname,u),u)*.
% 299.64/300.40 8075[0:Obv:8053.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,u)* -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y),u)*.
% 299.64/300.40 8076[0:Obv:8050.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,u)* -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),x),u)*.
% 299.64/300.40 8079[0:SSi:8033.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),x,y),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.40 8149[0:Res:989.1,427.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Opreorder(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v,w,x),tc_Com_Opname,u),y,u)* -> c_lessequals(v,y,u).
% 299.64/300.40 8136[0:Res:4805.3,427.1] class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> c_lessequals(w,v,u)*.
% 299.64/300.40 8179[0:SSi:8111.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,tc_fun(x,tc_bool)),y,tc_fun(x,tc_bool))* -> c_lessequals(u,y,tc_fun(x,tc_bool)).
% 299.64/300.40 8197[0:Res:5887.1,146.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_HOL_Ouminus__class_Ouminus(z,u)),u),z,u)*.
% 299.64/300.40 8222[0:Res:5888.1,146.1] class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_HOL_Ouminus__class_Ouminus(z,u)),u),z,u)*.
% 299.64/300.40 8276[0:Res:989.1,426.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Oorder(u) || c_lessequals(v,w,u) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(w,x,y),tc_Com_Opname,u),u)*.
% 299.64/300.40 8249[0:Res:4714.3,426.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(v,w,u)*.
% 299.64/300.40 8247[0:Res:4722.3,426.1] class_Lattices_Oboolean__algebra(u) class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(v,w,u)*.
% 299.64/300.40 8312[0:SSi:8236.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v,x,y),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.40 8335[0:SpL:2267.1,76.1] || equal(u,v)* c_Finite__Set_Ofinite(u,w)* c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w).
% 299.64/300.40 8368[0:Res:149.1,279.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oinsert(v,u),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)))**.
% 299.64/300.40 8364[0:SpR:3229.1,149.1] || equal(u,c_in(v)) -> hBOOL(hAPP(hAPP(c_in(v),v_x),w)) hBOOL(hAPP(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))))*.
% 299.64/300.40 8362[0:SpR:2267.1,149.1] || equal(u,v)* -> hBOOL(hAPP(hAPP(c_in(w),x),u))* hBOOL(hAPP(hAPP(c_in(w),x),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))))*.
% 299.64/300.40 8509[0:SpL:584.0,355.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oinsert(v,u),w,x,y),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v).
% 299.64/300.40 8508[0:SpL:3229.1,355.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))* -> equal(v_x,w).
% 299.64/300.40 8619[0:SpL:8498.1,3484.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,w),v_x)** -> equal(v_x,w).
% 299.64/300.40 8587[0:SpR:8498.1,3346.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,w),c_Set_Oinsert(x,u))* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x))*.
% 299.64/300.40 8586[0:SpR:8498.1,3317.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_in(v),c_Set_Oinsert(w,u))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,v),x)))*.
% 299.64/300.40 8585[0:SpR:8498.1,3305.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(v,c_Set_Oinsert(w,u))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,x),v_Procs),v_x))*.
% 299.64/300.40 8578[0:SpR:8498.1,3291.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),v_x),v_Procs))*.
% 299.64/300.40 8577[0:SpR:8498.1,3285.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.40 8574[0:SpR:8498.1,3279.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v,u))* -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.40 8700[0:SpR:3229.1,335.2] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* c_Finite__Set_Ofinite(w,v) c_Finite__Set_Ofinite(v_x,v) -> c_Finite__Set_Ofinite(hAPP(u,v_x),v)*.
% 299.64/300.40 8698[0:SpR:3229.1,335.2] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) c_Finite__Set_Ofinite(v_x,v) c_Finite__Set_Ofinite(w,v) -> c_Finite__Set_Ofinite(hAPP(hAPP(u,v_x),w),v)*.
% 299.64/300.40 8995[0:SpL:8415.2,333.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname))** c_Finite__Set_Ofinite(v_x,u) -> c_Finite__Set_Ofinite(v,u).
% 299.64/300.40 8962[0:SpL:8415.2,333.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Finite__Set_Ofinite(hAPP(v_x,v),u)* -> c_Finite__Set_Ofinite(v_x,u).
% 299.64/300.40 8961[0:SpL:8415.2,332.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Finite__Set_Ofinite(hAPP(v_x,v),u)* -> c_Finite__Set_Ofinite(v,u).
% 299.64/300.40 8950[0:SpL:8415.2,3701.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 8949[0:SpL:8415.2,3330.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(v_x,v) -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.40 8948[0:SpL:8415.2,3726.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_in(tc_Com_Opname),v_x) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.40 8943[0:SpL:8415.2,3698.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(v,u)* equal(c_Com_Ocom_OBODY,v)* equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 8930[0:SpL:8415.2,682.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) c_lessequals(v_x,u,tc_fun(v,tc_bool))* -> hBOOL(hAPP(u,v_Procs)).
% 299.64/300.40 8917[0:SpL:8415.2,591.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(v_x,v_G)) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),v_x,t_a)*.
% 299.64/300.40 8909[0:SpR:8415.2,9.0] || equal(v_Procs,v_x) equal(c_Fun_Ocomp(u,v,w,x,y),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(u,hAPP(v,v_x)),v_x).
% 299.64/300.40 8890[0:SpR:8415.2,88.1] class_Lattices_Oboolean__algebra(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(c_Orderings_Otop__class_Otop(u),v_x).
% 299.64/300.40 8886[0:SpR:8415.2,499.0] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),v_x,u).
% 299.64/300.40 8879[0:SpR:8415.2,7253.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x))*.
% 299.64/300.40 8874[0:SpR:8415.2,8375.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) equal(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))* -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.40 8853[0:SpR:8415.2,499.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Com_Ocom_OBODY) -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),v_x),w),u)*.
% 299.64/300.40 8846[0:SpR:8415.2,499.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(u)) -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(hAPP(v_x,hAPP(c_Com_Ocom_OBODY,v)),w),u)*.
% 299.64/300.40 8841[0:SpR:8415.2,675.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.40 8830[0:SpR:8415.2,87.1] class_Lattices_Oboolean__algebra(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.40 8817[0:SpR:8415.2,676.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(hAPP(v_x,hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.40 8802[0:SpR:8415.2,1161.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.40 8799[0:SpR:8415.2,3339.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(v,u)* -> equal(c_Fun_Ofun__upd(v,v_x,v_x,w,x),v)**.
% 299.64/300.40 8798[0:SpR:8415.2,3316.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_in(v),u)* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.40 8795[0:SpR:8415.2,648.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.40 8790[0:SpR:8415.2,3284.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),v_x))*.
% 299.64/300.40 8783[0:SpR:8415.2,651.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.40 8766[0:SpR:8415.2,676.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),v_Procs))*.
% 299.64/300.40 8765[0:SpR:8415.2,675.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),v_Procs))*.
% 299.64/300.40 8764[0:SpR:8415.2,652.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(v_x,u)).
% 299.64/300.40 8762[0:SpR:8415.2,649.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs)))*.
% 299.64/300.40 8761[0:SpR:8415.2,650.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u)))*.
% 299.64/300.40 8751[0:SpR:8415.2,649.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(v_x,v_Procs)))*.
% 299.64/300.40 9069[0:Res:364.1,214.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oinsert(y,v),x)))*.
% 299.64/300.40 9061[0:SpL:2098.1,214.0] || c_lessequals(u,v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(w,u,t_a) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,u)),v))*.
% 299.64/300.40 9059[0:SpL:3229.1,214.0] || equal(u,c_Set_Oinsert(v,w))* c_lessequals(hAPP(u,v_x),x,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),v),x))*.
% 299.64/300.40 9173[0:SpR:9.0,8376.2] || equal(c_Fun_Ocomp(u,v,w,x,y),c_in(tc_Com_Opname))** equal(z,v_Procs) -> hBOOL(hAPP(hAPP(u,hAPP(v,v_x)),z))*.
% 299.64/300.40 9167[0:SpR:88.1,8376.2] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v))*.
% 299.64/300.40 9162[0:SpR:2098.1,8376.2] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname))** equal(v,v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(v_x,v))*.
% 299.64/300.40 9152[0:SpR:3586.1,8376.2] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname)) equal(w,v_Procs) -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.40 9141[0:SpR:8498.1,8376.2] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname))** equal(w,v_Procs) -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.40 9356[0:SpL:3229.1,347.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* c_Fun_Oinj__on(x,hAPP(u,v_x),v,y)* -> c_Fun_Oinj__on(x,w,v,y)*.
% 299.64/300.40 9353[0:SpL:3229.1,347.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) c_Fun_Oinj__on(w,hAPP(hAPP(u,v_x),x),v,y)* -> c_Fun_Oinj__on(w,v_x,v,y).
% 299.64/300.40 9415[0:SpL:3229.1,346.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* c_Fun_Oinj__on(x,hAPP(u,v_x),v,y)* -> c_Fun_Oinj__on(x,v_x,v,y).
% 299.64/300.40 9412[0:SpL:3229.1,346.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) c_Fun_Oinj__on(w,hAPP(hAPP(u,v_x),x),v,y)* -> c_Fun_Oinj__on(w,x,v,y).
% 299.64/300.40 9532[0:Res:448.1,251.1] class_Orderings_Olinorder(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(w,x,tc_fun(u,v))* c_lessequals(hAPP(x,y),hAPP(w,y),v)*.
% 299.64/300.40 9843[0:SpR:3229.1,98.1] || equal(u,c_Set_Oimage(v,w,x))* c_Fun_Oinj__on(v,v_x,w,x)* -> equal(c_Finite__Set_Ocard(hAPP(u,v_x),x),c_Finite__Set_Ocard(v_x,w))*.
% 299.64/300.40 9875[0:SpL:3229.1,447.0] || equal(u,c_Set_Oimage(v,w,x))* c_Finite__Set_Ofinite(hAPP(u,v_x),x)* c_Fun_Oinj__on(v,v_x,w,x)* -> c_Finite__Set_Ofinite(v_x,w).
% 299.64/300.40 10138[0:Res:448.1,431.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Fun_Oinj__on(v,w,u,x)* -> c_lessequals(w,y,tc_fun(u,tc_bool))* c_Fun_Oinj__on(v,y,u,x)*.
% 299.64/300.40 10106[0:Res:364.1,431.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,hAPP(c_Set_Oinsert(y,w),v),w,z)* -> c_Fun_Oinj__on(x,u,w,z)*.
% 299.64/300.40 10721[0:SpR:329.1,9566.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(v,hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u)),v),tc_bool)*.
% 299.64/300.40 10720[0:SpR:328.1,9566.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(v,hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v)),u),tc_bool)*.
% 299.64/300.40 10719[0:SpR:538.0,9566.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w)),v),tc_bool)*.
% 299.64/300.40 10717[0:SpR:599.0,9566.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(u,tc_bool))),tc_bool)*.
% 299.64/300.40 10906[0:SpL:353.0,214.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),y,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),w),y)).
% 299.64/300.40 10882[0:SpR:3586.1,353.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(w,u),v_x)),hAPP(c_Set_Oinsert(w,u),v_x))**.
% 299.64/300.40 10854[0:SpR:353.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(c_Set_Oinsert(y,v),hAPP(c_Set_Oinsert(u,v),z))))*.
% 299.64/300.40 10826[0:SpR:353.0,7539.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(y,v),w))),tc_fun(v,tc_bool))*.
% 299.64/300.40 11065[0:Res:83.0,357.1] || c_Finite__Set_Ofinite(u,v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(w,x,y),hAPP(c_Set_Ovimage(w,x,y),hAPP(c_Set_Oimage(z,v,y),u))),y)*.
% 299.64/300.40 11259[0:SpR:11176.1,584.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x,y),z),hAPP(u,hAPP(v,z)))**.
% 299.64/300.40 11258[0:SpR:11176.1,584.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,x,y),z),hAPP(hAPP(v,z),u))**.
% 299.64/300.40 11388[0:SpR:11177.1,584.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x,y,z),u),hAPP(u,hAPP(w,u)))*.
% 299.64/300.40 11387[0:SpR:11177.1,584.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,y,z),u),hAPP(hAPP(v,u),u))*.
% 299.64/300.40 11640[0:SpR:584.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_COMBS(u,v,w,x,y),z,tc_fun(x1,tc_bool)),x2),hAPP(hAPP(u,x2),hAPP(v,x2)),tc_bool)*.
% 299.64/300.40 11634[0:SpR:336.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool)*.
% 299.64/300.40 11623[0:SpR:584.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(u,v),w,tc_fun(x,tc_bool)),hAPP(y,v)),hAPP(c_COMBS(u,y,z,x1,x2),v),tc_bool)*.
% 299.64/300.40 11616[0:SpR:337.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,tc_fun(w,tc_bool)),x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool)*.
% 299.64/300.40 11609[0:SpR:540.1,9567.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(x,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v),tc_bool)*.
% 299.64/300.40 11608[0:SpR:539.1,9567.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(x,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v),tc_bool)*.
% 299.64/300.40 11607[0:SpR:297.2,9567.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,tc_fun(y,tc_bool)),w),w,tc_bool)*.
% 299.64/300.40 11598[0:SpR:299.2,9567.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,tc_fun(y,tc_bool)),v),w,tc_bool)*.
% 299.64/300.40 11590[0:SpR:25.1,9567.0] class_HOL_Ouminus(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w,tc_fun(x,tc_bool)),v_x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool)*.
% 299.64/300.40 11771[0:SSi:11770.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),hAPP(v,v_x),tc_bool),hAPP(v,v_x),tc_bool),c_HOL_Ominus__class_Ominus(hAPP(u,v_x),hAPP(v,v_x),tc_bool))**.
% 299.64/300.40 12678[0:Res:8376.2,519.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname))** equal(w,v_Procs) -> hBOOL(hAPP(v,w))* hBOOL(hAPP(v_x,w))*.
% 299.64/300.40 12993[0:Res:3316.1,501.0] || equal(c_in(u),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.64/300.40 12987[0:Res:9071.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v,t_a).
% 299.64/300.40 13104[0:SpL:10090.1,325.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v,tc_fun(u,tc_bool))* -> c_lessequals(v_x,v,tc_fun(u,tc_bool)).
% 299.64/300.40 13085[0:SpR:586.0,10090.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(u,hAPP(y,v_x)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.40 13084[0:SpR:585.0,10090.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(hAPP(u,v_x),y),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.40 13054[0:SpR:8415.2,10090.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.40 13049[0:SpR:445.1,10090.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(v_x,v) equal(hAPP(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.40 13167[0:Res:108.1,437.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),w)*.
% 299.64/300.40 13244[0:SpR:9493.1,353.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(v,t_a),u)),hAPP(c_Set_Oinsert(v,t_a),u))**.
% 299.64/300.40 13296[0:SpR:8415.2,13238.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(t_a)) equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(v_x,u))*.
% 299.64/300.40 13561[0:Res:11030.1,501.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.40 13547[0:SpR:297.2,11030.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))).
% 299.64/300.40 13544[0:SpR:586.0,11030.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_in(t_a))** -> hBOOL(hAPP(hAPP(u,hAPP(y,v_x)),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))*.
% 299.64/300.40 13543[0:SpR:585.0,11030.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))*.
% 299.64/300.40 13513[0:SpR:8415.2,11030.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_in(t_a),u) -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.40 13508[0:SpR:445.1,11030.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_in(t_a))** -> equal(v_x,v) hBOOL(hAPP(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))*.
% 299.64/300.40 13657[0:SpL:11473.0,3507.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.40 13656[0:SpL:11473.0,3499.1] || equal(c_in(u),hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.40 13653[0:SpL:11473.0,3484.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,w),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(v_x,w).
% 299.64/300.40 13624[0:SpR:11473.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(v),u),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 13623[0:SpR:11473.0,3317.1] || equal(c_in(u),hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(v_x,u),x)))*.
% 299.64/300.40 13622[0:SpR:11473.0,3305.1] || equal(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 13613[0:SpR:11473.0,8376.2] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_in(tc_Com_Opname))** equal(w,v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),w))*.
% 299.64/300.40 13612[0:SpR:11473.0,8415.2] || equal(v_Procs,v_x) equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.40 13611[0:SpR:11473.0,3291.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),c_Orderings_Otop__class_Otop(tc_bool)),v_Procs))*.
% 299.64/300.40 13610[0:SpR:11473.0,3285.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.40 13607[0:SpR:11473.0,3279.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_Procs),v_x)).
% 299.64/300.40 13682[0:SpR:8415.2,11499.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.40 13736[0:SpR:3229.1,544.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(v,v_x)),hAPP(v,v_x))**.
% 299.64/300.40 14030[0:SpR:3229.1,543.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(v,v_x)),hAPP(v,v_x))**.
% 299.64/300.40 14114[0:Res:13016.2,405.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,u)* -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.40 14113[0:Res:13016.2,427.1] class_Lattices_Olattice(u) class_Orderings_Opreorder(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v,u)* -> c_lessequals(v_x,v,u).
% 299.64/300.40 14112[0:Res:13016.2,426.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v,v_x,u) -> c_lessequals(v,c_Orderings_Otop__class_Otop(tc_bool),u)*.
% 299.64/300.40 14194[0:Res:176.0,2629.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,tc_Com_Opname,v),hAPP(c_Set_Oinsert(hAPP(u,v_x),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.40 14154[0:SpR:351.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_COMBK(w,x,y),u,z),hAPP(c_Set_Oinsert(w,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.64/300.40 14153[0:SpR:456.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(v,w)),hAPP(c_Set_Ovimage(c_Option_Othe(w),u,x),hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.64/300.40 14274[0:SpR:14216.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,y,z,x1),x2),hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(x,x2)))**.
% 299.64/300.40 14273[0:SpR:14216.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),y,z,x1),x2),hAPP(hAPP(u,x2),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.64/300.40 14319[0:SpR:11695.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),w),c_Orderings_Otop__class_Otop(tc_bool),x,y),hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)))**.
% 299.64/300.40 14365[0:Res:3284.1,170.1] class_Orderings_Olinorder(u) || equal(c_in(tc_Com_Opname),v) c_Finite__Set_Ofinite(hAPP(v,v_x),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(v,v_x),u),v_Procs,u)*.
% 299.64/300.40 14454[0:SpL:12944.0,3507.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,x),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),y,z)))* equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.40 14453[0:SpL:12944.0,3499.1] || equal(c_in(u),hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)))* hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.40 14450[0:SpL:12944.0,3484.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,y),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(v_x,y).
% 299.64/300.40 14421[0:SpR:12944.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,x),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),y,z)))* -> hBOOL(hAPP(hAPP(c_in(v),u),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 14420[0:SpR:12944.0,3317.1] || equal(c_in(u),hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(v_x,u),z)))*.
% 299.64/300.40 14419[0:SpR:12944.0,3305.1] || equal(u,hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,z),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 14410[0:SpR:12944.0,8376.2] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_in(tc_Com_Opname))** equal(y,v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),y))*.
% 299.64/300.40 14409[0:SpR:12944.0,8415.2] || equal(v_Procs,v_x) equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.40 14408[0:SpR:12944.0,3291.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,z),c_Orderings_Otop__class_Otop(tc_bool)),v_Procs))*.
% 299.64/300.40 14407[0:SpR:12944.0,3285.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)))*.
% 299.64/300.40 14404[0:SpR:12944.0,3279.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_Procs),v_x)).
% 299.64/300.40 14492[0:Res:3284.1,169.1] class_Orderings_Olinorder(u) || equal(c_in(tc_Com_Opname),v) c_Finite__Set_Ofinite(hAPP(v,v_x),u) -> c_lessequals(v_Procs,c_Finite__Set_Olinorder__class_OMax(hAPP(v,v_x),u),u)*.
% 299.64/300.40 14733[0:SpR:128.0,12687.1] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y)) hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),y))*.
% 299.64/300.40 14807[0:SSi:14806.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(w,x,v),u),tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))**.
% 299.64/300.40 14809[0:SSi:14808.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(w,x,v),u),tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))**.
% 299.64/300.40 15089[2:SpR:181.1,4250.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_Com_Ocom_OBODY)** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) c_Com_OWT(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.64/300.40 15081[0:SpR:181.1,3282.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) hBOOL(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.64/300.40 15163[0:SpR:8415.2,11611.0] || equal(v_Procs,v_x) equal(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(v_x,u,tc_bool).
% 299.64/300.40 15233[0:Res:446.1,437.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(x,w),v),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(x,w),u),w)*.
% 299.64/300.40 15193[0:SpR:2097.1,446.1] || hBOOL(hAPP(u,v)) c_lessequals(w,u,tc_fun(x,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v,x),w),u,tc_fun(x,tc_bool))*.
% 299.64/300.40 15644[0:Res:11030.1,278.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,v,u)))*.
% 299.64/300.40 15641[0:Res:3316.1,278.1] || equal(c_in(u),c_in(v)) hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),x,w,v)))*.
% 299.64/300.40 15812[0:SpR:586.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_COMBB(u,v,w,x),y),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(y,v_x)),tc_bool)).
% 299.64/300.40 15811[0:SpR:585.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_COMBC(u,v,w,x),y),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),y),tc_bool)).
% 299.64/300.40 15771[0:SpR:445.1,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Fun_Ofun__upd(u,v,w,x,y),tc_fun(t_a,tc_bool)),v_Procs)** -> equal(v_x,v) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)).
% 299.64/300.40 15872[0:Res:11030.1,277.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),v,u)))*.
% 299.64/300.40 15869[0:Res:3316.1,277.1] || equal(c_in(u),c_in(v)) hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w,v)))*.
% 299.64/300.40 15952[2:SpR:586.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_COMBB(u,v,w,x),y),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(y,v_x)),tc_bool)).
% 299.64/300.40 15951[2:SpR:585.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_COMBC(u,v,w,x),y),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),y),tc_bool)).
% 299.64/300.40 15917[2:SpR:8415.2,15483.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.40 15911[2:SpR:445.1,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Fun_Ofun__upd(u,v,w,x,y),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> equal(v_x,v) c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)).
% 299.64/300.40 16043[0:SSi:16039.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(v,v_x,tc_fun(u,tc_bool)) -> c_lessequals(v,c_Orderings_Otop__class_Otop(tc_bool),tc_fun(u,tc_bool))*.
% 299.64/300.40 16187[0:Res:15262.1,371.0] || equal(c_Set_Oinsert(u,v),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 16173[0:SpR:12944.0,15262.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))).
% 299.64/300.40 16169[0:SpR:9.0,15262.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_in(t_a))** -> hBOOL(hAPP(hAPP(u,hAPP(v,v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.40 16168[0:SpR:11473.0,15262.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))).
% 299.64/300.40 16158[0:SpR:88.1,15262.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.40 16150[0:SpR:2098.1,15262.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.40 16139[0:SpR:3586.1,15262.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_in(t_a)) -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.40 16127[0:SpR:8498.1,15262.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.40 16269[0:SpL:584.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_COMBS(u,v,w,x,y),v_Procs)** -> .
% 299.64/300.40 16252[0:SpL:540.1,16217.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> .
% 299.64/300.40 16251[0:SpL:539.1,16217.0] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> .
% 299.64/300.40 16250[0:SpL:297.2,16217.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs)** -> .
% 299.64/300.40 16241[0:SpL:299.2,16217.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs)** -> .
% 299.64/300.40 16230[0:SpL:25.1,16217.0] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_Procs) -> .
% 299.64/300.40 16468[0:SpL:9935.1,3698.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* equal(c_Com_Ocom_OBODY,u) equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 16465[0:SpL:9935.1,3493.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.40 16401[0:SpR:9935.1,3339.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* -> equal(c_Fun_Ofun__upd(u,v_x,c_Orderings_Otop__class_Otop(tc_bool),w,x),u)**.
% 299.64/300.40 16400[0:SpR:9935.1,3316.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.40 16397[0:SpR:9935.1,648.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.40 16394[0:SpR:9935.1,11030.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.40 16393[0:SpR:9935.1,10090.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.40 16388[0:SpR:9935.1,3284.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 16378[0:SpR:9935.1,651.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.40 16542[0:SpR:351.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_COMBK(y,z,x1),v,u),u)*.
% 299.64/300.40 16541[0:SpR:456.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Option_Ooption_OSome(w,x)),y))* -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Option_Othe(x),v,u),u)*.
% 299.64/300.40 16602[0:SSi:16593.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(x,y),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.64/300.40 16706[0:SpL:9936.1,3698.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* equal(c_Com_Ocom_OBODY,v) equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 16703[0:SpL:9936.1,3493.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname)) equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.40 16637[0:SpR:9936.1,3339.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* -> equal(c_Fun_Ofun__upd(v,v_x,c_Orderings_Otop__class_Otop(tc_bool),w,x),v)**.
% 299.64/300.40 16636[0:SpR:9936.1,3316.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.40 16633[0:SpR:9936.1,648.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.40 16630[0:SpR:9936.1,11030.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.40 16629[0:SpR:9936.1,10090.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.40 16624[0:SpR:9936.1,3284.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 16614[0:SpR:9936.1,651.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.40 16754[0:MRR:16738.3,429.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,v),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Finite__Set_Ofinite(v_x,v) -> c_Fun_Oinj__on(u,v_x,v,v)*.
% 299.64/300.40 16769[0:SpL:8415.2,16768.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) hBOOL(hAPP(v_G,v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v_na,v_x)))* -> c_Hoare__Mirabelle_Otriple__valid(v_na,v_Procs,t_a).
% 299.64/300.40 16775[0:SpL:321.0,390.0] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x,w,v),u,v,w)*.
% 299.64/300.40 16810[0:SpR:8415.2,16776.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_x,u,v,w),v_x,w,v)*.
% 299.64/300.40 16943[0:SpR:600.0,328.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v),v).
% 299.64/300.40 17170[0:SpL:17045.0,3507.1] || equal(c_Set_Oinsert(u,v),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x,tc_fun(y,tc_bool)))* equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.40 17169[0:SpL:17045.0,3499.1] || equal(c_in(u),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)))* hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.40 17165[0:SpL:17045.0,3484.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,x),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(v_x,x).
% 299.64/300.40 17135[0:SpR:17045.0,3346.1] || equal(c_Set_Oinsert(u,v),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x,tc_fun(y,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(v),u),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.40 17134[0:SpR:17045.0,3317.1] || equal(c_in(u),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)))* -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Set_Oinsert(v_x,u),y)))*.
% 299.64/300.40 17133[0:SpR:17045.0,3305.1] || equal(u,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,y),v_Procs),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.40 17126[0:SpR:17045.0,15262.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))).
% 299.64/300.40 17123[0:SpR:17045.0,8376.2] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_in(tc_Com_Opname))** equal(x,v_Procs) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),x))*.
% 299.64/300.40 17121[0:SpR:17045.0,3291.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_bool)),v_Procs))*.
% 299.64/300.40 17120[0:SpR:17045.0,3285.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)))*.
% 299.64/300.40 17117[0:SpR:17045.0,3279.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_Procs),v_x)).
% 299.64/300.40 17310[0:SpL:9.0,13272.0] || equal(hAPP(u,hAPP(v,v_x)),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Fun_Ocomp(u,v,w,x,y),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.64/300.40 17297[0:SpL:88.1,13272.0] class_Lattices_Oboolean__algebra(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.40 17358[0:Res:172.2,279.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(c_Set_Oinsert(c_Finite__Set_Olinorder__class_OMax(v,u),u),v),v)**.
% 299.64/300.40 17376[0:SpR:14526.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Option_Othe(v),w,tc_fun(x,tc_bool)),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.64/300.40 17461[0:SpL:9.0,16327.1] || equal(u,c_Fun_Ocomp(v,w,x,y,z))* equal(hAPP(v,hAPP(w,v_x)),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_Procs) -> .
% 299.64/300.40 17448[0:SpL:88.1,16327.1] class_Lattices_Oboolean__algebra(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(v,v_Procs) -> .
% 299.64/300.40 17476[0:Res:171.2,279.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(c_Set_Oinsert(c_Finite__Set_Olinorder__class_OMin(v,u),u),v),v)**.
% 299.64/300.40 17733[0:Res:9071.0,255.0] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),u),w)).
% 299.64/300.40 17728[0:Res:1157.0,255.0] || c_lessequals(hAPP(c_Set_Oimage(c_COMBK(u,v,w),tc_Com_Opname,x),v_Procs),y,tc_fun(x,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(x),u),y)).
% 299.64/300.40 17976[0:Res:687.1,11894.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_in(u),v),tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.40 17975[0:Res:686.1,11894.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_in(u),v),tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.40 17951[0:Res:510.1,11894.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.40 17950[0:Res:511.1,11894.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.40 18134[0:SpR:659.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.40 18297[0:SpL:15172.0,3698.2] || equal(u,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)))* equal(c_Com_Ocom_OBODY,u) equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.40 18293[0:SpL:15172.0,3493.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_in(tc_Com_Opname))** equal(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.40 18272[0:SpR:15172.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.40 18260[0:SpR:15172.0,3339.1] || equal(u,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)))* -> equal(c_Fun_Ofun__upd(u,v_x,c_Orderings_Obot__class_Obot(tc_bool),z,x1),u)**.
% 299.64/300.40 18259[0:SpR:15172.0,3316.1] || equal(c_in(u),c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)))* -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.40 18256[0:SpR:15172.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.40 18253[0:SpR:15172.0,11030.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))))*.
% 299.64/300.40 18252[0:SpR:15172.0,10090.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.40 18247[0:SpR:15172.0,3284.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(y),v_Procs),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.40 18237[0:SpR:15172.0,651.0] || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),tc_Com_Opname,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.64/300.40 18334[0:SpR:659.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,w),v)))*.
% 299.64/300.40 18523[0:Res:9246.0,255.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(v),x),w))*.
% 299.64/300.40 18591[0:Res:153.1,11894.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* equal(hAPP(c_Set_Ovimage(v,y,u),x),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))** -> .
% 299.64/300.40 18723[0:SpR:12944.0,9568.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y))),z),x1),tc_bool)*.
% 299.64/300.40 18719[0:SpR:9.0,9568.0] || -> c_lessequals(hAPP(u,hAPP(v,w)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Fun_Ocomp(u,v,y,z,x1)),x2),w),tc_bool)*.
% 299.64/300.40 18717[0:SpR:11499.0,9568.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x))),y),c_Orderings_Otop__class_Otop(tc_bool)),tc_bool)*.
% 299.64/300.40 18716[0:SpR:10090.1,9568.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(u,v_x)),w),c_Orderings_Otop__class_Otop(tc_bool)),tc_bool)*.
% 299.64/300.40 18711[0:SpR:105.0,9568.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Ovimage(w,u,x)),y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),tc_bool)*.
% 299.64/300.40 18710[0:SpR:1196.1,9568.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u))),w),c_Orderings_Otop__class_Otop(u)),tc_bool)*.
% 299.64/300.40 18707[0:SpR:38.0,9568.0] || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Ovimage(w,u,x)),y),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_bool)*.
% 299.64/300.40 18706[0:SpR:321.0,9568.0] || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oimage(w,x,u)),y),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_bool)*.
% 299.64/300.40 18704[0:SpR:1195.1,9568.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),w),c_Orderings_Obot__class_Obot(u)),tc_bool)*.
% 299.64/300.40 18702[0:SpR:11695.0,9568.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x))),y),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),x)),tc_bool)*.
% 299.64/300.40 18701[0:SpR:11473.0,9568.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))),x),y),tc_bool)*.
% 299.64/300.40 18684[0:SpR:87.1,9568.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),x),c_HOL_Ouminus__class_Ouminus(w,u)),tc_bool)*.
% 299.64/300.40 18683[0:SpR:88.1,9568.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u))),x),w),tc_bool)*.
% 299.64/300.40 18671[0:SpR:2098.1,9568.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a))),x),v),tc_bool)*.
% 299.64/300.40 18660[0:SpR:3586.1,9568.0] || equal(hAPP(c_in(u),v),v_Procs) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Set_Oinsert(v,u)),x),v_x),tc_bool)*.
% 299.64/300.40 18646[0:SpR:653.0,9568.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname)),w),v_Procs),tc_bool)*.
% 299.64/300.40 18642[0:SpR:9493.1,9568.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a)),w),u),tc_bool)*.
% 299.64/300.40 18640[0:SpR:8498.1,9568.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Set_Oinsert(x,v)),y),u),tc_bool)*.
% 299.64/300.40 18895[0:SSi:18863.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)) -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_Procs),tc_bool)*.
% 299.64/300.40 18896[0:SSi:18860.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)) -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_Procs),tc_bool)*.
% 299.64/300.40 19034[0:SpR:12944.0,9569.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,x),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),y,z))),x1),tc_bool)*.
% 299.64/300.40 19030[0:SpR:9.0,9569.0] || -> c_lessequals(hAPP(u,hAPP(v,w)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Fun_Ocomp(u,v,z,x1,x2)),w),tc_bool)*.
% 299.64/300.40 19028[0:SpR:11499.0,9569.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y))),c_Orderings_Otop__class_Otop(tc_bool)),tc_bool)*.
% 299.64/300.40 19027[0:SpR:10090.1,9569.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(u,v_x)),c_Orderings_Otop__class_Otop(tc_bool)),tc_bool)*.
% 299.64/300.40 19022[0:SpR:105.0,9569.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Ovimage(x,u,y)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),tc_bool)*.
% 299.64/300.40 19021[0:SpR:1196.1,9569.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u))),c_Orderings_Otop__class_Otop(u)),tc_bool)*.
% 299.64/300.40 19018[0:SpR:38.0,9569.0] || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Ovimage(x,u,y)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_bool)*.
% 299.64/300.40 19017[0:SpR:321.0,9569.0] || -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oimage(x,y,u)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_bool)*.
% 299.64/300.40 19015[0:SpR:1195.1,9569.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),c_Orderings_Obot__class_Obot(u)),tc_bool)*.
% 299.64/300.40 19013[0:SpR:11695.0,9569.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,x),c_Option_Othe(y))),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),y)),tc_bool)*.
% 299.64/300.40 19012[0:SpR:11473.0,9569.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))),y),tc_bool)*.
% 299.64/300.40 18995[0:SpR:87.1,9569.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x)),c_HOL_Ouminus__class_Ouminus(x,u)),tc_bool)*.
% 299.64/300.40 18994[0:SpR:88.1,9569.0] class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(x,u))),x),tc_bool)*.
% 299.64/300.40 18982[0:SpR:2098.1,9569.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a))),v),tc_bool)*.
% 299.64/300.40 18971[0:SpR:3586.1,9569.0] || equal(hAPP(c_in(u),v),v_Procs) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Set_Oinsert(v,u)),v_x),tc_bool)*.
% 299.64/300.40 18957[0:SpR:653.0,9569.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.40 18953[0:SpR:9493.1,9569.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_x,t_a)),u),tc_bool)*.
% 299.64/300.40 18951[0:SpR:8498.1,9569.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Set_Oinsert(y,v)),u),tc_bool)*.
% 299.64/300.40 19257[0:Rew:12524.1,19246.2] || c_lessequals(u,v,tc_bool)* equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_HOL_Ominus__class_Ominus(u,w,tc_bool),v)*.
% 299.64/300.40 19426[0:Res:15188.1,123.0] || c_Natural_Oevalc(u,v,w)* c_Natural_Oevalc(x,w,y)* -> c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSemi(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSKIP)),u),x),v,y)*.
% 299.64/300.40 19474[0:Res:9067.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,w,t_a).
% 299.64/300.40 19486[0:SpR:8415.2,19451.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))))*.
% 299.64/300.40 19500[0:SpR:8415.2,19440.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oinsert(v,u),v_x)))*.
% 299.64/300.40 19529[0:Res:19452.0,255.0] || c_lessequals(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v,tc_fun(t_a,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.64/300.40 19593[0:Res:19441.0,255.0] || c_lessequals(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),w,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),w)).
% 299.64/300.40 19626[0:Res:19436.1,255.0] || equal(u,v_Procs) c_lessequals(hAPP(c_Set_Oinsert(v,tc_Com_Opname),u),w,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),w)).
% 299.64/300.40 19678[0:Res:3282.1,496.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,v_x)),v_x))* c_Hoare__Mirabelle_Otriple__valid(v,u,t_a)*.
% 299.64/300.40 19688[0:SpL:2097.1,19641.0] || hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(u,v),w),u))* hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(u,v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oinsert(u,v),w,t_a).
% 299.64/300.40 19888[0:SpL:104.0,324.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* -> c_lessequals(v,x,tc_fun(w,tc_bool)).
% 299.64/300.40 19886[0:SpL:104.0,344.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.64/300.40 19826[0:SpR:104.0,517.1] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),w))*.
% 299.64/300.40 19908[0:SSi:19813.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.40 19917[0:SSi:19916.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.64/300.40 20080[0:SpL:2095.0,215.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.64/300.40 20202[0:Res:20152.0,430.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(x,c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool))*.
% 299.64/300.40 20222[0:SSi:20210.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* -> c_lessequals(u,w,tc_fun(x,tc_bool)).
% 299.64/300.40 20256[0:Res:20186.0,430.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(x,u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))*.
% 299.64/300.40 20271[0:SSi:20262.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* -> c_lessequals(u,c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)).
% 299.64/300.40 20385[0:Rew:20354.2,20313.3] class_Lattices_Obounded__lattice(u) class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> equal(c_Orderings_Obot__class_Obot(u),v).
% 299.64/300.40 20408[0:Rew:20341.1,20339.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> equal(c_HOL_Ominus__class_Ominus(y,v,tc_fun(u,tc_bool)),y)**.
% 299.64/300.40 20669[0:SSi:20610.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(u,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),x),tc_bool)*.
% 299.64/300.40 20670[0:SSi:20607.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(u,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v),x),tc_bool)*.
% 299.64/300.40 20824[0:Res:19748.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),w,u,tc_Com_Opname)))*.
% 299.64/300.40 20823[0:Res:19748.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),u,tc_Com_Opname)))*.
% 299.64/300.40 20899[0:SpR:317.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oinsert(x,u),hAPP(c_Set_Oimage(v,y,u),hAPP(c_Set_Oinsert(w,y),z)))))*.
% 299.64/300.40 20883[0:SpR:317.0,15367.0] || -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),w)*.
% 299.64/300.40 20865[0:SpR:317.0,9566.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oimage(u,v,w),x),y),hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(z,v),x)),y),tc_bool)*.
% 299.64/300.40 20829[0:SpR:317.0,318.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(hAPP(x,u),y),hAPP(c_Set_Oimage(x,v,y),w)),y)*.
% 299.64/300.40 21142[0:SpR:317.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),hAPP(c_Set_Oinsert(z,y),x1))),hAPP(u,hAPP(x,z))))*.
% 299.64/300.40 21118[0:SpR:12944.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y,z),hAPP(c_Set_Oinsert(x1,y),x2)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21114[0:SpR:9.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(u,hAPP(v,x2))))*.
% 299.64/300.40 21112[0:SpR:11499.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x,y),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),z)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21111[0:SpR:10090.1,20881.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),v),x)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21106[0:SpR:105.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x),z)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.40 21105[0:SpR:1196.1,20881.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),v),x)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.40 21102[0:SpR:38.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x),z)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))*.
% 299.64/300.40 21101[0:SpR:321.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(u,v,w),x,y),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),x),z)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.64/300.40 21099[0:SpR:1195.1,20881.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),v),x)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.40 21097[0:SpR:11695.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),x,y),hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),w),x),z)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21096[0:SpR:11473.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,x),hAPP(c_Set_Oinsert(y,w),z)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21079[0:SpR:87.1,20881.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(v,u),w),y)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.40 21078[0:SpR:88.1,20881.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),w,x),hAPP(c_Set_Oinsert(v,w),y)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.40 21077[0:SpR:17045.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x,y),hAPP(c_Set_Oinsert(z,x),x1)),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.40 21066[0:SpR:2098.1,20881.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,x),hAPP(c_Set_Oinsert(v,w),y)),v))*.
% 299.64/300.40 21055[0:SpR:3586.1,20881.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,x),hAPP(c_Set_Oinsert(v_x,w),y)),v_x))*.
% 299.64/300.40 21037[0:SpR:653.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,v),x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.40 21033[0:SpR:9493.1,20881.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,v),x)),u))*.
% 299.64/300.40 21031[0:SpR:8498.1,20881.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(w,v),x,y),hAPP(c_Set_Oinsert(u,x),z)),u))*.
% 299.64/300.40 21195[0:SpR:8415.2,21130.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),v_x),hAPP(u,v_Procs)))*.
% 299.64/300.40 21194[0:SpR:15172.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y,z),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.40 21191[0:SpR:586.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),z,x1),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(u,hAPP(y,v_Procs))))*.
% 299.64/300.40 21190[0:SpR:585.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBC(u,v,w,x),y),z,x1),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(hAPP(u,v_Procs),y)))*.
% 299.64/300.40 21185[0:SpR:9936.1,21130.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21183[0:SpR:9935.1,21130.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_Procs,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21151[0:SpR:445.1,21130.0] || -> equal(v_Procs,u) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(v,u,w,x,y),z,x1),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(v,v_Procs)))*.
% 299.64/300.40 21199[0:SpR:8415.2,21152.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),v_x),v_Procs))*.
% 299.64/300.40 21255[0:SpR:15172.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),t_a,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.40 21252[0:SpR:586.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),t_a,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),hAPP(u,hAPP(y,v_x))))*.
% 299.64/300.40 21251[0:SpR:585.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBC(u,v,w,x),y),t_a,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),hAPP(hAPP(u,v_x),y)))*.
% 299.64/300.40 21246[0:SpR:9936.1,21141.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21244[0:SpR:9935.1,21141.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21212[0:SpR:8415.2,21141.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.40 21206[0:SpR:445.1,21141.0] || -> equal(v_x,u) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(v,u,w,x,y),t_a,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),hAPP(v,v_x)))*.
% 299.64/300.40 21275[0:Res:13238.1,469.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,t_a)),v_x)**.
% 299.64/300.40 21274[0:Res:8375.1,469.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,u,y,v,w)),y)**.
% 299.64/300.40 21273[0:Res:545.1,469.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,x,hAPP(x,v),u,y)),hAPP(x,v))**.
% 299.64/300.40 21266[0:Res:652.1,469.0] || c_lessequals(v_Procs,hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),tc_fun(tc_Com_Opname,tc_bool))* -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,tc_Com_Opname)),v_x)**.
% 299.64/300.40 21620[0:SpL:21267.0,377.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),v_x),v) -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),v)*.
% 299.64/300.40 21612[0:SpL:21267.0,3484.1] || equal(c_Com_Ocom_OBODY,u) equal(hAPP(u,v_x),hAPP(c_Com_Ocom_OBODY,v_x))* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,v_x),tc_Com_Opname,v),v_x)**.
% 299.64/300.40 21502[0:SpR:21267.0,19744.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v_x),tc_Com_Opname,v),t_a)*.
% 299.64/300.40 21443[0:SpR:21267.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,x),v),y)),hAPP(u,v_x)))*.
% 299.64/300.40 21374[0:SpR:21267.0,9569.0] || -> c_lessequals(hAPP(u,v_x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,x)),tc_bool)*.
% 299.64/300.40 21373[0:SpR:21267.0,9568.0] || -> c_lessequals(hAPP(u,v_x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,x)),tc_bool)*.
% 299.64/300.40 21295[0:SpR:21267.0,378.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),v_x),v).
% 299.64/300.40 21802[0:SpR:12944.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),t_a,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21798[0:SpR:9.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),t_a,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(u,hAPP(v,v_x))))*.
% 299.64/300.40 21797[0:SpR:11473.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 21784[0:SpR:88.1,21143.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.40 21783[0:SpR:17045.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),t_a,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.40 21774[0:SpR:2098.1,21143.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.40 21763[0:SpR:3586.1,21143.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.40 21751[0:SpR:8498.1,21143.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.40 21867[0:SpR:9.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname,z),hAPP(c_Set_Oinsert(x1,tc_Com_Opname),v_Procs)),hAPP(u,hAPP(v,v_x))))*.
% 299.64/300.40 21853[0:SpR:88.1,21131.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.40 21843[0:SpR:2098.1,21131.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.40 21832[0:SpR:3586.1,21131.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.40 21820[0:SpR:8498.1,21131.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.40 21901[0:Res:13238.1,464.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,t_a)),v_x)**.
% 299.64/300.40 21900[0:Res:8375.1,464.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(x,y,u,v,w)),y)**.
% 299.64/300.40 21899[0:Res:545.1,464.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(w,hAPP(x,v),x,u,y)),hAPP(x,v))**.
% 299.64/300.40 21892[0:Res:652.1,464.0] || c_lessequals(v_Procs,hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),tc_fun(tc_Com_Opname,tc_bool))* -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,tc_Com_Opname)),v_x)**.
% 299.64/300.40 22248[0:SpL:21893.0,377.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),v_x),v) -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),v)*.
% 299.64/300.40 22240[0:SpL:21893.0,3484.1] || equal(c_Com_Ocom_OBODY,u) equal(hAPP(u,v_x),hAPP(c_Com_Ocom_OBODY,v_x))* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Ocom_OBODY,v_x),c_Com_Ocom_OBODY,tc_Com_Opname,v),v_x)**.
% 299.64/300.40 22128[0:SpR:21893.0,19744.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v_x),c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,v),t_a)*.
% 299.64/300.40 22069[0:SpR:21893.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,x),v),y)),hAPP(u,v_x)))*.
% 299.64/300.40 22000[0:SpR:21893.0,9569.0] || -> c_lessequals(hAPP(u,v_x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,x)),tc_bool)*.
% 299.64/300.40 21999[0:SpR:21893.0,9568.0] || -> c_lessequals(hAPP(u,v_x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,x)),tc_bool)*.
% 299.64/300.40 21921[0:SpR:21893.0,378.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),v_x),v).
% 299.64/300.40 22503[0:SpR:12944.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)),tc_Com_Opname,z),u),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 22499[0:SpR:9.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),tc_Com_Opname,x1),u),hAPP(v,hAPP(w,v_x))))*.
% 299.64/300.40 22498[0:SpR:11473.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_Com_Opname,x),u),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.40 22485[0:SpR:88.1,21126.1] class_Lattices_Oboolean__algebra(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,w),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.40 22484[0:SpR:17045.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)),tc_Com_Opname,y),u),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.40 22475[0:SpR:2098.1,21126.1] || equal(u,v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,w),u),v_x))*.
% 299.64/300.40 22464[0:SpR:3586.1,21126.1] || equal(hAPP(c_in(u),v),v_Procs) equal(w,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),tc_Com_Opname,x),w),v_x))*.
% 299.64/300.40 22452[0:SpR:8498.1,21126.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(w,u),tc_Com_Opname,x),v),v_x))*.
% 299.64/300.40 22598[0:SpR:158.0,318.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_Fun_Ocomp(y,u,w,z,v),v,z),x),z)*.
% 299.64/300.40 22677[0:Rew:9.0,22525.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))),hAPP(u,hAPP(x,v_x))))*.
% 299.64/300.40 22678[0:Rew:9.0,22523.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,tc_Com_Opname,v),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs))),hAPP(u,hAPP(x,v_x))))*.
% 299.64/300.40 22680[0:Rew:9.0,22516.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,tc_Com_Opname,w),u)),hAPP(v,hAPP(y,v_x))))*.
% 299.64/300.40 22874[0:SpL:3294.1,325.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v,tc_fun(u,tc_bool))* -> c_lessequals(v_x,v,tc_fun(u,tc_bool)).
% 299.64/300.40 22847[0:SpL:3294.1,296.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v,u) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v,u)*.
% 299.64/300.40 22834[0:SpR:14216.0,3294.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_in(t_a))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.40 22833[0:SpR:11176.1,3294.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a)) -> equal(hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 22831[0:SpR:11177.1,3294.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 22810[0:SpR:331.0,3294.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_in(t_a))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.40 22809[0:SpR:302.1,3294.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(t_a))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 22796[0:SpR:15476.0,3294.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_in(t_a)) -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.40 22760[0:SpR:3294.1,294.2] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) c_lessequals(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),u)* -> c_lessequals(v,c_Orderings_Obot__class_Obot(tc_bool),u).
% 299.64/300.40 22746[0:SpR:3294.1,9567.0] || equal(c_in(t_a),u) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)*.
% 299.64/300.40 23046[0:Rew:9.0,23035.1] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),z)),v_Procs)** -> hBOOL(hAPP(z,hAPP(x,hAPP(u,v_x)))).
% 299.64/300.40 23138[2:Rew:9.0,23134.1] || equal(c_Fun_Ocomp(u,c_Fun_Ocomp(v,w,x,y,z),y,x1,z),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(u,hAPP(v,hAPP(w,v_x)))).
% 299.64/300.40 23139[0:Rew:9.0,23133.1] || equal(c_Fun_Ocomp(u,c_Fun_Ocomp(v,w,x,y,z),y,x1,z),v_Procs)** -> hBOOL(hAPP(u,hAPP(v,hAPP(w,v_x)))).
% 299.64/300.40 23140[2:Rew:9.0,23131.1] || equal(c_Fun_Ocomp(c_Fun_Ocomp(u,v,w,x,y),z,y,x,x1),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(u,hAPP(v,hAPP(z,v_x)))).
% 299.64/300.40 23141[0:Rew:9.0,23130.1] || equal(c_Fun_Ocomp(c_Fun_Ocomp(u,v,w,x,y),z,y,x,x1),v_Procs)** -> hBOOL(hAPP(u,hAPP(v,hAPP(z,v_x)))).
% 299.64/300.40 23150[0:Res:22737.2,427.1] class_Lattices_Olattice(u) class_Orderings_Opreorder(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v,u)* -> c_lessequals(v_x,v,u).
% 299.64/300.40 23149[0:Res:22737.2,426.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) c_lessequals(v,v_x,u) -> c_lessequals(v,c_Orderings_Obot__class_Obot(tc_bool),u)*.
% 299.64/300.40 23167[0:SSi:23164.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_lessequals(v,v_x,tc_fun(u,tc_bool)) -> c_lessequals(v,c_Orderings_Obot__class_Obot(tc_bool),tc_fun(u,tc_bool))*.
% 299.64/300.40 23214[0:SpL:14216.0,3487.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> .
% 299.64/300.40 23213[0:SpL:11176.1,3487.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.40 23189[0:SpL:302.1,3487.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.40 23176[0:SpL:15476.0,3487.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.40 23291[0:SpL:14216.0,3489.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_in(tc_Com_Opname))** hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.40 23290[0:SpL:11176.1,3489.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname)) hBOOL(hAPP(u,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.40 23288[0:SpL:11177.1,3489.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.40 23266[0:SpL:302.1,3489.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.40 23253[0:SpL:15476.0,3489.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.40 23995[0:SpR:23912.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v,u),u)*.
% 299.64/300.40 23984[0:SpR:23912.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,w),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.64/300.40 24224[0:SpR:3229.1,542.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)))* -> equal(hAPP(hAPP(u,v_x),hAPP(hAPP(u,v_x),w)),hAPP(hAPP(u,v_x),w))**.
% 299.64/300.40 24222[0:SpR:8415.2,542.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(v_x,hAPP(v_x,v)),hAPP(v_x,v))**.
% 299.64/300.40 24396[0:Rew:610.0,24322.2] || c_Fun_Oinj__on(c_COMBK(u,v,w),x,w,v)* -> equal(x,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(c_Finite__Set_Ocard(x,w),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 299.64/300.40 24728[0:SpL:24020.1,515.0] || equal(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(v_x,y))* -> equal(v,v_x).
% 299.64/300.40 24727[0:SpL:24020.1,514.0] || equal(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(v_x,y))* -> equal(w,v_x).
% 299.64/300.40 24726[0:SpL:24020.1,513.0] || equal(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(v_x,y))* -> equal(x,y).
% 299.64/300.40 24710[0:SpL:24020.1,515.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),v_x)** -> equal(v,w)*.
% 299.64/300.40 24709[0:SpL:24020.1,514.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),v_x)** -> equal(v_x,x).
% 299.64/300.40 24708[0:SpL:24020.1,513.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),v_x)** -> equal(v_x,y).
% 299.64/300.40 24655[0:SpR:329.1,24020.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,v_x),v_x).
% 299.64/300.40 24654[0:SpR:328.1,24020.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(u,v_x),v_x).
% 299.64/300.40 24652[0:SpR:538.0,24020.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),v_x),v_x)**.
% 299.64/300.40 24562[0:SpR:24020.1,474.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(hAPP(u,v_x),w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.40 24830[0:Obv:24814.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w)* -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x),x)**.
% 299.64/300.40 24923[0:Res:9258.0,467.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),tc_bool))* equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,t_a),v_x)),v_x)**.
% 299.64/300.40 25095[0:SpL:23902.1,324.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(v_x,v,tc_fun(u,tc_bool)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v,tc_fun(u,tc_bool))*.
% 299.64/300.40 25061[0:SpR:584.0,23902.1] || equal(c_COMBS(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.40 25034[0:SpR:540.1,23902.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.40 25033[0:SpR:539.1,23902.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.40 25032[0:SpR:297.2,23902.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.40 25023[0:SpR:299.2,23902.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v,c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.40 25012[0:SpR:25.1,23902.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.40 25131[0:Res:252.1,133.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),c_Com_Ocom_OSKIP),w),t_a)* equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,w,c_Com_Ocom_OSKIP,u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(v,w,c_Com_Ocom_OSKIP,u)).
% 299.64/300.40 25611[0:Res:9566.0,24120.1] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),w),x),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),w),x),hAPP(w,x)).
% 299.64/300.40 25670[0:Rew:25611.1,25620.1] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x),x).
% 299.64/300.40 25728[0:Res:168.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w),t_a)* -> c_Hoare__Mirabelle_Ohoare__valids(x,v,t_a) c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,v),t_a)*.
% 299.64/300.40 25992[0:SpL:339.0,346.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),w,z)* -> c_Fun_Oinj__on(u,y,w,z).
% 299.64/300.40 25985[0:SpL:339.0,333.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v).
% 299.64/300.40 26239[0:SpL:338.0,347.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),w,z)* -> c_Fun_Oinj__on(u,x,w,z).
% 299.64/300.40 26230[0:SpL:338.0,332.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),x),v).
% 299.64/300.40 26140[0:SpR:338.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(c_Set_Oinsert(v,u),y)))))*.
% 299.64/300.40 26139[0:SpR:338.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(y,v),z))),hAPP(u,y)))*.
% 299.64/300.40 26312[0:Res:23960.1,427.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Opreorder(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v,u)* -> c_lessequals(v_x,v,u).
% 299.64/300.40 26311[0:Res:23960.1,426.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Oorder(u) || c_lessequals(v,v_x,u) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),u)*.
% 299.64/300.40 26301[0:SpR:8415.2,23960.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,u),u)*.
% 299.64/300.40 26324[0:SSi:26305.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* -> c_lessequals(v_x,v,tc_fun(u,tc_bool)).
% 299.64/300.40 26447[0:Res:24941.2,427.1] class_Lattices_Olattice(u) class_Orderings_Opreorder(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v_x,v,u) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v,u)*.
% 299.64/300.40 26446[0:Res:24941.2,426.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v,c_Orderings_Obot__class_Obot(tc_bool),u)* -> c_lessequals(v,v_x,u).
% 299.64/300.40 26553[0:SpL:8415.2,24122.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(v_x,u),c_Orderings_Obot__class_Obot(tc_bool))** -> c_lessequals(v_x,v,tc_bool)*.
% 299.64/300.40 26708[0:SpL:8415.2,24123.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(v_x,u),c_Orderings_Obot__class_Obot(tc_bool)) -> c_lessequals(u,v,tc_bool)*.
% 299.64/300.40 26760[0:SpR:8415.2,23997.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(v_x,u,tc_fun(v,tc_bool)),v_x),v_x,tc_bool)*.
% 299.64/300.40 27006[0:Res:526.1,175.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),y))* -> equal(hAPP(u,y),x).
% 299.64/300.40 27048[0:Res:23946.1,496.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,v_x)),v_x))* c_Hoare__Mirabelle_Otriple__valid(u,v_Procs,t_a).
% 299.64/300.40 27040[0:Res:23946.1,255.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),u))*.
% 299.64/300.40 27088[0:Res:526.1,280.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(w,v),x))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,w,y,tc_fun(z,tc_bool)),x))*.
% 299.64/300.40 27290[7:Res:27207.1,496.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)** -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,v_x)),v_x))* c_Hoare__Mirabelle_Otriple__valid(v,u,t_a)*.
% 299.64/300.40 27242[7:SpR:181.1,27207.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_x)** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) hBOOL(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.64/300.40 27307[7:MRR:24366.2,27297.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))** equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_Procs)** -> .
% 299.64/300.40 27308[7:MRR:24289.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_Procs))*.
% 299.64/300.40 27331[7:MRR:11287.3,27297.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(hAPP(v_x,v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))* -> .
% 299.64/300.40 27336[7:MRR:24283.0,27297.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_Com_Opname,x),v_Procs),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))*.
% 299.64/300.40 27345[7:MRR:24309.1,27297.0] || equal(u,c_Set_Oimage(c_COMBK(v,w,x),x,w))* -> equal(hAPP(u,v_x),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.64/300.40 27360[7:MRR:17853.0,27303.2] || equal(v_Procs,v_x) equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_x).
% 299.64/300.40 27387[0:Res:545.1,470.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(w,hAPP(x,v),x,u,y)),w))*.
% 299.64/300.40 27384[0:Res:526.1,470.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),y)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(x,y,u,v,w)),x))*.
% 299.64/300.40 27447[0:Res:545.1,466.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,x,hAPP(x,v),u,y)),w))*.
% 299.64/300.40 27444[0:Res:526.1,466.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),y)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,u,y,v,w)),x))*.
% 299.64/300.40 27870[7:SpR:586.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_COMBB(u,v,w,x),y),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(y,v_x)),tc_bool)).
% 299.64/300.40 27869[7:SpR:585.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_COMBC(u,v,w,x),y),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),y),tc_bool)).
% 299.64/300.40 27818[7:SpR:445.1,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Fun_Ofun__upd(u,v,w,x,y),tc_fun(t_a,tc_bool)),v_x)** -> equal(v_x,v) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)).
% 299.64/300.40 27929[0:Res:468.0,527.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(y,v,w),x)) hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(x,u,y,v,w)))*.
% 299.64/300.40 28022[0:SpR:15172.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),tc_Com_Opname,y)),v_Procs))*.
% 299.64/300.40 28017[0:SpR:586.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,hAPP(v,v_x)),hAPP(c_COMBB(u,w,x,y),v),tc_Com_Opname,z)),v_Procs))*.
% 299.64/300.40 28016[0:SpR:585.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(u,v_x),v),hAPP(c_COMBC(u,w,x,y),v),tc_Com_Opname,z)),v_Procs))*.
% 299.64/300.40 28010[0:SpR:9936.1,27381.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.40 28006[0:SpR:9935.1,27381.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.40 27971[0:SpR:8415.2,27381.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.40 27965[0:SpR:445.1,27381.0] || -> equal(v_x,u) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),c_Fun_Ofun__upd(v,u,w,x,y),tc_Com_Opname,z)),v_Procs))*.
% 299.64/300.40 28112[7:MRR:28045.0,27297.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_Com_Opname,x)))*.
% 299.64/300.40 28259[0:SpR:8415.2,28056.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,v)))*.
% 299.64/300.40 28325[0:SpR:15172.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,y)),v_Procs))*.
% 299.64/300.40 28320[0:SpR:586.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_COMBB(u,v,w,x),y),hAPP(u,hAPP(y,v_x)),tc_Com_Opname,z)),v_Procs))*.
% 299.64/300.40 28319[0:SpR:585.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_COMBC(u,v,w,x),y),hAPP(hAPP(u,v_x),y),tc_Com_Opname,z)),v_Procs))*.
% 299.64/300.40 28313[0:SpR:9936.1,27441.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.40 28309[0:SpR:9935.1,27441.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.40 28273[0:SpR:8415.2,27441.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.40 28267[0:SpR:445.1,27441.0] || -> equal(v_x,u) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ofun__upd(v,u,w,x,y),hAPP(v,v_x),tc_Com_Opname,z)),v_Procs))*.
% 299.64/300.40 28416[7:MRR:28348.0,27297.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_Com_Opname,x)))*.
% 299.64/300.40 28573[0:SpL:118.0,3952.0] || equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,v_x,w,x,y),y,z,x),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(x1,x2),hAPP(u,w))* -> .
% 299.64/300.40 28435[0:SpR:118.0,10705.0] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(c_Set_Oinsert(w,x),c_Fun_Ocomp(u,c_Fun_Ofun__upd(y,z,v,x1,x2),x2,x3,x1)),z),tc_bool)*.
% 299.64/300.40 28595[0:SpR:177.1,117.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),w)**.
% 299.64/300.40 28658[0:SpR:8415.2,28359.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,v)))*.
% 299.64/300.41 28784[0:SpR:15172.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),tc_Com_Opname,y),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28779[0:SpR:586.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,hAPP(v,v_x)),hAPP(c_COMBB(u,w,x,y),v),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28778[0:SpR:585.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(u,v_x),v),hAPP(c_COMBC(u,w,x,y),v),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28772[0:SpR:9936.1,28031.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28768[0:SpR:9935.1,28031.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28732[0:SpR:8415.2,28031.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28726[0:SpR:445.1,28031.0] || -> equal(v_x,u) equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),c_Fun_Ofun__upd(v,u,w,x,y),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28711[0:SpR:28031.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),v_Procs))*.
% 299.64/300.41 28705[0:SpR:28031.0,353.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))**.
% 299.64/300.41 28684[0:SpR:28031.0,9569.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(w,v_x),w,tc_Com_Opname,x),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.41 28683[0:SpR:28031.0,9568.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w),tc_Com_Opname)),x),v_Procs),tc_bool)*.
% 299.64/300.41 28939[0:SpR:15172.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,y),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28934[0:SpR:586.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_COMBB(u,v,w,x),y),hAPP(u,hAPP(y,v_x)),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28933[0:SpR:585.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_COMBC(u,v,w,x),y),hAPP(hAPP(u,v_x),y),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28927[0:SpR:9936.1,28334.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28923[0:SpR:9935.1,28334.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28887[0:SpR:8415.2,28334.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28881[0:SpR:445.1,28334.0] || -> equal(v_x,u) equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ofun__upd(v,u,w,x,y),hAPP(v,v_x),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28866[0:SpR:28334.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),v_Procs))*.
% 299.64/300.41 28860[0:SpR:28334.0,353.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))**.
% 299.64/300.41 28839[0:SpR:28334.0,9569.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,hAPP(w,v_x),tc_Com_Opname,x),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.41 28838[0:SpR:28334.0,9568.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w),tc_Com_Opname)),x),v_Procs),tc_bool)*.
% 299.64/300.41 29211[0:Obv:29040.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),u)*.
% 299.64/300.41 29223[0:SSi:29161.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.41 29224[0:SSi:29160.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.41 29228[0:SSi:29076.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),u)),v),tc_bool)*.
% 299.64/300.41 29229[0:SSi:29068.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_Set_Oinsert(v_x,tc_Com_Opname))),v_Procs),tc_bool)*.
% 299.64/300.41 29423[7:SpL:27278.1,3484.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_Com_Ocom_OBODY) equal(hAPP(c_Com_Ocom_OBODY,w),v_x)** -> equal(v_x,w).
% 299.64/300.41 29404[7:SpR:27278.1,20881.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,x),hAPP(c_Set_Oinsert(v_x,w),y)),v_x))*.
% 299.64/300.41 29398[7:SpR:27278.1,353.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(w,u),v_x)),hAPP(c_Set_Oinsert(w,u),v_x))**.
% 299.64/300.41 29375[7:SpR:27278.1,9569.0] || equal(hAPP(c_in(u),v),v_x) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Set_Oinsert(v,u)),v_x),tc_bool)*.
% 299.64/300.41 29374[7:SpR:27278.1,9568.0] || equal(hAPP(c_in(u),v),v_x) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Set_Oinsert(v,u)),x),v_x),tc_bool)*.
% 299.64/300.41 29366[7:SpR:27278.1,3346.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(w,x),c_Set_Oinsert(v,u))* -> hBOOL(hAPP(hAPP(c_in(x),w),v_x))*.
% 299.64/300.41 29365[7:SpR:27278.1,21126.1] || equal(hAPP(c_in(u),v),v_x) equal(w,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),tc_Com_Opname,x),w),v_x))*.
% 299.64/300.41 29364[7:SpR:27278.1,3317.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_in(w),c_Set_Oinsert(v,u))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,w),x)))*.
% 299.64/300.41 29363[7:SpR:27278.1,3305.1] || equal(hAPP(c_in(u),v),v_x)** equal(w,c_Set_Oinsert(v,u))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,tc_Com_Opname,x),v_Procs),v_x))*.
% 299.64/300.41 29350[7:SpR:27278.1,21131.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.41 29349[7:SpR:27278.1,21143.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.41 29343[7:SpR:27278.1,15262.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_in(t_a)) -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.41 29340[7:SpR:27278.1,8376.2] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname)) equal(w,v_Procs) -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.41 29338[7:SpR:27278.1,3291.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),v_x),v_Procs))*.
% 299.64/300.41 29337[7:SpR:27278.1,3285.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.41 29333[7:SpR:27278.1,3279.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v,u)) -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.41 29733[0:Obv:29706.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y,u)* -> c_lessequals(x,y,u).
% 299.64/300.41 29736[0:Obv:29585.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w)),u)*.
% 299.64/300.41 29737[0:Obv:29561.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),u)*.
% 299.64/300.41 29950[0:SpL:27043.1,3698.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** equal(u,c_Set_Oinsert(v_Procs,v))* equal(c_Com_Ocom_OBODY,u) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 29922[0:SpR:27043.1,7253.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x))*.
% 299.64/300.41 29887[0:SpR:27043.1,3339.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(u,c_Set_Oinsert(v_Procs,v))* -> equal(c_Fun_Ofun__upd(u,v_x,v_x,w,x),u)**.
% 299.64/300.41 29886[0:SpR:27043.1,3316.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_in(u),c_Set_Oinsert(v_Procs,v))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.41 29883[0:SpR:27043.1,648.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,v),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.41 29879[0:SpR:27043.1,21893.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v)),v_x)**.
% 299.64/300.41 29878[0:SpR:27043.1,28031.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 29876[0:SpR:27043.1,27381.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.41 29873[0:SpR:27043.1,21267.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_Procs,u),v_x,tc_Com_Opname,v)),v_x)**.
% 299.64/300.41 29872[0:SpR:27043.1,28334.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_Procs,u),v_x,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 29870[0:SpR:27043.1,27441.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_Procs,u),v_x,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.41 29869[0:SpR:27043.1,21141.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.41 29867[0:SpR:27043.1,11030.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(v_Procs,u),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.41 29866[0:SpR:27043.1,10090.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.41 29855[2:SpR:27043.1,15483.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_Procs,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.41 29849[0:SpR:27043.1,651.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.41 30343[0:Obv:30068.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w)),u)*.
% 299.64/300.41 30363[0:SSi:30298.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.41 30364[0:SSi:30297.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.41 30367[0:Rew:13749.2,30232.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_HOL_Ouminus__class_Ouminus(v,u))),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.41 30370[0:Rew:30368.2,29124.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),w)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.41 30377[0:SSi:30132.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y)),v),tc_bool)*.
% 299.64/300.41 30378[0:SSi:30122.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),w)),v_Procs),tc_bool)*.
% 299.64/300.41 30504[0:Res:28009.0,255.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)),u))*.
% 299.64/300.41 30516[0:Res:28312.0,255.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)),u))*.
% 299.64/300.41 30905[0:Obv:30867.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y,u)* -> c_lessequals(w,y,u).
% 299.64/300.41 30909[0:Obv:30670.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),u)*.
% 299.64/300.41 30910[0:Obv:30623.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w)),u)*.
% 299.64/300.41 30927[0:Rew:14043.2,30794.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_HOL_Ouminus__class_Ouminus(v,u))),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.41 30930[0:Rew:30928.2,29648.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),w)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.41 30935[0:Rew:525.1,30703.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z))**.
% 299.64/300.41 31093[0:SpR:28771.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_Procs))*.
% 299.64/300.41 31066[0:SpR:28771.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v,w),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.41 31179[0:SpR:28926.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_Procs))*.
% 299.64/300.41 31152[0:SpR:28926.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v,w),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.41 31236[0:SSi:31233.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.41 31289[0:Res:15261.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,t_a),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.64/300.41 31263[0:Res:267.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(c_Set_Oinsert(x,w),y)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.64/300.41 31257[0:Res:8366.1,356.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oimage(c_COMBK(v,w,tc_Com_Opname),tc_Com_Opname,w),u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.64/300.41 31351[0:Res:23961.0,255.0] || c_lessequals(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_Procs),v,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v_x),v)).
% 299.64/300.41 31433[0:MRR:31422.1,9408.1] || equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w),c_Orderings_Otop__class_Otop(tc_bool)) -> c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)),t_a)*.
% 299.64/300.41 31434[0:MRR:31420.1,9408.1] || equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w),c_Orderings_Otop__class_Otop(tc_bool)) -> c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)),t_a)*.
% 299.64/300.41 31507[0:SpL:12944.0,24254.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31501[0:SpL:9.0,24254.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(u,hAPP(v,v_x)),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31500[0:SpL:11473.0,24254.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31481[0:SpL:88.1,24254.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31478[0:SpL:17045.0,24254.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31468[0:SpL:2098.1,24254.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a).
% 299.64/300.41 31457[0:SpL:3586.1,24254.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31456[7:SpL:27278.1,24254.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31443[0:SpL:8498.1,24254.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31511[0:MRR:31474.0,15145.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31538[0:Res:3346.1,473.0] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(w,x,v)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Hilbert__Choice_Oinv__into(v_x,w,x,v),u)),v_x))*.
% 299.64/300.41 31531[0:Res:8366.1,473.0] || equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,tc_Com_Opname),v_x)),w))*.
% 299.64/300.41 31559[0:SSi:31556.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(v,c_Orderings_Obot__class_Obot(tc_bool),tc_fun(u,tc_bool))* -> c_lessequals(v,v_x,tc_fun(u,tc_bool)).
% 299.64/300.41 31681[0:SSi:31658.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs))),v_x))*.
% 299.64/300.41 31727[0:SSi:31700.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w))),v_x))*.
% 299.64/300.41 31846[7:SpL:584.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_COMBS(u,v,w,x,y),v_x)** -> .
% 299.64/300.41 31815[7:SpL:540.1,31778.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> .
% 299.64/300.41 31814[7:SpL:539.1,31778.0] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> .
% 299.64/300.41 31813[7:SpL:297.2,31778.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)** -> .
% 299.64/300.41 31804[7:SpL:299.2,31778.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)** -> .
% 299.64/300.41 31792[7:SpL:25.1,31778.0] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_x) -> .
% 299.64/300.41 31946[7:MRR:31878.2,27297.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))** equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_x)** -> .
% 299.64/300.41 32018[0:SpL:383.1,16339.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(v,v_x,u,w,x),y,z,w,x),v_Procs)** -> equal(v_x,y).
% 299.64/300.41 32016[0:SpL:383.1,3340.0] || equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v_x,v,w,x),y,z,w,x),x1)* -> equal(v_x,y) equal(hAPP(x1,v_x),v)*.
% 299.64/300.41 32015[0:SpL:383.1,3732.0] || equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v_x,v,w,x),y,z,w,x),c_in(tc_Com_Opname))** -> equal(v_x,y) hBOOL(hAPP(v,v_Procs)).
% 299.64/300.41 31973[0:SpR:383.1,28065.0] || -> equal(v_x,u) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_Fun_Ofun__upd(c_Fun_Ofun__upd(w,v_x,v,x,y),u,z,x,y),tc_Com_Opname,x1)))*.
% 299.64/300.41 31971[0:SpR:383.1,28368.0] || -> equal(v_x,u) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ofun__upd(c_Fun_Ofun__upd(v,v_x,w,x,y),u,z,x,y),w,tc_Com_Opname,x1)))*.
% 299.64/300.41 31970[0:SpR:383.1,1166.0] || -> equal(v_x,u) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(c_Fun_Ofun__upd(v,v_x,w,x,y),u,z,x,y),tc_Com_Opname,x1),v_Procs),w))*.
% 299.64/300.41 32081[7:SpL:383.1,31899.1] || equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(v,v_x,u,w,x),y,z,w,x),v_x)** -> equal(y,v_x).
% 299.64/300.41 32176[0:SpR:21893.0,31323.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v_Procs,v_x),v_Procs,tc_Com_Opname,u)),hAPP(v_Procs,v_x),tc_bool)*.
% 299.64/300.41 32175[0:SpR:21267.0,31323.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_Procs,hAPP(v_Procs,v_x),tc_Com_Opname,u)),hAPP(v_Procs,v_x),tc_bool)*.
% 299.64/300.41 32251[0:SSi:32225.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))),v_x))*.
% 299.64/300.41 32665[0:Res:31533.0,255.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))),u))*.
% 299.64/300.41 32659[0:SpR:12944.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),tc_Com_Opname,y),c_Orderings_Otop__class_Otop(tc_bool))),v_Procs))*.
% 299.64/300.41 32653[0:SpR:9.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname,z),hAPP(u,hAPP(v,v_x)))),v_Procs))*.
% 299.64/300.41 32652[0:SpR:11473.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_Com_Opname,w),c_Orderings_Otop__class_Otop(tc_bool))),v_Procs))*.
% 299.64/300.41 32633[0:SpR:88.1,31533.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u))),v_Procs))*.
% 299.64/300.41 32630[0:SpR:17045.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),tc_Com_Opname,x),c_Orderings_Obot__class_Obot(tc_bool))),v_Procs))*.
% 299.64/300.41 32620[0:SpR:2098.1,31533.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,v),v_x)),v_Procs))*.
% 299.64/300.41 32609[0:SpR:3586.1,31533.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x)),v_Procs))*.
% 299.64/300.41 32608[7:SpR:27278.1,31533.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x)),v_Procs))*.
% 299.64/300.41 32595[0:SpR:8498.1,31533.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x)),v_Procs))*.
% 299.64/300.41 32723[0:SpR:329.1,32669.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),v_x)))*.
% 299.64/300.41 32722[0:SpR:328.1,32669.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),u)))*.
% 299.64/300.41 32719[0:SpR:538.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))))*.
% 299.64/300.41 32823[0:MRR:32765.0,420.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)) -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),w)**.
% 299.64/300.41 33164[0:SSi:33132.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),v,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),w),v_x))*.
% 299.64/300.41 33165[0:SSi:33129.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),v,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v),v_x))*.
% 299.64/300.41 33315[0:SpR:12944.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),tc_Com_Opname,y),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33309[0:SpR:9.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname,z),hAPP(u,hAPP(v,v_x))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33308[0:SpR:11473.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_Com_Opname,w),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33289[0:SpR:88.1,32668.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33286[0:SpR:17045.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),tc_Com_Opname,x),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33276[0:SpR:2098.1,32668.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,v),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33265[0:SpR:3586.1,32668.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33264[7:SpR:27278.1,32668.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33251[0:SpR:8498.1,32668.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33235[0:SpR:32668.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_Procs))*.
% 299.64/300.41 33207[0:SpR:32668.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),w,x),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.41 33397[0:Res:678.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(tc_Com_Opname),v_x),t_a) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v)),u))* c_Hoare__Mirabelle_Otriple__valid(v,v_Procs,t_a).
% 299.64/300.41 33485[7:SpL:1259.2,27247.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ozero__class_Ozero(u),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v_x)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.64/300.41 33601[0:SpR:12944.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)),tc_Com_Opname,z)))*.
% 299.64/300.41 33595[0:SpR:9.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,hAPP(w,v_x)),c_Fun_Ocomp(v,w,x,y,z),tc_Com_Opname,x1)))*.
% 299.64/300.41 33594[0:SpR:11473.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_Com_Opname,x)))*.
% 299.64/300.41 33575[0:SpR:88.1,28704.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,w)))*.
% 299.64/300.41 33572[0:SpR:17045.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)),tc_Com_Opname,y)))*.
% 299.64/300.41 33562[0:SpR:2098.1,28704.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,w)))*.
% 299.64/300.41 33551[0:SpR:3586.1,28704.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v,u),tc_Com_Opname,x)))*.
% 299.64/300.41 33550[7:SpR:27278.1,28704.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v,u),tc_Com_Opname,x)))*.
% 299.64/300.41 33537[0:SpR:8498.1,28704.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(w,u),tc_Com_Opname,x)))*.
% 299.64/300.41 33692[0:SpR:12944.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,z)))*.
% 299.64/300.41 33686[0:SpR:9.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ocomp(v,w,x,y,z),hAPP(v,hAPP(w,v_x)),tc_Com_Opname,x1)))*.
% 299.64/300.41 33685[0:SpR:11473.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x)))*.
% 299.64/300.41 33666[0:SpR:88.1,28859.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,w)))*.
% 299.64/300.41 33663[0:SpR:17045.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,y)))*.
% 299.64/300.41 33653[0:SpR:2098.1,28859.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),v_x,tc_Com_Opname,w)))*.
% 299.64/300.41 33642[0:SpR:3586.1,28859.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),v_x,tc_Com_Opname,x)))*.
% 299.64/300.41 33641[7:SpR:27278.1,28859.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),v_x,tc_Com_Opname,x)))*.
% 299.64/300.41 33628[0:SpR:8498.1,28859.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(w,u),v_x,tc_Com_Opname,x)))*.
% 299.64/300.41 33777[7:SpL:9.0,31886.1] || equal(u,c_Fun_Ocomp(v,w,x,y,z))* equal(hAPP(v,hAPP(w,v_x)),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_x) -> .
% 299.64/300.41 33757[7:SpL:88.1,31886.1] class_Lattices_Oboolean__algebra(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(v,v_x) -> .
% 299.64/300.41 33899[0:SpL:118.0,24636.0] || equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,v_x,w,x,y),y,z,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(u,w),v_x),v_x).
% 299.64/300.41 34293[0:SpL:24914.0,527.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,w),hAPP(c_in(u),v_x))))*.
% 299.64/300.41 34241[0:SpR:11177.1,24914.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),v_x)),v_x)**.
% 299.64/300.41 34205[0:SpR:3586.1,24914.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x)),v_x)**.
% 299.64/300.41 34204[7:SpR:27278.1,24914.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x)),v_x)**.
% 299.64/300.41 34197[0:SpR:365.1,24914.0] class_Orderings_Obot(u) || -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,v),c_Orderings_Obot__class_Obot(u))),c_Orderings_Obot__class_Obot(u))**.
% 299.64/300.41 34196[0:SpR:397.1,24914.0] class_Orderings_Otop(u) || -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u))),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.41 34191[0:SpR:8498.1,24914.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x)),v_x)**.
% 299.64/300.41 33975[0:SpR:24914.0,526.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(v),tc_Com_Opname,w),hAPP(c_in(v),v_x))))* -> hBOOL(hAPP(hAPP(c_in(v),v_x),u)).
% 299.64/300.41 33912[0:SpR:24914.0,376.0] || -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),hAPP(c_Set_Oinsert(u,v),v_x),tc_fun(v,tc_bool))*.
% 299.64/300.41 34449[0:Rew:25660.1,34402.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),c_Orderings_Obot__class_Obot(tc_bool)) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),v_x),u)**.
% 299.64/300.41 34761[0:SpL:34428.0,3489.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_in(tc_Com_Opname))** hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)))) -> .
% 299.64/300.41 34711[0:SpR:34428.0,3294.1] || equal(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_in(t_a))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.41 34820[0:Res:27383.0,255.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y)),u))*.
% 299.64/300.41 34830[0:Res:27443.0,255.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y)),u))*.
% 299.64/300.41 34910[0:SpR:12944.0,28053.1] || equal(u,hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),u,tc_Com_Opname,z)))*.
% 299.64/300.41 34904[0:SpR:9.0,28053.1] || equal(u,c_Fun_Ocomp(v,w,x,y,z))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,hAPP(w,v_x)),u,tc_Com_Opname,x1)))*.
% 299.64/300.41 34903[0:SpR:11473.0,28053.1] || equal(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),u,tc_Com_Opname,x)))*.
% 299.64/300.41 34884[0:SpR:88.1,28053.1] class_Lattices_Oboolean__algebra(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),v,tc_Com_Opname,w)))*.
% 299.64/300.41 34881[0:SpR:17045.0,28053.1] || equal(u,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),u,tc_Com_Opname,y)))*.
% 299.64/300.41 34871[0:SpR:2098.1,28053.1] || equal(u,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,v_x),tc_Hoare__Mirabelle_Otriple(t_a)))* -> c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,w)))*.
% 299.64/300.41 34859[0:SpR:3586.1,28053.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(w,c_Set_Oinsert(v,u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,w,tc_Com_Opname,x)))*.
% 299.64/300.41 34858[7:SpR:27278.1,28053.1] || equal(hAPP(c_in(u),v),v_x)** equal(w,c_Set_Oinsert(v,u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,w,tc_Com_Opname,x)))*.
% 299.64/300.41 34845[0:SpR:8498.1,28053.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(v,c_Set_Oinsert(w,u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v,tc_Com_Opname,x)))*.
% 299.64/300.41 34989[0:SpR:12944.0,28356.1] || equal(u,hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,z)))*.
% 299.64/300.41 34983[0:SpR:9.0,28356.1] || equal(u,c_Fun_Ocomp(v,w,x,y,z))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(v,hAPP(w,v_x)),tc_Com_Opname,x1)))*.
% 299.64/300.41 34982[0:SpR:11473.0,28356.1] || equal(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x)))*.
% 299.64/300.41 34963[0:SpR:88.1,28356.1] class_Lattices_Oboolean__algebra(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,c_Orderings_Otop__class_Otop(u),tc_Com_Opname,w)))*.
% 299.64/300.41 34960[0:SpR:17045.0,28356.1] || equal(u,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,y)))*.
% 299.64/300.41 34950[0:SpR:2098.1,28356.1] || equal(u,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,v_x),tc_Hoare__Mirabelle_Otriple(t_a)))* -> c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,w)))*.
% 299.64/300.41 34938[0:SpR:3586.1,28356.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(w,c_Set_Oinsert(v,u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,v_x,tc_Com_Opname,x)))*.
% 299.64/300.41 34937[7:SpR:27278.1,28356.1] || equal(hAPP(c_in(u),v),v_x)** equal(w,c_Set_Oinsert(v,u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,v_x,tc_Com_Opname,x)))*.
% 299.64/300.41 34924[0:SpR:8498.1,28356.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(v,c_Set_Oinsert(w,u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,v_x,tc_Com_Opname,x)))*.
% 299.64/300.41 35051[0:SpR:28755.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),y,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),v_Procs))*.
% 299.64/300.41 35023[0:SpR:28755.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),y,z),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.41 35140[0:SpR:28910.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),y,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),v_Procs))*.
% 299.64/300.41 35112[0:SpR:28910.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),y,z),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.41 35185[0:SpR:410.0,341.0] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(y,w),u),v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.41 35480[0:SpR:113.0,115.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),x),v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))),v)*.
% 299.64/300.41 35646[0:Rew:586.0,35643.1] || c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),w,v,tc_fun(x,tc_bool)),x)* -> c_Finite__Set_Ofinite(hAPP(w,hAPP(u,v_x)),x).
% 299.64/300.41 35681[0:SpR:338.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(x,u),y))),x))*.
% 299.64/300.41 35675[0:SpR:317.0,26119.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oinsert(y,x),z))),hAPP(w,y)))*.
% 299.64/300.41 36697[0:SpR:55.1,36605.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),v),u,tc_fun(t_a,tc_bool)),tc_Com_Opname,tc_bool))*.
% 299.64/300.41 36781[0:Rew:11.0,36750.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Oinsert(u,v),w),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.64/300.41 36892[7:SpL:66.0,27293.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),v_x)** -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),v_x)).
% 299.64/300.41 36891[0:SpL:66.0,4964.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),v_Procs)** -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),v_x)).
% 299.64/300.41 36846[0:SpR:66.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),y),hAPP(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),y),tc_bool)*.
% 299.64/300.41 37564[0:SpR:9935.1,36690.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Set_Oinsert(v_x,t_a))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,tc_bool))*.
% 299.64/300.41 38233[0:MRR:38202.0,420.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(x,v,tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.41 38324[0:SSi:38287.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),u),v)) c_Finite__Set_Ofinite(v,tc_bool) -> c_lessequals(u,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,tc_bool,tc_bool),tc_bool)*.
% 299.64/300.41 38867[7:MRR:38684.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),x))*.
% 299.64/300.41 38938[7:MRR:38873.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),x,t_a)*.
% 299.64/300.41 40164[4:Res:38631.1,449.0] || c_lessequals(v_x,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w),tc_bool) -> c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)),t_a)*.
% 299.64/300.41 40175[4:SSi:40137.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v)))*.
% 299.64/300.41 40260[4:Res:38632.1,449.0] || c_lessequals(v_x,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w),tc_bool) -> c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)),t_a)*.
% 299.64/300.41 40270[4:SSi:40235.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)))*.
% 299.64/300.41 40285[0:Res:13387.1,398.0] || equal(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> c_lessequals(v,w,tc_fun(u,tc_bool))*.
% 299.64/300.41 40284[0:Res:13385.1,398.0] || equal(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** -> c_lessequals(w,v,tc_fun(u,tc_bool))*.
% 299.64/300.41 40847[4:SSi:40778.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(w,v,tc_bool)* c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),tc_bool)* -> hBOOL(v).
% 299.64/300.41 41140[4:SSi:41039.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(w,v,tc_bool)* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(v).
% 299.64/300.41 41402[0:Res:678.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_in(tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.64/300.41 41504[4:SpR:584.0,38236.1] || equal(c_COMBS(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_Com_Opname,tc_bool))*.
% 299.64/300.41 41472[4:SpR:540.1,38236.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_Com_Opname,tc_bool))*.
% 299.64/300.41 41471[4:SpR:539.1,38236.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_Com_Opname,tc_bool))*.
% 299.64/300.41 41461[4:SpR:299.2,38236.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,tc_bool))*.
% 299.64/300.41 41448[4:SpR:25.1,38236.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_Com_Opname,tc_bool))*.
% 299.64/300.41 41746[0:Res:499.0,494.1] || hBOOL(hAPP(hAPP(u,v),w))* c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,x),w,c_HOL_Ozero__class_Ozero(tc_nat),y)* -> hBOOL(hAPP(hAPP(z,v),y))*.
% 299.64/300.41 42193[0:SSi:42141.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),w),v_x),tc_bool),u),tc_bool,tc_bool))*.
% 299.64/300.41 42194[0:SSi:42137.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) equal(c_Orderings_Otop__class_Otop(tc_bool),v) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,hAPP(c_Set_Oinsert(v,tc_bool),u),tc_bool,tc_bool),v)**.
% 299.64/300.41 42291[4:SpL:8415.2,40680.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(u)*.
% 299.64/300.41 42306[4:SpL:8415.2,38697.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.41 42319[4:SpL:8415.2,38886.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.41 42554[4:SpR:8415.2,40590.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.41 42551[4:SpR:8415.2,40590.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),w))*.
% 299.64/300.41 42790[4:SpR:8415.2,40591.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v))*.
% 299.64/300.41 42787[4:SpR:8415.2,40591.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),w))*.
% 299.64/300.41 42837[4:SpR:8415.2,40601.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(v_x,u),v,w),tc_Com_Opname,tc_bool))*.
% 299.64/300.41 43148[4:SpR:8415.2,42609.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.41 43145[4:SpR:8415.2,42609.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),w,t_a)*.
% 299.64/300.41 43191[4:SpR:8415.2,42829.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v,t_a)*.
% 299.64/300.41 43188[4:SpR:8415.2,42829.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),w,t_a)*.
% 299.64/300.41 43364[4:SpL:8415.2,42582.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(v_x,u,tc_fun(v,tc_bool))* -> hBOOL(hAPP(u,w))*.
% 299.64/300.41 43600[4:SpL:8415.2,43176.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(v_x,u,tc_fun(v,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(u,w,t_a)*.
% 299.64/300.41 43868[0:SpR:584.0,38131.1] || hBOOL(hAPP(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(w,x),u,y,z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v)))*.
% 299.64/300.41 44025[4:SpL:383.1,38706.0] || equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v_x,v,w,x),y,z,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(y,v_x) hBOOL(hAPP(v,x1))*.
% 299.64/300.41 44036[4:SpL:383.1,38895.0] || equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v_x,v,w,x),y,z,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(y,v_x) c_Hoare__Mirabelle_Ohoare__valids(v,x1,t_a)*.
% 299.64/300.41 44634[0:SpR:533.0,35656.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),u)),v_x))*.
% 299.64/300.41 44627[0:SpR:542.0,35656.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_x))*.
% 299.64/300.41 44748[0:SpR:532.0,36599.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),w)),x)),v_x))*.
% 299.64/300.41 45190[0:SpR:533.0,36600.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(v_x,t_a),x))),v_x))*.
% 299.64/300.41 45462[0:Res:45357.1,3863.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname)))*.
% 299.64/300.41 45478[0:Rew:586.0,45439.0] || hBOOL(hAPP(u,hAPP(v,v_x))) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_COMBB(u,w,x,y),v),tc_Com_Opname))))*.
% 299.64/300.41 45479[0:Rew:585.0,45438.0] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_COMBC(u,w,x,y),v),tc_Com_Opname)),v))*.
% 299.64/300.41 45707[0:SpR:532.0,44625.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),w)),v_x))*.
% 299.64/300.41 45986[0:Res:8369.1,45899.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),tc_Com_Opname)),v))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),v_x)).
% 299.64/300.41 46002[0:Rew:586.0,45954.1] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_COMBB(u,w,x,y),v),tc_Com_Opname))))* -> hBOOL(hAPP(u,hAPP(v,v_x))).
% 299.64/300.41 46003[0:Rew:585.0,45953.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_COMBC(u,v,w,x),y),tc_Com_Opname)),y))* -> hBOOL(hAPP(hAPP(u,v_x),y)).
% 299.64/300.41 46672[4:SpL:15172.0,46565.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.41 46667[4:SpL:586.0,46565.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)),hAPP(u,hAPP(y,v_x)))* -> .
% 299.64/300.41 46666[4:SpL:585.0,46565.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)),hAPP(hAPP(u,v_x),y))* -> .
% 299.64/300.41 46660[4:SpL:9936.1,46565.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.41 46656[4:SpL:9935.1,46565.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.41 46609[4:SpL:445.1,46565.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)),hAPP(u,v_x))* -> equal(v_x,v).
% 299.64/300.41 46817[0:SSi:46745.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(tc_Com_Opname,tc_bool))* equal(u,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),w),v_x))*.
% 299.64/300.41 46818[0:SSi:46742.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(tc_Com_Opname,tc_bool))* equal(u,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v),v_x))*.
% 299.64/300.41 46911[0:SSi:46884.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),v_x))*.
% 299.64/300.41 46912[0:SSi:46881.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v),v_x))*.
% 299.64/300.41 47287[4:SpR:8415.2,47138.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,tc_bool)))*.
% 299.64/300.41 47420[4:SpR:8415.2,47319.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,tc_bool)),u))*.
% 299.64/300.41 47464[4:SpR:8415.2,47458.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,tc_bool)),u,t_a)*.
% 299.64/300.41 47468[4:SpL:8415.2,47318.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,tc_bool),u,tc_bool)* -> hBOOL(u).
% 299.64/300.41 48165[4:SpR:12944.0,39023.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,z),c_Orderings_Otop__class_Otop(tc_bool)),x1))*.
% 299.64/300.41 48159[4:SpR:9.0,39023.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(u,hAPP(v,v_x))),x2))*.
% 299.64/300.41 48158[4:SpR:11473.0,39023.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),c_Orderings_Otop__class_Otop(tc_bool)),y))*.
% 299.64/300.41 48138[4:SpR:88.1,39023.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(u)),x))*.
% 299.64/300.41 48135[4:SpR:17045.0,39023.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_bool)),z))*.
% 299.64/300.41 48125[4:SpR:2098.1,39023.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),x))*.
% 299.64/300.41 48113[4:SpR:3586.1,39023.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),v_x),y))*.
% 299.64/300.41 48112[7:SpR:27278.1,39023.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),v_x),y))*.
% 299.64/300.41 48099[4:SpR:8498.1,39023.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),v_x),y))*.
% 299.64/300.41 48280[4:SpR:12944.0,39064.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(y,z),c_Orderings_Otop__class_Otop(tc_bool)),x1,t_a)*.
% 299.64/300.41 48274[4:SpR:9.0,39064.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(z,x1),hAPP(u,hAPP(v,v_x))),x2,t_a)*.
% 299.64/300.41 48273[4:SpR:11473.0,39064.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),c_Orderings_Otop__class_Otop(tc_bool)),y,t_a)*.
% 299.64/300.41 48253[4:SpR:88.1,39064.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(u)),x,t_a)*.
% 299.64/300.41 48250[4:SpR:17045.0,39064.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_bool)),z,t_a)*.
% 299.64/300.41 48240[4:SpR:2098.1,39064.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),v_x),x,t_a)*.
% 299.64/300.41 48228[4:SpR:3586.1,39064.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),v_x),y,t_a)*.
% 299.64/300.41 48227[7:SpR:27278.1,39064.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),v_x),y,t_a)*.
% 299.64/300.41 48214[4:SpR:8498.1,39064.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),v_x),y,t_a)*.
% 299.64/300.41 48724[4:SpR:338.0,42357.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(y,tc_bool)),v_x))*.
% 299.64/300.41 48992[0:Con:48976.3] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.64/300.41 49086[0:SpR:49017.1,20881.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,v),x)),v_Procs))*.
% 299.64/300.41 49080[0:SpR:49017.1,353.0] || -> hBOOL(hAPP(u,v_x)) equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))**.
% 299.64/300.41 49057[0:SpR:49017.1,9569.0] || -> hBOOL(hAPP(u,v_x)) c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.41 49056[0:SpR:49017.1,9568.0] || -> hBOOL(hAPP(u,v_x)) c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname)),w),v_Procs),tc_bool)*.
% 299.64/300.41 49053[0:SpR:49017.1,415.0] || -> hBOOL(hAPP(u,v_x)) equal(c_Fun_Ofun__upd(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v_Procs,v_Procs,v,w),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname))**.
% 299.64/300.41 49339[0:Res:49314.1,255.0] || hBOOL(hAPP(u,v_x)) c_lessequals(v_Procs,v,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)),v))*.
% 299.64/300.41 49404[0:SpR:49342.1,7253.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_Procs))*.
% 299.64/300.41 49375[0:SpR:49342.1,21130.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.41 50424[0:SpR:223.1,423.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),y))*.
% 299.64/300.41 51372[0:SpR:9.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(u,hAPP(v,v_x)),hAPP(hAPP(c_Set_Oinsert(w,t_a),c_Fun_Ocomp(u,v,x,y,z)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 51351[0:SpR:88.1,51231.0] class_Lattices_Oboolean__algebra(u) || -> equal(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 51337[0:SpR:2098.1,51231.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(v,t_a),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 51325[0:SpR:3586.1,51231.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(w,t_a),c_Set_Oinsert(v,u)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 51324[7:SpR:27278.1,51231.0] || equal(hAPP(c_in(u),v),v_x) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(w,t_a),c_Set_Oinsert(v,u)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 51310[0:SpR:8498.1,51231.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(v,t_a),c_Set_Oinsert(w,u)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 51452[7:Rew:9.0,51445.1] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),z)),v_x)** -> hBOOL(hAPP(z,hAPP(x,hAPP(u,v_x)))).
% 299.64/300.41 51461[0:SpR:118.0,32700.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,v_x,w,x,y),y,z,x),tc_Com_Opname,x1),hAPP(u,w))))*.
% 299.64/300.41 51860[4:Res:40792.1,45899.0] || c_lessequals(v_x,hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Set_Oinsert(v,w),u),tc_Com_Opname)),tc_bool)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x)).
% 299.64/300.41 51975[0:Rew:10463.0,51929.1,10463.0,51929.1] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w,x),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(c_List_Ofoldl(y,c_Orderings_Obot__class_Obot(tc_bool),z,x,x1),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 51976[0:Rew:9911.0,51928.1,9911.0,51928.1] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w,x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_List_Ofoldl(y,c_Orderings_Otop__class_Otop(tc_bool),z,x,x1),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.41 52244[7:Rew:9.0,52241.1] || equal(c_Fun_Ocomp(c_Fun_Ocomp(u,v,w,x,y),z,y,x,x1),v_x)** -> hBOOL(hAPP(u,hAPP(v,hAPP(z,v_x)))).
% 299.64/300.41 52245[7:Rew:9.0,52240.1] || equal(c_Fun_Ocomp(u,c_Fun_Ocomp(v,w,x,y,z),y,x1,z),v_x)** -> hBOOL(hAPP(u,hAPP(v,hAPP(w,v_x)))).
% 299.64/300.41 52271[0:SpL:338.0,35720.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),y,tc_fun(u,tc_bool))* -> hBOOL(hAPP(y,w)).
% 299.64/300.41 52268[0:SpL:317.0,35720.0] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),z,tc_fun(w,tc_bool))* -> hBOOL(hAPP(z,hAPP(u,x))).
% 299.64/300.41 52352[0:SSi:52321.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y),u))*.
% 299.64/300.41 52353[0:SSi:52318.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x),u))*.
% 299.64/300.41 52708[2:SSi:52700.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.41 52709[2:SSi:52699.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.41 52788[0:SpR:24019.2,24914.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(v_x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_x,tc_Com_Opname,u),v_x)),v_x)**.
% 299.64/300.41 53010[0:Res:23739.1,278.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,v,u,w)))*.
% 299.64/300.41 53009[0:Res:23739.1,277.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,v_x,u,w)))*.
% 299.64/300.41 52996[0:Res:23739.1,170.1] class_Orderings_Olinorder(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_x,u),v_Procs,u)*.
% 299.64/300.41 52995[0:Res:23739.1,169.1] class_Orderings_Olinorder(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(v_Procs,c_Finite__Set_Olinorder__class_OMax(v_x,u),u)*.
% 299.64/300.41 53053[0:SpR:23955.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w)),v_x,tc_bool)*.
% 299.64/300.41 53031[0:SpR:23955.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),v_x,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))**.
% 299.64/300.41 53185[0:SpR:23958.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w)),v_x,tc_bool)*.
% 299.64/300.41 53163[0:SpR:23958.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))**.
% 299.64/300.41 53371[0:Res:31543.0,278.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,u,tc_Com_Opname)))*.
% 299.64/300.41 53370[0:Res:31543.0,277.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.41 53363[0:Res:31543.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname)*.
% 299.64/300.41 53362[0:Res:31543.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.41 53443[0:SpR:33303.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v,tc_fun(w,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.41 53785[0:Res:7226.0,278.1] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(c_Option_Othe(w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),z,u,y)))*.
% 299.64/300.41 53784[0:Res:7226.0,277.1] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oimage(c_Option_Othe(x),y,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u,z)))*.
% 299.64/300.41 53780[0:Res:7226.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oimage(c_Option_Othe(v),w,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,x,t_a)*.
% 299.64/300.41 54157[0:SpL:52997.1,16217.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(v_Procs,u),v_Procs)** -> .
% 299.64/300.41 54156[7:SpL:52997.1,31778.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oinsert(v_Procs,u),v_x)** -> .
% 299.64/300.41 54131[0:SpR:52997.1,9567.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_Procs,u),v,tc_fun(w,tc_bool)),v_x),v_x,tc_bool)*.
% 299.64/300.41 54080[0:SpR:52997.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_Procs,v),tc_Com_Opname,u),u)*.
% 299.64/300.41 54072[0:SpR:52997.1,23902.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.41 54743[0:SpR:13749.2,9567.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.41 54717[0:SpR:13749.2,415.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(u),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.64/300.41 55217[0:SpR:14043.2,9567.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.41 55191[0:SpR:14043.2,415.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(u),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.64/300.41 55513[0:SpR:540.1,54593.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool)*.
% 299.64/300.41 55512[0:SpR:539.1,54593.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool)*.
% 299.64/300.41 55633[0:Rew:181.1,55515.0] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),w),v_x))* c_lessequals(x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_bool)*.
% 299.64/300.41 56020[0:SpL:586.0,55174.1] || equal(u,hAPP(c_COMBB(v,w,x,y),z))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(v,hAPP(z,v_x)))* -> .
% 299.64/300.41 56019[0:SpL:585.0,55174.1] || equal(u,hAPP(c_COMBC(v,w,x,y),z))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(hAPP(v,v_x),z))* -> .
% 299.64/300.41 55960[0:SpL:445.1,55174.1] || equal(u,c_Fun_Ofun__upd(v,w,x,y,z))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(v,v_x))* -> equal(v_x,w).
% 299.64/300.41 55938[0:SpL:586.0,55174.1] || equal(hAPP(c_COMBB(u,v,w,x),y),z)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(y,v_x)),tc_bool),hAPP(z,v_x))* -> .
% 299.64/300.41 55937[0:SpL:585.0,55174.1] || equal(hAPP(c_COMBC(u,v,w,x),y),z)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),y),tc_bool),hAPP(z,v_x))* -> .
% 299.64/300.41 55877[0:SpL:445.1,55174.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),z)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(z,v_x))* -> equal(v_x,v).
% 299.64/300.41 56333[0:SpL:30368.2,16217.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> .
% 299.64/300.41 56332[7:SpL:30368.2,31778.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> .
% 299.64/300.41 56331[0:SpL:30368.2,3929.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.41 56221[0:SpR:30368.2,9567.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(w,tc_bool)),x),c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.41 56171[0:SpR:30368.2,683.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),v)*.
% 299.64/300.41 56167[4:SpR:30368.2,38236.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(u),tc_Com_Opname,tc_bool))*.
% 299.64/300.41 56162[0:SpR:30368.2,23902.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.41 56775[0:SpL:30928.2,16217.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> .
% 299.64/300.41 56774[7:SpL:30928.2,31778.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> .
% 299.64/300.41 56773[0:SpL:30928.2,3929.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.41 56663[0:SpR:30928.2,9567.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(w,tc_bool)),x),c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.41 56612[0:SpR:30928.2,683.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),v)*.
% 299.64/300.41 56608[4:SpR:30928.2,38236.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(u),tc_Com_Opname,tc_bool))*.
% 299.64/300.41 56603[0:SpR:30928.2,23902.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.41 57808[0:SSi:57774.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_bool)* -> equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v).
% 299.64/300.41 57971[0:SpL:12944.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(c_Set_Oinsert(x,y),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),z,x1)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> .
% 299.64/300.41 57965[0:SpL:9.0,55910.1] || equal(c_COMBK(u,v,w),c_Fun_Ocomp(x,y,z,x1,x2))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(x,hAPP(y,v_x))) -> .
% 299.64/300.41 57964[0:SpL:11473.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> .
% 299.64/300.41 57944[0:SpL:88.1,55910.1] class_Lattices_Oboolean__algebra(u) || equal(c_COMBK(v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_Orderings_Otop__class_Otop(u)) -> .
% 299.64/300.41 57940[0:SpL:17045.0,55910.1] || equal(c_COMBK(u,v,w),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y,tc_fun(z,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) -> .
% 299.64/300.41 57930[0:SpL:2098.1,55910.1] || equal(c_COMBK(u,v,w),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,v_x),tc_Hoare__Mirabelle_Otriple(t_a)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(x,v_x,t_a).
% 299.64/300.41 57915[0:SpL:3586.1,55910.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_COMBK(w,x,y),c_Set_Oinsert(v,u))* equal(c_HOL_Ouminus__class_Ouminus(w,tc_bool),v_x) -> .
% 299.64/300.41 57914[7:SpL:27278.1,55910.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_COMBK(w,x,y),c_Set_Oinsert(v,u))* equal(c_HOL_Ouminus__class_Ouminus(w,tc_bool),v_x) -> .
% 299.64/300.41 57900[0:SpL:8498.1,55910.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_COMBK(v,w,x),c_Set_Oinsert(y,u))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),v_x) -> .
% 299.64/300.41 58122[0:SpL:9.0,55992.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_COMBK(z,x1,x2))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),z)* -> .
% 299.64/300.41 58101[0:SpL:88.1,55992.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v) -> .
% 299.64/300.41 58087[0:SpL:2098.1,55992.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v) -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a).
% 299.64/300.41 58072[0:SpL:3586.1,55992.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w) -> .
% 299.64/300.41 58071[7:SpL:27278.1,55992.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w) -> .
% 299.64/300.41 58057[0:SpL:8498.1,55992.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w) -> .
% 299.64/300.41 58258[7:MRR:58162.1,27297.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool),w,x),c_Set_Oimage(c_COMBK(u,v,y),y,v))* -> .
% 299.64/300.41 58390[0:Res:5887.1,5005.2] class_Lattices_Oupper__semilattice(u) class_Orderings_Otop(u) class_Orderings_Oorder(u) || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.41 58389[0:Res:5888.1,5005.2] class_Lattices_Olattice(u) class_Orderings_Otop(u) class_Orderings_Oorder(u) || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.41 58507[0:SpL:52997.1,58248.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_COMBK(v_x,u,v),c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_Procs,w),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.41 58502[0:SpL:584.0,58248.0] || equal(c_COMBK(hAPP(hAPP(u,v_x),hAPP(v,v_x)),w,x),c_HOL_Ouminus__class_Ouminus(c_COMBS(u,v,y,z,x1),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.41 58482[0:SpL:337.0,58248.0] || equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.41 58469[0:SpL:540.1,58248.0] class_Lattices_Olattice(u) || equal(c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),w,x),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)))** -> .
% 299.64/300.41 58468[0:SpL:539.1,58248.0] class_Lattices_Oupper__semilattice(u) || equal(c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),w,x),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)))** -> .
% 299.64/300.41 58467[0:SpL:297.2,58248.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(c_COMBK(v_x,w,x),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.41 58460[0:SpL:30368.2,58248.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_COMBK(c_Orderings_Otop__class_Otop(u),v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.41 58459[0:SpL:30928.2,58248.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_COMBK(c_Orderings_Otop__class_Otop(u),v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.41 58456[0:SpL:299.2,58248.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_COMBK(v,w,x),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.41 58450[0:SpL:24019.2,58248.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_COMBK(v_x,u,v),c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.41 58441[0:SpL:25.1,58248.0] class_HOL_Ouminus(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),w,x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.41 58534[0:SpL:8415.2,58177.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v,w),v_x)** -> .
% 299.64/300.41 58601[0:Res:10771.1,19641.0] || hBOOL(hAPP(hAPP(c_in(u),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Set_Oinsert(v,u),w),x)),w))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,u),w),x,t_a).
% 299.64/300.41 58648[0:SpL:383.1,58188.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v,w),c_Fun_Ofun__upd(c_Fun_Ofun__upd(x,v_x,u,y,z),x1,x2,y,z))* -> equal(x1,v_x).
% 299.64/300.41 58640[0:SpL:2771.1,58188.0] || equal(u,v) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),w,x),c_Fun_Ofun__upd(y,v_x,hAPP(v,v_x),z,x1))* -> .
% 299.64/300.41 58659[0:SpL:383.1,58637.0] || equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),u,v),c_Fun_Ofun__upd(c_Fun_Ofun__upd(w,v_x,c_Orderings_Obot__class_Obot(tc_bool),x,y),z,x1,x,y))* -> equal(z,v_x).
% 299.64/300.41 58664[0:SpL:383.1,58638.0] || equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),c_Fun_Ofun__upd(c_Fun_Ofun__upd(w,v_x,c_Orderings_Otop__class_Otop(tc_bool),x,y),z,x1,x,y))* -> equal(z,v_x).
% 299.64/300.41 59117[4:MRR:58701.1,6340.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Oinsert(v,u),w)))*.
% 299.64/300.41 59118[7:MRR:58700.1,6340.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Oinsert(v,u),w)))*.
% 299.64/300.41 59161[0:SpL:383.1,58636.0] || equal(c_COMBK(u,v,w),c_Fun_Ofun__upd(c_Fun_Ofun__upd(x,v_x,c_HOL_Ouminus__class_Ouminus(u,tc_bool),y,z),x1,x2,y,z))* -> equal(x1,v_x).
% 299.64/300.41 59157[0:SpL:2771.1,58636.0] || equal(u,v) equal(c_COMBK(hAPP(v,v_x),w,x),c_Fun_Ofun__upd(y,v_x,c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),z,x1))* -> .
% 299.64/300.41 59627[4:MRR:59209.1,6340.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(v,u),x)))*.
% 299.64/300.41 59628[7:MRR:59208.1,6340.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(v,u),x)))*.
% 299.64/300.41 59921[0:SSi:59852.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),w) -> c_lessequals(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))*.
% 299.64/300.41 60165[0:SpL:2771.1,60048.2] || equal(u,v)* equal(w,hAPP(v,v_x))* equal(x,w)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),x)* -> .
% 299.64/300.41 60234[0:SpL:9.0,58170.1] || equal(u,c_Fun_Ocomp(v,w,x,y,z))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(v,hAPP(w,v_x)),tc_bool),x1,x2),u)* -> .
% 299.64/300.41 60213[0:SpL:88.1,58170.1] class_Lattices_Oboolean__algebra(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),w,x),v)* -> .
% 299.64/300.41 60199[0:SpL:2098.1,58170.1] || equal(u,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,v_x),tc_Hoare__Mirabelle_Otriple(t_a)))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),u)* -> c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a).
% 299.64/300.41 60184[0:SpL:3586.1,58170.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(w,c_Set_Oinsert(v,u))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),x,y),w)* -> .
% 299.64/300.41 60183[7:SpL:27278.1,58170.1] || equal(hAPP(c_in(u),v),v_x)** equal(w,c_Set_Oinsert(v,u))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),x,y),w)* -> .
% 299.64/300.41 60169[0:SpL:8498.1,58170.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(v,c_Set_Oinsert(w,u))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),x,y),v)* -> .
% 299.64/300.41 60468[0:SpR:5882.1,9567.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,tc_fun(x1,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.41 60467[0:SpR:5882.1,7253.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.41 60979[7:SSi:60971.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) -> .
% 299.64/300.41 61215[0:SSi:61207.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_Procs) -> .
% 299.64/300.41 61658[0:Res:5887.1,8141.2] class_Lattices_Oupper__semilattice(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),c_Orderings_Otop__class_Otop(u)),u)*.
% 299.64/300.41 61657[0:Res:5888.1,8141.2] class_Lattices_Olattice(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),c_Orderings_Otop__class_Otop(u)),u)*.
% 299.64/300.41 61923[0:SpL:331.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 61922[0:SpL:302.1,15487.1] class_Lattices_Obounded__lattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 61912[0:SpL:34428.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 61992[0:Rew:2990.0,61967.1] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 61993[0:Rew:3014.0,61955.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 61994[0:Rew:3014.0,61951.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 62034[0:SSi:62026.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_Procs) -> .
% 299.64/300.41 62189[0:Res:23754.0,278.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),v_Procs),w,u,v)))*.
% 299.64/300.41 62188[0:Res:23754.0,277.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,w),v_Procs),u,w)))*.
% 299.64/300.41 62184[0:Res:23754.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.41 62395[0:SSi:62357.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_bool)*.
% 299.64/300.41 62490[0:Res:62365.2,12719.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** equal(w,c_HOL_Ominus__class_Ominus(u,v,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(w,x,tc_bool),u,tc_bool)*.
% 299.64/300.41 63681[0:Res:62368.3,427.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_Orderings_Opreorder(u) || equal(v,w)* c_lessequals(w,x,u)* -> c_lessequals(v,x,u)*.
% 299.64/300.41 63780[0:SSi:63622.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(v,w)* c_lessequals(w,x,tc_fun(u,tc_bool))* -> c_lessequals(v,x,tc_fun(u,tc_bool))*.
% 299.64/300.41 64059[0:Res:63953.0,430.0] || c_lessequals(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.41 64079[0:SSi:64070.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* -> c_lessequals(u,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),tc_fun(tc_Com_Opname,tc_bool)).
% 299.64/300.41 64106[0:Res:679.1,431.0] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,w) -> c_Fun_Oinj__on(v,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),tc_Com_Opname,w)*.
% 299.64/300.41 64209[0:SpR:10463.0,646.1] || c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.41 64208[0:SpR:9911.0,646.1] || c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool)),v_x)**.
% 299.64/300.41 64167[0:SpR:646.1,7253.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.41 64155[0:SpR:646.1,9566.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(w,x),c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v)),hAPP(u,v_x)),tc_bool)*.
% 299.64/300.41 64376[0:SpR:10463.0,645.1] || c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.41 64375[0:SpR:9911.0,645.1] || c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool)),v_x)**.
% 299.64/300.41 64334[0:SpR:645.1,7253.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.41 64322[0:SpR:645.1,9566.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(w,x),c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v)),hAPP(u,v_x)),tc_bool)*.
% 299.64/300.41 64552[0:SpL:14216.0,24257.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_in(tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.41 64550[0:SpL:11176.1,24257.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(u,c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.41 64516[0:SpL:302.1,24257.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.41 64497[0:SpL:15476.0,24257.1] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.41 64597[0:SpR:26782.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)*.
% 299.64/300.41 64596[0:SpR:26782.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.41 64663[7:SSi:64655.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))** equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)),v_x) -> .
% 299.64/300.41 64709[0:Res:27986.0,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,u,tc_Com_Opname)))*.
% 299.64/300.41 64708[0:Res:27986.0,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.41 64699[0:Res:27986.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname)*.
% 299.64/300.41 64698[0:Res:27986.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.41 64729[0:Res:27987.0,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,u,tc_Com_Opname)))*.
% 299.64/300.41 64728[0:Res:27987.0,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.41 64719[0:Res:27987.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname)*.
% 299.64/300.41 64718[0:Res:27987.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.41 64749[0:Res:28288.0,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,u,tc_Com_Opname)))*.
% 299.64/300.41 64748[0:Res:28288.0,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.41 64739[0:Res:28288.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname)*.
% 299.64/300.41 64738[0:Res:28288.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.41 64769[0:Res:28289.0,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,u,tc_Com_Opname)))*.
% 299.64/300.41 64768[0:Res:28289.0,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,u,tc_Com_Opname)))*.
% 299.64/300.41 64759[0:Res:28289.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname)*.
% 299.64/300.41 64758[0:Res:28289.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.41 64834[0:SpR:28747.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,tc_fun(x,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.41 64954[0:SpR:28748.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,tc_fun(x,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.41 65074[0:SpR:28902.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,tc_fun(x,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.41 65194[0:SpR:28903.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,tc_fun(x,tc_bool)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.41 65569[0:Rew:65404.1,30143.1] class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z))**.
% 299.64/300.41 66535[0:SpL:8415.2,66188.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 66700[0:SpR:1188.2,9566.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u))),c_HOL_Ozero__class_Ozero(u)),tc_bool)*.
% 299.64/300.41 67455[0:SpR:1189.2,9566.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u))),c_HOL_Ozero__class_Ozero(u)),tc_bool)*.
% 299.64/300.41 69830[0:Res:67118.3,405.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)* -> equal(c_HOL_Ozero__class_Ozero(u),v).
% 299.64/300.41 69829[0:Res:67118.3,427.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_Orderings_Opreorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)* -> c_lessequals(w,v,u)*.
% 299.64/300.41 70089[0:Res:1103.1,11883.0] || hBOOL(hAPP(hAPP(c_in(u),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)))),w))* -> c_Hoare__Mirabelle_Ohoare__valids(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),t_a).
% 299.64/300.41 70094[4:MRR:70071.2,6340.0] || equal(v_Procs,v_x) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(v),v_x),u))* -> .
% 299.64/300.41 70143[0:Res:68748.3,405.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)* -> equal(c_HOL_Ozero__class_Ozero(u),v).
% 299.64/300.41 70142[0:Res:68748.3,427.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_Orderings_Opreorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)* -> c_lessequals(w,v,u)*.
% 299.64/300.41 70402[0:Res:153.1,70070.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,v_x)),w)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Ovimage(v,t_a,u),w),v_x),tc_bool))* -> .
% 299.64/300.41 70395[0:Res:510.1,70070.1] || hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),tc_bool))* -> .
% 299.64/300.41 70394[0:Res:511.1,70070.1] || hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u),v_x),tc_bool))* -> .
% 299.64/300.41 70697[0:SpL:538.0,70400.1] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool))* -> .
% 299.64/300.41 70913[0:SpL:584.0,6582.0] || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),z)** -> c_lessequals(hAPP(v,z),z,tc_fun(u,tc_bool))*.
% 299.64/300.41 71068[0:SpR:410.0,7568.0] || -> c_lessequals(hAPP(u,v),hAPP(c_Set_Oinsert(w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,y),z),u,y,tc_fun(x,tc_bool))),tc_fun(x,tc_bool))*.
% 299.64/300.41 71324[0:Res:7538.0,214.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(x,u),hAPP(c_Set_Oinsert(v,u),y)))))*.
% 299.64/300.41 71305[0:Res:7538.0,431.0] || c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),y)),v,z)* -> c_Fun_Oinj__on(u,y,v,z).
% 299.64/300.41 71476[7:MRR:71370.2,27297.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool))* equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_x)** -> .
% 299.64/300.41 72099[0:SpR:3294.1,7830.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_bool)),tc_fun(u,tc_bool))*.
% 299.64/300.41 72094[0:SpR:584.0,7830.0] || -> c_lessequals(hAPP(u,v),hAPP(c_Set_Oinsert(w,x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u,y,z,x1),v)),tc_fun(x,tc_bool))*.
% 299.64/300.41 72076[0:SpR:600.0,7830.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v)),tc_fun(w,tc_bool))*.
% 299.64/300.41 72500[4:MRR:72474.2,6340.0] || equal(v_Procs,v_x) equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(w),v_x),u))*.
% 299.64/300.41 73060[7:Res:71608.1,473.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_x) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,t_a),v_x)),w))*.
% 299.64/300.41 73047[7:Res:71608.1,356.0] || equal(u,v_x) -> equal(hAPP(c_Set_Oimage(c_COMBK(v,w,t_a),t_a,w),u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.64/300.41 74295[7:SpL:71835.1,347.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a))** c_Fun_Oinj__on(w,v_x,u,x)* -> c_Fun_Oinj__on(w,v,u,x)*.
% 299.64/300.41 74246[7:SpL:71835.1,447.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_Finite__Set_Ofinite(v_x,w) c_Fun_Oinj__on(u,v_x,v,w)* -> c_Finite__Set_Ofinite(v_x,v).
% 299.64/300.41 74210[7:SpL:71835.1,347.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) c_Fun_Oinj__on(v,hAPP(v_x,w),u,x)* -> c_Fun_Oinj__on(v,v_x,u,x).
% 299.64/300.41 74209[7:SpL:71835.1,346.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) c_Fun_Oinj__on(v,hAPP(v_x,w),u,x)* -> c_Fun_Oinj__on(v,w,u,x).
% 299.64/300.41 74199[7:SpL:71835.1,214.0] || equal(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(u,v)) c_lessequals(v_x,w,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),u),w))*.
% 299.64/300.41 74127[7:SpL:71835.1,355.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> equal(v_x,v).
% 299.64/300.41 73601[7:SpR:71835.1,98.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_Fun_Oinj__on(u,v_x,v,w)* -> equal(c_Finite__Set_Ocard(v_x,w),c_Finite__Set_Ocard(v_x,v)).
% 299.64/300.41 73237[7:SpR:71835.1,335.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) c_Finite__Set_Ofinite(v_x,u) c_Finite__Set_Ofinite(v,u) -> c_Finite__Set_Ofinite(hAPP(v_x,v),u)*.
% 299.64/300.41 74478[7:MRR:74269.1,6340.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_Set_Oinsert(v_x,t_a))** c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,v_x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a)*.
% 299.64/300.41 74479[7:MRR:74265.2,6340.0] || equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,x,w,u)))*.
% 299.64/300.41 74480[7:MRR:74264.2,6340.0] || equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_x,w,u)))*.
% 299.64/300.41 74481[7:MRR:74259.2,6340.0] class_Orderings_Olinorder(u) || equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,t_a)) c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_x,u),v,u)*.
% 299.64/300.41 74482[7:MRR:74258.2,6340.0] class_Orderings_Olinorder(u) || equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,t_a)) c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(v_x,u),u)*.
% 299.64/300.41 74483[7:Rew:71835.1,74129.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,v)) hBOOL(hAPP(v_x,c_HOL_Ominus__class_Ominus(w,v,tc_fun(u,tc_bool))))* -> .
% 299.64/300.41 74499[7:MRR:73230.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x)**.
% 299.64/300.41 74967[7:MRR:74828.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x))*.
% 299.64/300.41 75398[0:SpR:3294.1,7820.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(tc_bool)),u)*.
% 299.64/300.41 75393[0:SpR:584.0,7820.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,y,z,x1),w)),u)*.
% 299.64/300.41 75590[0:Obv:75511.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v))),u)*.
% 299.64/300.41 75591[0:Obv:75510.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y))),u)*.
% 299.64/300.41 75719[7:SpR:71883.1,474.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v_x,v,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))))*.
% 299.64/300.41 75684[7:SpR:71883.1,646.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Fun_Oinj__on(v_x,v_Procs,tc_Com_Opname,u) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,v_x,tc_Com_Opname,u),v_x),v_x)**.
% 299.64/300.41 75678[7:SpR:71883.1,645.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Fun_Oinj__on(v_x,v_Procs,tc_Com_Opname,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_x,tc_Com_Opname,u),v_x),v_x)**.
% 299.64/300.41 76064[0:SSi:76063.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w))),v_x))*.
% 299.64/300.41 76143[0:SpR:9915.0,9566.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBS(c_Set_Ovimage(w,x,y),z,x1,x2,x3)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),tc_bool)*.
% 299.64/300.41 76529[0:SpR:3294.1,29199.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(tc_bool)),u)*.
% 299.64/300.41 76524[0:SpR:584.0,29199.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,y,z,x1),w)),u)*.
% 299.64/300.41 76714[0:Obv:76573.0] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v))),u)*.
% 299.64/300.41 76760[7:SpR:317.0,71682.1] || equal(hAPP(c_Set_Oimage(u,v,w),x),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(y,v),x)),v_x))*.
% 299.64/300.41 77077[0:Obv:76928.0] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y))),u)*.
% 299.64/300.41 77188[7:SpL:328.1,74788.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)** equal(u,w)* -> hBOOL(w)*.
% 299.64/300.41 77184[7:SpL:538.0,74788.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),w)* -> hBOOL(w)*.
% 299.64/300.41 77233[0:SpR:8415.2,801.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* -> equal(c_Fun_Ofun__upd(v_x,v_x,v_x,v,w),v_x)**.
% 299.64/300.41 77400[0:Res:2399.2,112.1] class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)*.
% 299.64/300.41 77328[0:SpR:140.1,2399.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.41 77327[0:SpR:137.1,2399.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.41 77592[0:Res:2429.2,112.1] class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)*.
% 299.64/300.41 77520[0:SpR:140.1,2429.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.41 77519[0:SpR:137.1,2429.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.41 77911[0:Res:23881.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v,w),x,y,z),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.41 77910[0:Res:21234.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(c_COMBK(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,x),t_a,y),z,x1,x2),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.41 77909[0:Res:21173.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(c_COMBK(hAPP(c_in(tc_Com_Opname),v_x),v,w),x,y),z,x1,x2),hAPP(c_in(tc_Com_Opname),v_x)))*.
% 299.64/300.41 77908[0:Res:7284.0,5892.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(c_COMBK(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,x),v,y),z,x1,x2),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.41 77857[0:SpL:1188.2,5892.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y),c_HOL_Ozero__class_Ozero(u)))*.
% 299.64/300.41 77856[0:SpL:1189.2,5892.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) -> hBOOL(hAPP(c_COMBS(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y),c_HOL_Ozero__class_Ozero(u)))*.
% 299.64/300.41 77694[0:SpL:300.1,5892.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(v,v))* -> hBOOL(hAPP(c_COMBS(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,y,z),v))*.
% 299.64/300.41 78001[7:MRR:34373.1,77996.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(tc_Com_Opname),v_x),tc_Com_Opname,u),hAPP(hAPP(c_in(tc_Com_Opname),v_x),v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.41 78331[7:SpR:78167.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,x),u,w),v)))*.
% 299.64/300.41 78327[7:SpR:78167.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,w),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.41 78515[4:Res:77988.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),t_a) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v)),u))* c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.64/300.41 78509[4:Res:77988.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(w,tc_bool))))*.
% 299.64/300.41 78756[4:Res:78665.1,278.1] || equal(hAPP(hAPP(c_in(u),v),w),v_x)** hBOOL(hAPP(x,v))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,y,x,u)))*.
% 299.64/300.41 78755[4:Res:78665.1,277.1] || equal(hAPP(hAPP(c_in(u),v),w),v_x)** hBOOL(hAPP(x,v))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,w,x,u)))*.
% 299.64/300.41 78739[4:Res:78665.1,501.0] || equal(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),v_x)** c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.64/300.41 78694[4:Res:78665.1,147.1] || equal(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))),v_x)** hBOOL(hAPP(hAPP(c_in(u),v),x)) -> .
% 299.64/300.41 78689[4:Res:78665.1,170.1] class_Orderings_Olinorder(u) || equal(hAPP(hAPP(c_in(u),v),w),v_x)** c_Finite__Set_Ofinite(w,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(w,u),v,u)*.
% 299.64/300.41 78688[4:Res:78665.1,169.1] class_Orderings_Olinorder(u) || equal(hAPP(hAPP(c_in(u),v),w),v_x)** c_Finite__Set_Ofinite(w,u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(w,u),u)*.
% 299.64/300.41 78872[0:SpR:158.0,11064.1] || c_Finite__Set_Ofinite(u,v) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(w,x,y),hAPP(c_Set_Oimage(z,v,x),u)),x1,tc_fun(y,tc_bool)),y)*.
% 299.64/300.41 79079[0:Res:78077.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w)),u))* c_Hoare__Mirabelle_Otriple__valid(w,v_Procs,t_a).
% 299.64/300.41 79109[7:Res:78199.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),v_x),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w)),u))* c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.64/300.41 79103[7:Res:78199.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_in(x),u,tc_fun(w,tc_bool))))*.
% 299.64/300.41 79947[0:SpR:23902.1,21268.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(u,v_x),v_x,v,w)),v_x)**.
% 299.64/300.41 79937[0:SpR:301.1,21268.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v,w,x)),v)**.
% 299.64/300.41 79865[0:SpR:525.1,21268.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v,w,x)),v)**.
% 299.64/300.41 79864[0:SpR:65404.1,21268.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v,w,x)),v)**.
% 299.64/300.41 79823[0:SpR:2097.1,21268.0] || hBOOL(hAPP(u,v)) -> equal(hAPP(c_Set_Oinsert(v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(v,w),u,x,y)),u)**.
% 299.64/300.41 79529[0:SpR:21268.0,9566.0] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(c_Set_Oinsert(w,x),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),u,hAPP(u,v),y,z)),tc_bool)*.
% 299.64/300.41 80369[0:Rew:99.1,79650.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,hAPP(u,y),x,z),y)**.
% 299.64/300.41 81141[0:SpR:23902.1,21894.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v_x,hAPP(u,v_x),v,w)),v_x)**.
% 299.64/300.41 81131[0:SpR:301.1,21894.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x)),v)**.
% 299.64/300.41 81059[0:SpR:525.1,21894.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x)),v)**.
% 299.64/300.41 81058[0:SpR:65404.1,21894.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x)),v)**.
% 299.64/300.41 81017[0:SpR:2097.1,21894.0] || hBOOL(hAPP(u,v)) -> equal(hAPP(c_Set_Oinsert(v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,c_Set_Oinsert(v,w),x,y)),u)**.
% 299.64/300.41 80722[0:SpR:21894.0,9566.0] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(c_Set_Oinsert(w,x),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(u,v),u,y,z)),tc_bool)*.
% 299.64/300.41 81564[0:Rew:99.1,80844.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(u,y),u,x,z),y)**.
% 299.64/300.41 82171[7:SpR:78597.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oinsert(v_x,t_a),u,v,w,x),c_Set_Oinsert(v_x,y)),hAPP(c_Set_Oinsert(v_x,y),hAPP(u,c_Set_Oinsert(v_x,y))))*.
% 299.64/300.41 82170[7:SpR:78597.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oinsert(v_x,t_a),v,w,x),c_Set_Oinsert(v_x,y)),hAPP(hAPP(u,c_Set_Oinsert(v_x,y)),c_Set_Oinsert(v_x,y)))*.
% 299.64/300.41 82738[0:Res:23960.1,7671.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),u)*.
% 299.64/300.41 82694[0:Res:989.1,7671.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(w,x,y),tc_Com_Opname,u),u)*.
% 299.64/300.41 82813[0:Obv:82687.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* c_lessequals(x,v,u)* -> c_lessequals(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y),u)*.
% 299.64/300.41 82814[0:Obv:82684.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* c_lessequals(x,v,u)* -> c_lessequals(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w),u)*.
% 299.64/300.41 82851[7:Res:77991.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oinsert(v,w),v_x))),hAPP(c_Set_Oinsert(v,w),v_x)))* c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.41 82837[7:Res:77991.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(c_Set_Oinsert(x,y),v_x)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.64/300.41 82936[0:SpR:158.0,22513.1] || c_Finite__Set_Ofinite(u,v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(w,x,y),hAPP(c_Set_Oimage(z,x1,x),hAPP(c_Set_Oimage(x2,v,x1),u))),y)*.
% 299.64/300.41 83108[7:SpL:5924.0,74788.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_x)** equal(hAPP(hAPP(u,v_x),v),x2)* -> hBOOL(x2)*.
% 299.64/300.41 83097[0:SpL:5924.0,3506.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(x2,x3),hAPP(hAPP(u,v_x),v))* -> .
% 299.64/300.41 83031[0:SpR:5924.0,9566.0] || -> c_lessequals(hAPP(hAPP(u,v),w),hAPP(hAPP(c_Set_Oinsert(x,y),c_COMBS(u,c_COMBK(w,z,x1),x2,x3,x4)),v),tc_bool)*.
% 299.64/300.41 83006[0:SpR:5924.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname,x2),hAPP(hAPP(u,v_x),v))))*.
% 299.64/300.41 82982[0:SpR:5924.0,24020.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(hAPP(u,v_x),v),v_x),v_x).
% 299.64/300.41 83285[7:MRR:83203.0,27297.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(u,v,w),w,v),x,y),v_x),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))*.
% 299.64/300.41 83428[7:SpL:5961.0,74788.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_x)** equal(hAPP(u,hAPP(x,v_x)),x2)* -> hBOOL(x2)*.
% 299.64/300.41 83417[0:SpL:5961.0,3506.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(x2,x3),hAPP(u,hAPP(x,v_x)))* -> .
% 299.64/300.41 83362[0:SpR:5961.0,9566.0] || -> c_lessequals(hAPP(u,hAPP(v,w)),hAPP(hAPP(c_Set_Oinsert(x,y),c_COMBS(c_COMBK(u,z,x1),v,x2,x3,x4)),w),tc_bool)*.
% 299.64/300.41 83336[0:SpR:5961.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(c_COMBK(u,v,w),x,y,z,x1),tc_Com_Opname,x2),hAPP(u,hAPP(x,v_x)))))*.
% 299.64/300.41 83312[0:SpR:5961.0,24020.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(u,hAPP(x,v_x)),v_x),v_x).
% 299.64/300.41 83740[0:SpR:5899.0,9566.0] || -> c_lessequals(hAPP(c_COMBS(u,v,w,x,y),z),hAPP(hAPP(c_Set_Oinsert(x1,x2),c_COMBS(u,v,x3,x4,x5)),z),tc_bool)*.
% 299.64/300.41 84227[7:SpL:5961.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),v_x) equal(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),v_x)** -> .
% 299.64/300.41 84226[7:SpL:5924.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool),v_x) equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_x)** -> .
% 299.64/300.41 84202[7:SpL:328.1,78767.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)** -> .
% 299.64/300.41 84198[7:SpL:538.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x) -> .
% 299.64/300.41 84416[0:SpL:2936.0,10287.0] || equal(c_Fun_Ofun__upd(hAPP(c_in(t_a),v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),u,v,w),hAPP(c_in(t_a),v_x))** -> equal(c_Orderings_Obot__class_Obot(tc_bool),u).
% 299.64/300.41 84886[4:SpL:8385.1,78744.0] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(v_x,tc_Com_Opname),u),v_Procs) equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(v_x,tc_Com_Opname),u),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oinsert(v_x,tc_Com_Opname),u,t_a)*.
% 299.64/300.41 85007[0:Res:84957.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oinsert(v,w),v))),hAPP(c_Set_Oinsert(v,w),v)))* c_Hoare__Mirabelle_Otriple__valid(u,v,t_a).
% 299.64/300.41 84993[0:Res:84957.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(c_Set_Oinsert(x,y),x)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.64/300.41 85128[0:Rew:35438.0,85025.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_COMBB(u,v,tc_fun(w,tc_bool),tc_Com_Opname),c_COMBK(x,v,tc_Com_Opname)),tc_Com_Opname,tc_fun(w,tc_bool)),hAPP(u,x))**.
% 299.64/300.41 85131[0:MRR:85087.1,49657.0] || c_Fun_Oinj__on(c_COMBK(u,v,tc_Com_Opname),v_Procs,tc_Com_Opname,v) -> c_Fun_Oinj__on(c_Fun_Ocomp(w,c_COMBK(u,v,tc_Com_Opname),v,x,tc_Com_Opname),v_Procs,tc_Com_Opname,x)*.
% 299.64/300.41 85135[0:Rew:31256.0,85134.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),w)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.64/300.41 85222[0:SpL:819.1,10287.0] class_Orderings_Otop(u) || equal(c_Fun_Ofun__upd(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x,v,w,x),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)))** -> equal(c_Orderings_Otop__class_Otop(u),v).
% 299.64/300.41 85273[0:SpL:824.1,10287.0] class_Orderings_Obot(u) || equal(c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x,v,w,x),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)))** -> equal(c_Orderings_Obot__class_Obot(u),v).
% 299.64/300.41 85309[0:SpL:3229.1,26240.0] || equal(u,c_Set_Oinsert(v,w))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(u,v_x)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.41 85776[0:SpR:3229.1,9066.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(hAPP(u,v_x),hAPP(c_Set_Oinsert(w,v),x))))*.
% 299.64/300.41 85769[0:SpR:49342.1,9066.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)))*.
% 299.64/300.41 85766[0:SpR:32668.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.64/300.41 85765[0:SpR:28910.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),y),v_Procs)))*.
% 299.64/300.41 85764[0:SpR:28926.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)))*.
% 299.64/300.41 85760[0:SpR:28755.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),y),v_Procs)))*.
% 299.64/300.41 85759[0:SpR:28771.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)))*.
% 299.64/300.41 85753[0:SpR:27043.1,9066.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)))*.
% 299.64/300.41 85742[0:SpR:2098.1,9066.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),v)))*.
% 299.64/300.41 85739[0:SpR:3229.1,9066.0] || equal(u,c_Set_Oinsert(v,w)) -> hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(u,v_x))))*.
% 299.64/300.41 85864[0:Con:85816.1] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,w),x),u,w)),hAPP(c_Set_Oinsert(v,w),x)))*.
% 299.64/300.41 85933[0:SpL:3229.1,13582.0] || equal(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)))* hBOOL(hAPP(u,v_x))* hBOOL(hAPP(hAPP(c_in(x),v_x),w))* -> .
% 299.64/300.41 86129[7:MRR:86020.2,27297.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool))* equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_Procs)** -> .
% 299.64/300.41 86592[0:Res:19823.1,3929.0] || hBOOL(hAPP(u,v_x)) equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.41 86581[0:SpR:2267.1,19823.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)* hBOOL(hAPP(v,y))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),y))*.
% 299.64/300.41 86654[0:Res:86261.1,473.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,t_a),v_x)),w))*.
% 299.64/300.41 86641[0:Res:86261.1,356.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oimage(c_COMBK(v,w,t_a),t_a,w),u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.64/300.41 86772[4:SpL:5961.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),v_x) equal(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),v_Procs)** -> .
% 299.64/300.41 86771[4:SpL:5924.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool),v_x) equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_Procs)** -> .
% 299.64/300.41 86747[4:SpL:328.1,86106.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_Procs)** -> .
% 299.64/300.41 86743[4:SpL:538.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs) -> .
% 299.64/300.41 86863[0:SpR:317.0,86345.1] || equal(hAPP(c_Set_Oimage(u,v,w),x),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(y,v),x)),v_x))*.
% 299.64/300.41 87091[0:MRR:86972.1,214.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.64/300.41 87095[0:Rew:26873.0,86957.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(x,w),v),tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.64/300.41 87339[7:SpR:584.0,71492.1] || equal(c_COMBS(u,v,w,x,y),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(u,v_x),hAPP(v,v_x))),z))*.
% 299.64/300.41 87318[7:SpR:337.0,71492.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v))*.
% 299.64/300.41 87305[7:SpR:540.1,71492.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),w))*.
% 299.64/300.41 87304[7:SpR:539.1,71492.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),w))*.
% 299.64/300.41 87296[7:SpR:30368.2,71492.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v))*.
% 299.64/300.41 87295[7:SpR:30928.2,71492.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v))*.
% 299.64/300.41 87292[7:SpR:299.2,71492.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w))*.
% 299.64/300.41 87279[7:SpR:25.1,71492.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)),w))*.
% 299.64/300.41 87415[7:SSi:87367.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) equal(v,v_x) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,hAPP(c_Set_Oinsert(hAPP(v,v_x),tc_bool),u),tc_bool,tc_bool))*.
% 299.64/300.41 87487[7:SpR:584.0,71493.1] || equal(c_COMBS(u,v,w,x,y),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(u,v_x),hAPP(v,v_x))),z,t_a)*.
% 299.64/300.41 87466[7:SpR:337.0,71493.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,t_a)*.
% 299.64/300.41 87453[7:SpR:540.1,71493.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),w,t_a)*.
% 299.64/300.41 87452[7:SpR:539.1,71493.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),w,t_a)*.
% 299.64/300.41 87444[7:SpR:30368.2,71493.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.41 87443[7:SpR:30928.2,71493.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.41 87440[7:SpR:299.2,71493.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,t_a)*.
% 299.64/300.41 87427[7:SpR:25.1,71493.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)),w,t_a)*.
% 299.64/300.41 87527[0:SpL:769.0,10287.0] || equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v,w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v))** -> equal(v,w).
% 299.64/300.41 87617[7:SpR:584.0,71679.1] || equal(c_COMBS(u,v,w,x,y),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(hAPP(u,v_x),hAPP(v,v_x))))*.
% 299.64/300.41 87596[7:SpR:337.0,71679.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.41 87583[7:SpR:540.1,71679.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.41 87582[7:SpR:539.1,71679.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.41 87574[7:SpR:30368.2,71679.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.41 87573[7:SpR:30928.2,71679.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.41 87570[7:SpR:299.2,71679.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v))*.
% 299.64/300.41 87557[7:SpR:25.1,71679.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)))*.
% 299.64/300.41 87745[7:SpL:21893.0,74399.0] || equal(hAPP(c_in(u),v_x),c_Set_Oinsert(v_x,t_a)) -> hBOOL(hAPP(v_x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,v)))*.
% 299.64/300.41 87743[7:SpL:21267.0,74399.0] || equal(hAPP(c_in(u),v_x),c_Set_Oinsert(v_x,t_a)) -> hBOOL(hAPP(v_x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,v)))*.
% 299.64/300.41 87788[0:Obv:87762.0] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,w) equal(c_HOL_Ouminus__class_Ouminus(v,u),w)* -> equal(c_HOL_Ouminus__class_Ouminus(w,u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.41 87943[0:Obv:87920.0] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,w) equal(c_HOL_Ouminus__class_Ouminus(v,u),w)* -> equal(c_HOL_Ouminus__class_Ouminus(w,u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.41 88294[0:SpR:3229.1,7227.0] || equal(u,c_in(v)) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(c_COMBK(v_x,w,x),y,v),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.64/300.41 88586[0:Res:448.1,8306.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))* c_lessequals(x,v,tc_fun(u,tc_bool)).
% 299.64/300.41 88679[7:SpL:5961.0,88086.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(x2,hAPP(u,hAPP(x,v_x)),tc_bool))* -> .
% 299.64/300.41 88678[7:SpL:5924.0,88086.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(x2,hAPP(hAPP(u,v_x),v),tc_bool))* -> .
% 299.64/300.41 88655[7:SpL:329.1,88086.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(w,v_x,tc_bool))* -> .
% 299.64/300.41 88654[7:SpL:328.1,88086.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(w,u,tc_bool))* -> .
% 299.64/300.41 88650[7:SpL:538.0,88086.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x) hBOOL(c_HOL_Ominus__class_Ominus(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool))* -> .
% 299.64/300.41 89020[0:Res:14196.0,3929.0] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(u,v_x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.41 88980[7:SpR:78597.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),u,v),hAPP(c_Set_Oinsert(c_Set_Oinsert(v_x,w),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),c_Set_Oinsert(v_x,w)))*.
% 299.64/300.41 88868[0:SpR:525.1,14196.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v))*.
% 299.64/300.41 88867[0:SpR:65404.1,14196.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v))*.
% 299.64/300.41 88861[0:SpR:3229.1,14196.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,w,x),hAPP(c_Set_Oinsert(hAPP(u,v_x),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_x))*.
% 299.64/300.41 88828[7:SpR:71455.1,14196.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),u))*.
% 299.64/300.41 88827[0:SpR:86109.1,14196.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),u))*.
% 299.64/300.41 88826[0:SpR:8385.1,14196.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),u))*.
% 299.64/300.41 89055[0:Res:78099.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),t_a)*.
% 299.64/300.41 89047[0:Res:78099.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u)*.
% 299.64/300.41 89046[0:Res:78099.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Finite__Set_Olinorder__class_OMax(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u),u)*.
% 299.64/300.41 89161[0:SpL:339.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))),v)* -> c_Finite__Set_Ofinite(y,v).
% 299.64/300.41 89124[0:SpL:3229.1,25984.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(x,v),hAPP(u,v_x)),v)* -> c_Finite__Set_Ofinite(v_x,v).
% 299.64/300.41 89117[0:SpL:3229.1,25984.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(u,v_x),x)),v)* -> c_Finite__Set_Ofinite(x,v).
% 299.64/300.41 89387[7:SpR:78590.1,584.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(c_COMBS(c_Set_Oinsert(v_x,t_a),v,w,x,y),u),hAPP(u,hAPP(v,u)))*.
% 299.64/300.41 89386[7:SpR:78590.1,584.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(c_COMBS(v,c_Set_Oinsert(v_x,t_a),w,x,y),u),hAPP(hAPP(v,u),u))*.
% 299.64/300.41 89385[7:SpR:78590.1,1103.1] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oinsert(v_x,t_a)),c_Set_Oinsert(v_x,t_a)) -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Oinsert(v_x,t_a),t_a)* hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oinsert(v_x,t_a))).
% 299.64/300.41 89713[7:Res:89344.1,467.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,t_a),v_x)),v_x)**.
% 299.64/300.41 89910[0:SpR:3229.1,26183.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) -> equal(hAPP(hAPP(u,v_x),hAPP(c_Set_Oinsert(w,v),v_x)),hAPP(c_Set_Oinsert(w,v),v_x))**.
% 299.64/300.41 89852[0:SpR:26183.0,8376.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(tc_Com_Opname)) equal(hAPP(c_Set_Oinsert(v,u),v_x),v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(v,u),v_x))*.
% 299.64/300.41 89960[0:SSi:89849.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),hAPP(hAPP(c_Set_Oinsert(v,t_a),u),v_x)),hAPP(hAPP(c_Set_Oinsert(v,t_a),u),v_x))**.
% 299.64/300.41 90177[4:SpR:78660.1,584.0] || equal(hAPP(u,v_x),v_x) -> equal(hAPP(c_COMBS(c_Set_Oinsert(v_x,t_a),v,w,x,y),u),hAPP(u,hAPP(v,u)))*.
% 299.64/300.41 90176[4:SpR:78660.1,584.0] || equal(hAPP(u,v_x),v_x) -> equal(hAPP(c_COMBS(v,c_Set_Oinsert(v_x,t_a),w,x,y),u),hAPP(hAPP(v,u),u))*.
% 299.64/300.41 90175[4:SpR:78660.1,1103.1] || equal(hAPP(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oinsert(v_x,t_a)),v_x),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Oinsert(v_x,t_a),t_a) hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oinsert(v_x,t_a))).
% 299.64/300.41 90655[0:SpL:338.0,26231.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))),v)* -> c_Finite__Set_Ofinite(x,v).
% 299.64/300.41 90623[0:SpL:3229.1,26231.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(x,v),hAPP(u,v_x)),v)* -> c_Finite__Set_Ofinite(w,v).
% 299.64/300.41 90616[0:SpL:3229.1,26231.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(u,v_x),x)),v)* -> c_Finite__Set_Ofinite(v_x,v).
% 299.64/300.41 90791[0:Res:448.1,26480.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,c_HOL_Ominus__class_Ominus(w,v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* c_lessequals(w,v,tc_fun(u,tc_bool)).
% 299.64/300.41 90771[0:SpL:647.0,26480.0] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v_Procs,tc_fun(tc_Com_Opname,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool)).
% 299.64/300.41 90857[4:Res:90134.1,467.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),v_x) -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,t_a),v_x)),v_x)**.
% 299.64/300.41 90934[4:SpL:540.1,90278.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))* -> .
% 299.64/300.41 90933[4:SpL:539.1,90278.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))* -> .
% 299.64/300.41 91095[0:SpR:44588.1,21894.0] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x)),v)**.
% 299.64/300.41 91094[0:SpR:44588.1,21268.0] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v,w,x)),v)**.
% 299.64/300.41 91347[0:Rew:91288.1,91188.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y,z),c_Orderings_Obot__class_Obot(u)),hAPP(v,hAPP(w,c_Orderings_Obot__class_Obot(u))))**.
% 299.64/300.41 91348[0:Rew:91288.1,91187.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),c_Orderings_Obot__class_Obot(u)),hAPP(hAPP(v,c_Orderings_Obot__class_Obot(u)),w))**.
% 299.64/300.41 91803[0:SpL:834.1,10287.0] class_Lattices_Obounded__lattice(u) || equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(u),w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))** -> equal(v,w).
% 299.64/300.41 91874[4:Rew:9.0,91850.1] || equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname))),v_x)** -> hBOOL(hAPP(u,hAPP(v,v_x))).
% 299.64/300.41 92347[0:SpL:3229.1,5022.0] || equal(u,c_Set_Oinsert(v,w))* c_lessequals(hAPP(u,v_x),v_x,tc_fun(w,tc_bool))* -> equal(hAPP(c_Set_Oinsert(v,w),v_x),v_x)**.
% 299.64/300.41 92416[0:Rew:7593.1,92386.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),x,tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Oinsert(w,v),x),x).
% 299.64/300.41 92417[0:Rew:92416.1,7593.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),x,tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Oinsert(u,v),x),x).
% 299.64/300.41 92589[0:SpL:5227.1,521.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x)* equal(c_Suc(y),c_Suc(w))* -> equal(y,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x))*.
% 299.64/300.41 92710[7:Res:82151.1,519.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(t_a))** -> hBOOL(hAPP(v,c_Set_Oinsert(v_x,w)))* hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,w)))*.
% 299.64/300.41 92689[7:Res:82151.1,255.0] || equal(c_in(t_a),c_in(u)) c_lessequals(c_Set_Oinsert(v_x,v),w,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v_x),w)).
% 299.64/300.41 92668[7:SpR:52997.1,82151.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(v_Procs,u),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,v)))*.
% 299.64/300.41 92663[7:SpR:584.0,82151.1] || equal(c_COMBS(u,v,w,x,y),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_Set_Oinsert(v_x,z)))*.
% 299.64/300.41 92629[7:SpR:540.1,82151.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Set_Oinsert(v_x,w)))*.
% 299.64/300.41 92628[7:SpR:539.1,82151.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Set_Oinsert(v_x,w)))*.
% 299.64/300.41 92627[7:SpR:297.2,82151.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,w)))*.
% 299.64/300.41 92620[7:SpR:30368.2,82151.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Set_Oinsert(v_x,v)))*.
% 299.64/300.41 92619[7:SpR:30928.2,82151.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Set_Oinsert(v_x,v)))*.
% 299.64/300.41 92616[7:SpR:299.2,82151.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a))** -> hBOOL(hAPP(v,c_Set_Oinsert(v_x,w)))*.
% 299.64/300.41 92603[7:SpR:25.1,82151.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_Set_Oinsert(v_x,w)))*.
% 299.64/300.41 92788[0:SpR:3229.1,5876.0] || equal(u,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z))* -> c_lessequals(hAPP(w,v_x),hAPP(u,v_x),tc_fun(v,tc_bool))*.
% 299.64/300.41 93328[4:SpR:52997.1,85556.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v_x,v),tc_bool)*.
% 299.64/300.41 93323[4:SpR:584.0,85556.1] || equal(c_COMBS(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(hAPP(hAPP(u,v_x),hAPP(v,v_x)),z),tc_bool)*.
% 299.64/300.41 93289[4:SpR:540.1,85556.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),w),tc_bool)*.
% 299.64/300.41 93288[4:SpR:539.1,85556.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),w),tc_bool)*.
% 299.64/300.41 93287[4:SpR:297.2,85556.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v_x,w),tc_bool)*.
% 299.64/300.41 93280[4:SpR:30368.2,85556.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(c_Orderings_Otop__class_Otop(u),v),tc_bool)*.
% 299.64/300.41 93279[4:SpR:30928.2,85556.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(c_Orderings_Otop__class_Otop(u),v),tc_bool)*.
% 299.64/300.41 93276[4:SpR:299.2,85556.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v,w),tc_bool)*.
% 299.64/300.41 93263[4:SpR:25.1,85556.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),w),tc_bool)*.
% 299.64/300.41 93511[0:SpR:584.0,86147.1] || equal(c_COMBS(u,v,w,x,y),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(u,v_x),hAPP(v,v_x))),z))*.
% 299.64/300.41 93490[0:SpR:337.0,86147.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v))*.
% 299.64/300.41 93477[0:SpR:540.1,86147.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),w))*.
% 299.64/300.41 93476[0:SpR:539.1,86147.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),w))*.
% 299.64/300.41 93468[0:SpR:30368.2,86147.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v))*.
% 299.64/300.41 93467[0:SpR:30928.2,86147.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v))*.
% 299.64/300.41 93464[0:SpR:299.2,86147.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w))*.
% 299.64/300.41 93451[0:SpR:25.1,86147.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)),w))*.
% 299.64/300.41 93588[0:SSi:93539.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) equal(v,v_Procs) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,hAPP(c_Set_Oinsert(hAPP(v,v_x),tc_bool),u),tc_bool,tc_bool))*.
% 299.64/300.41 93662[0:SpR:584.0,86148.1] || equal(c_COMBS(u,v,w,x,y),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(u,v_x),hAPP(v,v_x))),z,t_a)*.
% 299.64/300.41 93641[0:SpR:337.0,86148.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,t_a)*.
% 299.64/300.41 93628[0:SpR:540.1,86148.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),w,t_a)*.
% 299.64/300.41 93627[0:SpR:539.1,86148.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),w,t_a)*.
% 299.64/300.41 93619[0:SpR:30368.2,86148.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.41 93618[0:SpR:30928.2,86148.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(u)),v,t_a)*.
% 299.64/300.41 93615[0:SpR:299.2,86148.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,t_a)*.
% 299.64/300.41 93602[0:SpR:25.1,86148.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)),w,t_a)*.
% 299.64/300.41 93693[0:SpL:3229.1,7462.1] || equal(u,c_Set_Oinsert(v,w))* c_lessequals(x,v_x,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(u,v_x),w)* -> c_Finite__Set_Ofinite(x,w).
% 299.64/300.41 93806[0:SpR:584.0,86342.1] || equal(c_COMBS(u,v,w,x,y),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(hAPP(u,v_x),hAPP(v,v_x))))*.
% 299.64/300.41 93785[0:SpR:337.0,86342.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.41 93772[0:SpR:540.1,86342.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.41 93771[0:SpR:539.1,86342.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.41 93763[0:SpR:30368.2,86342.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.41 93762[0:SpR:30928.2,86342.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.41 93759[0:SpR:299.2,86342.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v))*.
% 299.64/300.41 93746[0:SpR:25.1,86342.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)))*.
% 299.64/300.41 94021[0:SpR:3229.1,10791.0] || equal(u,c_Set_Oinsert(v,w)) -> c_lessequals(hAPP(u,v_x),hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),v_x)),tc_fun(w,tc_bool))*.
% 299.64/300.41 93998[7:SpR:71455.1,10791.0] || equal(hAPP(c_Set_Oinsert(u,t_a),v),v_x) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),v),hAPP(c_Set_Oinsert(u,t_a),v),tc_fun(t_a,tc_bool))*.
% 299.64/300.41 93997[0:SpR:86109.1,10791.0] || equal(hAPP(c_Set_Oinsert(u,t_a),v),v_Procs) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),v),hAPP(c_Set_Oinsert(u,t_a),v),tc_fun(t_a,tc_bool))*.
% 299.64/300.41 93994[0:SpR:8385.1,10791.0] || equal(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v),v_Procs) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),hAPP(c_Set_Oinsert(u,tc_Com_Opname),v),tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.41 93954[0:SpR:3229.1,10791.0] || equal(u,c_Set_Oinsert(v,w))* -> c_lessequals(hAPP(c_Set_Oinsert(x,w),v_x),hAPP(c_Set_Oinsert(x,w),hAPP(u,v_x)),tc_fun(w,tc_bool))*.
% 299.64/300.41 94192[0:Res:14364.3,24120.1] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) equal(v,c_Orderings_Obot__class_Obot(tc_bool)) -> equal(c_Finite__Set_Olinorder__class_OMin(u,tc_bool),v).
% 299.64/300.41 94324[0:Res:14491.3,36406.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,hAPP(hAPP(c_Set_Oinsert(v_x,t_a),v),v_x)))* c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.64/300.41 684[0:Res:589.0,479.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,v,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)))*.
% 299.64/300.41 685[0:Res:589.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)))*.
% 299.64/300.41 665[0:Res:589.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(w,v_x))) -> hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,w,tc_Com_Opname,tc_fun(u,tc_bool))))*.
% 299.64/300.41 1101[0:SpR:653.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w),c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname))**.
% 299.64/300.41 1551[0:SpL:141.1,134.1] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ominus__class_Ominus(w,v,u))* -> equal(c_HOL_Ominus__class_Ominus(w,v,u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.41 2249[0:Res:1157.0,279.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oimage(c_COMBK(u,w,x),tc_Com_Opname,v),v_Procs)),hAPP(c_Set_Oimage(c_COMBK(u,w,x),tc_Com_Opname,v),v_Procs))**.
% 299.64/300.41 2574[0:Rew:585.0,2571.0] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_COMBC(u,x,y,z),v),tc_Com_Opname)),v))*.
% 299.64/300.41 2575[0:Rew:585.0,2570.0] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_COMBC(u,x,y,z),v),tc_Com_Opname)),v))*.
% 299.64/300.41 2585[0:Rew:586.0,2582.0] || hBOOL(hAPP(u,hAPP(v,v_x))) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_COMBB(u,x,y,z),v),tc_Com_Opname))))*.
% 299.64/300.41 2586[0:Rew:586.0,2581.0] || hBOOL(hAPP(u,hAPP(v,v_x))) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_COMBB(u,x,y,z),v),tc_Com_Opname))))*.
% 299.64/300.41 2599[0:SpR:445.1,415.0] || -> equal(u,v) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(w,v,x,y,z),u,hAPP(w,u),x1,x2),c_Fun_Ofun__upd(w,v,x,y,z))**.
% 299.64/300.41 2643[0:SpR:337.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.41 2640[0:SpR:337.0,651.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.41 2750[0:SpR:26.1,25.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_HOL_Ouminus(u) || -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),u),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x))**.
% 299.64/300.41 2749[0:SpR:27.1,25.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_HOL_Ouminus(u) || -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),u),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x))**.
% 299.64/300.41 2748[0:SpR:1561.1,25.1] class_OrderedGroup_Oab__group__add(tc_fun(t_a,u)) class_HOL_Ouminus(u) || -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),u),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x))**.
% 299.64/300.41 2747[0:SpR:73.1,25.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_HOL_Ouminus(u) || -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x),u),hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x))**.
% 299.64/300.41 2746[0:SpR:74.1,25.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_HOL_Ouminus(u) || -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x),u),hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x))**.
% 299.64/300.41 2745[0:SpR:25.1,415.0] class_HOL_Ouminus(u) || -> equal(c_Fun_Ofun__upd(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_x,c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),w,x),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)))**.
% 299.64/300.41 2744[0:SpR:25.1,648.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u)),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u)),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.41 2741[0:SpR:25.1,651.0] class_HOL_Ouminus(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.41 2775[0:Rew:25.1,2759.3] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_HOL_Ouminus(u) || equal(v,w) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u))*.
% 299.64/300.41 2776[0:Rew:25.1,2758.3] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_HOL_Ouminus(u) || equal(v,w) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u))*.
% 299.64/300.41 3200[0:SpR:586.0,2771.1] || equal(hAPP(c_COMBB(u,v,w,x),y),z)* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(z,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(y,v_x)),tc_bool))*.
% 299.64/300.41 3199[0:SpR:585.0,2771.1] || equal(hAPP(c_COMBC(u,v,w,x),y),z)* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(z,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),y),tc_bool))*.
% 299.64/300.41 3182[0:SpR:445.1,2771.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),z)* -> equal(v_x,v) equal(c_HOL_Ouminus__class_Ouminus(hAPP(z,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.41 3649[0:SpR:540.1,648.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.41 3644[0:SpR:540.1,651.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.41 3801[0:SpR:539.1,648.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.41 3795[0:SpR:539.1,651.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.41 3913[0:SpR:141.1,53.2] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ominus__class_Ominus(v,w,u),u) -> c_lessequals(c_HOL_Ominus__class_Ominus(w,v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.41 3912[0:SpR:1605.2,53.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.41 3911[0:SpR:1628.2,53.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.41 3905[0:SpR:1421.2,53.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)* -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.41 3904[0:SpR:1409.2,53.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)* -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.41 3977[0:SpR:141.1,41.2] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ominus__class_Ominus(w,v,u),u).
% 299.64/300.41 3976[0:SpR:1605.2,41.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.41 3975[0:SpR:1628.2,41.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.41 3969[0:SpR:1421.2,41.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.41 3968[0:SpR:1409.2,41.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.41 4007[0:SpL:1605.2,54.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u)*.
% 299.64/300.41 4006[0:SpL:1628.2,54.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u)*.
% 299.64/300.41 4000[0:SpL:1421.2,54.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.41 3999[0:SpL:1409.2,54.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.41 4051[0:SpL:1605.2,42.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.41 4050[0:SpL:1628.2,42.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.41 4044[0:SpL:1421.2,42.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u)* -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.41 4043[0:SpL:1409.2,42.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.41 4198[0:SpR:299.2,648.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v_Procs)))*.
% 299.64/300.41 4192[0:SpR:299.2,651.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.41 4292[0:SpR:297.2,648.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v_Procs)))*.
% 299.64/300.41 4285[0:SpR:297.2,651.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.41 4420[0:SpR:540.1,3284.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.41 4419[0:SpR:539.1,3284.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.41 4418[0:SpR:297.2,3284.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),v_x))*.
% 299.64/300.41 4411[0:SpR:299.2,3284.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),v))*.
% 299.64/300.41 4405[0:SpR:25.1,3284.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)))*.
% 299.64/300.41 4468[0:SpL:540.1,3493.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.41 4467[0:SpL:539.1,3493.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.41 4459[0:SpL:299.2,3493.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname))** equal(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.41 4453[0:SpL:25.1,3493.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_in(tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.41 4517[0:SpR:540.1,3316.1] class_Lattices_Olattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.41 4516[0:SpR:539.1,3316.1] class_Lattices_Oupper__semilattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.41 4515[0:SpR:297.2,3316.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.41 4508[0:SpR:299.2,3316.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> hBOOL(hAPP(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.41 4502[0:SpR:25.1,3316.1] class_HOL_Ouminus(u) || equal(c_in(v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u))) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.41 4612[0:SpR:141.1,111.2] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ominus__class_Ominus(w,x,u),u) -> c_lessequals(c_HOL_Ominus__class_Ominus(x,w,u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.41 4611[0:SpR:1605.2,111.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(x,w,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(x,u),u)*.
% 299.64/300.41 4610[0:SpR:1628.2,111.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(x,w,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(x,u),u)*.
% 299.64/300.41 4607[0:SpR:1259.2,111.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) c_lessequals(w,v,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(w,u),u)*.
% 299.64/300.41 4604[0:SpR:1421.2,111.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(w,v,u)* -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ouminus__class_Ouminus(w,u),u)*.
% 299.64/300.41 4603[0:SpR:1409.2,111.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(w,v,u)* -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ouminus__class_Ouminus(w,u),u)*.
% 299.64/300.41 4587[0:SpR:141.1,111.2] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),x,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(x,u),c_HOL_Ominus__class_Ominus(w,v,u),u)*.
% 299.64/300.41 4586[0:SpR:1605.2,111.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(w,x,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(x,u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.41 4585[0:SpR:1628.2,111.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(w,x,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(x,u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.41 4582[0:SpR:1259.2,111.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) c_lessequals(v,w,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(w,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.41 4579[0:SpR:1421.2,111.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(v,w,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(w,u),c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.41 4578[0:SpR:1409.2,111.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(v,w,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(w,u),c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.41 4656[0:SpL:337.0,3698.2] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* equal(c_Com_Ocom_OBODY,u) equal(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 4653[0:SpL:540.1,3698.2] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* equal(c_Com_Ocom_OBODY,v) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.41 4652[0:SpL:539.1,3698.2] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* equal(c_Com_Ocom_OBODY,v) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.41 4651[0:SpL:297.2,3698.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* equal(c_Com_Ocom_OBODY,w) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 4644[0:SpL:299.2,3698.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* equal(c_Com_Ocom_OBODY,w) equal(v,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 4637[0:SpL:25.1,3698.2] class_HOL_Ouminus(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u)))* equal(c_Com_Ocom_OBODY,v) equal(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.41 4673[0:SpL:1605.2,146.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),x,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(x,u),w,u)*.
% 299.64/300.41 4672[0:SpL:1628.2,146.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),x,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(x,u),w,u)*.
% 299.64/300.41 4669[0:SpL:1259.2,146.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(w,u),v,u)*.
% 299.64/300.41 4666[0:SpL:1421.2,146.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(c_Orderings_Otop__class_Otop(u),w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(w,u),v,u)*.
% 299.64/300.41 4665[0:SpL:1409.2,146.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(c_Orderings_Obot__class_Obot(u),w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(w,u),v,u)*.
% 299.64/300.41 4768[0:SpL:1605.2,144.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(x,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(x,u),u)*.
% 299.64/300.41 4767[0:SpL:1628.2,144.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(x,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(x,u),u)*.
% 299.64/300.41 4764[0:SpL:1259.2,144.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,u),u)*.
% 299.64/300.41 4761[0:SpL:1421.2,144.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(w,c_Orderings_Otop__class_Otop(u),u) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,u),u)*.
% 299.64/300.41 4760[0:SpL:1409.2,144.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(w,c_Orderings_Obot__class_Obot(u),u) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,u),u)*.
% 299.64/300.41 4920[0:SpL:141.1,112.1] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ouminus__class_Ouminus(x,u),u)* -> c_lessequals(x,c_HOL_Ominus__class_Ominus(w,v,u),u).
% 299.64/300.41 4919[0:SpL:1605.2,112.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(x,u),u)* -> c_lessequals(x,w,u)*.
% 299.64/300.41 4918[0:SpL:1628.2,112.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(x,u),u)* -> c_lessequals(x,w,u)*.
% 299.64/300.41 4915[0:SpL:1259.2,112.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(w,u),u)* -> c_lessequals(w,v,u)*.
% 299.64/300.41 4912[0:SpL:1421.2,112.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ouminus__class_Ouminus(w,u),u)* -> c_lessequals(w,v,u)*.
% 299.64/300.41 4911[0:SpL:1409.2,112.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(c_Orderings_Obot__class_Obot(u),c_HOL_Ouminus__class_Ouminus(w,u),u)* -> c_lessequals(w,v,u)*.
% 299.64/300.41 4895[0:SpL:141.1,112.1] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ominus__class_Ominus(w,x,u),u)* -> c_lessequals(c_HOL_Ominus__class_Ominus(x,w,u),v,u).
% 299.64/300.41 4894[0:SpL:1605.2,112.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(c_HOL_Ouminus__class_Ouminus(x,u),c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,x,u)*.
% 299.64/300.41 4893[0:SpL:1628.2,112.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* c_lessequals(c_HOL_Ouminus__class_Ouminus(x,u),c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,x,u)*.
% 299.64/300.41 4890[0:SpL:1259.2,112.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) c_lessequals(c_HOL_Ouminus__class_Ouminus(w,u),c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(v,w,u)*.
% 299.64/300.41 4887[0:SpL:1421.2,112.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) c_lessequals(c_HOL_Ouminus__class_Ouminus(w,u),c_Orderings_Otop__class_Otop(u),u)* -> c_lessequals(v,w,u)*.
% 299.64/300.41 4886[0:SpL:1409.2,112.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) c_lessequals(c_HOL_Ouminus__class_Ouminus(w,u),c_Orderings_Obot__class_Obot(u),u)* -> c_lessequals(v,w,u)*.
% 299.64/300.41 4966[0:Res:687.1,3863.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname)))*.
% 299.64/300.41 4965[0:Res:686.1,3863.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname)))*.
% 299.64/300.41 5014[0:Res:4790.2,405.1] class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),v,u)* -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),v).
% 299.64/300.41 5000[0:Res:4703.2,405.1] class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),u)* -> equal(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u)).
% 299.64/300.41 5112[0:SpR:337.0,3339.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* -> equal(c_Fun_Ofun__upd(u,v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,x),u)**.
% 299.64/300.41 5109[0:SpR:540.1,3339.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> equal(c_Fun_Ofun__upd(v,v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),x,y),v)**.
% 299.64/300.41 5108[0:SpR:539.1,3339.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> equal(c_Fun_Ofun__upd(v,v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),x,y),v)**.
% 299.64/300.41 5107[0:SpR:297.2,3339.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> equal(c_Fun_Ofun__upd(w,v_x,v_x,x,y),w)**.
% 299.64/300.41 5100[0:SpR:299.2,3339.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> equal(c_Fun_Ofun__upd(w,v_x,v,x,y),w)**.
% 299.64/300.41 5093[0:SpR:25.1,3339.1] class_HOL_Ouminus(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u))) -> equal(c_Fun_Ofun__upd(v,v_x,c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u),x,y),v)**.
% 299.64/300.41 5725[0:Res:503.1,123.0] || c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,u),v,w)* c_Natural_Oevalc(x,w,y)* -> c_Natural_Oevalc(c_Com_Ocom_OSemi(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u)),x),v,y)*.
% 299.64/300.41 5989[0:SpL:584.0,371.0] || hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),x1))* -> hBOOL(hAPP(x1,hAPP(w,x1)))* equal(u,hAPP(w,x1)).
% 299.64/300.41 5984[0:SpL:584.0,298.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),hAPP(v,z))** -> c_lessequals(z,hAPP(v,z),u)*.
% 299.64/300.41 5983[0:SpL:584.0,3698.2] || equal(u,c_COMBS(v,w,x,y,z))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(hAPP(v,v_x),hAPP(w,v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.41 5982[0:SpL:584.0,3493.1] || equal(c_COMBS(u,v,w,x,y),c_in(tc_Com_Opname))** equal(hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))* -> .
% 299.64/300.41 5976[0:SpR:9.0,584.0] || -> equal(hAPP(c_COMBS(c_Fun_Ocomp(u,v,w,x,y),z,x1,x2,x3),x4),hAPP(hAPP(u,hAPP(v,x4)),hAPP(z,x4)))*.
% 299.64/300.41 5971[0:SpR:303.1,584.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y,z),c_Orderings_Otop__class_Otop(u)),hAPP(c_Orderings_Otop__class_Otop(u),hAPP(w,c_Orderings_Otop__class_Otop(u))))**.
% 299.64/300.41 5962[0:SpR:88.1,584.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),w,x,y,z),v),hAPP(c_Orderings_Otop__class_Otop(u),hAPP(w,v)))**.
% 299.64/300.41 5956[0:SpR:2098.1,584.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) equal(hAPP(c_COMBS(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,x,y,z),v),hAPP(v,hAPP(w,v)))**.
% 299.64/300.41 5939[0:SpR:9.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Fun_Ocomp(v,w,x,y,z),x1,x2,x3),x4),hAPP(hAPP(u,x4),hAPP(v,hAPP(w,x4))))*.
% 299.64/300.41 5934[0:SpR:303.1,584.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),c_Orderings_Otop__class_Otop(u)),hAPP(hAPP(v,c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u)))**.
% 299.64/300.41 5925[0:SpR:88.1,584.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),x,y,z),w),hAPP(hAPP(v,w),c_Orderings_Otop__class_Otop(u)))**.
% 299.64/300.41 5919[0:SpR:2098.1,584.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) equal(hAPP(c_COMBS(w,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),x,y,z),v),hAPP(hAPP(w,v),v))**.
% 299.64/300.41 5889[0:SpR:584.0,297.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,hAPP(w,v),u)* -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),v),hAPP(w,v))**.
% 299.64/300.41 5870[0:SpR:584.0,3339.1] || equal(u,c_COMBS(v,w,x,y,z))* -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(hAPP(v,v_x),hAPP(w,v_x)),x1,x2),u)**.
% 299.64/300.41 5869[0:SpR:584.0,3316.1] || equal(c_in(u),c_COMBS(v,w,x,y,z))* -> hBOOL(hAPP(hAPP(hAPP(v,v_x),hAPP(w,v_x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.41 5866[0:SpR:584.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(v,v_x),hAPP(w,v_x))),hAPP(c_Set_Oimage(c_COMBS(v,w,x,y,z),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.41 5864[0:SpR:584.0,3284.1] || equal(c_COMBS(u,v,w,x,y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(z),v_Procs),hAPP(hAPP(u,v_x),hAPP(v,v_x))))*.
% 299.64/300.41 5858[0:SpR:584.0,651.0] || -> c_lessequals(hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBS(u,v,w,x,y),tc_Com_Opname,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.64/300.41 6331[0:SpR:586.0,3279.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(hAPP(u,hAPP(y,v_x)),v_Procs),v_x))*.
% 299.64/300.41 6330[0:SpR:585.0,3279.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(hAPP(hAPP(u,v_x),y),v_Procs),v_x))*.
% 299.64/300.41 6304[0:SpR:445.1,3279.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> equal(v_x,v) hBOOL(hAPP(hAPP(hAPP(u,v_x),v_Procs),v_x))*.
% 299.64/300.41 6472[0:SpL:538.0,3929.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.41 6436[0:SpR:538.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y,z,x1),v))*.
% 299.64/300.41 6418[0:SpR:538.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname,u),u)*.
% 299.64/300.41 6514[0:SpR:586.0,3285.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(u,hAPP(y,v_x)),hAPP(c_Set_Oinsert(z,tc_Com_Opname),v_Procs)))*.
% 299.64/300.41 6513[0:SpR:585.0,3285.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),y),hAPP(c_Set_Oinsert(z,tc_Com_Opname),v_Procs)))*.
% 299.64/300.41 6485[0:SpR:445.1,3285.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_in(tc_Com_Opname))** -> equal(v_x,v) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oinsert(z,tc_Com_Opname),v_Procs)))*.
% 299.64/300.41 6663[0:SpR:329.1,3316.1] || c_lessequals(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_fun(v,tc_bool))* equal(c_in(u),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))).
% 299.64/300.41 6635[0:SpR:329.1,5875.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(v,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y,z,x1),v))*.
% 299.64/300.41 6617[0:SpR:329.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || c_lessequals(v,v_x,tc_fun(w,tc_bool)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),tc_Com_Opname,u),u)*.
% 299.64/300.41 6753[0:SpR:586.0,3291.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(u,hAPP(y,v_x))),v_Procs))*.
% 299.64/300.41 6752[0:SpR:585.0,3291.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(hAPP(u,v_x),y)),v_Procs))*.
% 299.64/300.41 6723[0:SpR:445.1,3291.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_in(tc_Com_Opname))** -> equal(v_x,v) hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(u,v_x)),v_Procs))*.
% 299.64/300.41 6836[0:SpL:328.1,3929.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) hBOOL(u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.41 6779[0:SpR:328.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || c_lessequals(v_x,v,tc_fun(w,tc_bool)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),tc_Com_Opname,u),u)*.
% 299.64/300.41 6884[0:SpL:586.0,3484.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Com_Ocom_OBODY)** equal(hAPP(u,hAPP(y,v_x)),hAPP(c_Com_Ocom_OBODY,z))* -> equal(v_x,z).
% 299.64/300.41 6883[0:SpL:585.0,3484.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Com_Ocom_OBODY)** equal(hAPP(hAPP(u,v_x),y),hAPP(c_Com_Ocom_OBODY,z))* -> equal(v_x,z).
% 299.64/300.41 6853[0:SpL:445.1,3484.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Com_Ocom_OBODY)** equal(hAPP(u,v_x),hAPP(c_Com_Ocom_OBODY,z))* -> equal(v_x,v) equal(v_x,z).
% 299.64/300.41 6923[0:SpL:297.2,3499.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),u)* equal(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(u)) hBOOL(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) -> .
% 299.64/300.41 6920[0:SpL:586.0,3499.1] || equal(c_in(u),hAPP(c_COMBB(v,w,x,y),z))* hBOOL(hAPP(hAPP(v,hAPP(z,v_x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.41 6919[0:SpL:585.0,3499.1] || equal(c_in(u),hAPP(c_COMBC(v,w,x,y),z))* hBOOL(hAPP(hAPP(hAPP(v,v_x),z),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.41 6889[0:SpL:445.1,3499.1] || equal(c_in(u),c_Fun_Ofun__upd(v,w,x,y,z))* hBOOL(hAPP(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> equal(v_x,w).
% 299.64/300.41 7141[0:SpR:586.0,3305.1] || equal(u,hAPP(c_COMBB(v,w,x,y),z))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x1),v_Procs),hAPP(v,hAPP(z,v_x))))*.
% 299.64/300.41 7140[0:SpR:585.0,3305.1] || equal(u,hAPP(c_COMBC(v,w,x,y),z))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x1),v_Procs),hAPP(hAPP(v,v_x),z)))*.
% 299.64/300.41 7110[0:SpR:445.1,3305.1] || equal(u,c_Fun_Ofun__upd(v,w,x,y,z))* -> equal(v_x,w) hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x1),v_Procs),hAPP(v,v_x)))*.
% 299.64/300.41 7184[0:SpR:586.0,3317.1] || equal(c_in(u),hAPP(c_COMBB(v,w,x,y),z))* -> hBOOL(hAPP(hAPP(v,hAPP(z,v_x)),hAPP(c_Set_Oinsert(v_x,u),x1)))*.
% 299.64/300.41 7183[0:SpR:585.0,3317.1] || equal(c_in(u),hAPP(c_COMBC(v,w,x,y),z))* -> hBOOL(hAPP(hAPP(hAPP(v,v_x),z),hAPP(c_Set_Oinsert(v_x,u),x1)))*.
% 299.64/300.41 7153[0:SpR:445.1,3317.1] || equal(c_in(u),c_Fun_Ofun__upd(v,w,x,y,z))* -> equal(v_x,w) hBOOL(hAPP(hAPP(v,v_x),hAPP(c_Set_Oinsert(v_x,u),x1)))*.
% 299.64/300.41 7247[0:SpR:336.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.41 7220[0:SpR:331.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.41 7200[0:SpR:3744.1,474.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.41 7308[0:SpR:584.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,v,w,x,y),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),hAPP(hAPP(u,x2),hAPP(v,x2))))*.
% 299.64/300.41 7282[0:SpR:540.1,7253.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v)))*.
% 299.64/300.41 7281[0:SpR:539.1,7253.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v)))*.
% 299.64/300.41 7280[0:SpR:297.2,7253.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),w))*.
% 299.64/300.41 7266[0:SpR:25.1,7253.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)))*.
% 299.64/300.41 7346[0:SpL:586.0,3507.1] || equal(c_Set_Oinsert(u,v),hAPP(c_COMBB(w,x,y,z),x1))* equal(hAPP(w,hAPP(x1,v_x)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.41 7345[0:SpL:585.0,3507.1] || equal(c_Set_Oinsert(u,v),hAPP(c_COMBC(w,x,y,z),x1))* equal(hAPP(hAPP(w,v_x),x1),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.41 7315[0:SpL:445.1,3507.1] || equal(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,y,z,x1))* equal(hAPP(w,v_x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> equal(v_x,x).
% 299.64/300.41 7517[0:SpR:586.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(c_COMBB(w,x,y,z),x1))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(w,hAPP(x1,v_x))))*.
% 299.64/300.41 7516[0:SpR:585.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(c_COMBC(w,x,y,z),x1))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(hAPP(w,v_x),x1)))*.
% 299.64/300.41 7486[0:SpR:445.1,3346.1] || equal(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,y,z,x1))* -> equal(v_x,x) hBOOL(hAPP(hAPP(c_in(v),u),hAPP(w,v_x)))*.
% 299.64/300.41 7596[0:Res:7539.0,2092.0] || -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))),hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))**.
% 299.64/300.41 7678[0:SSi:7657.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(u,x))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v),x))*.
% 299.64/300.41 7741[0:SSi:7721.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(u,x))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),x))*.
% 299.64/300.41 8083[0:SpR:584.0,7284.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oimage(c_COMBK(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w,x),v,y),u,z,x1,x2),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.41 8170[0:Res:4801.2,427.1] class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),u),v,u)* -> c_lessequals(w,v,u)*.
% 299.64/300.41 8151[0:Res:49.2,427.1] class_OrderedGroup_Olordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)* -> c_lessequals(v,w,u).
% 299.64/300.41 8150[0:Res:45.2,427.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)* -> c_lessequals(v,w,u).
% 299.64/300.41 8130[0:Res:47.2,427.1] class_OrderedGroup_Olordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(v,w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.41 8129[0:Res:43.2,427.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(v,w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.41 8180[0:SSi:8116.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(x,y,w),hAPP(c_Set_Ovimage(x,y,w),u)),v,tc_fun(w,tc_bool))*.
% 299.64/300.41 8220[0:Res:5888.1,427.1] class_Lattices_Olattice(u) class_Orderings_Opreorder(u) || c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),x1,u)* -> c_lessequals(z,x1,u).
% 299.64/300.41 8278[0:Res:49.2,426.1] class_OrderedGroup_Olordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(w,v,u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.41 8277[0:Res:45.2,426.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(w,v,u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.41 8274[0:Res:5888.1,426.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(v,w,u) -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),w),u)*.
% 299.64/300.41 8255[0:Res:47.2,426.1] class_OrderedGroup_Olordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,v,u).
% 299.64/300.41 8254[0:Res:43.2,426.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,v,u).
% 299.64/300.41 8313[0:SSi:8241.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Ovimage(v,w,x),y)),tc_fun(x,tc_bool))* -> c_lessequals(u,y,tc_fun(x,tc_bool)).
% 299.64/300.41 8609[0:SpR:8498.1,584.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(hAPP(c_COMBS(c_Set_Oinsert(w,v),x,y,z,x1),u),hAPP(u,hAPP(x,u)))*.
% 299.64/300.41 8608[0:SpR:8498.1,584.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(hAPP(c_COMBS(w,c_Set_Oinsert(x,v),y,z,x1),u),hAPP(hAPP(w,u),u))*.
% 299.64/300.41 8607[0:SpR:8498.1,1103.1] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oinsert(v,w)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Oinsert(v,w),t_a)* hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oinsert(v,w))).
% 299.64/300.41 8720[0:SpR:584.0,335.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(hAPP(w,u),v) -> c_Finite__Set_Ofinite(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),u),v)*.
% 299.64/300.41 8956[0:SpL:8415.2,279.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,v)) -> equal(hAPP(c_Set_Oinsert(v_x,u),v),v)**.
% 299.64/300.41 8952[0:SpL:8415.2,3331.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(v_x,v) -> equal(hAPP(v,v_x),v_x)**.
% 299.64/300.41 8951[0:SpL:8415.2,3727.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(c_in(tc_Com_Opname),v_x) -> hBOOL(hAPP(v_x,v_Procs))*.
% 299.64/300.41 8946[0:SpL:8415.2,3945.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_Com_Ocom_OBODY,v_x) equal(c_Com_Ocom_OSemi(v,w),v_x)** -> .
% 299.64/300.41 8945[0:SpL:8415.2,3499.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_in(v),u)* hBOOL(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.41 8942[0:SpL:8415.2,3484.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_Com_Ocom_OBODY,u) equal(hAPP(c_Com_Ocom_OBODY,v),v_x)** -> equal(v_x,v).
% 299.64/300.41 8926[0:SpL:8415.2,3303.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(hAPP(v_x,v_Procs),u) -> hBOOL(hAPP(u,v_x))*.
% 299.64/300.41 8925[0:SpL:8415.2,1944.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v_x,v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.41 8916[0:SpR:8415.2,5877.0] || equal(v_Procs,v_x) equal(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Com_Ocom_OBODY,v,w,x),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(v_x,y),u)*.
% 299.64/300.41 8915[0:SpR:8415.2,586.0] || equal(v_Procs,v_x) equal(c_COMBB(u,v,w,x),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(u,hAPP(v_x,y)),hAPP(v_x,y))**.
% 299.64/300.41 8914[0:SpR:8415.2,585.0] || equal(v_Procs,v_x) equal(c_COMBC(u,v,w,x),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(hAPP(u,y),v_x),hAPP(v_x,y))**.
% 299.64/300.41 8912[0:SpR:8415.2,5877.0] || equal(v_Procs,v_x) equal(hAPP(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Com_Ocom_OBODY,v,w,x),y),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),v_x,u).
% 299.64/300.41 8911[0:SpR:8415.2,586.0] || equal(v_Procs,v_x) equal(hAPP(c_COMBB(u,v,w,x),y),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(u,hAPP(y,v_x)),v_x).
% 299.64/300.41 8910[0:SpR:8415.2,585.0] || equal(v_Procs,v_x) equal(hAPP(c_COMBC(u,v,w,x),y),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(hAPP(u,v_x),y),v_x).
% 299.64/300.41 8811[0:SpR:8415.2,1157.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(c_COMBK(v_x,v,w),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.41 8805[0:SpR:8415.2,3346.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_Set_Oinsert(v,w),u)* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x))*.
% 299.64/300.41 8803[0:SpR:8415.2,1162.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.41 8801[0:SpR:8415.2,3317.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_in(v),u)* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,v),w)))*.
% 299.64/300.41 8800[0:SpR:8415.2,3305.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(v,u)* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.41 8792[0:SpR:8415.2,3291.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),v_Procs))*.
% 299.64/300.41 8791[0:SpR:8415.2,3285.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.41 8788[0:SpR:8415.2,3279.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u)* -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.41 8770[0:SpR:8415.2,7599.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),v_Procs))*.
% 299.64/300.41 8755[0:SpR:8415.2,445.1] || equal(v_Procs,v_x) equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(v_x,v) equal(hAPP(u,v_x),v_x).
% 299.64/300.41 9028[0:Rew:8415.2,8813.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(v_x,v)) hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))))*.
% 299.64/300.41 9175[0:SpR:586.0,8376.2] || equal(hAPP(c_COMBB(u,v,w,x),y),c_in(tc_Com_Opname))** equal(z,v_Procs) -> hBOOL(hAPP(hAPP(u,hAPP(y,v_x)),z))*.
% 299.64/300.41 9174[0:SpR:585.0,8376.2] || equal(hAPP(c_COMBC(u,v,w,x),y),c_in(tc_Com_Opname))** equal(z,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(u,v_x),y),z))*.
% 299.64/300.41 9149[0:SpR:8415.2,8376.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_in(tc_Com_Opname),u) equal(v,v_Procs) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.41 9143[0:SpR:445.1,8376.2] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_in(tc_Com_Opname))** equal(z,v_Procs) -> equal(v_x,v) hBOOL(hAPP(hAPP(u,v_x),z))*.
% 299.64/300.41 9224[0:Res:9071.0,279.0] || -> equal(hAPP(c_Set_Oinsert(u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)))**.
% 299.64/300.41 9220[0:SpR:8415.2,9071.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_x,u),tc_Com_Opname,tc_fun(u,tc_bool))))*.
% 299.64/300.41 9435[0:SpL:584.0,346.0] || c_Fun_Oinj__on(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),x1),v,x2)* -> c_Fun_Oinj__on(u,hAPP(w,x1),v,x2).
% 299.64/300.41 9463[0:SpR:302.1,9268.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))**.
% 299.64/300.41 9537[0:Res:309.1,251.1] class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),y),w),x),v)*.
% 299.64/300.41 9536[0:Res:306.1,251.1] class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),y),w),x),v)*.
% 299.64/300.41 9534[0:Res:310.1,251.1] class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),w),y),x),v)*.
% 299.64/300.41 9533[0:Res:305.1,251.1] class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),w),y),x),v)*.
% 299.64/300.41 10419[0:SpL:3229.1,590.0] || equal(u,v_P) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(u,v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(v_Q,v_x)),t_a)* -> .
% 299.64/300.41 10416[0:SpL:3229.1,590.0] || equal(u,c_Com_Ocom_OBODY) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(u,v_x)),hAPP(v_Q,v_x)),t_a)* -> .
% 299.64/300.41 10413[0:SpL:3229.1,590.0] || equal(u,v_Q) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(u,v_x)),t_a)* -> .
% 299.64/300.41 10490[0:SpL:3229.1,454.0] || equal(u,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v))* hBOOL(hAPP(u,v_x))* -> c_Hoare__Mirabelle_Ohoare__valids(v_x,w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v_x,w),v,t_a)*.
% 299.64/300.41 10487[0:SpL:3229.1,454.0] || equal(u,c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(hAPP(u,v_x),v))* -> c_Hoare__Mirabelle_Ohoare__valids(v,w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v,w),v_x,t_a)*.
% 299.64/300.41 10597[0:SpL:3229.1,57.1] class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) equal(hAPP(hAPP(v,v_x),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_HOL_Ozero__class_Ozero(u))** -> equal(c_HOL_Ozero__class_Ozero(u),v_x).
% 299.64/300.41 10657[0:SpL:3229.1,505.0] || equal(u,c_Com_Obody) c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(u,v_x)),v,w,x)* -> c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_x),v,c_Suc(w),x).
% 299.64/300.41 10770[0:Res:254.1,279.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(x,u),w)),hAPP(c_Set_Oinsert(x,u),w))**.
% 299.64/300.41 10766[0:SpR:3229.1,254.1] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oinsert(x,v),w)))*.
% 299.64/300.41 10760[0:SpR:3229.1,254.1] || equal(u,c_Set_Oinsert(v,w))* hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),x),hAPP(u,v_x)))*.
% 299.64/300.41 10910[0:SpL:353.0,7600.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(x,v),y))),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(w,v),y),v).
% 299.64/300.41 10909[0:SpL:353.0,360.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),y)),w,z)* -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),y),w,z).
% 299.64/300.41 10905[0:SpL:353.0,4382.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),x),v_x)) equal(w,v_x).
% 299.64/300.41 10881[0:SpR:3229.1,353.0] || equal(u,c_Set_Oinsert(v,w)) -> equal(hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),v_x)),hAPP(c_Set_Oinsert(x,w),hAPP(u,v_x)))*.
% 299.64/300.41 10878[0:SpR:369.0,353.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(u,v),x))),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(u,v),x)))**.
% 299.64/300.41 10832[0:SpR:353.0,7460.1] || c_lessequals(v_Procs,hAPP(c_Set_Oinsert(u,tc_Com_Opname),v),tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v)),v_x))*.
% 299.64/300.41 10831[0:SpR:353.0,8385.1] || equal(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v)),hAPP(c_Set_Oinsert(u,tc_Com_Opname),v))**.
% 299.64/300.41 11086[0:Res:448.1,357.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,w) -> c_lessequals(hAPP(c_Set_Oimage(x,w,u),v),y,tc_fun(u,tc_bool))* c_Finite__Set_Ofinite(y,u).
% 299.64/300.41 11060[0:SpL:3229.1,357.1] || equal(u,c_Set_Oimage(v,w,x))* c_Finite__Set_Ofinite(v_x,w) c_lessequals(y,hAPP(u,v_x),tc_fun(x,tc_bool))* -> c_Finite__Set_Ofinite(y,x).
% 299.64/300.41 11312[0:SpL:584.0,345.0] || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> equal(z,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.64/300.41 11363[0:SpR:11177.1,474.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.41 11563[0:SSi:11552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w)* -> c_lessequals(v,w,tc_bool)*.
% 299.64/300.41 11564[0:SSi:11551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w)* -> c_lessequals(u,w,tc_bool)*.
% 299.64/300.41 11619[0:SpR:329.1,9567.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,tc_fun(y,tc_bool)),v),v,tc_bool)*.
% 299.64/300.41 11618[0:SpR:328.1,9567.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,tc_fun(y,tc_bool)),u),v,tc_bool)*.
% 299.64/300.41 11617[0:SpR:538.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,tc_fun(x,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v),tc_bool)*.
% 299.64/300.41 11615[0:SpR:599.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool)*.
% 299.64/300.41 11749[0:SpL:130.1,3483.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Com_Ocom_OBODY) equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.41 11740[0:SpR:1.1,130.1] class_OrderedGroup_Oab__group__add(tc_fun(t_a,u)) class_HOL_Ominus(u) || -> equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(v,v_x),u),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x))**.
% 299.64/300.41 11739[0:SpR:4.1,130.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_HOL_Ominus(u) || -> equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(v,v_x),u),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x))**.
% 299.64/300.41 11737[0:SpR:3.1,130.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_HOL_Ominus(u) || -> equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),u),hAPP(v,v_x))**.
% 299.64/300.41 12039[0:SpL:584.0,325.0] || c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),x1,tc_fun(u,tc_bool))* -> c_lessequals(z,x1,tc_fun(u,tc_bool)).
% 299.64/300.41 12089[0:SSi:12075.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),x1)),tc_fun(v,tc_bool))*.
% 299.64/300.41 12440[0:SSi:12426.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),u)),tc_fun(v,tc_bool))*.
% 299.64/300.41 12688[0:MRR:3888.2,12687.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(v,c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),w))*.
% 299.64/300.41 12999[0:Res:8376.2,501.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) equal(u,v_Procs) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.64/300.41 12995[0:Res:3285.1,501.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.41 12994[0:Res:3317.1,501.0] || equal(c_in(u),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,hAPP(c_Set_Oinsert(v_x,u),w)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.64/300.41 12981[0:Res:474.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(v,x),t_a)*.
% 299.64/300.41 13086[0:SpR:584.0,10090.1] || equal(c_COMBS(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.41 13072[0:SpR:540.1,10090.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.41 13071[0:SpR:539.1,10090.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.41 13070[0:SpR:297.2,10090.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.41 13061[0:SpR:299.2,10090.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.41 13052[0:SpR:25.1,10090.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.41 13020[0:SpR:10090.1,474.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(u,v_x),w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.41 13159[0:SpR:81.0,108.1] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.41 13180[0:SSi:13169.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),x),hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),x),tc_bool)*.
% 299.64/300.41 13258[0:SpR:9493.1,584.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(c_COMBS(c_Set_Oinsert(v_x,t_a),v,w,x,y),u),hAPP(u,hAPP(v,u)))*.
% 299.64/300.41 13257[0:SpR:9493.1,584.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(c_COMBS(v,c_Set_Oinsert(v_x,t_a),w,x,y),u),hAPP(hAPP(v,u),u))*.
% 299.64/300.41 13256[0:SpR:9493.1,1103.1] || equal(hAPP(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oinsert(v_x,t_a)),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Oinsert(v_x,t_a),t_a) hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oinsert(v_x,t_a))).
% 299.64/300.41 13354[0:SpL:81.0,109.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> c_lessequals(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)).
% 299.64/300.41 13334[0:SpL:79.0,109.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,tc_fun(v,tc_bool)).
% 299.64/300.41 13549[0:SpR:329.1,11030.1] || c_lessequals(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_fun(v,tc_bool))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_in(t_a)) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))).
% 299.64/300.41 13545[0:SpR:584.0,11030.1] || equal(c_COMBS(u,v,w,x,y),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))*.
% 299.64/300.41 13531[0:SpR:540.1,11030.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.41 13530[0:SpR:539.1,11030.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.41 13529[0:SpR:297.2,11030.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.41 13520[0:SpR:299.2,11030.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a))** -> hBOOL(hAPP(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.41 13511[0:SpR:25.1,11030.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.41 13643[0:SpR:11473.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,x,y,z),x1),hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(w,x1)))**.
% 299.64/300.41 13642[0:SpR:11473.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),x,y,z),x1),hAPP(hAPP(u,x1),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.64/300.41 13668[0:MRR:13667.0,826.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))),hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))**.
% 299.64/300.41 13675[0:SpR:11499.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.64/300.41 13770[0:SpR:3229.1,544.1] class_Lattices_Olattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u))* -> equal(hAPP(hAPP(v,v_x),hAPP(hAPP(v,v_x),w)),hAPP(hAPP(v,v_x),w))**.
% 299.64/300.41 13768[0:SpR:8415.2,544.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* -> equal(hAPP(v_x,hAPP(v_x,v)),hAPP(v_x,v))**.
% 299.64/300.41 13865[0:SpL:540.1,11759.0] class_Lattices_Olattice(u) || hBOOL(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(w,v_x),tc_bool))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)).
% 299.64/300.41 13864[0:SpL:539.1,11759.0] class_Lattices_Oupper__semilattice(u) || hBOOL(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(w,v_x),tc_bool))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)).
% 299.64/300.41 14065[0:SpR:3229.1,543.1] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u))* -> equal(hAPP(hAPP(v,v_x),hAPP(hAPP(v,v_x),w)),hAPP(hAPP(v,v_x),w))**.
% 299.64/300.41 14063[0:SpR:8415.2,543.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* -> equal(hAPP(v_x,hAPP(v_x,v)),hAPP(v_x,v))**.
% 299.64/300.41 14149[0:SpR:10463.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),u,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.64/300.41 14148[0:SpR:9911.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.64/300.41 14263[0:SpR:14216.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.64/300.41 14259[0:SpR:14216.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,c_Orderings_Otop__class_Otop(tc_bool),y,z),hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))**.
% 299.64/300.41 14380[0:Res:8376.2,170.1] class_Orderings_Olinorder(u) || equal(c_in(tc_Com_Opname),c_in(u)) equal(v,v_Procs) c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),v_x,u)*.
% 299.64/300.41 14379[0:Res:168.0,170.1] class_Orderings_Olinorder(tc_Hoare__Mirabelle_Otriple(t_a)) || c_Finite__Set_Ofinite(u,tc_Hoare__Mirabelle_Otriple(t_a)) -> c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a) c_lessequals(c_Finite__Set_Olinorder__class_OMin(u,tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,u),tc_Hoare__Mirabelle_Otriple(t_a))*.
% 299.64/300.41 14366[0:Res:3346.1,170.1] class_Orderings_Olinorder(u) || equal(c_Set_Oinsert(v,u),w) c_Finite__Set_Ofinite(hAPP(w,v_x),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(w,v_x),u),v,u)*.
% 299.64/300.41 14438[0:SpR:12944.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y,z,x1,x2),x3),hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(y,x3)))**.
% 299.64/300.41 14437[0:SpR:12944.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)),z,x1,x2),x3),hAPP(hAPP(u,x3),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.64/300.41 14465[0:MRR:14464.0,826.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x))),hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)))**.
% 299.64/300.41 14507[0:Res:8376.2,169.1] class_Orderings_Olinorder(u) || equal(c_in(tc_Com_Opname),c_in(u)) equal(v,v_Procs) c_Finite__Set_Ofinite(v,u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.64/300.41 14506[0:Res:168.0,169.1] class_Orderings_Olinorder(tc_Hoare__Mirabelle_Otriple(t_a)) || c_Finite__Set_Ofinite(u,tc_Hoare__Mirabelle_Otriple(t_a)) -> c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a) c_lessequals(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,u),c_Finite__Set_Olinorder__class_OMax(u,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a))*.
% 299.64/300.41 14493[0:Res:3346.1,169.1] class_Orderings_Olinorder(u) || equal(c_Set_Oinsert(v,u),w) c_Finite__Set_Ofinite(hAPP(w,v_x),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(hAPP(w,v_x),u),u)*.
% 299.64/300.41 14764[0:SpL:128.0,4439.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)),v_Procs)** -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),hAPP(u,v_x))).
% 299.64/300.41 15210[0:SpR:9987.0,446.1] || c_lessequals(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(t_a,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(t_a,tc_bool))*.
% 299.64/300.41 15199[0:SpR:2093.0,446.1] || c_lessequals(u,hAPP(c_in(tc_Com_Opname),v_x),tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_Procs,v),u),hAPP(c_in(tc_Com_Opname),v_x),tc_fun(v,tc_bool))*.
% 299.64/300.41 15198[0:SpR:3744.1,446.1] || equal(c_in(tc_Com_Opname),c_in(u)) c_lessequals(v,v_Procs,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,u),v),v_Procs,tc_fun(u,tc_bool))*.
% 299.64/300.41 15240[0:SSi:15236.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(x,w),u),y),hAPP(hAPP(c_Set_Oinsert(x,w),v),y),tc_bool)*.
% 299.64/300.41 15534[0:Rew:15475.0,15441.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.41 15653[0:Res:8376.2,278.1] || equal(c_in(tc_Com_Opname),c_in(u)) equal(v,v_Procs) hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,x,w,u)))*.
% 299.64/300.41 15643[0:Res:3285.1,278.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),x,v,u)))*.
% 299.64/300.41 15642[0:Res:3317.1,278.1] || equal(c_in(u),c_in(v)) hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v_x,u),x),y,w,v)))*.
% 299.64/300.41 15628[0:Res:474.0,278.1] || hBOOL(hAPP(u,hAPP(v,w)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(v,x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),z,u,y)))*.
% 299.64/300.41 15813[0:SpR:584.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBS(u,v,w,x,y),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_bool)).
% 299.64/300.41 15801[0:SpR:337.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool)).
% 299.64/300.41 15796[0:SpR:540.1,15482.1] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))*.
% 299.64/300.41 15795[0:SpR:539.1,15482.1] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))*.
% 299.64/300.41 15785[0:SpR:299.2,15482.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool)).
% 299.64/300.41 15774[0:SpR:25.1,15482.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool)).
% 299.64/300.41 15881[0:Res:8376.2,277.1] || equal(c_in(tc_Com_Opname),c_in(u)) equal(v,v_Procs) hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v,w,u)))*.
% 299.64/300.41 15871[0:Res:3285.1,277.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs),v,u)))*.
% 299.64/300.41 15870[0:Res:3317.1,277.1] || equal(c_in(u),c_in(v)) hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(v_x,u),y),w,v)))*.
% 299.64/300.41 15856[0:Res:474.0,277.1] || hBOOL(hAPP(u,hAPP(v,w)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oimage(v,y,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u,z)))*.
% 299.64/300.41 15953[2:SpR:584.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBS(u,v,w,x,y),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_bool)).
% 299.64/300.41 15941[2:SpR:337.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool)).
% 299.64/300.41 15936[2:SpR:540.1,15483.1] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))*.
% 299.64/300.41 15935[2:SpR:539.1,15483.1] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))*.
% 299.64/300.41 15934[2:SpR:297.2,15483.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.41 15925[2:SpR:299.2,15483.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v,tc_bool)).
% 299.64/300.41 15914[2:SpR:25.1,15483.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool)).
% 299.64/300.41 16011[0:SpL:10090.1,515.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(w,v)*.
% 299.64/300.41 16006[0:SpL:10090.1,515.0] || equal(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(c_Orderings_Otop__class_Otop(tc_bool),y))* -> equal(v,v_x).
% 299.64/300.41 16119[0:SpL:10090.1,514.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(x,v_x).
% 299.64/300.41 16192[0:Res:15262.1,278.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),w,v,u)))*.
% 299.64/300.41 16191[0:Res:15262.1,277.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v,u)))*.
% 299.64/300.41 16189[0:Res:15262.1,501.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.41 16171[0:SpR:586.0,15262.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_in(t_a))** -> hBOOL(hAPP(hAPP(u,hAPP(y,v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.41 16170[0:SpR:585.0,15262.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.41 16136[0:SpR:8415.2,15262.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_in(t_a),u) -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.41 16130[0:SpR:445.1,15262.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_in(t_a))** -> equal(v_x,v) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.41 16260[0:SpL:329.1,16217.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_Procs)** -> .
% 299.64/300.41 16259[0:SpL:328.1,16217.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_Procs)** -> .
% 299.64/300.41 16258[0:SpL:538.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs) -> .
% 299.64/300.41 16310[0:SpL:10090.1,513.0] || equal(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(c_Orderings_Otop__class_Otop(tc_bool),y))* -> equal(x,y).
% 299.64/300.41 16471[0:SpL:9935.1,3507.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w))* equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.41 16470[0:SpL:9935.1,3499.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.41 16466[0:SpL:9935.1,3484.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,v),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(v_x,v).
% 299.64/300.41 16458[0:SpR:8415.2,9935.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* -> equal(hAPP(v_x,u),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.41 16404[0:SpR:9935.1,3346.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w))* -> hBOOL(hAPP(hAPP(c_in(v),u),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.41 16403[0:SpR:9935.1,3317.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(v_x,u),w)))*.
% 299.64/300.41 16402[0:SpR:9935.1,3305.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.41 16395[0:SpR:9935.1,15262.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.41 16392[0:SpR:9935.1,8376.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v))*.
% 299.64/300.41 16390[0:SpR:9935.1,3291.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_bool)),v_Procs))*.
% 299.64/300.41 16389[0:SpR:9935.1,3285.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.41 16386[0:SpR:9935.1,3279.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_Procs),v_x))*.
% 299.64/300.41 16536[0:SpR:10463.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),v,u),u)*.
% 299.64/300.41 16535[0:SpR:9911.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),v,u),u)*.
% 299.64/300.41 16603[0:SSi:16592.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(y,x),u,tc_fun(x,tc_bool))))*.
% 299.64/300.41 16604[0:SSi:16591.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),y)* -> c_Finite__Set_Ofinite(hAPP(x,v),y)*.
% 299.64/300.41 16709[0:SpL:9936.1,3507.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> .
% 299.64/300.41 16708[0:SpL:9936.1,3499.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.41 16704[0:SpL:9936.1,3484.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Com_Ocom_OBODY) equal(hAPP(c_Com_Ocom_OBODY,v),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(v_x,v).
% 299.64/300.41 16696[0:SpR:8415.2,9936.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* -> equal(hAPP(v_x,u),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.41 16640[0:SpR:9936.1,3346.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* -> hBOOL(hAPP(hAPP(c_in(w),v),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.41 16639[0:SpR:9936.1,3317.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(v_x,v),w)))*.
% 299.64/300.41 16638[0:SpR:9936.1,3305.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.41 16631[0:SpR:9936.1,15262.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.41 16628[0:SpR:9936.1,8376.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname)) equal(v,v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v))*.
% 299.64/300.41 16627[0:SpR:9936.1,8415.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.64/300.41 16626[0:SpR:9936.1,3291.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_bool)),v_Procs))*.
% 299.64/300.41 16625[0:SpR:9936.1,3285.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.41 16622[0:SpR:9936.1,3279.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_Procs),v_x))*.
% 299.64/300.41 16765[0:SpL:8415.2,12979.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,v_x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v_Procs,t_a).
% 299.64/300.41 16978[0:SpL:600.0,346.0] || c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v,y)* -> c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),v,y).
% 299.64/300.41 16933[0:SpR:600.0,335.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,u,tc_fun(v,tc_bool)),v) -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v)*.
% 299.64/300.41 16995[0:Res:9952.1,427.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Opreorder(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,u),w,u)* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),w,u).
% 299.64/300.41 16994[0:Res:9952.1,426.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Oorder(u) || c_lessequals(v,c_Orderings_Otop__class_Otop(tc_bool),u) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,u),u)*.
% 299.64/300.41 17007[0:SSi:16988.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),w,tc_fun(v,tc_bool)).
% 299.64/300.41 17020[0:Res:10531.1,427.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Opreorder(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,u),w,u)* -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),w,u).
% 299.64/300.41 17019[0:Res:10531.1,426.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Oorder(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(tc_bool),u) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,u),u)*.
% 299.64/300.41 17026[0:SSi:17013.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),w,tc_fun(v,tc_bool)).
% 299.64/300.41 17097[0:Res:511.1,2629.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),u)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.41 17096[0:SpR:584.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),v))* -> hBOOL(hAPP(c_COMBS(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x,y,z),v))*.
% 299.64/300.41 17150[0:SpR:17045.0,584.0] || -> equal(hAPP(c_COMBS(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x,y,z,x1),x2),hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(x,x2)))**.
% 299.64/300.41 17149[0:SpR:17045.0,584.0] || -> equal(hAPP(c_COMBS(u,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)),y,z,x1),x2),hAPP(hAPP(u,x2),c_Orderings_Obot__class_Obot(tc_bool)))**.
% 299.64/300.41 17254[0:Res:510.1,2629.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),u)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.41 17253[0:SpR:584.0,510.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(c_COMBS(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x,y,z),v))*.
% 299.64/300.41 17312[0:SpL:586.0,13272.0] || equal(hAPP(u,hAPP(v,v_x)),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_COMBB(u,w,x,y),v),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.64/300.41 17311[0:SpL:585.0,13272.0] || equal(hAPP(hAPP(u,v_x),v),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_COMBC(u,w,x,y),v),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.64/300.41 17268[0:SpL:445.1,13272.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Fun_Ofun__upd(u,v,w,x,y),z)* -> equal(v_x,v) hBOOL(hAPP(z,v_x))*.
% 299.64/300.41 17463[0:SpL:586.0,16327.1] || equal(u,hAPP(c_COMBB(v,w,x,y),z))* equal(hAPP(v,hAPP(z,v_x)),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_Procs) -> .
% 299.64/300.41 17462[0:SpL:585.0,16327.1] || equal(u,hAPP(c_COMBC(v,w,x,y),z))* equal(hAPP(hAPP(v,v_x),z),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_Procs) -> .
% 299.64/300.41 17419[0:SpL:445.1,16327.1] || equal(u,c_Fun_Ofun__upd(v,w,x,y,z))* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_Procs) -> equal(v_x,w).
% 299.64/300.41 17690[0:SSi:17615.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(hAPP(x,v),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.41 17743[0:Res:11030.1,255.0] || equal(c_in(t_a),c_in(u)) c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v_x),w)).
% 299.64/300.41 17739[0:Res:3316.1,255.0] || equal(c_in(u),c_in(v)) c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),v_x),w)).
% 299.64/300.41 17849[2:SpR:188.1,4250.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))).
% 299.64/300.41 17839[0:SpR:188.1,3282.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_Procs)** -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))).
% 299.64/300.41 17927[0:SpL:8415.2,11894.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))* hBOOL(hAPP(v_x,v))* -> .
% 299.64/300.41 18005[0:SpL:584.0,263.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oinsert(v,u),w,x,y),z))* -> hBOOL(hAPP(hAPP(c_in(u),z),z))* equal(z,v).
% 299.64/300.41 18171[0:SpR:351.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBK(x,y,z),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.64/300.41 18169[0:SpR:456.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(v,w)),x)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Option_Othe(w),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.64/300.41 18301[0:SpL:15172.0,3507.1] || equal(c_Set_Oinsert(u,v),c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),y,tc_fun(z,tc_bool)))* equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.41 18299[0:SpL:15172.0,3499.1] || equal(c_in(u),c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)))* hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.41 18294[0:SpL:15172.0,3484.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,y),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(v_x,y).
% 299.64/300.41 18263[0:SpR:15172.0,3346.1] || equal(c_Set_Oinsert(u,v),c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),y,tc_fun(z,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(v),u),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.41 18262[0:SpR:15172.0,3317.1] || equal(c_in(u),c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)))* -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Set_Oinsert(v_x,u),z)))*.
% 299.64/300.41 18261[0:SpR:15172.0,3305.1] || equal(u,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,z),v_Procs),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.41 18254[0:SpR:15172.0,15262.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))).
% 299.64/300.41 18251[0:SpR:15172.0,8376.2] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_in(tc_Com_Opname))** equal(y,v_Procs) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),y))*.
% 299.64/300.41 18249[0:SpR:15172.0,3291.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_bool)),v_Procs))*.
% 299.64/300.41 18248[0:SpR:15172.0,3285.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)))*.
% 299.64/300.41 18245[0:SpR:15172.0,3279.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_Procs),v_x)).
% 299.64/300.41 18371[0:SpR:351.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_COMBK(y,z,x1),u,x),w)))*.
% 299.64/300.41 18369[0:SpR:456.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(v,w)),x)) -> hBOOL(hAPP(hAPP(c_in(y),v),hAPP(c_Set_Oimage(c_Option_Othe(w),u,y),x)))*.
% 299.64/300.41 18447[0:SpL:584.0,156.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Ovimage(v,u,w),x,y,z),x1))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(v,x1)),x1))*.
% 299.64/300.41 18479[0:Res:1103.1,8513.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),t_a)* equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v).
% 299.64/300.41 18471[0:SpL:584.0,8513.0] || hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> equal(hAPP(w,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),u).
% 299.64/300.41 18517[0:SpR:8415.2,9246.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))))* hBOOL(hAPP(v,v_x)).
% 299.64/300.41 18584[0:Res:153.1,2629.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,v_x)),w)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,tc_Com_Opname,u),w),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.41 18583[0:SpR:584.0,153.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),w))* -> hBOOL(hAPP(c_COMBS(c_in(x),c_Set_Ovimage(v,x,u),y,z,x1),w))*.
% 299.64/300.41 18725[0:SpR:10063.0,9568.0] || -> c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_bool)*.
% 299.64/300.41 18721[0:SpR:586.0,9568.0] || -> c_lessequals(hAPP(u,hAPP(v,w)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_COMBB(u,y,z,x1),v)),x2),w),tc_bool)*.
% 299.64/300.41 18720[0:SpR:585.0,9568.0] || -> c_lessequals(hAPP(hAPP(u,v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_COMBC(u,y,z,x1),w)),x2),v),tc_bool)*.
% 299.64/300.41 18697[0:SpR:9936.1,9568.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),w),x),tc_bool)*.
% 299.64/300.41 18695[0:SpR:9935.1,9568.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),u),tc_bool)*.
% 299.64/300.41 18657[0:SpR:8415.2,9568.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x),tc_bool)*.
% 299.64/300.41 18649[0:SpR:369.0,9568.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Set_Oinsert(u,v)),y),hAPP(c_Set_Oinsert(u,v),w)),tc_bool)*.
% 299.64/300.41 18648[0:SpR:2089.0,9568.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),w),hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs)),tc_bool)*.
% 299.64/300.41 18643[0:SpR:445.1,9568.0] || -> equal(u,v) c_lessequals(hAPP(w,u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Fun_Ofun__upd(w,v,y,z,x1)),x2),u),tc_bool)*.
% 299.64/300.41 18634[0:SpR:8415.2,9568.0] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(hAPP(v,v_x),v_x,tc_bool).
% 299.64/300.41 18600[0:SpR:8415.2,9568.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(hAPP(v,w),hAPP(v_x,w),tc_bool)*.
% 299.64/300.41 18597[0:SpR:8415.2,9568.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(hAPP(v_x,v),hAPP(hAPP(v_x,w),v),tc_bool)*.
% 299.64/300.41 18748[0:SpR:8415.2,18644.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(v_Procs,hAPP(v_x,v_Procs),tc_bool).
% 299.64/300.41 18794[0:SpR:8415.2,18763.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(v_Procs,hAPP(hAPP(v_x,c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.41 19036[0:SpR:10063.0,9569.0] || -> c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_bool)*.
% 299.64/300.41 19032[0:SpR:586.0,9569.0] || -> c_lessequals(hAPP(u,hAPP(v,w)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_COMBB(u,z,x1,x2),v)),w),tc_bool)*.
% 299.64/300.41 19031[0:SpR:585.0,9569.0] || -> c_lessequals(hAPP(hAPP(u,v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_COMBC(u,z,x1,x2),w)),v),tc_bool)*.
% 299.64/300.41 19008[0:SpR:9936.1,9569.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),x),tc_bool)*.
% 299.64/300.41 19006[0:SpR:9935.1,9569.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),u),tc_bool)*.
% 299.64/300.41 18968[0:SpR:8415.2,9569.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x),tc_bool)*.
% 299.64/300.41 18960[0:SpR:369.0,9569.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Set_Oinsert(u,v)),hAPP(c_Set_Oinsert(u,v),w)),tc_bool)*.
% 299.64/300.41 18959[0:SpR:2089.0,9569.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(v_x,tc_Com_Opname)),hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs)),tc_bool)*.
% 299.64/300.41 18954[0:SpR:445.1,9569.0] || -> equal(u,v) c_lessequals(hAPP(w,u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Fun_Ofun__upd(w,v,z,x1,x2)),u),tc_bool)*.
% 299.64/300.41 18945[0:SpR:8415.2,9569.0] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(hAPP(w,v_x),v_x,tc_bool).
% 299.64/300.41 18908[0:SpR:8415.2,9569.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(hAPP(v,w),hAPP(hAPP(v_x,v),w),tc_bool)*.
% 299.64/300.41 19059[0:SpR:8415.2,10697.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(v,w),v_x),v_x),tc_bool)*.
% 299.64/300.41 19259[0:Rew:12927.1,19248.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,tc_bool),tc_bool)* -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),u).
% 299.64/300.41 19280[0:SpR:87.1,304.3] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)* -> c_lessequals(c_Orderings_Otop__class_Otop(u),w,u).
% 299.64/300.41 19463[0:SpR:8415.2,9067.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v_x,u),w))))*.
% 299.64/300.41 19445[0:SpR:8415.2,9067.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Set_Oinsert(u,v)) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oinsert(w,v),v_x)))*.
% 299.64/300.41 19525[0:SpR:8415.2,19452.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))))*.
% 299.64/300.41 19559[0:SpL:1.1,36.1] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u))** c_lessequals(w,v,u) -> c_lessequals(x,x,u)*.
% 299.64/300.41 19558[0:SpL:4.1,36.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u))** c_lessequals(w,v,u) -> c_lessequals(x,x,u)*.
% 299.64/300.41 19556[0:SpL:3.1,36.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),x)* c_lessequals(w,v,u) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),x,u)*.
% 299.64/300.41 19543[0:SpL:1.1,36.1] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u))** c_lessequals(x,x,u)* -> c_lessequals(w,v,u).
% 299.64/300.41 19542[0:SpL:4.1,36.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u))** c_lessequals(x,x,u)* -> c_lessequals(w,v,u).
% 299.64/300.41 19540[0:SpL:3.1,36.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ominus__class_Ominus(w,x,u))* c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)* -> c_lessequals(x,w,u).
% 299.64/300.41 19588[0:SpR:8415.2,19441.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))))*.
% 299.64/300.41 19620[0:SpR:8415.2,19436.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) equal(u,v_Procs) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),u)))*.
% 299.64/300.41 19613[0:SpR:353.0,19436.1] || equal(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v),v_Procs) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v))))*.
% 299.64/300.41 19664[0:Res:3284.1,496.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,hAPP(u,v_x))),hAPP(u,v_x)))* c_Hoare__Mirabelle_Otriple__valid(v,v_Procs,t_a).
% 299.64/300.41 19724[0:Res:34.1,19641.0] || hBOOL(hAPP(u,hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Set_Ovimage(v,w,x),u),y))))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Ovimage(v,w,x),u),y,t_a).
% 299.64/300.41 19714[0:SpL:9.0,19641.0] || hBOOL(hAPP(u,hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Fun_Ocomp(u,v,w,x,y),z))))* -> c_Hoare__Mirabelle_Ohoare__valids(c_Fun_Ocomp(u,v,w,x,y),z,t_a).
% 299.64/300.41 19694[0:SpL:299.2,19641.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v,u)* hBOOL(v) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,t_a).
% 299.64/300.41 19885[0:SpL:104.0,327.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v)** -> c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool)).
% 299.64/300.41 19855[0:SpR:135.0,104.0] || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w))**.
% 299.64/300.41 19828[0:SpR:104.0,329.1] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool)) -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),w)**.
% 299.64/300.41 19819[0:SpR:104.0,538.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))**.
% 299.64/300.41 20014[0:SpL:64.0,377.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v)*.
% 299.64/300.41 19958[0:SpR:64.0,378.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,w),u),w).
% 299.64/300.41 20068[0:SpL:2097.1,215.0] || hBOOL(hAPP(u,v))* c_Hoare__Mirabelle_Ohoare__derivs(w,u,x)* -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(x),tc_bool))),x)*.
% 299.64/300.41 20206[0:Res:20152.0,390.0] || -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(u,v,w,x),c_HOL_Ominus__class_Ominus(y,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(v,w,x),u),tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),x,w)*.
% 299.64/300.41 20393[0:Rew:20314.2,20316.3] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y)* -> equal(w,v).
% 299.64/300.41 20404[0:Rew:438.1,20337.2] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),y)**.
% 299.64/300.41 20405[0:Rew:438.1,20336.2] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),y)**.
% 299.64/300.41 20692[0:SpR:8415.2,10705.0] || equal(v_Procs,v_x) equal(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,v_x,x,y,z)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(x,v_x,tc_bool).
% 299.64/300.41 20816[0:Res:19748.0,255.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v)).
% 299.64/300.41 20864[0:SpR:317.0,212.1] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),y)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(z,v),x)),y))*.
% 299.64/300.41 21135[0:SpR:8415.2,20881.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Set_Oinsert(u,v)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,v,x),v_x),hAPP(w,u)))*.
% 299.64/300.41 21121[0:SpR:10063.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,v),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u),w)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.41 21119[0:SpR:15172.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y,z),hAPP(c_Set_Oinsert(x1,y),x2)),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.41 21116[0:SpR:586.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(u,hAPP(y,x2))))*.
% 299.64/300.41 21115[0:SpR:585.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBC(u,v,w,x),y),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(hAPP(u,x2),y)))*.
% 299.64/300.41 21092[0:SpR:9936.1,20881.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_Set_Oinsert(x,v),y)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.41 21090[0:SpR:9935.1,20881.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),hAPP(c_Set_Oinsert(u,w),y)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.41 21075[0:SpR:14526.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),x,y),hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),u),x),z)),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.41 21052[0:SpR:8415.2,20881.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(v_x,v),x)),v_x))*.
% 299.64/300.41 21040[0:SpR:369.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),y),w),z)),hAPP(c_Set_Oinsert(u,v),y)))*.
% 299.64/300.41 21039[0:SpR:2089.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),u),x)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.41 21034[0:SpR:445.1,20881.0] || -> equal(u,v) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,y,z),x1,x2),hAPP(c_Set_Oinsert(u,x1),x3)),hAPP(w,u)))*.
% 299.64/300.41 21192[0:SpR:584.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,v,w,x,y),z,x1),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(hAPP(u,v_Procs),hAPP(v,v_Procs))))*.
% 299.64/300.41 21177[0:SpR:337.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,w),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.41 21170[0:SpR:540.1,21130.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_Procs),v)))*.
% 299.64/300.41 21169[0:SpR:539.1,21130.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_Procs),v)))*.
% 299.64/300.41 21168[0:SpR:297.2,21130.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_Procs,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.41 21159[0:SpR:299.2,21130.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_Procs,v,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_in(tc_Com_Opname),v_x)),v))*.
% 299.64/300.41 21253[0:SpR:584.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,v,w,x,y),t_a,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),hAPP(hAPP(u,v_x),hAPP(v,v_x))))*.
% 299.64/300.41 21238[0:SpR:337.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.41 21231[0:SpR:540.1,21141.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.41 21230[0:SpR:539.1,21141.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.41 21229[0:SpR:297.2,21141.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),v_x))*.
% 299.64/300.41 21220[0:SpR:299.2,21141.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),v))*.
% 299.64/300.41 21209[0:SpR:25.1,21141.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)))*.
% 299.64/300.41 21568[0:SpL:21267.0,502.0] || c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x)),u,v) -> c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Obody,hAPP(c_Com_Obody,v_x),tc_Com_Opname,w)),u,v)*.
% 299.64/300.41 21564[0:SpL:21267.0,348.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_x),u,v,w) -> equal(c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,v_x),tc_Com_Opname,x),v,u,w)),v)**.
% 299.64/300.41 21395[0:SpR:21267.0,15367.0] || -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),tc_fun(v,tc_bool)),v)*.
% 299.64/300.41 21355[0:SpR:21267.0,87.1] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.41 21299[0:SpR:21267.0,9566.0] || -> c_lessequals(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),x),hAPP(hAPP(c_Set_Oinsert(u,v),v_x),x),tc_bool)*.
% 299.64/300.41 21289[0:SpR:21267.0,503.1] || c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Obody,hAPP(c_Com_Obody,v_x),tc_Com_Opname,u)),v,w)* -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x)),v,w).
% 299.64/300.41 21803[0:SpR:15172.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),t_a,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.41 21800[0:SpR:586.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),t_a,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(u,hAPP(y,v_x))))*.
% 299.64/300.41 21799[0:SpR:585.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBC(u,v,w,x),y),t_a,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(u,v_x),y)))*.
% 299.64/300.41 21794[0:SpR:9936.1,21143.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.41 21792[0:SpR:9935.1,21143.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.41 21760[0:SpR:8415.2,21143.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.41 21754[0:SpR:445.1,21143.0] || -> equal(v_x,u) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(v,u,w,x,y),t_a,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(v,v_x)))*.
% 299.64/300.41 21810[0:SpR:8415.2,21035.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_Procs,u),c_Set_Oinsert(v_x,tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),v_x),v_Procs))*.
% 299.64/300.41 21869[0:SpR:586.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),tc_Com_Opname,z),hAPP(c_Set_Oinsert(x1,tc_Com_Opname),v_Procs)),hAPP(u,hAPP(y,v_x))))*.
% 299.64/300.41 21868[0:SpR:585.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBC(u,v,w,x),y),tc_Com_Opname,z),hAPP(c_Set_Oinsert(x1,tc_Com_Opname),v_Procs)),hAPP(hAPP(u,v_x),y)))*.
% 299.64/300.41 21861[0:SpR:9935.1,21131.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.41 21829[0:SpR:8415.2,21131.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.41 21823[0:SpR:445.1,21131.0] || -> equal(v_x,u) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(v,u,w,x,y),tc_Com_Opname,z),hAPP(c_Set_Oinsert(x1,tc_Com_Opname),v_Procs)),hAPP(v,v_x)))*.
% 299.64/300.41 22195[0:SpL:21893.0,502.0] || c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x)),u,v) -> c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Obody,v_x),c_Com_Obody,tc_Com_Opname,w)),u,v)*.
% 299.64/300.41 22191[0:SpL:21893.0,348.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_x),u,v,w) -> equal(c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Ocom_OBODY,v_x),c_Com_Ocom_OBODY,tc_Com_Opname,x),v,u,w)),v)**.
% 299.64/300.41 22021[0:SpR:21893.0,15367.0] || -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),tc_fun(v,tc_bool)),v)*.
% 299.64/300.41 21981[0:SpR:21893.0,87.1] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.41 21925[0:SpR:21893.0,9566.0] || -> c_lessequals(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),x),hAPP(hAPP(c_Set_Oinsert(u,v),v_x),x),tc_bool)*.
% 299.64/300.41 21915[0:SpR:21893.0,503.1] || c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Obody,v_x),c_Com_Obody,tc_Com_Opname,u)),v,w)* -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x)),v,w).
% 299.64/300.41 22382[0:SpR:8415.2,21689.1] class_Lattices_Obounded__lattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),v_x,tc_Com_Opname,v),v_x)**.
% 299.64/300.41 22388[0:SpR:8415.2,21704.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),v_x,tc_Com_Opname,v),v_x)**.
% 299.64/300.41 22442[0:SpR:8415.2,22318.1] class_Lattices_Obounded__lattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),v_x)**.
% 299.64/300.41 22448[0:SpR:8415.2,22333.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),v_x)**.
% 299.64/300.41 22504[0:SpR:15172.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)),tc_Com_Opname,z),u),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.41 22501[0:SpR:586.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBB(v,w,x,y),z),tc_Com_Opname,x1),u),hAPP(v,hAPP(z,v_x))))*.
% 299.64/300.41 22500[0:SpR:585.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_COMBC(v,w,x,y),z),tc_Com_Opname,x1),u),hAPP(hAPP(v,v_x),z)))*.
% 299.64/300.41 22495[0:SpR:9936.1,21126.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,w),v),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.41 22493[0:SpR:9935.1,21126.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),tc_Com_Opname,w),u),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.41 22461[0:SpR:8415.2,21126.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v),v_x))*.
% 299.64/300.41 22455[0:SpR:445.1,21126.1] || equal(u,v_Procs) -> equal(v_x,v) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,y,z),tc_Com_Opname,x1),u),hAPP(w,v_x)))*.
% 299.64/300.41 22656[0:SpL:158.0,319.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> equal(z,c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))).
% 299.64/300.41 22601[0:SpR:158.0,97.1] || c_Fun_Oinj__on(u,v,w,x) -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(c_Fun_Othe__inv__into(v,u,w,x),u,x,w,w),w,w),v),v)**.
% 299.64/300.41 22692[0:SpR:584.0,21173.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oimage(c_COMBK(hAPP(u,hAPP(c_in(tc_Com_Opname),v_x)),v,w),x,y),u,z,x1,x2),hAPP(c_in(tc_Com_Opname),v_x)))*.
% 299.64/300.41 22697[0:SpR:584.0,21234.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oimage(c_COMBK(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w,x),t_a,y),u,z,x1,x2),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.41 22885[0:SpL:3294.1,515.0] || equal(c_Hoare__Mirabelle_Otriple_Otriple(u),c_in(t_a)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(c_Orderings_Obot__class_Obot(tc_bool),y))* -> equal(v,v_x).
% 299.64/300.41 22883[0:SpL:3294.1,513.0] || equal(c_Hoare__Mirabelle_Otriple_Otriple(u),c_in(t_a)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(c_Orderings_Obot__class_Obot(tc_bool),y))* -> equal(x,y).
% 299.64/300.41 22876[0:SpL:3294.1,346.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_Fun_Oinj__on(v,c_Orderings_Obot__class_Obot(tc_bool),u,w) -> c_Fun_Oinj__on(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),u,w)*.
% 299.64/300.41 22866[0:SpL:3294.1,515.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_in(t_a))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(v,w)*.
% 299.64/300.41 22865[0:SpL:3294.1,514.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_in(t_a))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(v_x,x).
% 299.64/300.41 22841[0:SpR:12944.0,3294.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_in(t_a))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.41 22836[0:SpR:9.0,3294.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_in(t_a))** -> equal(hAPP(hAPP(u,hAPP(v,v_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 22835[0:SpR:11473.0,3294.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_in(t_a))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.41 22822[0:SpR:88.1,3294.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_in(t_a))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 22821[0:SpR:17045.0,3294.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_in(t_a))** -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.41 22812[0:SpR:2098.1,3294.1] || equal(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a))** -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 22801[0:SpR:3586.1,3294.1] || equal(hAPP(c_in(u),v),v_Procs)** equal(c_Set_Oinsert(v,u),c_in(t_a)) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 22789[0:SpR:8498.1,3294.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x)** equal(c_Set_Oinsert(v,u),c_in(t_a))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 22743[0:SpR:3294.1,474.0] || equal(c_in(t_a),u) -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(hAPP(u,v_x),w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.41 22742[0:SpR:3294.1,335.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_Finite__Set_Ofinite(v_x,u) c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),u)* -> c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_bool),u).
% 299.64/300.41 23047[0:Rew:9.0,23034.1] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),z)),x1))* -> hBOOL(hAPP(z,hAPP(x,hAPP(u,x1)))).
% 299.64/300.41 23048[0:Rew:9.0,22907.0] || hBOOL(hAPP(u,hAPP(v,hAPP(w,x)))) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(w,y,z),hAPP(c_Set_Ovimage(v,z,x1),u)),x))*.
% 299.64/300.41 23222[0:SpL:12944.0,3487.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> .
% 299.64/300.41 23216[0:SpL:9.0,3487.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.41 23215[0:SpL:11473.0,3487.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> .
% 299.64/300.41 23202[0:SpL:88.1,3487.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> .
% 299.64/300.41 23201[0:SpL:17045.0,3487.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> .
% 299.64/300.41 23299[0:SpL:12944.0,3489.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_in(tc_Com_Opname))** hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)))) -> .
% 299.64/300.41 23293[0:SpL:9.0,3489.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_in(tc_Com_Opname))** hBOOL(hAPP(hAPP(u,hAPP(v,v_x)),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.41 23292[0:SpL:11473.0,3489.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_in(tc_Com_Opname))** hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)))) -> .
% 299.64/300.41 23279[0:SpL:88.1,3489.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_in(tc_Com_Opname))** hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.41 23278[0:SpL:17045.0,3489.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_in(tc_Com_Opname))** hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)))) -> .
% 299.64/300.41 23612[0:SSi:23611.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)),hAPP(v,v_x)),c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)),v_x),tc_bool))**.
% 299.64/300.41 23787[0:SpR:23682.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,u),u)*.
% 299.64/300.41 23776[0:SpR:23682.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,w),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.64/300.41 23880[0:SpR:23840.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_bool)),w)) -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v,u),u)*.
% 299.64/300.41 23869[0:SpR:23840.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,w),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.64/300.41 23986[0:SpR:23912.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,x),w)))*.
% 299.64/300.41 23985[0:SpR:23912.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.41 24187[0:SpR:3229.1,542.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(u,v_x)),hAPP(u,v_x))**.
% 299.64/300.41 24922[0:Res:13238.1,467.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,t_a),v_x)),v_x)**.
% 299.64/300.41 24921[0:Res:8375.1,467.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(x,u,v,w),y)),y)**.
% 299.64/300.41 24920[0:Res:545.1,467.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(x,hAPP(c_Hilbert__Choice_Oinv__into(w,x,u,y),hAPP(x,v))),hAPP(x,v))**.
% 299.64/300.41 24913[0:Res:652.1,467.0] || c_lessequals(v_Procs,hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),tc_fun(tc_Com_Opname,tc_bool))* -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,tc_Com_Opname),v_x)),v_x)**.
% 299.64/300.41 25105[0:SpL:23902.1,514.0] || equal(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(v_x,y))* -> equal(w,c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.41 25086[0:SpL:23902.1,513.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),v_x)** -> equal(c_Orderings_Obot__class_Obot(tc_bool),y).
% 299.64/300.41 25047[0:SpR:329.1,23902.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.41 25046[0:SpR:328.1,23902.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(u,c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.41 25044[0:SpR:538.0,23902.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.41 25135[0:Res:252.1,250.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),x),t_a) c_Natural_Oevalc(w,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(v,x,w,u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,x,w,u))*.
% 299.64/300.41 25672[0:SSi:25604.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(w,v,tc_bool)* equal(v,c_Orderings_Obot__class_Obot(tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),v)*.
% 299.64/300.41 25720[0:Res:3283.1,455.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__valids(u,v_Procs,t_a) c_Hoare__Mirabelle_Otriple__valid(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.64/300.41 25713[0:Res:3284.1,455.0] || equal(c_in(tc_Com_Opname),u) c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(u,v_x),t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,v_Procs,t_a).
% 299.64/300.41 25920[0:SpR:339.0,9568.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),w),x),hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)),x),tc_bool)*.
% 299.64/300.41 26082[0:SpR:338.0,9569.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),w),x),hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),w)),x),tc_bool)*.
% 299.64/300.41 26379[0:Res:124.0,85.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))*.
% 299.64/300.41 26531[0:Res:84.1,1051.0] || c_lessequals(c_HOL_Ominus__class_Ominus(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)),v,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_x))*.
% 299.64/300.41 26785[0:Res:23997.0,12719.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ominus__class_Ominus(u,v,tc_bool)),w,tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_bool)),y,tc_bool),u,tc_bool)*.
% 299.64/300.41 26972[2:SpL:8415.2,23941.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.41 27010[0:Res:9258.0,175.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Ovimage(u,t_a,v),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),v_x),tc_bool))* equal(hAPP(u,v_x),w).
% 299.64/300.41 27034[0:SpR:8415.2,26317.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,tc_bool),v_x)**.
% 299.64/300.41 27103[0:Res:9258.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool)) hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,u,t_a,tc_fun(x,tc_bool)),v))*.
% 299.64/300.41 27096[0:Res:3283.1,280.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(v,v_x),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,u,tc_fun(x,tc_bool)),w))*.
% 299.64/300.41 27241[7:SpR:188.1,27207.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x)** -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))).
% 299.64/300.41 27303[7:MRR:15093.3,27297.0] || equal(v_Procs,v_x) equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)).
% 299.64/300.41 27309[7:MRR:24362.2,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(x,y),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.41 27329[7:MRR:24616.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x),v_x)**.
% 299.64/300.41 27390[0:Res:9258.0,470.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),tc_bool)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,t_a)),w))*.
% 299.64/300.41 27450[0:Res:9258.0,466.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),tc_bool)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,t_a)),w))*.
% 299.64/300.41 27871[7:SpR:584.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBS(u,v,w,x,y),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_bool)).
% 299.64/300.41 27852[7:SpR:337.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool)).
% 299.64/300.41 27843[7:SpR:540.1,27219.1] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))*.
% 299.64/300.41 27842[7:SpR:539.1,27219.1] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))*.
% 299.64/300.41 27832[7:SpR:299.2,27219.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool)).
% 299.64/300.41 27821[7:SpR:25.1,27219.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool)).
% 299.64/300.41 28018[0:SpR:584.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_COMBS(u,v,w,x,y),tc_Com_Opname,z)),v_Procs))*.
% 299.64/300.41 27999[0:SpR:337.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.41 27990[0:SpR:540.1,27381.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.41 27989[0:SpR:539.1,27381.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.41 27988[0:SpR:297.2,27381.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.41 27979[0:SpR:299.2,27381.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.41 27968[0:SpR:25.1,27381.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.41 28122[0:SpR:465.1,1158.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs)) hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),hAPP(c_Fun_Ofun__upd(v,u,x,tc_Com_Opname,w),v_x)))*.
% 299.64/300.41 28321[0:SpR:584.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(u,v,w,x,y),hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_Com_Opname,z)),v_Procs))*.
% 299.64/300.41 28302[0:SpR:337.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.41 28292[0:SpR:540.1,27441.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.41 28291[0:SpR:539.1,27441.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.41 28290[0:SpR:297.2,27441.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x,tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.41 28281[0:SpR:299.2,27441.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v,tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.41 28270[0:SpR:25.1,27441.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.41 28780[0:SpR:584.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_COMBS(u,v,w,x,y),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28761[0:SpR:337.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28751[0:SpR:540.1,28031.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28750[0:SpR:539.1,28031.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28749[0:SpR:297.2,28031.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28740[0:SpR:299.2,28031.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28729[0:SpR:25.1,28031.0] class_HOL_Ouminus(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28935[0:SpR:584.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(u,v,w,x,y),hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28916[0:SpR:337.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28906[0:SpR:540.1,28334.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28905[0:SpR:539.1,28334.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28904[0:SpR:297.2,28334.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x,tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28895[0:SpR:299.2,28334.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v,tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 28884[0:SpR:25.1,28334.0] class_HOL_Ouminus(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 29212[0:SSi:29196.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)).
% 299.64/300.41 29234[0:SSi:29075.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),u)),v))*.
% 299.64/300.41 29355[7:SpR:27278.1,3294.1] || equal(hAPP(c_in(u),v),v_x)** equal(c_Set_Oinsert(v,u),c_in(t_a)) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 29945[0:SpL:27043.1,3484.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,v),v_x)** -> equal(v_x,v).
% 299.64/300.41 29927[0:SpR:27043.1,20881.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),v_x))*.
% 299.64/300.41 29921[0:SpR:27043.1,353.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),hAPP(c_Set_Oinsert(v,u),v_x)),hAPP(c_Set_Oinsert(v,u),v_x))**.
% 299.64/300.41 29900[0:SpR:27043.1,9569.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_Procs,w)),v_x),tc_bool)*.
% 299.64/300.41 29899[0:SpR:27043.1,9568.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_Procs,v)),w),v_x),tc_bool)*.
% 299.64/300.41 29891[0:SpR:27043.1,3346.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(u,v),c_Set_Oinsert(v_Procs,w))* -> hBOOL(hAPP(hAPP(c_in(v),u),v_x))*.
% 299.64/300.41 29890[0:SpR:27043.1,21126.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,v),tc_Com_Opname,w),u),v_x))*.
% 299.64/300.41 29889[0:SpR:27043.1,3317.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_in(u),c_Set_Oinsert(v_Procs,v))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,u),w)))*.
% 299.64/300.41 29888[0:SpR:27043.1,3305.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(u,c_Set_Oinsert(v_Procs,v))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.41 29875[0:SpR:27043.1,21131.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.41 29874[0:SpR:27043.1,21143.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.41 29868[0:SpR:27043.1,15262.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(v_Procs,u),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.41 29858[0:SpR:27043.1,3279.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_Procs,u))* -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.41 30347[0:SSi:30318.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),v).
% 299.64/300.41 30386[0:SSi:30131.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y)),v))*.
% 299.64/300.41 30495[0:Rew:30493.2,20471.2] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v),y)**.
% 299.64/300.41 30501[0:SpR:8415.2,28009.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u)),v_Procs))*.
% 299.64/300.41 30513[0:SpR:8415.2,28312.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u)),v_Procs))*.
% 299.64/300.41 31042[0:Rew:31040.2,20470.2] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v),y)**.
% 299.64/300.41 31108[0:SpR:8415.2,28771.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 31098[0:SpR:28771.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,v),x)),v_Procs))*.
% 299.64/300.41 31092[0:SpR:28771.0,353.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))**.
% 299.64/300.41 31071[0:SpR:28771.0,9569.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.41 31070[0:SpR:28771.0,9568.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),tc_Com_Opname)),w),v_Procs),tc_bool)*.
% 299.64/300.41 31194[0:SpR:8415.2,28926.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,u),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 31184[0:SpR:28926.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,v),x)),v_Procs))*.
% 299.64/300.41 31178[0:SpR:28926.0,353.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))**.
% 299.64/300.41 31157[0:SpR:28926.0,9569.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.41 31156[0:SpR:28926.0,9568.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v),tc_Com_Opname)),w),v_Procs),tc_bool)*.
% 299.64/300.41 31220[0:SpR:8415.2,23934.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_Procs),u,v),v_x),v_Procs))*.
% 299.64/300.41 31223[0:SpR:8415.2,23936.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v_x,tc_Com_Opname,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.64/300.41 31272[0:Res:526.1,356.0] || hBOOL(hAPP(u,v))* -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,y),y,x),u),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.64/300.41 31260[0:Res:648.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(c_Set_Oimage(x,tc_Com_Opname,w),v_Procs)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.64/300.41 31336[0:SpR:8415.2,23954.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,t_a,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x))*.
% 299.64/300.41 31354[0:Res:23961.0,279.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_Procs)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_Procs))**.
% 299.64/300.41 31346[0:SpR:8415.2,23961.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.41 31343[0:SpR:8415.2,23961.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v_x,tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.41 31431[0:MRR:31421.1,820.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w),tc_bool) -> c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)),t_a)*.
% 299.64/300.41 31432[0:MRR:31419.1,820.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w),tc_bool) -> c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)),t_a)*.
% 299.64/300.41 31439[0:SpL:8415.2,24034.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(u,v_x) equal(c_Com_Ocom_OBODY,u)* equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31510[0:SpL:27043.1,24254.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31508[0:SpL:15172.0,24254.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_bool),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31503[0:SpL:586.0,24254.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(u,hAPP(y,v_x)),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31502[0:SpL:585.0,24254.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(u,v_x),y),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31496[0:SpL:9936.1,24254.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31492[0:SpL:9935.1,24254.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(tc_bool),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31453[0:SpL:8415.2,24254.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 31447[0:SpL:445.1,24254.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(u,v_x),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> equal(v_x,v).
% 299.64/300.41 31539[0:Res:545.1,473.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Hilbert__Choice_Oinv__into(w,x,u,y),hAPP(x,v))),w))*.
% 299.64/300.41 31536[0:Res:526.1,473.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),y)) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(x,u,v,w),y)),x))*.
% 299.64/300.41 31832[7:SpL:329.1,31778.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)** -> .
% 299.64/300.41 31831[7:SpL:328.1,31778.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)** -> .
% 299.64/300.41 31828[7:SpL:538.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x) -> .
% 299.64/300.41 32012[0:SpL:383.1,3952.0] || equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v_x,v,w,x),y,z,w,x),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(x1,x2),v)* -> equal(v_x,y).
% 299.64/300.41 31980[0:SpR:383.1,10705.0] || -> equal(u,v) c_lessequals(w,hAPP(hAPP(c_Set_Oinsert(x,y),c_Fun_Ofun__upd(c_Fun_Ofun__upd(z,u,w,x1,x2),v,x3,x1,x2)),u),tc_bool)*.
% 299.64/300.41 32183[0:SpR:584.0,31323.0] || -> c_lessequals(hAPP(c_COMBS(c_Set_Oinsert(v_x,tc_Com_Opname),u,v,w,x),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),hAPP(v_Procs,hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))),tc_bool)*.
% 299.64/300.41 32180[0:SpR:8415.2,31323.0] || equal(v_Procs,v_x) equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),c_Set_Oinsert(v_x,tc_Com_Opname))** -> c_lessequals(v_x,hAPP(v_Procs,v_x),tc_bool).
% 299.64/300.41 32172[0:SpR:8415.2,31323.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),v_Procs) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v_x),v_x,tc_bool)*.
% 299.64/300.41 32264[0:Res:23753.1,427.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Opreorder(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v,u)* -> c_lessequals(v_x,v,u).
% 299.64/300.41 32263[0:Res:23753.1,426.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Oorder(u) || c_lessequals(v,v_x,u) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),u)*.
% 299.64/300.41 32276[0:SSi:32257.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* -> c_lessequals(v_x,v,tc_fun(u,tc_bool)).
% 299.64/300.41 32328[0:SpL:336.0,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v)))* hBOOL(hAPP(hAPP(c_in(v),w),x))* -> hBOOL(hAPP(u,w))*.
% 299.64/300.41 32455[0:SpR:8415.2,28058.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,v)))*.
% 299.64/300.41 32591[0:SpR:8415.2,28361.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,v)))*.
% 299.64/300.41 32662[0:SpR:27043.1,31533.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),v_x)),v_Procs))*.
% 299.64/300.41 32660[0:SpR:15172.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),tc_Com_Opname,y),c_Orderings_Obot__class_Obot(tc_bool))),v_Procs))*.
% 299.64/300.41 32655[0:SpR:586.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_COMBB(u,v,w,x),y),tc_Com_Opname,z),hAPP(u,hAPP(y,v_x)))),v_Procs))*.
% 299.64/300.41 32654[0:SpR:585.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_COMBC(u,v,w,x),y),tc_Com_Opname,z),hAPP(hAPP(u,v_x),y))),v_Procs))*.
% 299.64/300.41 32648[0:SpR:9936.1,31533.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool))),v_Procs))*.
% 299.64/300.41 32644[0:SpR:9935.1,31533.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool))),v_Procs))*.
% 299.64/300.41 32605[0:SpR:8415.2,31533.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),v_x)),v_Procs))*.
% 299.64/300.41 32599[0:SpR:445.1,31533.0] || -> equal(v_x,u) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ofun__upd(v,u,w,x,y),tc_Com_Opname,z),hAPP(v,v_x))),v_Procs))*.
% 299.64/300.41 32745[7:MRR:32679.0,27297.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_Com_Opname,x),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))))*.
% 299.64/300.41 32871[0:SpR:475.1,10813.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oimage(z,u,y),w)),hAPP(z,v)))*.
% 299.64/300.41 33053[0:SpR:8415.2,32691.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_x,tc_Com_Opname,v),v_x)))*.
% 299.64/300.41 33318[0:SpR:27043.1,32668.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33316[0:SpR:15172.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),tc_Com_Opname,y),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33311[0:SpR:586.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_COMBB(u,v,w,x),y),tc_Com_Opname,z),hAPP(u,hAPP(y,v_x))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33310[0:SpR:585.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_COMBC(u,v,w,x),y),tc_Com_Opname,z),hAPP(hAPP(u,v_x),y)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33304[0:SpR:9936.1,32668.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33300[0:SpR:9935.1,32668.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33261[0:SpR:8415.2,32668.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33255[0:SpR:445.1,32668.0] || -> equal(v_x,u) equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ofun__upd(v,u,w,x,y),tc_Com_Opname,z),hAPP(v,v_x)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 33240[0:SpR:32668.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),v_Procs))*.
% 299.64/300.41 33234[0:SpR:32668.0,353.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))**.
% 299.64/300.41 33212[0:SpR:32668.0,9569.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,w,tc_Com_Opname,x),hAPP(w,v_x)),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.41 33211[0:SpR:32668.0,9568.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x)),tc_Com_Opname)),x),v_Procs),tc_bool)*.
% 299.64/300.41 33400[0:Res:264.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v)),u))* c_Hoare__Mirabelle_Otriple__valid(v,w,t_a)*.
% 299.64/300.41 33444[0:SpR:8415.2,23882.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(v_x,u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),v_x,tc_bool)*.
% 299.64/300.41 33604[0:SpR:27043.1,28704.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_Procs,v),tc_Com_Opname,w)))*.
% 299.64/300.41 33602[0:SpR:15172.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)),tc_Com_Opname,z)))*.
% 299.64/300.41 33597[0:SpR:586.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,hAPP(w,v_x)),hAPP(c_COMBB(v,x,y,z),w),tc_Com_Opname,x1)))*.
% 299.64/300.41 33596[0:SpR:585.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(v,v_x),w),hAPP(c_COMBC(v,x,y,z),w),tc_Com_Opname,x1)))*.
% 299.64/300.41 33590[0:SpR:9936.1,28704.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,w)))*.
% 299.64/300.41 33586[0:SpR:9935.1,28704.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),tc_Com_Opname,w)))*.
% 299.64/300.41 33547[0:SpR:8415.2,28704.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,w)))*.
% 299.64/300.41 33541[0:SpR:445.1,28704.0] || -> equal(v_x,u) hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(w,v_x),c_Fun_Ofun__upd(w,u,x,y,z),tc_Com_Opname,x1)))*.
% 299.64/300.41 33695[0:SpR:27043.1,28859.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_Procs,v),v_x,tc_Com_Opname,w)))*.
% 299.64/300.41 33693[0:SpR:15172.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,z)))*.
% 299.64/300.41 33688[0:SpR:586.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_COMBB(v,w,x,y),z),hAPP(v,hAPP(z,v_x)),tc_Com_Opname,x1)))*.
% 299.64/300.41 33687[0:SpR:585.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_COMBC(v,w,x,y),z),hAPP(hAPP(v,v_x),z),tc_Com_Opname,x1)))*.
% 299.64/300.41 33681[0:SpR:9936.1,28859.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))*.
% 299.64/300.41 33677[0:SpR:9935.1,28859.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))*.
% 299.64/300.41 33638[0:SpR:8415.2,28859.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,w)))*.
% 299.64/300.41 33632[0:SpR:445.1,28859.0] || -> equal(v_x,u) hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ofun__upd(w,u,x,y,z),hAPP(w,v_x),tc_Com_Opname,x1)))*.
% 299.64/300.41 33779[7:SpL:586.0,31886.1] || equal(u,hAPP(c_COMBB(v,w,x,y),z))* equal(hAPP(v,hAPP(z,v_x)),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_x) -> .
% 299.64/300.41 33778[7:SpL:585.0,31886.1] || equal(u,hAPP(c_COMBC(v,w,x,y),z))* equal(hAPP(hAPP(v,v_x),z),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_x) -> .
% 299.64/300.41 33723[7:SpL:445.1,31886.1] || equal(u,c_Fun_Ofun__upd(v,w,x,y,z))* equal(hAPP(v,v_x),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_x) -> equal(v_x,w).
% 299.64/300.41 33839[0:SpR:584.0,23881.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))),v,w),u,x,y,z),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.41 33831[0:SpR:8415.2,23881.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,u,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x))*.
% 299.64/300.41 33898[0:SpL:383.1,24636.0] || equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v_x,v,w,x),y,z,w,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(y,v_x) equal(hAPP(v,v_x),v_x).
% 299.64/300.41 34336[0:SpL:24914.0,377.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),v_x),v) -> c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),v)*.
% 299.64/300.41 34326[0:SpL:24914.0,3484.1] || equal(c_Com_Ocom_OBODY,u) equal(hAPP(u,v_x),hAPP(c_Com_Ocom_OBODY,v_x))* -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Ocom_OBODY,tc_Com_Opname,v),hAPP(c_Com_Ocom_OBODY,v_x)),v_x)**.
% 299.64/300.41 34258[0:SpR:27043.1,24914.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),v_x)),v_x)**.
% 299.64/300.41 34185[0:SpR:24914.0,19744.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v_x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,v),hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v_x)),t_a)*.
% 299.64/300.41 34102[0:SpR:24914.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,x),hAPP(u,v_x)),v),y)),hAPP(u,v_x)))*.
% 299.64/300.41 34019[0:SpR:24914.0,9569.0] || -> c_lessequals(hAPP(u,v_x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,x),hAPP(u,v_x))),tc_bool)*.
% 299.64/300.41 34018[0:SpR:24914.0,9568.0] || -> c_lessequals(hAPP(u,v_x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,x),hAPP(u,v_x))),tc_bool)*.
% 299.64/300.41 33957[0:SpR:24914.0,31323.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_Procs,tc_Com_Opname,u),hAPP(v_Procs,v_x))),hAPP(v_Procs,v_x),tc_bool)*.
% 299.64/300.41 33916[0:SpR:24914.0,378.1] || c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),v_x),v).
% 299.64/300.41 34653[0:SpL:55.1,418.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(v),u),x)).
% 299.64/300.41 34605[0:SpR:55.1,267.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool))))*.
% 299.64/300.41 34741[0:SpR:34428.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.41 34785[7:SpL:353.0,27282.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),v_x)** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),x),v_x)) equal(w,v_x).
% 299.64/300.41 34913[0:SpR:27043.1,28053.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(u,c_Set_Oinsert(v_Procs,v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,w)))*.
% 299.64/300.41 34911[0:SpR:15172.0,28053.1] || equal(u,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),u,tc_Com_Opname,z)))*.
% 299.64/300.41 34906[0:SpR:586.0,28053.1] || equal(u,hAPP(c_COMBB(v,w,x,y),z))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,hAPP(z,v_x)),u,tc_Com_Opname,x1)))*.
% 299.64/300.41 34905[0:SpR:585.0,28053.1] || equal(u,hAPP(c_COMBC(v,w,x,y),z))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(v,v_x),z),u,tc_Com_Opname,x1)))*.
% 299.64/300.41 34899[0:SpR:9936.1,28053.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),v,tc_Com_Opname,w)))*.
% 299.64/300.41 34895[0:SpR:9935.1,28053.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),u,tc_Com_Opname,w)))*.
% 299.64/300.41 34855[0:SpR:8415.2,28053.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(v,u)* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v,tc_Com_Opname,w)))*.
% 299.64/300.41 34849[0:SpR:445.1,28053.1] || equal(u,c_Fun_Ofun__upd(v,w,x,y,z))* -> equal(v_x,w) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),u,tc_Com_Opname,x1)))*.
% 299.64/300.41 34992[0:SpR:27043.1,28356.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(u,c_Set_Oinsert(v_Procs,v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,w)))*.
% 299.64/300.41 34990[0:SpR:15172.0,28356.1] || equal(u,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,z)))*.
% 299.64/300.41 34985[0:SpR:586.0,28356.1] || equal(u,hAPP(c_COMBB(v,w,x,y),z))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(v,hAPP(z,v_x)),tc_Com_Opname,x1)))*.
% 299.64/300.41 34984[0:SpR:585.0,28356.1] || equal(u,hAPP(c_COMBC(v,w,x,y),z))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(hAPP(v,v_x),z),tc_Com_Opname,x1)))*.
% 299.64/300.41 34978[0:SpR:9936.1,28356.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))*.
% 299.64/300.41 34974[0:SpR:9935.1,28356.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))*.
% 299.64/300.41 34934[0:SpR:8415.2,28356.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(v,u)* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,v_x,tc_Com_Opname,w)))*.
% 299.64/300.41 34928[0:SpR:445.1,28356.1] || equal(u,c_Fun_Ofun__upd(v,w,x,y,z))* -> equal(v_x,w) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(v,v_x),tc_Com_Opname,x1)))*.
% 299.64/300.41 35056[0:SpR:28755.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),y,z),hAPP(c_Set_Oinsert(v_Procs,y),x1)),v_Procs))*.
% 299.64/300.41 35050[0:SpR:28755.0,353.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs))**.
% 299.64/300.41 35028[0:SpR:28755.0,9569.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,w,c_COMBK(w,x,y),tc_Com_Opname,z),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.41 35027[0:SpR:28755.0,9568.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y),tc_Com_Opname)),z),v_Procs),tc_bool)*.
% 299.64/300.41 35145[0:SpR:28910.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),y,z),hAPP(c_Set_Oinsert(v_Procs,y),x1)),v_Procs))*.
% 299.64/300.41 35139[0:SpR:28910.0,353.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs))**.
% 299.64/300.41 35117[0:SpR:28910.0,9569.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(w,x,y),w,tc_Com_Opname,z),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.41 35116[0:SpR:28910.0,9568.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y),tc_Com_Opname)),z),v_Procs),tc_bool)*.
% 299.64/300.41 35434[0:SpL:410.0,347.0] || c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),y,w,tc_fun(z,tc_bool)),z,x1)* -> c_Fun_Oinj__on(u,hAPP(y,v),z,x1).
% 299.64/300.41 35425[0:SpL:410.0,332.0] || c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),y)* -> c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool)),y).
% 299.64/300.41 35531[7:SpL:113.0,27293.0] || equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))),v_x)** -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),v_x)).
% 299.64/300.41 35530[0:SpL:113.0,4964.0] || equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),v_x)).
% 299.64/300.41 35482[0:SpR:113.0,9567.0] || -> c_lessequals(hAPP(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))),z),hAPP(hAPP(c_Set_Ovimage(u,v,w),x),z),tc_bool)*.
% 299.64/300.41 35693[0:SpR:8415.2,26119.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> hBOOL(hAPP(hAPP(v_x,hAPP(c_Set_Oinsert(v,u),w)),v))*.
% 299.64/300.41 35665[0:SpR:8415.2,26119.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Set_Oinsert(u,v)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),u))*.
% 299.64/300.41 36890[0:SpL:66.0,3863.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),y))* -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),y)).
% 299.64/300.41 36958[0:Con:36940.2] || equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(t_a,tc_bool)),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.64/300.41 37534[0:SpR:299.2,36690.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,tc_bool))*.
% 299.64/300.41 37729[0:SpR:540.1,36342.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.41 37728[0:SpR:539.1,36342.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.41 38325[0:SSi:38296.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),u),v)) c_Finite__Set_Ofinite(v,tc_bool) -> c_lessequals(u,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool),v,tc_bool,tc_bool),tc_bool)*.
% 299.64/300.41 38326[0:SSi:38286.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u)) c_Finite__Set_Ofinite(u,tc_bool) -> c_lessequals(v,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,u,tc_bool,tc_bool),tc_bool)*.
% 299.64/300.41 40366[4:Res:10697.0,40016.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v_x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v_x)))*.
% 299.64/300.41 40585[4:Res:10697.0,40105.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),x)))*.
% 299.64/300.41 41424[0:Res:15261.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),v)) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(t_a,tc_bool))))*.
% 299.64/300.41 41397[0:Res:658.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(w,tc_Com_Opname),u,tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.64/300.41 41489[4:SpR:328.1,38236.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool)).
% 299.64/300.41 41485[4:SpR:538.0,38236.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_Com_Opname,tc_bool))*.
% 299.64/300.41 42195[0:SSi:42180.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(w,tc_bool),u),tc_bool,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** -> c_lessequals(w,x,tc_bool)*.
% 299.64/300.41 42653[0:SpR:161.0,342.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.41 42623[0:SpR:161.0,341.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.41 42888[4:SSi:42858.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(v_x,tc_bool),u),tc_bool,tc_bool),w,x),tc_Com_Opname,tc_bool))*.
% 299.64/300.41 43471[0:SpR:507.0,342.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),tc_fun(w,tc_bool))*.
% 299.64/300.41 43440[0:SpR:507.0,341.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x)),tc_fun(w,tc_bool))*.
% 299.64/300.41 43693[0:SpR:162.0,342.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),tc_fun(v,tc_bool))*.
% 299.64/300.41 43662[0:SpR:162.0,341.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),x)),tc_fun(v,tc_bool))*.
% 299.64/300.41 43877[0:Res:38131.1,19641.0] || hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x,t_a)*.
% 299.64/300.41 44512[0:Res:10697.0,36528.1] || equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(v_Procs,v_x))),hAPP(v_Procs,v_x)))*.
% 299.64/300.41 44628[0:SpR:338.0,35656.1] || equal(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v)),v_x))*.
% 299.64/300.41 45247[0:SpR:353.0,37394.1] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,t_a),v),v_x)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(w,t_a),v)),tc_Com_Opname,tc_bool))*.
% 299.64/300.41 45371[0:MRR:45370.1,264.0] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,u,x))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool)),u,x)))*.
% 299.64/300.41 45516[4:SpL:8415.2,38699.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x) -> hBOOL(hAPP(v_x,v))*.
% 299.64/300.41 45660[4:SpL:8415.2,38888.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a)*.
% 299.64/300.41 45705[0:SpR:339.0,44625.1] || equal(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),w)),v_x))*.
% 299.64/300.41 46066[0:SpR:353.0,36802.1] || equal(hAPP(c_Set_Oinsert(u,v),w),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool))) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(x,v),w)),v_x))*.
% 299.64/300.41 46525[4:SpR:353.0,42029.1] || equal(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(x,v),w)),v_x))*.
% 299.64/300.41 46668[4:SpL:584.0,46565.1] || equal(c_COMBS(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)),hAPP(hAPP(u,v_x),hAPP(v,v_x)))* -> .
% 299.64/300.41 46636[4:SpL:540.1,46565.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))* -> .
% 299.64/300.41 46635[4:SpL:539.1,46565.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))* -> .
% 299.64/300.41 46625[4:SpL:299.2,46565.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),v)* -> .
% 299.64/300.41 46612[4:SpL:25.1,46565.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))* -> .
% 299.64/300.41 46701[0:Res:446.1,44639.0] || c_lessequals(u,v,tc_fun(tc_Com_Opname,tc_bool))* equal(hAPP(c_Set_Oinsert(w,tc_Com_Opname),u),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v),v_x))*.
% 299.64/300.41 46697[0:Res:108.1,44639.0] || c_lessequals(u,v,tc_fun(tc_Com_Opname,tc_bool))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.41 47463[4:SSi:47442.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool),tc_bool),u),tc_bool,tc_bool))*.
% 299.64/300.41 48167[4:SpR:27043.1,39023.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),x))*.
% 299.64/300.41 48166[4:SpR:15172.0,39023.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_bool)),x1))*.
% 299.64/300.41 48161[4:SpR:586.0,39023.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(u,hAPP(y,v_x))),x2))*.
% 299.64/300.41 48160[4:SpR:585.0,39023.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(hAPP(u,v_x),y)),x2))*.
% 299.64/300.41 48154[4:SpR:9936.1,39023.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_bool)),x))*.
% 299.64/300.41 48150[4:SpR:9935.1,39023.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_bool)),x))*.
% 299.64/300.41 48109[4:SpR:8415.2,39023.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),x))*.
% 299.64/300.41 48103[4:SpR:445.1,39023.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(v_x,v) hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(u,v_x)),x2))*.
% 299.64/300.41 48282[4:SpR:27043.1,39064.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),v_x),x,t_a)*.
% 299.64/300.41 48281[4:SpR:15172.0,39064.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_bool)),x1,t_a)*.
% 299.64/300.41 48276[4:SpR:586.0,39064.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(z,x1),hAPP(u,hAPP(y,v_x))),x2,t_a)*.
% 299.64/300.41 48275[4:SpR:585.0,39064.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(z,x1),hAPP(hAPP(u,v_x),y)),x2,t_a)*.
% 299.64/300.41 48269[4:SpR:9936.1,39064.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_bool)),x,t_a)*.
% 299.64/300.41 48265[4:SpR:9935.1,39064.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_bool)),x,t_a)*.
% 299.64/300.41 48224[4:SpR:8415.2,39064.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),v_x),x,t_a)*.
% 299.64/300.41 48218[4:SpR:445.1,39064.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(v_x,v) c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(z,x1),hAPP(u,v_x)),x2,t_a)*.
% 299.64/300.41 48528[4:SpR:8415.2,40606.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),hAPP(v_x,y)))*.
% 299.64/300.41 49317[0:Con:49301.3] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)),w))*.
% 299.64/300.41 49409[0:SpR:49342.1,20881.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,v),x)),v_Procs))*.
% 299.64/300.41 49403[0:SpR:49342.1,353.0] || hBOOL(hAPP(u,v_x)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))**.
% 299.64/300.41 49380[0:SpR:49342.1,9569.0] || hBOOL(hAPP(u,v_x)) -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.41 49379[0:SpR:49342.1,9568.0] || hBOOL(hAPP(u,v_x)) -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname)),w),v_Procs),tc_bool)*.
% 299.64/300.41 49376[0:SpR:49342.1,415.0] || hBOOL(hAPP(u,v_x)) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v_Procs,v_Procs,v,w),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname))**.
% 299.64/300.41 50182[4:SpR:8415.2,43372.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),x))*.
% 299.64/300.41 50213[4:SpR:8415.2,43608.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),x,t_a)*.
% 299.64/300.41 50381[0:SSi:50347.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),u),v))* c_Finite__Set_Ofinite(v,tc_bool) hBOOL(w) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,v,tc_bool,tc_bool))*.
% 299.64/300.41 50763[0:SSi:50730.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),u),v))* c_Finite__Set_Ofinite(v,tc_bool) hBOOL(u) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,v,tc_bool,tc_bool))*.
% 299.64/300.41 51163[0:SpR:353.0,26873.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(x,v),w)),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.64/300.41 51380[0:SpR:27043.1,51231.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_Procs,v)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 51374[0:SpR:586.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(u,hAPP(v,v_x)),hAPP(hAPP(c_Set_Oinsert(w,t_a),hAPP(c_COMBB(u,x,y,z),v)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 51373[0:SpR:585.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(u,v_x),v),hAPP(hAPP(c_Set_Oinsert(w,t_a),hAPP(c_COMBC(u,x,y,z),v)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 51320[0:SpR:8415.2,51231.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(v,t_a),u),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 51314[0:SpR:445.1,51231.0] || -> equal(v_x,u) equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(hAPP(c_Set_Oinsert(w,t_a),c_Fun_Ofun__upd(v,u,x,y,z)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 51302[0:SpR:8415.2,51231.0] || equal(v_Procs,v_x) equal(hAPP(c_Set_Oinsert(u,t_a),v),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),v_x,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 51284[0:SpR:353.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(u,t_a),v),v_x),hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(w,t_a),v)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.41 51444[7:SpL:128.0,27284.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)),v_x)** -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),hAPP(u,v_x))).
% 299.64/300.41 51460[0:SpR:383.1,32700.0] || -> equal(u,v_x) hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ofun__upd(c_Fun_Ofun__upd(v,v_x,w,x,y),u,z,x,y),tc_Com_Opname,x1),w)))*.
% 299.64/300.41 51477[0:SpL:353.0,33513.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(x,v),w)),v),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.41 51788[4:Res:40244.1,19641.0] || c_lessequals(v_x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),y),tc_bool)* -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),y,t_a).
% 299.64/300.41 51806[4:SpR:353.0,40792.1] || c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(u,v),w),x),tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(y,v),w)),x))*.
% 299.64/300.41 51978[0:Rew:9924.0,51956.1,9924.0,51956.1] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_List_Ofoldl(x,c_Orderings_Otop__class_Otop(tc_bool),y,w,z),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.41 52258[0:SpL:8415.2,35720.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Set_Oinsert(u,v))* c_lessequals(v_x,w,tc_fun(v,tc_bool))* -> hBOOL(hAPP(w,u))*.
% 299.64/300.41 52479[0:Res:37898.1,19641.0] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),y)))* -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),y,t_a).
% 299.64/300.41 52797[0:SpR:24019.2,3339.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(u,v_x) -> equal(c_Fun_Ofun__upd(u,v_x,v_x,v,w),u)**.
% 299.64/300.41 53004[0:Res:23739.1,496.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,v_x)),v_x))* c_Hoare__Mirabelle_Otriple__valid(u,v_Procs,t_a).
% 299.64/300.41 52994[0:Res:23739.1,255.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),u))*.
% 299.64/300.41 53361[0:Res:31543.0,255.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x)),u))*.
% 299.64/300.41 53442[0:SpR:33303.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_Procs))*.
% 299.64/300.41 53413[0:SpR:33303.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v,w),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.41 53571[0:SSi:53552.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.41 53574[0:SSi:53549.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.41 53759[0:Res:7226.0,255.0] || c_lessequals(hAPP(c_Set_Oimage(c_Option_Othe(u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),x,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),y),x))*.
% 299.64/300.41 53808[0:SpR:53771.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Option_Othe(u),v,w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Option_Othe(u),x,z),v),x1)),y))*.
% 299.64/300.41 53793[0:SpR:53771.0,9569.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Option_Othe(x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),u,c_Option_Othe(x),y,z)),tc_bool)*.
% 299.64/300.41 53792[0:SpR:53771.0,9568.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Option_Othe(w)),x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),u,c_Option_Othe(w),y,z)),tc_bool)*.
% 299.64/300.41 53839[0:SpR:53772.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Option_Othe(u),v,w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Option_Othe(u),y,x,z),v),x1)),y))*.
% 299.64/300.41 53824[0:SpR:53772.0,9569.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Option_Othe(x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Option_Othe(x),u,y,z)),tc_bool)*.
% 299.64/300.41 53823[0:SpR:53772.0,9568.0] || -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Option_Othe(w)),x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Option_Othe(w),u,y,z)),tc_bool)*.
% 299.64/300.41 54169[0:SpL:52997.1,3698.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(u,c_Set_Oinsert(v_Procs,v))* equal(c_Com_Ocom_OBODY,u) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 54130[0:SpR:52997.1,7253.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x))*.
% 299.64/300.41 54085[0:SpR:52997.1,3339.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(u,c_Set_Oinsert(v_Procs,v))* -> equal(c_Fun_Ofun__upd(u,v_x,v_x,w,x),u)**.
% 299.64/300.41 54084[0:SpR:52997.1,3316.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_in(u),c_Set_Oinsert(v_Procs,v))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.41 54081[0:SpR:52997.1,648.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,v),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.41 54070[0:SpR:52997.1,21893.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v)),v_x)**.
% 299.64/300.41 54069[0:SpR:52997.1,28031.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 54067[0:SpR:52997.1,27381.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.41 54064[0:SpR:52997.1,21267.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_Procs,u),v_x,tc_Com_Opname,v)),v_x)**.
% 299.64/300.41 54063[0:SpR:52997.1,28334.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_Procs,u),v_x,tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 54061[0:SpR:52997.1,27441.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_Procs,u),v_x,tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.41 54060[0:SpR:52997.1,21141.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x))*.
% 299.64/300.41 54058[0:SpR:52997.1,11030.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(v_Procs,u),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.41 54057[0:SpR:52997.1,10090.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.41 54043[2:SpR:52997.1,15483.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_Procs,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.41 54037[0:SpR:52997.1,651.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.41 55527[0:SpR:538.0,54593.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool)*.
% 299.64/300.41 55639[7:MRR:55638.1,27297.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(w,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool)*.
% 299.64/300.41 55759[0:SpL:540.1,55605.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.41 55758[0:SpL:539.1,55605.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.41 55822[0:Rew:181.1,55761.0] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(v),w),v_x))*.
% 299.64/300.41 56021[0:SpL:584.0,55174.1] || equal(u,c_COMBS(v,w,x,y,z))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(hAPP(v,v_x),hAPP(w,v_x)))* -> .
% 299.64/300.41 56001[0:SpL:337.0,55174.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* -> .
% 299.64/300.41 55988[0:SpL:540.1,55174.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w))* -> .
% 299.64/300.41 55987[0:SpL:539.1,55174.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w))* -> .
% 299.64/300.41 55977[0:SpL:299.2,55174.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool),v)* -> .
% 299.64/300.41 55963[0:SpL:25.1,55174.1] class_HOL_Ouminus(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u))) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u))* -> .
% 299.64/300.41 55939[0:SpL:584.0,55174.1] || equal(c_COMBS(u,v,w,x,y),z)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_bool),hAPP(z,v_x))* -> .
% 299.64/300.41 55919[0:SpL:337.0,55174.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v)* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool),hAPP(v,v_x))* -> .
% 299.64/300.41 55906[0:SpL:540.1,55174.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),hAPP(w,v_x))* -> .
% 299.64/300.41 55905[0:SpL:539.1,55174.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),hAPP(w,v_x))* -> .
% 299.64/300.41 55895[0:SpL:299.2,55174.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),hAPP(w,v_x))* -> .
% 299.64/300.41 55880[0:SpL:25.1,55174.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w) equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool),hAPP(w,v_x))* -> .
% 299.64/300.41 56351[0:SpL:30368.2,55174.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Otop__class_Otop(u))* -> .
% 299.64/300.41 56347[0:SpL:30368.2,3698.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_Com_Ocom_OBODY,v) equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 56346[4:SpL:30368.2,46565.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(u))* -> .
% 299.64/300.41 56337[0:SpL:30368.2,3493.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.41 56334[0:SpL:30368.2,55174.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v)* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),hAPP(v,v_x))* -> .
% 299.64/300.41 56195[0:SpR:30368.2,415.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,c_Orderings_Otop__class_Otop(u),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))**.
% 299.64/300.41 56176[0:SpR:30368.2,3339.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> equal(c_Fun_Ofun__upd(v,v_x,c_Orderings_Otop__class_Otop(u),w,x),v)**.
% 299.64/300.41 56175[0:SpR:30368.2,3316.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.41 56172[0:SpR:30368.2,648.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.41 56159[0:SpR:30368.2,28031.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 56157[0:SpR:30368.2,27381.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.41 56153[0:SpR:30368.2,28334.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 56151[0:SpR:30368.2,27441.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.41 56150[0:SpR:30368.2,21141.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.41 56148[0:SpR:30368.2,11030.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.41 56147[0:SpR:30368.2,10090.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.41 56138[0:SpR:30368.2,3284.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.41 56133[2:SpR:30368.2,15483.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)).
% 299.64/300.41 56131[0:SpR:30368.2,15482.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)).
% 299.64/300.41 56130[7:SpR:30368.2,27219.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)).
% 299.64/300.41 56127[0:SpR:30368.2,651.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.41 56123[0:SpR:30368.2,21130.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.41 56793[0:SpL:30928.2,55174.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_Orderings_Otop__class_Otop(u))* -> .
% 299.64/300.41 56789[0:SpL:30928.2,3698.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_Com_Ocom_OBODY,v) equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 56788[4:SpL:30928.2,46565.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(u))* -> .
% 299.64/300.41 56779[0:SpL:30928.2,3493.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.41 56776[0:SpL:30928.2,55174.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v)* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),hAPP(v,v_x))* -> .
% 299.64/300.41 56637[0:SpR:30928.2,415.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,c_Orderings_Otop__class_Otop(u),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))**.
% 299.64/300.41 56617[0:SpR:30928.2,3339.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> equal(c_Fun_Ofun__upd(v,v_x,c_Orderings_Otop__class_Otop(u),w,x),v)**.
% 299.64/300.41 56616[0:SpR:30928.2,3316.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.41 56613[0:SpR:30928.2,648.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),v_Procs)))*.
% 299.64/300.41 56600[0:SpR:30928.2,28031.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 56598[0:SpR:30928.2,27381.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.41 56594[0:SpR:30928.2,28334.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.41 56592[0:SpR:30928.2,27441.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v)),v_Procs))*.
% 299.64/300.41 56591[0:SpR:30928.2,21141.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.41 56589[0:SpR:30928.2,11030.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.41 56588[0:SpR:30928.2,10090.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.41 56579[0:SpR:30928.2,3284.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.41 56574[2:SpR:30928.2,15483.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)).
% 299.64/300.41 56572[0:SpR:30928.2,15482.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)).
% 299.64/300.41 56571[7:SpR:30928.2,27219.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)).
% 299.64/300.41 56568[0:SpR:30928.2,651.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.41 56564[0:SpR:30928.2,21130.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.41 57758[4:SpL:8415.2,57560.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),v_x),v_x),c_HOL_Ouminus__class_Ouminus(v_x,tc_bool))** -> .
% 299.64/300.41 57835[0:Res:47.2,4203.2] class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),c_Orderings_Obot__class_Obot(u)).
% 299.64/300.41 57834[0:Res:43.2,4203.2] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),c_Orderings_Obot__class_Obot(u)).
% 299.64/300.41 57974[0:SpL:27043.1,55910.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** equal(c_COMBK(u,v,w),c_Set_Oinsert(v_Procs,x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) -> .
% 299.64/300.41 57972[0:SpL:15172.0,55910.1] || equal(c_COMBK(u,v,w),c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),x,y),z,tc_fun(x1,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) -> .
% 299.64/300.41 57967[0:SpL:586.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(c_COMBB(x,y,z,x1),x2))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(x,hAPP(x2,v_x))) -> .
% 299.64/300.41 57966[0:SpL:585.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(c_COMBC(x,y,z,x1),x2))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(hAPP(x,v_x),x2)) -> .
% 299.64/300.41 57960[0:SpL:9936.1,55910.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(c_COMBK(v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> .
% 299.64/300.41 57956[0:SpL:9935.1,55910.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(c_COMBK(u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> .
% 299.64/300.41 57910[0:SpL:8415.2,55910.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) equal(c_COMBK(v,w,x),u)* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),v_x) -> .
% 299.64/300.41 57904[0:SpL:445.1,55910.1] || equal(c_COMBK(u,v,w),c_Fun_Ofun__upd(x,y,z,x1,x2))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(x,v_x)) -> equal(v_x,y).
% 299.64/300.41 57898[0:SpL:2771.1,55910.1] || equal(u,v)* equal(c_COMBK(hAPP(v,v_x),w,x),y)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(y,v_x))* -> .
% 299.64/300.41 58018[0:Res:49.2,4229.2] class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),c_Orderings_Otop__class_Otop(u)).
% 299.64/300.41 58017[0:Res:45.2,4229.2] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),c_Orderings_Otop__class_Otop(u)).
% 299.64/300.41 58131[0:SpL:27043.1,55992.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v) -> .
% 299.64/300.41 58124[0:SpL:586.0,55992.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_COMBK(z,x1,x2))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(y,v_x)),tc_bool),z) -> .
% 299.64/300.41 58123[0:SpL:585.0,55992.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_COMBK(z,x1,x2))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),y),tc_bool),z) -> .
% 299.64/300.41 58067[0:SpL:8415.2,55992.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) equal(u,c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v) -> .
% 299.64/300.41 58061[0:SpL:445.1,55992.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_COMBK(z,x1,x2))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),z) -> equal(v_x,v).
% 299.64/300.41 58284[0:Res:47.2,4996.2] class_OrderedGroup_Olordered__ab__group__add(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),c_Orderings_Obot__class_Obot(u)).
% 299.64/300.41 58283[0:Res:43.2,4996.2] class_OrderedGroup_Oordered__ab__group__add(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),c_Orderings_Obot__class_Obot(u)).
% 299.64/300.41 58393[0:Res:49.2,5005.2] class_OrderedGroup_Olordered__ab__group__add(u) class_Orderings_Otop(u) class_Orderings_Oorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),c_Orderings_Otop__class_Otop(u)).
% 299.64/300.41 58392[0:Res:45.2,5005.2] class_OrderedGroup_Oordered__ab__group__add(u) class_Orderings_Otop(u) class_Orderings_Oorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),c_Orderings_Otop__class_Otop(u)).
% 299.64/300.41 58488[0:SpL:329.1,58248.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(c_COMBK(v_x,w,x),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.41 58487[0:SpL:328.1,58248.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(c_COMBK(u,w,x),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.41 58483[0:SpL:538.0,58248.0] || equal(c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),w,x),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_fun(t_a,tc_bool)))** -> .
% 299.64/300.41 58604[0:Res:10771.1,45899.0] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Set_Oinsert(v,u),w),tc_Com_Opname)),w))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),w),v_x)).
% 299.64/300.41 59038[4:Res:40606.0,15629.0] || -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),y)))*.
% 299.64/300.41 58991[0:Res:12687.1,15629.0] || -> hBOOL(hAPP(u,v))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),x)))*.
% 299.64/300.41 58789[0:SpL:105.0,15629.0] || hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))) -> hBOOL(hAPP(c_Set_Ovimage(v,u,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Set_Ovimage(v,u,w),x)))*.
% 299.64/300.41 58779[0:SpL:38.0,15629.0] || hBOOL(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) -> hBOOL(hAPP(c_Set_Ovimage(v,u,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Set_Ovimage(v,u,w),x)))*.
% 299.64/300.41 58778[0:SpL:321.0,15629.0] || hBOOL(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) -> hBOOL(hAPP(c_Set_Oimage(v,w,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Set_Oimage(v,w,u),x)))*.
% 299.64/300.41 58775[0:SpL:301.1,15629.0] class_Lattices_Obounded__lattice(u) || hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))*.
% 299.64/300.41 58706[0:SpL:525.1,15629.0] class_Lattices_Oupper__semilattice(u) || hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))*.
% 299.64/300.41 58665[0:SpL:2097.1,15629.0] || hBOOL(hAPP(u,v))* hBOOL(u) -> hBOOL(hAPP(c_Set_Oinsert(v,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Set_Oinsert(v,w),x)))*.
% 299.64/300.41 59119[4:MRR:58811.1,6340.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Set_Oinsert(v_Procs,u),v)))*.
% 299.64/300.41 59546[4:Res:40606.0,15857.0] || -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),z)))*.
% 299.64/300.41 59499[0:Res:12687.1,15857.0] || -> hBOOL(hAPP(u,v))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),y)))*.
% 299.64/300.41 59297[0:SpL:105.0,15857.0] || hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))) -> hBOOL(hAPP(c_Set_Ovimage(v,u,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Ovimage(v,u,w),y)))*.
% 299.64/300.41 59287[0:SpL:38.0,15857.0] || hBOOL(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) -> hBOOL(hAPP(c_Set_Ovimage(v,u,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Ovimage(v,u,w),y)))*.
% 299.64/300.41 59286[0:SpL:321.0,15857.0] || hBOOL(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) -> hBOOL(hAPP(c_Set_Oimage(v,w,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oimage(v,w,u),y)))*.
% 299.64/300.41 59283[0:SpL:301.1,15857.0] class_Lattices_Obounded__lattice(u) || hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))*.
% 299.64/300.41 59214[0:SpL:525.1,15857.0] class_Lattices_Oupper__semilattice(u) || hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))*.
% 299.64/300.41 59173[0:SpL:2097.1,15857.0] || hBOOL(hAPP(u,v))* hBOOL(u) -> hBOOL(hAPP(c_Set_Oinsert(v,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(v,w),y)))*.
% 299.64/300.41 59629[4:MRR:59319.1,6340.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v_Procs,u),w)))*.
% 299.64/300.41 59727[0:SpL:8415.2,58179.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v,w),v_x)** -> .
% 299.64/300.41 59755[0:SpL:338.0,21018.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(y,v),z))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> .
% 299.64/300.41 59801[0:Res:57755.3,427.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Olordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.41 59983[0:SpL:2771.1,57894.0] || equal(u,v)* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),w,x),y)* equal(hAPP(v,v_x),hAPP(y,v_x))* -> .
% 299.64/300.41 60092[0:Res:4718.2,4996.2] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_Orderings_Obot__class_Obot(u)).
% 299.64/300.41 60057[0:SpR:1628.2,4718.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.41 60053[0:SpR:1421.2,4718.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)) c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) -> c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)*.
% 299.64/300.41 60052[0:SpR:1409.2,4718.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) -> c_lessequals(c_Orderings_Obot__class_Obot(u),v,u)*.
% 299.64/300.41 60243[0:SpL:27043.1,58170.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(u,c_Set_Oinsert(v_Procs,v))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),u)* -> .
% 299.64/300.41 60236[0:SpL:586.0,58170.1] || equal(u,hAPP(c_COMBB(v,w,x,y),z))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(v,hAPP(z,v_x)),tc_bool),x1,x2),u)* -> .
% 299.64/300.41 60235[0:SpL:585.0,58170.1] || equal(u,hAPP(c_COMBC(v,w,x,y),z))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(v,v_x),z),tc_bool),x1,x2),u)* -> .
% 299.64/300.41 60179[0:SpL:8415.2,58170.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(v,u)* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),v)* -> .
% 299.64/300.41 60173[0:SpL:445.1,58170.1] || equal(u,c_Fun_Ofun__upd(v,w,x,y,z))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),x1,x2),u)* -> equal(v_x,w).
% 299.64/300.41 60324[0:Res:4803.2,5005.2] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Otop(u) class_Orderings_Oorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),c_Orderings_Otop__class_Otop(u)).
% 299.64/300.41 60278[0:SpR:1628.2,4803.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ozero__class_Ozero(u)) c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.41 60274[0:SpR:1421.2,4803.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Obot__class_Obot(u),c_HOL_Ozero__class_Ozero(u)) c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.41 60273[0:SpR:1409.2,4803.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.41 60786[0:SSi:60772.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,y,z,x1),v),tc_fun(w,tc_bool))*.
% 299.64/300.41 61422[0:Res:61338.3,427.1] class_Lattices_Obounded__lattice(u) class_Lattices_Oupper__semilattice(u) class_Orderings_Opreorder(u) || equal(c_Orderings_Otop__class_Otop(u),v) c_lessequals(v,w,u)* -> c_lessequals(x,w,u)*.
% 299.64/300.41 61669[0:Res:4803.2,8141.2] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),u)*.
% 299.64/300.41 61661[0:Res:49.2,8141.2] class_OrderedGroup_Olordered__ab__group__add(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),u)*.
% 299.64/300.41 61660[0:Res:45.2,8141.2] class_OrderedGroup_Oordered__ab__group__add(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),u)*.
% 299.64/300.41 61789[0:SpR:11167.1,7253.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_Procs))*.
% 299.64/300.41 61771[0:SpR:11167.1,21130.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),w,x),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.41 61960[0:SpL:9.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Fun_Ocomp(u,v,w,x,y),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 61939[0:SpL:88.1,15487.1] class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 61925[0:SpL:2098.1,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a).
% 299.64/300.41 61910[0:SpL:3586.1,15487.1] || equal(hAPP(c_in(u),v),v_Procs) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 61909[7:SpL:27278.1,15487.1] || equal(hAPP(c_in(u),v),v_x) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 61895[0:SpL:8498.1,15487.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.41 62103[2:SpL:8415.2,62081.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) equal(c_Com_Ocom_OBODY,v_x) -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.41 62147[0:SSi:62144.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.41 62163[0:Res:23754.0,255.0] || c_lessequals(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs),v,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v_x),v)).
% 299.64/300.41 62196[0:Rew:23682.0,62170.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v_Procs,tc_Com_Opname,u) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x),v_x)**.
% 299.64/300.41 62282[0:Res:4790.2,4246.1] class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),v) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),v,u)*.
% 299.64/300.41 62256[0:Res:4703.2,4246.1] class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || equal(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u)) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),u)*.
% 299.64/300.41 62617[0:Res:4790.2,4340.1] class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),v,u)* -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(u),u),v).
% 299.64/300.41 62591[0:Res:4703.2,4340.1] class_Orderings_Otop(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u),u)* -> equal(v,c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),u)).
% 299.64/300.41 63433[0:SpR:1605.2,4719.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u))* c_lessequals(w,x,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),x,u)*.
% 299.64/300.41 63432[0:SpR:1628.2,4719.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u))* c_lessequals(w,x,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),x,u)*.
% 299.64/300.41 63427[0:SpR:1259.2,4719.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) c_lessequals(v,w,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u)*.
% 299.64/300.41 63424[0:SpR:1421.2,4719.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u)) c_lessequals(v,w,u)* -> c_lessequals(c_Orderings_Otop__class_Otop(u),w,u)*.
% 299.64/300.41 63423[0:SpR:1409.2,4719.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)) c_lessequals(v,w,u)* -> c_lessequals(c_Orderings_Obot__class_Obot(u),w,u)*.
% 299.64/300.41 63781[0:SSi:63657.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(hAPP(c_Set_Oimage(v,u,u),w),w)** c_Finite__Set_Ofinite(w,u) -> c_Fun_Oinj__on(v,w,u,u).
% 299.64/300.41 63782[0:SSi:63656.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))) -> c_lessequals(w,v,tc_fun(u,tc_bool))*.
% 299.64/300.41 63783[0:SSi:63627.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(v,hAPP(c_Set_Oimage(w,x,u),y)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(y,w,x,u),v,u,x)*.
% 299.64/300.41 63883[0:Res:4804.2,8141.2] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u)*.
% 299.64/300.41 63836[0:SpR:1605.2,4804.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u))* c_lessequals(x,w,u)* -> c_lessequals(x,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.41 63835[0:SpR:1628.2,4804.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,u))* c_lessequals(x,w,u)* -> c_lessequals(x,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.41 63830[0:SpR:1259.2,4804.2] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) c_lessequals(w,v,u)* -> c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.41 63827[0:SpR:1421.2,4804.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Obot__class_Obot(u)) c_lessequals(w,v,u)* -> c_lessequals(w,c_Orderings_Otop__class_Otop(u),u)*.
% 299.64/300.41 63826[0:SpR:1409.2,4804.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)) c_lessequals(w,v,u)* -> c_lessequals(w,c_Orderings_Obot__class_Obot(u),u)*.
% 299.64/300.41 64034[0:SpR:353.0,63953.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v),v_Procs,tc_fun(tc_Com_Opname,tc_bool)),hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v)),tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.41 64168[0:SpR:646.1,9567.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,tc_fun(x,tc_bool)),hAPP(u,v_x)),v_x,tc_bool)*.
% 299.64/300.41 64335[0:SpR:645.1,9567.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,tc_fun(x,tc_bool)),hAPP(u,v_x)),v_x,tc_bool)*.
% 299.64/300.41 64560[0:SpL:12944.0,24257.1] || equal(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_in(tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.41 64554[0:SpL:9.0,24257.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(u,hAPP(v,v_x)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.41 64553[0:SpL:11473.0,24257.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_in(tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.41 64533[0:SpL:88.1,24257.1] class_Lattices_Oboolean__algebra(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.41 64529[0:SpL:17045.0,24257.1] || equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_bool),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.41 64564[0:MRR:64525.0,15145.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.41 64697[0:Res:27986.0,255.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w)),u))*.
% 299.64/300.41 64717[0:Res:27987.0,255.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w)),u))*.
% 299.64/300.41 64737[0:Res:28288.0,255.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)),u))*.
% 299.64/300.41 64757[0:Res:28289.0,255.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w)),u))*.
% 299.64/300.41 64833[0:SpR:28747.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_Procs))*.
% 299.64/300.41 64803[0:SpR:28747.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.41 64953[0:SpR:28748.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_Procs))*.
% 299.64/300.41 64923[0:SpR:28748.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.41 65073[0:SpR:28902.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_Procs))*.
% 299.64/300.41 65043[0:SpR:28902.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.41 65193[0:SpR:28903.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_Procs))*.
% 299.64/300.41 65163[0:SpR:28903.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.41 66211[0:SpL:65404.1,15629.0] class_Lattices_Olattice(u) || hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))*.
% 299.64/300.41 66210[0:SpL:65404.1,15857.0] class_Lattices_Olattice(u) || hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))*.
% 299.64/300.41 66724[0:SpR:1188.2,9567.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,tc_fun(w,tc_bool)),c_HOL_Ozero__class_Ozero(u)),c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.41 67479[0:SpR:1189.2,9567.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,tc_fun(w,tc_bool)),c_HOL_Ozero__class_Ozero(u)),c_Orderings_Otop__class_Otop(u),tc_bool)*.
% 299.64/300.41 68453[0:Rew:1250.3,68236.5,1409.2,68236.5] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Ogroup__add(u) class_Orderings_Obot(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.41 70346[0:SpL:8415.2,65954.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u))* equal(c_in(tc_Com_Opname),v_x) -> hBOOL(hAPP(v_x,v_Procs))*.
% 299.64/300.42 70375[0:SpL:8415.2,70070.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(t_a)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))* hBOOL(hAPP(v_x,u)) -> .
% 299.64/300.42 70468[0:SpL:55.1,70390.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(t_a,tc_bool)),v_x),tc_bool))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.64/300.42 71508[7:SpR:71455.1,353.0] || equal(hAPP(c_Set_Oinsert(u,t_a),v),v_x) -> equal(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),hAPP(c_Set_Oinsert(u,t_a),v))**.
% 299.64/300.42 72493[0:Res:1103.1,12554.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),t_a) hBOOL(hAPP(hAPP(c_in(x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)))),v))*.
% 299.64/300.42 74173[7:SpL:71835.1,57.1] class_OrderedGroup_Olordered__ab__group__add(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) equal(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_x,u)),c_HOL_Ozero__class_Ozero(u))** -> equal(c_HOL_Ozero__class_Ozero(u),v_x).
% 299.64/300.42 74113[7:SpL:71835.1,590.0] || equal(c_Set_Oinsert(v_x,t_a),v_P) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_x),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(v_Q,v_x)),t_a)* -> .
% 299.64/300.42 74112[7:SpL:71835.1,590.0] || equal(c_Set_Oinsert(v_x,t_a),c_Com_Ocom_OBODY) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),v_x),hAPP(v_Q,v_x)),t_a)* -> .
% 299.64/300.42 74111[7:SpL:71835.1,590.0] || equal(c_Set_Oinsert(v_x,t_a),v_Q) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_x),t_a)* -> .
% 299.64/300.42 73979[7:SpL:71835.1,357.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a))** c_Finite__Set_Ofinite(v_x,v) c_lessequals(x,v_x,tc_fun(w,tc_bool))* -> c_Finite__Set_Ofinite(x,w).
% 299.64/300.42 73966[7:SpL:71835.1,505.0] || equal(c_Set_Oinsert(v_x,t_a),c_Com_Obody) c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),v_x),u,v,w)* -> c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_x),u,c_Suc(v),w).
% 299.64/300.42 73957[7:SpL:71835.1,454.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(v_x,u)) -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(u,v),v_x,t_a)*.
% 299.64/300.42 73681[7:SpR:71835.1,353.0] || equal(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(u,v)) -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),hAPP(c_Set_Oinsert(w,v),v_x))**.
% 299.64/300.42 74486[7:MRR:74257.1,6340.0] || equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,t_a)) c_lessequals(v_x,w,tc_fun(u,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),v),w))*.
% 299.64/300.42 74487[7:Rew:71835.1,74132.2] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,u),w)))* -> hBOOL(hAPP(v_x,w)) equal(v_x,v).
% 299.64/300.42 74488[7:Rew:71835.1,74120.3] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,v)) c_lessequals(v,w,tc_fun(u,tc_bool))* -> hBOOL(hAPP(v_x,w)).
% 299.64/300.42 74491[7:Rew:71835.1,73510.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))*.
% 299.64/300.42 74492[7:Rew:71835.1,73509.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v)))*.
% 299.64/300.42 75166[7:Res:84.1,71908.0] || c_lessequals(c_HOL_Ominus__class_Ominus(v_x,u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x))*.
% 299.64/300.42 75609[0:SSi:75608.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),w).
% 299.64/300.42 76276[0:SpR:10469.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),x2,tc_fun(x3,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)*.
% 299.64/300.42 76406[0:SpR:10470.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,tc_fun(x3,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool),tc_bool)*.
% 299.64/300.42 77214[7:MRR:77136.2,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_x)** equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),x)* -> hBOOL(x)*.
% 299.64/300.42 77406[0:Res:2399.2,38189.0] class_Orderings_Olinorder(tc_bool) class_OrderedGroup_Olordered__ab__group__add(tc_bool) || hBOOL(u) -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_HOL_Ouminus__class_Ouminus(u,tc_bool)))*.
% 299.64/300.42 77405[0:Res:2399.2,38190.0] class_Orderings_Olinorder(tc_bool) class_OrderedGroup_Olordered__ab__group__add(tc_bool) || hBOOL(u) -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_bool)),v))*.
% 299.64/300.42 77403[0:Res:2399.2,50366.0] class_Orderings_Olinorder(tc_bool) class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v,tc_bool)* hBOOL(u) -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),u,tc_bool) hBOOL(v).
% 299.64/300.42 77437[0:MRR:77368.4,1811.1] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(tc_Com_Opname,tc_bool)) || equal(u,v_Procs) -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(tc_Com_Opname,tc_bool)),u,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.42 77638[7:Res:77503.0,15629.0] || -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname),u)))*.
% 299.64/300.42 77637[7:Res:77503.0,15857.0] || -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(t_a),v_x),tc_Com_Opname),v)))*.
% 299.64/300.42 77900[0:Res:9246.0,5892.0] || -> hBOOL(hAPP(u,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))))* hBOOL(hAPP(c_COMBS(c_in(w),c_in(v),x,y,z),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))))*.
% 299.64/300.42 77754[0:SpL:11177.1,5892.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(u,u))* -> hBOOL(hAPP(c_COMBS(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,y,z),u))*.
% 299.64/300.42 78182[7:Res:77996.0,479.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,w,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w)))*.
% 299.64/300.42 78181[7:Res:77996.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_x,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)))*.
% 299.64/300.42 78216[7:Rew:78167.0,78195.1] || equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname,u),v_x),v_Procs)** -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,tc_Com_Opname),tc_Com_Opname,u),v_x),v_x).
% 299.64/300.42 78538[4:MRR:9464.0,78524.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))**.
% 299.64/300.42 78577[4:MRR:34685.0,78524.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u)),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u))**.
% 299.64/300.42 78697[4:Res:78665.1,156.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y)),v_x)** -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,v)),y)).
% 299.64/300.42 78687[4:Res:78665.1,255.0] || equal(hAPP(hAPP(c_in(u),v),w),v_x)** c_lessequals(w,x,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),x))*.
% 299.64/300.42 78679[4:Res:78665.1,263.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)),v_x)** -> hBOOL(hAPP(hAPP(c_in(u),v),x)) equal(v,w).
% 299.64/300.42 78863[0:SpR:97.1,11064.1] || c_Fun_Oinj__on(u,v,w,x) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,w,x),v),x)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(v,y,tc_fun(w,tc_bool)),w)*.
% 299.64/300.42 79019[0:Res:15630.1,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,hAPP(c_in(u),v),x),v))*.
% 299.64/300.42 79239[0:Res:15858.1,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(w,y),z),hAPP(c_in(u),v),y),v))*.
% 299.64/300.42 80090[7:SpL:21268.0,27279.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(v_x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(u),hAPP(c_in(u),v),w,x)))*.
% 299.64/300.42 80072[0:SpL:21268.0,3587.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(v_x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(u),hAPP(c_in(u),v),w,x)))*.
% 299.64/300.42 79959[0:SpR:9987.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,w)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.64/300.42 79957[0:SpR:2095.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(u,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,x)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.64/300.42 79939[0:SpR:330.0,21268.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v,w,x)),v)**.
% 299.64/300.42 79874[0:SpR:414.0,21268.0] || -> equal(hAPP(c_Fun_Ofun__upd(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Fun_Ofun__upd(u,v,w,x,y),w,z,x1)),w)**.
% 299.64/300.42 79834[0:SpR:34427.0,21268.0] || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v_x,v,w)),v_x)**.
% 299.64/300.42 79833[0:SpR:2093.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_Procs,u),hAPP(c_in(tc_Com_Opname),v_x),v,w)),hAPP(c_in(tc_Com_Opname),v_x))**.
% 299.64/300.42 79831[0:SpR:3744.1,21268.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(hAPP(c_Set_Oinsert(v_x,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,u),v_Procs,v,w)),v_Procs)**.
% 299.64/300.42 79648[0:SpR:21268.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,hAPP(u,y),x,z)),hAPP(u,y),tc_bool)*.
% 299.64/300.42 79528[0:SpR:21268.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(u,v),w),u,x,y,z),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),u,hAPP(u,v),x1,x2)))*.
% 299.64/300.42 79448[0:SpR:21268.0,267.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(u),hAPP(c_in(u),v),w,x),u),y)))*.
% 299.64/300.42 81285[7:SpL:21894.0,27279.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(v_x,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(u),v),c_in(u),w,x)))*.
% 299.64/300.42 81267[0:SpL:21894.0,3587.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(v_x,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(u),v),c_in(u),w,x)))*.
% 299.64/300.42 81153[0:SpR:9987.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),u,w)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.64/300.42 81151[0:SpR:2095.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(u,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(u,v),w,x)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.64/300.42 81133[0:SpR:330.0,21894.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x)),v)**.
% 299.64/300.42 81068[0:SpR:414.0,21894.0] || -> equal(hAPP(c_Fun_Ofun__upd(u,v,w,x,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),w,c_Fun_Ofun__upd(u,v,w,x,y),z,x1)),w)**.
% 299.64/300.42 81028[0:SpR:34427.0,21894.0] || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v_x,c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v,w)),v_x)**.
% 299.64/300.42 81027[0:SpR:2093.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x),c_Set_Oinsert(v_Procs,u),v,w)),hAPP(c_in(tc_Com_Opname),v_x))**.
% 299.64/300.42 81025[0:SpR:3744.1,21894.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(hAPP(c_Set_Oinsert(v_x,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v_Procs,c_Set_Oinsert(v_x,u),v,w)),v_Procs)**.
% 299.64/300.42 80842[0:SpR:21894.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(u,y),u,x,z)),hAPP(u,y),tc_bool)*.
% 299.64/300.42 80721[0:SpR:21894.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(u,v),w),u,x,y,z),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(u,v),u,x1,x2)))*.
% 299.64/300.42 80641[0:SpR:21894.0,267.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(u),v),c_in(u),w,x),u),y)))*.
% 299.64/300.42 81757[0:Res:5075.1,447.0] || c_Finite__Set_Ofinite(u,v) c_Fun_Oinj__on(w,hAPP(c_Set_Ovimage(w,x,v),u),x,v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(w,x,v),u),x).
% 299.64/300.42 82739[0:Res:23753.1,7671.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),u)*.
% 299.64/300.42 82706[0:Res:10531.1,7671.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(tc_bool),u) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,u),u)*.
% 299.64/300.42 82705[0:Res:9952.1,7671.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_Orderings_Otop__class_Otop(tc_bool),u) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,u),u)*.
% 299.64/300.42 82702[0:Res:49.2,7671.1] class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(w,v,u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.42 82701[0:Res:45.2,7671.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(w,v,u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.42 82665[0:Res:47.2,7671.1] class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,v,u).
% 299.64/300.42 82664[0:Res:43.2,7671.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,v,u).
% 299.64/300.42 82849[7:Res:77991.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,w),v_x),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,x)),u))* c_Hoare__Mirabelle_Otriple__valid(x,v_x,t_a).
% 299.64/300.42 82843[7:Res:77991.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(x,y),u,tc_fun(w,tc_bool))))*.
% 299.64/300.42 82916[0:SpR:97.1,22513.1] || c_Fun_Oinj__on(u,v,w,x) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,w,x),v),x)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(y,w,z),v),z)*.
% 299.64/300.42 83106[0:SpL:5924.0,58248.0] || equal(c_COMBK(hAPP(hAPP(u,v_x),v),w,x),c_HOL_Ouminus__class_Ouminus(c_COMBS(u,c_COMBK(v,y,z),x1,x2,x3),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.42 83091[0:SpL:5924.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_Procs)** -> .
% 299.64/300.42 83090[7:SpL:5924.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_x)** -> .
% 299.64/300.42 83088[0:SpL:5924.0,3929.0] || hBOOL(hAPP(hAPP(u,v_x),v)) equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2)* -> hBOOL(hAPP(x2,v_x))*.
% 299.64/300.42 83054[0:SpR:5924.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,tc_fun(x3,tc_bool)),x4),hAPP(hAPP(u,x4),v),tc_bool)*.
% 299.64/300.42 83030[0:SpR:5924.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(u,v),w),x),c_COMBS(u,c_COMBK(w,y,z),x1,x2,x3),x4,x5,x6),v))*.
% 299.64/300.42 83015[0:SpR:5924.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(hAPP(v,v_x),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2),tc_Com_Opname,u),u)*.
% 299.64/300.42 83010[4:SpR:5924.0,38236.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(u,v_x),v),tc_Com_Opname,tc_bool))*.
% 299.64/300.42 83004[0:SpR:5924.0,23902.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(hAPP(u,v_x),v),c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.42 83278[7:SpR:465.1,78357.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(w,u,x),v_x),hAPP(c_Fun_Ofun__upd(w,v,y,u,x),v_x)))*.
% 299.64/300.42 83426[0:SpL:5961.0,58248.0] || equal(c_COMBK(hAPP(u,hAPP(v,v_x)),w,x),c_HOL_Ouminus__class_Ouminus(c_COMBS(c_COMBK(u,y,z),v,x1,x2,x3),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.42 83411[0:SpL:5961.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),v_Procs)** -> .
% 299.64/300.42 83410[7:SpL:5961.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),v_x)** -> .
% 299.64/300.42 83408[0:SpL:5961.0,3929.0] || hBOOL(hAPP(u,hAPP(v,v_x))) equal(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),x2)* -> hBOOL(hAPP(x2,v_x))*.
% 299.64/300.42 83379[0:SpR:5961.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2,tc_fun(x3,tc_bool)),x4),hAPP(u,hAPP(x,x4)),tc_bool)*.
% 299.64/300.42 83361[0:SpR:5961.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(u,hAPP(v,w)),x),c_COMBS(c_COMBK(u,y,z),v,x1,x2,x3),x4,x5,x6),w))*.
% 299.64/300.42 83346[0:SpR:5961.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(v,hAPP(w,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBS(c_COMBK(v,x,y),w,z,x1,x2),tc_Com_Opname,u),u)*.
% 299.64/300.42 83340[4:SpR:5961.0,38236.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(u,hAPP(x,v_x)),tc_Com_Opname,tc_bool))*.
% 299.64/300.42 83334[0:SpR:5961.0,23902.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(u,hAPP(x,v_x)),c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.64/300.42 83764[0:SpR:5899.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_COMBS(u,v,w,x,y),z,tc_fun(x1,tc_bool)),x2),hAPP(c_COMBS(u,v,x3,x4,x5),x2),tc_bool)*.
% 299.64/300.42 83739[0:SpR:5899.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_COMBS(u,v,w,x,y),z),x1),c_COMBS(u,v,x2,x3,x4),x5,x6,x7),z))*.
% 299.64/300.42 84253[7:MRR:84154.2,27297.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool),v_x)** equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_x)** -> .
% 299.64/300.42 84884[4:SpL:2097.1,78744.0] || hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(u,v),w),u))* equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(u,v),w),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oinsert(u,v),w,t_a).
% 299.64/300.42 85005[0:Res:84957.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,w),v),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,x)),u))* c_Hoare__Mirabelle_Otriple__valid(x,v,t_a)*.
% 299.64/300.42 84999[0:Res:84957.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v,y),u,tc_fun(x,tc_bool))))*.
% 299.64/300.42 84969[0:SpR:353.0,84957.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),x),w),x))))*.
% 299.64/300.42 85036[0:SpR:644.0,9566.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(hAPP(c_Set_Oinsert(w,x),c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v)),v_Procs),tc_bool)*.
% 299.64/300.42 85317[0:SpL:317.0,26240.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oinsert(y,x),z))),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.42 85460[4:SpR:78507.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Set_Oinsert(v_x,u),v,w)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))**.
% 299.64/300.42 85459[4:SpR:78507.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,w)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))**.
% 299.64/300.42 85437[4:SpR:78507.0,446.1] || c_lessequals(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,v),u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(v,tc_bool))*.
% 299.64/300.42 85767[0:SpR:33303.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)))*.
% 299.64/300.42 85763[0:SpR:28903.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.64/300.42 85762[0:SpR:28902.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.64/300.42 85758[0:SpR:28748.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.64/300.42 85757[0:SpR:28747.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.64/300.42 85752[0:SpR:52997.1,9066.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)))*.
% 299.64/300.42 85865[0:Con:85835.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oinsert(v,w),x),u,w)),hAPP(c_Set_Oinsert(v,w),x)))*.
% 299.64/300.42 86163[0:SpR:86109.1,353.0] || equal(hAPP(c_Set_Oinsert(u,t_a),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),hAPP(c_Set_Oinsert(u,t_a),v))**.
% 299.64/300.42 86551[7:Rew:78167.0,86297.1,78167.0,86297.0] || equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),v_x),v_Procs)** -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),v_x),v_x).
% 299.64/300.42 86798[7:MRR:86699.2,27297.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool),v_x)** equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_Procs)** -> .
% 299.64/300.42 86986[0:SpR:32817.1,117.0] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.64/300.42 87155[7:Res:82177.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,t_a),c_Set_Oinsert(v_x,x)),u,t_a,tc_fun(y,tc_bool)),v))*.
% 299.64/300.42 87225[0:MRR:87199.1,418.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),x),tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> .
% 299.64/300.42 87348[7:SpR:5961.0,71492.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,hAPP(x,v_x))),x2))*.
% 299.64/300.42 87347[7:SpR:5924.0,71492.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(u,v_x),v)),x2))*.
% 299.64/300.42 87323[7:SpR:328.1,71492.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w))*.
% 299.64/300.42 87319[7:SpR:538.0,71492.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)),w))*.
% 299.64/300.42 87496[7:SpR:5961.0,71493.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,hAPP(x,v_x))),x2,t_a)*.
% 299.64/300.42 87495[7:SpR:5924.0,71493.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(u,v_x),v)),x2,t_a)*.
% 299.64/300.42 87471[7:SpR:328.1,71493.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,t_a)*.
% 299.64/300.42 87467[7:SpR:538.0,71493.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)),w,t_a)*.
% 299.64/300.42 87626[7:SpR:5961.0,71679.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x2),hAPP(u,hAPP(x,v_x))))*.
% 299.64/300.42 87625[7:SpR:5924.0,71679.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x2),hAPP(hAPP(u,v_x),v)))*.
% 299.64/300.42 87601[7:SpR:328.1,71679.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u))*.
% 299.64/300.42 87597[7:SpR:538.0,71679.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)))*.
% 299.64/300.42 87742[7:SpL:24914.0,74399.0] || equal(hAPP(c_in(u),v_x),c_Set_Oinsert(v_x,t_a)) -> hBOOL(hAPP(v_x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),hAPP(c_in(u),v_x))))*.
% 299.64/300.42 88424[0:Res:8176.1,431.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,v,w,y)* -> c_Fun_Oinj__on(x,c_HOL_Ominus__class_Ominus(u,z,tc_fun(w,tc_bool)),w,y)*.
% 299.64/300.42 88558[0:Res:8176.1,8306.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,y,tc_fun(x,tc_bool)),v,tc_fun(x,tc_bool))*.
% 299.64/300.42 88712[7:MRR:88606.2,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool))* -> .
% 299.64/300.42 88947[0:SpR:2935.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_in(t_a),v_x),u,v),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))))*.
% 299.64/300.42 88940[0:SpR:301.1,14196.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.42 88935[0:SpR:24020.1,14196.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_x))*.
% 299.64/300.42 88869[0:SpR:300.1,14196.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),x))*.
% 299.64/300.42 88856[0:SpR:365.1,14196.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_x))*.
% 299.64/300.42 88855[0:SpR:397.1,14196.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_x))*.
% 299.64/300.42 88824[0:SpR:2097.1,14196.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v,w),x,y),hAPP(c_Set_Oinsert(u,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),u))*.
% 299.64/300.42 89056[0:Res:78099.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* c_Hoare__Mirabelle_Otriple__valid(u,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),t_a)*.
% 299.64/300.42 89050[0:Res:78099.0,280.1] || hBOOL(hAPP(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,y,tc_fun(z,tc_bool)),w))*.
% 299.64/300.42 89177[0:SpL:3294.1,25984.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_bool)),u)* -> c_Finite__Set_Ofinite(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),u).
% 299.64/300.42 89172[0:SpL:584.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),x1)),v)* -> c_Finite__Set_Ofinite(hAPP(w,x1),v).
% 299.64/300.42 89154[0:SpL:600.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),v)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),v).
% 299.64/300.42 89569[7:SpL:78590.1,19641.0] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(v_x,t_a),u),c_Set_Oinsert(v_x,t_a)) hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(v_x,t_a),u)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oinsert(v_x,t_a),u,t_a)*.
% 299.64/300.42 89354[7:SpR:78590.1,21894.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,c_Set_Oinsert(v_x,t_a),v,w)),u)**.
% 299.64/300.42 89353[7:SpR:78590.1,21268.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),u,v,w)),u)**.
% 299.64/300.42 89350[7:SpR:78590.1,474.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.42 89332[7:SpR:78590.1,446.1] || equal(c_Set_Oinsert(v_x,t_a),u) c_lessequals(v,u,tc_fun(t_a,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),v),u,tc_fun(t_a,tc_bool))*.
% 299.64/300.42 89662[7:Rew:78167.0,89479.1,78167.0,89479.0] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),c_Set_Oinsert(v_x,t_a))** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),v_x).
% 299.64/300.42 89663[7:Rew:78167.0,89477.1,78167.0,89477.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,t_a),v_x,tc_Com_Opname,u),c_Set_Oinsert(v_x,t_a))** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,t_a),v_x,tc_Com_Opname,u),v_x).
% 299.64/300.42 89720[7:Res:89344.1,280.1] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(v,v_x),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,t_a,tc_fun(x,tc_bool)),w))*.
% 299.64/300.42 89716[7:Res:89344.1,175.0] || equal(hAPP(c_Set_Ovimage(u,t_a,v),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(u,v_x),w).
% 299.64/300.42 89712[7:Res:89344.1,470.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),c_Set_Oinsert(v_x,t_a)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,t_a)),w))*.
% 299.64/300.42 89711[7:Res:89344.1,466.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),c_Set_Oinsert(v_x,t_a)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,t_a)),w))*.
% 299.64/300.42 89766[0:SpR:26183.0,9566.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)),hAPP(c_Set_Oinsert(u,v),w)),tc_bool)*.
% 299.64/300.42 90360[4:SpL:78660.1,19641.0] || equal(hAPP(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(v_x,t_a),u),v_x),v_x)** hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(v_x,t_a),u)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oinsert(v_x,t_a),u,t_a).
% 299.64/300.42 90144[4:SpR:78660.1,21894.0] || equal(hAPP(u,v_x),v_x) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,c_Set_Oinsert(v_x,t_a),v,w)),u)**.
% 299.64/300.42 90143[4:SpR:78660.1,21268.0] || equal(hAPP(u,v_x),v_x) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),u,v,w)),u)**.
% 299.64/300.42 90140[4:SpR:78660.1,474.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.42 90122[4:SpR:78660.1,446.1] || equal(hAPP(u,v_x),v_x) c_lessequals(v,u,tc_fun(t_a,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),v),u,tc_fun(t_a,tc_bool))*.
% 299.64/300.42 90439[7:Rew:78167.0,90270.1,78167.0,90270.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),v_x),v_x)** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),v_x).
% 299.64/300.42 90440[7:Rew:78167.0,90268.1,78167.0,90268.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,t_a),v_x,tc_Com_Opname,u),v_x),v_x)** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,t_a),v_x,tc_Com_Opname,u),v_x).
% 299.64/300.42 90600[4:Rew:130.1,90462.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),v_x) -> hBOOL(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))*.
% 299.64/300.42 90669[0:SpL:410.0,26231.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),y),z,x,tc_fun(v,tc_bool))),v)* -> c_Finite__Set_Ofinite(hAPP(z,w),v).
% 299.64/300.42 90734[4:Rew:1250.3,90726.4] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Ogroup__add(u) class_Orderings_Obot(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) equal(c_HOL_Ozero__class_Ozero(u),v_x) -> hBOOL(c_HOL_Ozero__class_Ozero(u))*.
% 299.64/300.42 90864[4:Res:90134.1,280.1] || equal(hAPP(u,v_x),v_x) hBOOL(hAPP(hAPP(v,v_x),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,t_a,tc_fun(x,tc_bool)),w))*.
% 299.64/300.42 90860[4:Res:90134.1,175.0] || equal(hAPP(hAPP(c_Set_Ovimage(u,t_a,v),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),v_x),v_x)** -> equal(hAPP(u,v_x),w).
% 299.64/300.42 90856[4:Res:90134.1,470.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),v_x) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,t_a)),w))*.
% 299.64/300.42 90855[4:Res:90134.1,466.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),v_x) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,t_a)),w))*.
% 299.64/300.42 90948[4:SpL:538.0,90278.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool))* -> .
% 299.64/300.42 91042[7:MRR:91041.2,27297.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool))* -> .
% 299.64/300.42 91213[0:SpL:44588.1,15629.0] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))*.
% 299.64/300.42 91212[0:SpL:44588.1,15857.0] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))*.
% 299.64/300.42 91321[0:Rew:91288.1,91102.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.42 91876[4:Rew:586.0,91852.1] || equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_COMBB(u,w,x,y),v),tc_Com_Opname))),v_x)** -> hBOOL(hAPP(u,hAPP(v,v_x))).
% 299.64/300.42 91877[4:Rew:585.0,91851.1] || equal(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_COMBC(u,v,w,x),y),tc_Com_Opname)),y),v_x)** -> hBOOL(hAPP(hAPP(u,v_x),y)).
% 299.64/300.42 91937[0:SpR:79073.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v_Procs,u),v,x)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.64/300.42 91936[0:SpR:79073.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_Procs,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,x)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.64/300.42 91915[0:SpR:79073.0,446.1] || c_lessequals(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_Procs,w),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.42 92090[7:SpR:79101.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(w),v_x),c_Set_Oinsert(v_x,u),v,x)),hAPP(c_in(w),v_x))**.
% 299.64/300.42 92089[7:SpR:79101.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,u),hAPP(c_in(w),v_x),v,x)),hAPP(c_in(w),v_x))**.
% 299.64/300.42 92067[7:SpR:79101.0,446.1] || c_lessequals(u,hAPP(c_in(v),v_x),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,w),u),hAPP(c_in(v),v_x),tc_fun(w,tc_bool))*.
% 299.64/300.42 92531[7:Res:10697.0,92132.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(hAPP(c_in(x),v_x),v_x))),hAPP(hAPP(c_in(x),v_x),v_x)))*.
% 299.64/300.42 92583[0:SpL:5227.1,522.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x) c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),y,z) -> c_Hoare__Mirabelle_Otriple__valid(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),y,z)*.
% 299.64/300.42 92691[7:Res:82151.1,170.1] class_Orderings_Olinorder(u) || equal(c_in(t_a),c_in(u)) c_Finite__Set_Ofinite(c_Set_Oinsert(v_x,v),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_Set_Oinsert(v_x,v),u),v_x,u)*.
% 299.64/300.42 92690[7:Res:82151.1,169.1] class_Orderings_Olinorder(u) || equal(c_in(t_a),c_in(u)) c_Finite__Set_Ofinite(c_Set_Oinsert(v_x,v),u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(c_Set_Oinsert(v_x,v),u),u)*.
% 299.64/300.42 92672[7:SpR:5961.0,82151.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_in(t_a))** -> hBOOL(hAPP(hAPP(u,hAPP(x,v_x)),c_Set_Oinsert(v_x,x2)))*.
% 299.64/300.42 92671[7:SpR:5924.0,82151.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),v),c_Set_Oinsert(v_x,x2)))*.
% 299.64/300.42 92648[7:SpR:329.1,82151.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Set_Oinsert(v_x,w)))*.
% 299.64/300.42 92647[7:SpR:328.1,82151.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(t_a))** -> hBOOL(hAPP(u,c_Set_Oinsert(v_x,w)))*.
% 299.64/300.42 92643[7:SpR:538.0,82151.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_Set_Oinsert(v_x,w)))*.
% 299.64/300.42 93193[0:SpR:5878.1,9566.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(hAPP(v,c_Orderings_Obot__class_Obot(u)),hAPP(hAPP(c_Set_Oinsert(w,x),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,y,z,x1)),c_Orderings_Obot__class_Obot(u)),tc_bool)*.
% 299.64/300.42 93357[4:SpR:338.0,85556.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),w)),tc_bool)*.
% 299.64/300.42 93352[4:SpR:536.1,85556.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)),tc_bool)*.
% 299.64/300.42 93351[4:SpR:535.1,85556.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)),tc_bool)*.
% 299.64/300.42 93332[4:SpR:5961.0,85556.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(hAPP(u,hAPP(x,v_x)),x2),tc_bool)*.
% 299.64/300.42 93331[4:SpR:5924.0,85556.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(hAPP(hAPP(u,v_x),v),x2),tc_bool)*.
% 299.64/300.42 93308[4:SpR:329.1,85556.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(v_x,w),tc_bool)*.
% 299.64/300.42 93307[4:SpR:328.1,85556.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(u,w),tc_bool)*.
% 299.64/300.42 93303[4:SpR:538.0,85556.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),w),tc_bool)*.
% 299.64/300.42 93520[0:SpR:5961.0,86147.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,hAPP(x,v_x))),x2))*.
% 299.64/300.42 93519[0:SpR:5924.0,86147.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(u,v_x),v)),x2))*.
% 299.64/300.42 93495[0:SpR:328.1,86147.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w))*.
% 299.64/300.42 93491[0:SpR:538.0,86147.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)),w))*.
% 299.64/300.42 93671[0:SpR:5961.0,86148.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,hAPP(x,v_x))),x2,t_a)*.
% 299.64/300.42 93670[0:SpR:5924.0,86148.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(u,v_x),v)),x2,t_a)*.
% 299.64/300.42 93646[0:SpR:328.1,86148.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,t_a)*.
% 299.64/300.42 93642[0:SpR:538.0,86148.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)),w,t_a)*.
% 299.64/300.42 93815[0:SpR:5961.0,86342.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x2),hAPP(u,hAPP(x,v_x))))*.
% 299.64/300.42 93814[0:SpR:5924.0,86342.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x2),hAPP(hAPP(u,v_x),v)))*.
% 299.64/300.42 93790[0:SpR:328.1,86342.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u))*.
% 299.64/300.42 93786[0:SpR:538.0,86342.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)))*.
% 299.64/300.42 93992[0:SpR:2097.1,10791.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),x)) -> c_lessequals(hAPP(c_Set_Oinsert(x,v),w),hAPP(c_Set_Oinsert(u,v),w),tc_fun(v,tc_bool))*.
% 299.64/300.42 94186[0:Res:14364.3,17530.1] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) equal(c_Finite__Set_Olinorder__class_OMin(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(c_Orderings_Otop__class_Otop(tc_bool),v).
% 299.64/300.42 94322[4:Res:14491.3,47318.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool)))* c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.64/300.42 94312[0:Res:14491.3,17530.1] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) equal(c_Orderings_Otop__class_Otop(tc_bool),v) -> equal(c_Finite__Set_Olinorder__class_OMax(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.42 909[0:SpR:331.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))**.
% 299.64/300.42 1107[0:SpR:331.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),t_a)* hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))).
% 299.64/300.42 2101[0:Res:1103.1,279.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a) equal(hAPP(c_Set_Oinsert(w,v),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(v),w))),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(v),w)))**.
% 299.64/300.42 2572[0:SpR:585.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_COMBC(v,w,x,y),z),t_a) hBOOL(hAPP(hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_COMBC(v,w,x,y),z))),z))*.
% 299.64/300.42 2569[0:SpR:585.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_COMBC(u,v,w,x),y),z,hAPP(hAPP(u,z),y),x1,x2),hAPP(c_COMBC(u,v,w,x),y))**.
% 299.64/300.42 2583[0:SpR:586.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_COMBB(v,w,x,y),z),t_a) hBOOL(hAPP(v,hAPP(z,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_COMBB(v,w,x,y),z)))))*.
% 299.64/300.42 2580[0:SpR:586.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_COMBB(u,v,w,x),y),z,hAPP(u,hAPP(y,z)),x1,x2),hAPP(c_COMBB(u,v,w,x),y))**.
% 299.64/300.42 2717[0:SpR:336.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v))**.
% 299.64/300.42 3197[0:SpR:337.0,2771.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v)* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool))*.
% 299.64/300.42 3187[0:SpR:25.1,2771.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool))*.
% 299.64/300.42 3650[0:SpR:540.1,2771.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))*.
% 299.64/300.42 3802[0:SpR:539.1,2771.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))*.
% 299.64/300.42 4199[0:SpR:299.2,2771.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool))*.
% 299.64/300.42 4711[0:Res:49.2,146.1] class_OrderedGroup_Olordered__ab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),v,u)*.
% 299.64/300.42 4710[0:Res:45.2,146.1] class_OrderedGroup_Oordered__ab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),v,u)*.
% 299.64/300.42 4793[0:Res:47.2,144.1] class_OrderedGroup_Olordered__ab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),u)*.
% 299.64/300.42 4792[0:Res:43.2,144.1] class_OrderedGroup_Oordered__ab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),u)*.
% 299.64/300.42 5013[0:Res:49.2,405.1] class_OrderedGroup_Olordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),v).
% 299.64/300.42 5012[0:Res:45.2,405.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),v).
% 299.64/300.42 5010[0:Res:309.1,405.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),w,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),w).
% 299.64/300.42 5008[0:Res:310.1,405.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v).
% 299.64/300.42 4999[0:Res:47.2,405.1] class_OrderedGroup_Olordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),v).
% 299.64/300.42 4998[0:Res:43.2,405.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),v).
% 299.64/300.42 5024[0:SSi:4983.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),w,tc_fun(u,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),w).
% 299.64/300.42 5025[0:SSi:4982.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v,tc_fun(u,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v).
% 299.64/300.42 5511[0:Rew:25.1,5430.3] class_OrderedGroup_Opordered__ab__group__add(tc_fun(t_a,u)) class_Orderings_Oorder(tc_fun(t_a,u)) class_HOL_Ouminus(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),u),hAPP(v,v_x))**.
% 299.64/300.42 5978[0:SpR:586.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_COMBB(u,v,w,x),y),z,x1,x2,x3),x4),hAPP(hAPP(u,hAPP(y,x4)),hAPP(z,x4)))*.
% 299.64/300.42 5977[0:SpR:585.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_COMBC(u,v,w,x),y),z,x1,x2,x3),x4),hAPP(hAPP(hAPP(u,x4),y),hAPP(z,x4)))*.
% 299.64/300.42 5972[0:SpR:1196.1,584.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w,x,y),c_Orderings_Otop__class_Otop(u)),hAPP(c_Orderings_Otop__class_Otop(u),hAPP(v,c_Orderings_Otop__class_Otop(u))))**.
% 299.64/300.42 5970[0:SpR:2935.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_in(t_a),v_x),u,v,w,x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))))**.
% 299.64/300.42 5966[0:SpR:1195.1,584.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w,x,y),c_Orderings_Obot__class_Obot(u)),hAPP(c_Orderings_Otop__class_Otop(u),hAPP(v,c_Orderings_Obot__class_Obot(u))))**.
% 299.64/300.42 5943[0:SpR:445.1,584.0] || -> equal(u,v) equal(hAPP(c_COMBS(c_Fun_Ofun__upd(w,v,x,y,z),x1,x2,x3,x4),u),hAPP(hAPP(w,u),hAPP(x1,u)))*.
% 299.64/300.42 5941[0:SpR:586.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_COMBB(v,w,x,y),z),x1,x2,x3),x4),hAPP(hAPP(u,x4),hAPP(v,hAPP(z,x4))))*.
% 299.64/300.42 5940[0:SpR:585.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_COMBC(v,w,x,y),z),x1,x2,x3),x4),hAPP(hAPP(u,x4),hAPP(hAPP(v,x4),z)))*.
% 299.64/300.42 5935[0:SpR:1196.1,584.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,x,y),c_Orderings_Otop__class_Otop(u)),hAPP(hAPP(v,c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u)))**.
% 299.64/300.42 5933[0:SpR:2935.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_in(t_a),v_x),v,w,x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),hAPP(hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))**.
% 299.64/300.42 5929[0:SpR:1195.1,584.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,x,y),c_Orderings_Obot__class_Obot(u)),hAPP(hAPP(v,c_Orderings_Obot__class_Obot(u)),c_Orderings_Otop__class_Otop(u)))**.
% 299.64/300.42 5906[0:SpR:445.1,584.0] || -> equal(u,v) equal(hAPP(c_COMBS(w,c_Fun_Ofun__upd(x,v,y,z,x1),x2,x3,x4),u),hAPP(hAPP(w,u),hAPP(x,u)))*.
% 299.64/300.42 5871[0:SpR:584.0,415.0] || -> equal(c_Fun_Ofun__upd(c_COMBS(u,v,w,x,y),z,hAPP(hAPP(u,z),hAPP(v,z)),x1,x2),c_COMBS(u,v,w,x,y))**.
% 299.64/300.42 5867[0:SpR:584.0,2771.1] || equal(u,c_COMBS(v,w,x,y,z))* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(v,v_x),hAPP(w,v_x)),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.42 6332[0:SpR:584.0,3279.1] || equal(c_COMBS(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(hAPP(hAPP(u,v_x),hAPP(v,v_x)),v_Procs),v_x))*.
% 299.64/300.42 6325[0:SpR:540.1,3279.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_Procs),v_x))*.
% 299.64/300.42 6324[0:SpR:539.1,3279.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_Procs),v_x))*.
% 299.64/300.42 6323[0:SpR:297.2,3279.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.42 6316[0:SpR:299.2,3279.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(v,v_Procs),v_x))*.
% 299.64/300.42 6309[0:SpR:25.1,3279.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),v_Procs),v_x))*.
% 299.64/300.42 6476[0:SpL:538.0,3698.2] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.42 6475[0:SpL:538.0,3493.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.42 6423[0:SpR:538.0,3339.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),x,y),u)**.
% 299.64/300.42 6422[0:SpR:538.0,3316.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.42 6419[0:SpR:538.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.42 6417[0:SpR:538.0,3284.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)))*.
% 299.64/300.42 6410[0:SpR:538.0,651.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.42 6517[0:SpR:297.2,3285.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)).
% 299.64/300.42 6515[0:SpR:584.0,3285.1] || equal(c_COMBS(u,v,w,x,y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),hAPP(v,v_x)),hAPP(c_Set_Oinsert(z,tc_Com_Opname),v_Procs)))*.
% 299.64/300.42 6506[0:SpR:540.1,3285.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.42 6505[0:SpR:539.1,3285.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.42 6504[0:SpR:297.2,3285.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.42 6497[0:SpR:299.2,3285.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.42 6490[0:SpR:25.1,3285.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.42 6586[0:SpL:584.0,327.0] || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),hAPP(v,z))** -> c_lessequals(z,hAPP(v,z),tc_fun(u,tc_bool))*.
% 299.64/300.42 6677[0:SpL:329.1,3698.2] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* equal(c_Com_Ocom_OBODY,w) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 6651[0:SpR:329.1,584.0] || c_lessequals(u,hAPP(v,u),tc_fun(w,tc_bool))* -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v,x,y,z),u),hAPP(v,u))**.
% 299.64/300.42 6622[0:SpR:329.1,3339.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> equal(c_Fun_Ofun__upd(w,v_x,v_x,x,y),w)**.
% 299.64/300.42 6621[0:SpR:329.1,3316.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.42 6618[0:SpR:329.1,648.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),v_Procs)))*.
% 299.64/300.42 6615[0:SpR:329.1,3284.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),v_x))*.
% 299.64/300.42 6608[0:SpR:329.1,651.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.42 6754[0:SpR:584.0,3291.1] || equal(c_COMBS(u,v,w,x,y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(hAPP(u,v_x),hAPP(v,v_x))),v_Procs))*.
% 299.64/300.42 6744[0:SpR:540.1,3291.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),v_Procs))*.
% 299.64/300.42 6743[0:SpR:539.1,3291.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),v_Procs))*.
% 299.64/300.42 6742[0:SpR:297.2,3291.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),v_x),v_Procs))*.
% 299.64/300.42 6735[0:SpR:299.2,3291.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),v),v_Procs))*.
% 299.64/300.42 6728[0:SpR:25.1,3291.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)),v_Procs))*.
% 299.64/300.42 6840[0:SpL:328.1,3698.2] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* equal(c_Com_Ocom_OBODY,w) equal(u,c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 6839[0:SpL:328.1,3493.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(tc_Com_Opname))** equal(u,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.42 6784[0:SpR:328.1,3339.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> equal(c_Fun_Ofun__upd(w,v_x,u,x,y),w)**.
% 299.64/300.42 6783[0:SpR:328.1,3316.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> hBOOL(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.42 6780[0:SpR:328.1,648.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),v_Procs)))*.
% 299.64/300.42 6776[0:SpR:328.1,3284.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),u))*.
% 299.64/300.42 6769[0:SpR:328.1,651.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.42 6885[0:SpL:584.0,3484.1] || equal(c_COMBS(u,v,w,x,y),c_Com_Ocom_OBODY)** equal(hAPP(hAPP(u,v_x),hAPP(v,v_x)),hAPP(c_Com_Ocom_OBODY,z))* -> equal(v_x,z).
% 299.64/300.42 6878[0:SpL:337.0,3484.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Com_Ocom_OBODY,v))* -> equal(v_x,v).
% 299.64/300.42 6874[0:SpL:540.1,3484.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(c_Com_Ocom_OBODY,w))* -> equal(v_x,w).
% 299.64/300.42 6873[0:SpL:539.1,3484.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(c_Com_Ocom_OBODY,w))* -> equal(v_x,w).
% 299.64/300.42 6872[0:SpL:297.2,3484.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,w),v_x)** -> equal(v_x,w).
% 299.64/300.42 6865[0:SpL:299.2,3484.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Com_Ocom_OBODY)** equal(v,hAPP(c_Com_Ocom_OBODY,w))* -> equal(v_x,w).
% 299.64/300.42 6858[0:SpL:25.1,3484.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Com_Ocom_OBODY) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),hAPP(c_Com_Ocom_OBODY,w))* -> equal(v_x,w).
% 299.64/300.42 6925[0:SpL:329.1,3499.1] || c_lessequals(v_x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_fun(v,tc_bool))* equal(c_in(u),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) hBOOL(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) -> .
% 299.64/300.42 6921[0:SpL:584.0,3499.1] || equal(c_in(u),c_COMBS(v,w,x,y,z))* hBOOL(hAPP(hAPP(hAPP(v,v_x),hAPP(w,v_x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.42 6910[0:SpL:540.1,3499.1] class_Lattices_Olattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.42 6909[0:SpL:539.1,3499.1] class_Lattices_Oupper__semilattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.42 6908[0:SpL:297.2,3499.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* hBOOL(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))* -> .
% 299.64/300.42 6901[0:SpL:299.2,3499.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* hBOOL(hAPP(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))* -> .
% 299.64/300.42 6894[0:SpL:25.1,3499.1] class_HOL_Ouminus(u) || equal(c_in(v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u))) hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.42 7142[0:SpR:584.0,3305.1] || equal(u,c_COMBS(v,w,x,y,z))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x1),v_Procs),hAPP(hAPP(v,v_x),hAPP(w,v_x))))*.
% 299.64/300.42 7135[0:SpR:337.0,3305.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v_Procs),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.42 7131[0:SpR:540.1,3305.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,x),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)))*.
% 299.64/300.42 7130[0:SpR:539.1,3305.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,x),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)))*.
% 299.64/300.42 7129[0:SpR:297.2,3305.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,tc_Com_Opname,x),v_Procs),v_x))*.
% 299.64/300.42 7122[0:SpR:299.2,3305.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,tc_Com_Opname,x),v_Procs),v))*.
% 299.64/300.42 7115[0:SpR:25.1,3305.1] class_HOL_Ouminus(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,x),v_Procs),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u)))*.
% 299.64/300.42 7187[0:SpR:297.2,3317.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,hAPP(c_Set_Oinsert(v_x,v),w),u)* equal(c_in(v),c_Lattices_Oupper__semilattice__class_Osup(u)) -> hBOOL(hAPP(c_Set_Oinsert(v_x,v),w)).
% 299.64/300.42 7185[0:SpR:584.0,3317.1] || equal(c_in(u),c_COMBS(v,w,x,y,z))* -> hBOOL(hAPP(hAPP(hAPP(v,v_x),hAPP(w,v_x)),hAPP(c_Set_Oinsert(v_x,u),x1)))*.
% 299.64/300.42 7174[0:SpR:540.1,3317.1] class_Lattices_Olattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),hAPP(c_Set_Oinsert(v_x,v),x)))*.
% 299.64/300.42 7173[0:SpR:539.1,3317.1] class_Lattices_Oupper__semilattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),hAPP(c_Set_Oinsert(v_x,v),x)))*.
% 299.64/300.42 7172[0:SpR:297.2,3317.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,w),x)))*.
% 299.64/300.42 7165[0:SpR:299.2,3317.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> hBOOL(hAPP(v,hAPP(c_Set_Oinsert(v_x,w),x)))*.
% 299.64/300.42 7158[0:SpR:25.1,3317.1] class_HOL_Ouminus(u) || equal(c_in(v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u))) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u),hAPP(c_Set_Oinsert(v_x,v),x)))*.
% 299.64/300.42 7248[0:SpR:9.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,x))),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,y,z,x1),x2,u),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)))))*.
% 299.64/300.42 7236[0:SpR:584.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_COMBS(v,w,x,y,z),x1)),hAPP(c_Set_Oimage(hAPP(v,x1),x2,u),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)))))*.
% 299.64/300.42 7222[0:SpR:2098.1,474.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),x,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.42 7212[0:SpR:3586.1,474.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),x,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.42 7292[0:SpR:329.1,7253.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),v))*.
% 299.64/300.42 7290[0:SpR:538.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v)))*.
% 299.64/300.42 7347[0:SpL:584.0,3507.1] || equal(c_Set_Oinsert(u,v),c_COMBS(w,x,y,z,x1))* equal(hAPP(hAPP(w,v_x),hAPP(x,v_x)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.42 7336[0:SpL:540.1,3507.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.42 7335[0:SpL:539.1,3507.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.42 7327[0:SpL:299.2,3507.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* equal(v,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> .
% 299.64/300.42 7320[0:SpL:25.1,3507.1] class_HOL_Ouminus(u) || equal(c_Set_Oinsert(v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,u)))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(x,v_x),u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.42 7518[0:SpR:584.0,3346.1] || equal(c_Set_Oinsert(u,v),c_COMBS(w,x,y,z,x1))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(hAPP(w,v_x),hAPP(x,v_x))))*.
% 299.64/300.42 7511[0:SpR:337.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(v),u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.42 7507[0:SpR:540.1,3346.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x)) -> hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),x)))*.
% 299.64/300.42 7506[0:SpR:539.1,3346.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x)) -> hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),x)))*.
% 299.64/300.42 7505[0:SpR:297.2,3346.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> hBOOL(hAPP(hAPP(c_in(x),w),v_x))*.
% 299.64/300.42 7498[0:SpR:299.2,3346.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> hBOOL(hAPP(hAPP(c_in(x),w),v))*.
% 299.64/300.42 7491[0:SpR:25.1,3346.1] class_HOL_Ouminus(u) || equal(c_Set_Oinsert(v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,u))) -> hBOOL(hAPP(hAPP(c_in(w),v),c_HOL_Ouminus__class_Ouminus(hAPP(x,v_x),u)))*.
% 299.64/300.42 7668[0:Res:294.2,146.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w),u),v,u)*.
% 299.64/300.42 7679[0:SSi:7664.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x),tc_fun(v,tc_bool))*.
% 299.64/300.42 7732[0:Res:293.2,146.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),u),v,u)*.
% 299.64/300.42 7742[0:SSi:7728.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y),tc_fun(v,tc_bool))*.
% 299.64/300.42 7836[0:SSi:7787.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool))* -> c_lessequals(w,hAPP(c_Set_Oinsert(y,u),x),tc_fun(u,tc_bool))*.
% 299.64/300.42 8080[0:SSi:8032.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool))* -> c_lessequals(v,hAPP(c_Set_Oinsert(y,u),x),tc_fun(u,tc_bool))*.
% 299.64/300.42 8162[0:Res:111.2,427.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(v,w,u)* c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),x,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(w,u),x,u)*.
% 299.64/300.42 8161[0:Res:41.2,427.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u).
% 299.64/300.42 8160[0:Res:52.2,427.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(v,w,u) c_lessequals(c_HOL_Ozero__class_Ozero(u),x,u) -> c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),x,u)*.
% 299.64/300.42 8156[0:Res:53.2,427.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)*.
% 299.64/300.42 8181[0:SSi:8110.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(hAPP(c_Set_Oinsert(x,w),v),y,tc_fun(w,tc_bool))* -> c_lessequals(u,y,tc_fun(w,tc_bool))*.
% 299.64/300.42 8289[0:Res:111.2,426.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,w,u)* c_lessequals(x,c_HOL_Ouminus__class_Ouminus(w,u),u)* -> c_lessequals(x,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.42 8288[0:Res:41.2,426.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.42 8287[0:Res:52.2,426.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,w,u) c_lessequals(x,c_HOL_Ominus__class_Ominus(v,w,u),u)* -> c_lessequals(x,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.42 8283[0:Res:53.2,426.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.42 8314[0:SSi:8235.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,u,tc_fun(w,tc_bool))* -> c_lessequals(x,hAPP(c_Set_Oinsert(y,w),v),tc_fun(w,tc_bool))*.
% 299.64/300.42 8598[0:SpR:8498.1,474.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> hBOOL(hAPP(hAPP(c_in(w),u),hAPP(c_Set_Oimage(c_Set_Oinsert(x,v),y,w),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.64/300.42 8987[0:SpL:8415.2,33.0] || equal(v_Procs,v_x) equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(v_x,x)) -> hBOOL(hAPP(v_x,hAPP(u,x)))*.
% 299.64/300.42 8964[0:SpL:8415.2,298.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) equal(hAPP(v_x,v),v) -> c_lessequals(v_x,v,u)*.
% 299.64/300.42 8929[0:SpL:8415.2,2629.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** hBOOL(hAPP(v_x,u)) -> .
% 299.64/300.42 8923[0:SpL:8415.2,502.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Com_Obody) c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),v_x),u,v)* -> c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,v_x),u,v).
% 299.64/300.42 8920[0:SpL:8415.2,348.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Com_Ocom_OBODY) c_Natural_Oevaln(v_x,u,v,w) -> equal(c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_x,v,u,w)),v)**.
% 299.64/300.42 8913[0:SpR:8415.2,584.0] || equal(v_Procs,v_x) equal(c_COMBS(u,v,w,x,y),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(hAPP(u,v_x),hAPP(v,v_x)),v_x)**.
% 299.64/300.42 8898[0:SpR:8415.2,517.1] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(v,w))* -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.42 8894[0:SpR:8415.2,337.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x).
% 299.64/300.42 8878[0:SpR:8415.2,83.0] || equal(v_Procs,v_x) equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),v_x),v_x,tc_fun(w,tc_bool))*.
% 299.64/300.42 8876[0:SpR:8415.2,518.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(v,w)) -> hBOOL(hAPP(hAPP(v_x,v),w))*.
% 299.64/300.42 8869[0:SpR:8415.2,299.2] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v,v_x,u)* -> equal(hAPP(v_x,v),v_x).
% 299.64/300.42 8868[0:SpR:8415.2,540.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(v_x,v))**.
% 299.64/300.42 8867[0:SpR:8415.2,539.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(v_x,v))**.
% 299.64/300.42 8861[0:SpR:8415.2,540.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_x)**.
% 299.64/300.42 8860[0:SpR:8415.2,539.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_x)**.
% 299.64/300.42 8838[0:SpR:8415.2,299.2] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** c_lessequals(v_x,v,u) -> equal(v_x,v).
% 299.64/300.42 8828[0:SpR:8415.2,297.2] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v_x,v,u)* -> equal(hAPP(v_x,v),v).
% 299.64/300.42 8819[0:SpR:8415.2,336.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.42 8777[0:SpR:8415.2,25.1] class_HOL_Ouminus(u) || equal(v_Procs,v_x) equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),v_x)**.
% 299.64/300.42 8769[0:SpR:8415.2,1588.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_x,u,v),tc_Com_Opname,tc_fun(w,tc_bool)),v_Procs))*.
% 299.64/300.42 8756[0:SpR:8415.2,34.1] || equal(v_Procs,v_x) equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(v_x,hAPP(u,x)))* -> hBOOL(hAPP(v_x,x)).
% 299.64/300.42 8753[0:SpR:8415.2,517.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(hAPP(v_x,w),v))*.
% 299.64/300.42 8739[0:SpR:8415.2,503.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Com_Obody) c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,v_x),u,v) -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),v_x),u,v)*.
% 299.64/300.42 9027[0:Rew:8965.4,8966.4] class_Lattices_Obounded__lattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) equal(hAPP(v_x,v),c_Orderings_Obot__class_Obot(u))* -> equal(v,v_x).
% 299.64/300.42 9176[0:SpR:584.0,8376.2] || equal(c_COMBS(u,v,w,x,y),c_in(tc_Com_Opname))** equal(z,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(u,v_x),hAPP(v,v_x)),z))*.
% 299.64/300.42 9165[0:SpR:540.1,8376.2] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname)) equal(w,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),w))*.
% 299.64/300.42 9164[0:SpR:539.1,8376.2] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname)) equal(w,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),w))*.
% 299.64/300.42 9163[0:SpR:297.2,8376.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname))** equal(w,v_Procs) -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.42 9156[0:SpR:299.2,8376.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname))** equal(w,v_Procs) -> hBOOL(hAPP(v,w))*.
% 299.64/300.42 9148[0:SpR:25.1,8376.2] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_in(tc_Com_Opname)) equal(w,v_Procs) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),w))*.
% 299.64/300.42 9545[0:Res:683.1,251.1] class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(hAPP(w,v_x),x),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,w,tc_Com_Opname,tc_fun(u,v)),x),v)*.
% 299.64/300.42 9530[0:Res:942.2,251.1] class_Lattices_Obounded__lattice(tc_fun(u,v)) class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,v)),x),v)*.
% 299.64/300.42 9529[0:Res:943.2,251.1] class_Lattices_Obounded__lattice(tc_fun(u,v)) class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,v)),x),v)*.
% 299.64/300.42 9528[0:Res:1176.2,251.1] class_Lattices_Oboolean__algebra(tc_fun(u,v)) class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,v)),x),v)*.
% 299.64/300.42 9527[0:Res:1177.2,251.1] class_Lattices_Oboolean__algebra(tc_fun(u,v)) class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,v)),x),v)*.
% 299.64/300.42 9516[0:Res:858.2,251.1] class_Lattices_Obounded__lattice(tc_fun(u,v)) class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,v)),w),hAPP(x,w),v)*.
% 299.64/300.42 9515[0:Res:867.2,251.1] class_Lattices_Obounded__lattice(tc_fun(u,v)) class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,v)),w),hAPP(x,w),v)*.
% 299.64/300.42 10269[0:SpR:395.0,3339.1] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),y) -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(y,v_x),w,x),c_Fun_Ofun__upd(u,v_x,v,w,x))*.
% 299.64/300.42 10493[0:Res:648.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oimage(u,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oimage(u,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),v),hAPP(u,v_x),t_a)*.
% 299.64/300.42 10515[4:MRR:10488.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_Set_Oinsert(v_x,tc_Com_Opname)) -> c_Hoare__Mirabelle_Ohoare__valids(v_x,v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v_x,v),u,t_a)*.
% 299.64/300.42 10602[0:SpL:297.2,57.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> equal(v,c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.42 10581[0:SpL:140.1,57.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),v),c_HOL_Ozero__class_Ozero(u))** -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.42 10749[0:SSi:10742.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),w),x),hAPP(w,x),tc_bool)* -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),w),x),hAPP(w,x)).
% 299.64/300.42 10774[0:Rew:8415.2,10764.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(w,u),v)))*.
% 299.64/300.42 10788[0:SSi:10781.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),v_Procs,tc_bool)* -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),v_Procs).
% 299.64/300.42 10908[0:SpL:353.0,442.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(w)),y)),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),y),w).
% 299.64/300.42 10904[0:SpL:353.0,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),y))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),x),y)) equal(w,y).
% 299.64/300.42 10883[0:SpR:2098.1,353.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) equal(hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),v)),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),v))**.
% 299.64/300.42 10843[0:SpR:353.0,9566.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),hAPP(hAPP(c_Set_Oinsert(y,z),c_Set_Oinsert(w,v)),hAPP(c_Set_Oinsert(u,v),x)),tc_bool)*.
% 299.64/300.42 10841[0:SpR:353.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(u,v),x)),y,z),c_Set_Oinsert(u,v))**.
% 299.64/300.42 10825[0:SpR:353.0,2097.1] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),x)) -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(x,v),w)),hAPP(c_Set_Oinsert(u,v),w))**.
% 299.64/300.42 11570[0:SpR:3229.1,229.0] || equal(u,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),v_x),c_Com_Ocom_OSKIP)) -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(u,v_x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.64/300.42 11567[0:SpR:3229.1,229.0] || equal(u,c_Hoare__Mirabelle_Otriple_Otriple(v)) -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(u,v_x),c_Com_Ocom_OSKIP),v_x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.64/300.42 11724[0:SpR:130.1,3229.1] class_HOL_Ominus(u) || equal(v,c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u))) -> equal(hAPP(v,v_x),c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u))*.
% 299.64/300.42 11713[0:SpR:130.1,3283.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),v_Procs))*.
% 299.64/300.42 11709[0:SpR:130.1,1158.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_Com_Opname,x),v_Procs),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)))*.
% 299.64/300.42 11879[0:SpL:3229.1,150.1] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) hBOOL(hAPP(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))))* -> .
% 299.64/300.42 11876[0:SpL:2267.1,150.1] || equal(u,v)* hBOOL(hAPP(hAPP(c_in(w),x),u))* hBOOL(hAPP(hAPP(c_in(w),x),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))))* -> .
% 299.64/300.42 12068[0:Res:448.1,325.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),tc_fun(u,tc_bool))* c_lessequals(w,v,tc_fun(u,tc_bool)).
% 299.64/300.42 12019[0:SpL:3229.1,325.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* c_lessequals(hAPP(u,v_x),x,tc_fun(v,tc_bool))* -> c_lessequals(w,x,tc_fun(v,tc_bool))*.
% 299.64/300.42 12016[0:SpL:3229.1,325.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) c_lessequals(hAPP(hAPP(u,v_x),w),x,tc_fun(v,tc_bool))* -> c_lessequals(v_x,x,tc_fun(v,tc_bool)).
% 299.64/300.42 12419[0:Res:448.1,324.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),tc_fun(u,tc_bool))* c_lessequals(x,v,tc_fun(u,tc_bool)).
% 299.64/300.42 12370[0:SpL:3229.1,324.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* c_lessequals(hAPP(u,v_x),x,tc_fun(v,tc_bool))* -> c_lessequals(v_x,x,tc_fun(v,tc_bool)).
% 299.64/300.42 12367[0:SpL:3229.1,324.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) c_lessequals(hAPP(hAPP(u,v_x),w),x,tc_fun(v,tc_bool))* -> c_lessequals(w,x,tc_fun(v,tc_bool)).
% 299.64/300.42 12551[0:SpL:3229.1,148.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(v),v_x),w)).
% 299.64/300.42 12669[0:Res:3316.1,519.0] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* -> hBOOL(hAPP(w,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))* hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.42 12664[0:SpL:3229.1,519.0] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(x,v_x)).
% 299.64/300.42 12635[0:SpL:3229.1,519.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(hAPP(u,v_x),x))* -> hBOOL(hAPP(w,x))* hBOOL(hAPP(v_x,x)).
% 299.64/300.42 12632[0:SpL:3229.1,519.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)))* hBOOL(hAPP(hAPP(hAPP(u,v_x),w),x))* -> hBOOL(hAPP(v_x,x)) hBOOL(hAPP(w,x)).
% 299.64/300.42 12800[0:Res:448.1,430.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_lessequals(v,w,tc_fun(u,tc_bool))* -> c_lessequals(v,x,tc_fun(u,tc_bool))* c_lessequals(x,w,tc_fun(u,tc_bool))*.
% 299.64/300.42 12965[0:SpR:3229.1,96.1] || equal(u,c_Set_Oimage(v,w,x)) c_Fun_Oinj__on(v,v_x,w,x) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(v_x,v,w,x),hAPP(u,v_x),x,w)*.
% 299.64/300.42 13079[0:SpR:329.1,10090.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.42 13078[0:SpR:328.1,10090.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(u,c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.42 13077[0:SpR:538.0,10090.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.42 13166[0:Res:108.1,436.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),x))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),x))*.
% 299.64/300.42 13241[0:SpR:9493.1,474.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.42 13563[0:Res:11030.1,519.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(t_a))** -> hBOOL(hAPP(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))* hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.42 13538[0:SpR:329.1,11030.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(t_a))** -> hBOOL(hAPP(v_x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.42 13537[0:SpR:328.1,11030.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(t_a))** -> hBOOL(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.42 13536[0:SpR:538.0,11030.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.42 13672[0:SpR:11499.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_bool),x,y),hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)))**.
% 299.64/300.42 13870[0:SpL:538.0,11759.0] || hBOOL(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),hAPP(w,v_x),tc_bool))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)).
% 299.64/300.42 14182[0:SpR:9925.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.64/300.42 14165[0:SpR:9924.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.64/300.42 14146[0:SpR:414.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_Fun_Ofun__upd(w,v,x,y,z),u,x1),hAPP(c_Set_Oinsert(x,x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.64/300.42 14138[0:SpR:524.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),u,x),hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.64/300.42 14428[0:SpR:12944.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)),z,u),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.64/300.42 14763[0:SpL:128.0,33.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)),y))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),hAPP(u,y))).
% 299.64/300.42 14694[0:SpR:128.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),z),tc_fun(v,tc_bool))))*.
% 299.64/300.42 14692[0:SpR:128.0,83.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.64/300.42 14686[0:SpR:128.0,34.1] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),hAPP(w,x))) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(w,y,v),u),tc_fun(y,tc_bool)),x))*.
% 299.64/300.42 15125[0:SpL:181.1,3483.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Com_Ocom_OSKIP) -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)).
% 299.64/300.42 15153[0:Rew:10463.0,15123.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_COMBS(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z,x1,x2),w),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 15232[0:Res:446.1,436.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_Set_Oinsert(x,w),u),y))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,w),v),y))*.
% 299.64/300.42 15207[0:SpR:3586.1,446.1] || equal(hAPP(c_in(u),v),v_Procs) c_lessequals(w,v_x,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v,u),w),v_x,tc_fun(u,tc_bool))*.
% 299.64/300.42 15196[0:SpR:9493.1,446.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(v,u,tc_fun(t_a,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),v),u,tc_fun(t_a,tc_bool))*.
% 299.64/300.42 15634[0:Res:149.1,278.1] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(hAPP(c_in(w),v),x))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),y,u,w)))*.
% 299.64/300.42 15803[0:SpR:328.1,15482.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)).
% 299.64/300.42 15802[0:SpR:538.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_fun(t_a,tc_bool)),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool))*.
% 299.64/300.42 15862[0:Res:149.1,277.1] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(hAPP(c_in(w),v),x))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),u,w)))*.
% 299.64/300.42 15944[2:SpR:329.1,15483.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool)).
% 299.64/300.42 15943[2:SpR:328.1,15483.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(u,tc_bool)).
% 299.64/300.42 15942[2:SpR:538.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool))*.
% 299.64/300.42 16010[0:SpL:584.0,515.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(c_COMBS(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),z,x1,x2,x3),x4))* -> equal(v,y).
% 299.64/300.42 16005[0:SpL:584.0,515.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),y,z,x1,x2),x3),x4))* -> equal(v,x3).
% 299.64/300.42 16118[0:SpL:584.0,514.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(c_COMBS(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),z,x1,x2,x3),x4))* -> equal(w,x4).
% 299.64/300.42 16114[0:SpL:10090.1,514.0] || equal(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(c_Orderings_Otop__class_Otop(tc_bool),y))* -> equal(w,c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.42 16175[0:SpR:297.2,15262.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))).
% 299.64/300.42 16172[0:SpR:584.0,15262.1] || equal(c_COMBS(u,v,w,x,y),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),hAPP(v,v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.42 16155[0:SpR:540.1,15262.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.42 16154[0:SpR:539.1,15262.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.42 16153[0:SpR:297.2,15262.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.42 16144[0:SpR:299.2,15262.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a))** -> hBOOL(hAPP(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.42 16133[0:SpR:25.1,15262.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.42 16315[0:SpL:10090.1,513.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(y,c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.42 16309[0:SpL:584.0,513.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),y,z,x1,x2),x3),x4))* -> equal(x,x4).
% 299.64/300.42 16325[0:SpL:130.1,16286.0] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_Orderings_Obot__class_Obot(tc_bool))** equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_Procs) -> .
% 299.64/300.42 16457[0:SpR:9935.1,584.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x,y,z),u),hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(w,u)))**.
% 299.64/300.42 16456[0:SpR:9935.1,584.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,y,z),u),hAPP(hAPP(v,u),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.64/300.42 16573[0:SpR:9925.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v,u),u)*.
% 299.64/300.42 16553[0:SpR:9924.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v,u),u)*.
% 299.64/300.42 16533[0:SpR:414.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Fun_Ofun__upd(z,w,y,x1,x2),v,u),u)*.
% 299.64/300.42 16524[0:SpR:524.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),w),v,u),u)*.
% 299.64/300.42 16695[0:SpR:9936.1,584.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x,y),z),hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(v,z)))**.
% 299.64/300.42 16694[0:SpR:9936.1,584.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,x,y),z),hAPP(hAPP(v,z),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.64/300.42 16781[0:Res:83.0,390.0] || -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(u,v,w,x),hAPP(c_Set_Oimage(y,z,x),hAPP(c_Set_Ovimage(y,z,x),hAPP(c_Set_Oimage(v,w,x),u))),x,w)*.
% 299.64/300.42 17140[0:SpR:17045.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.64/300.42 17249[0:SpR:10090.1,510.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_in(u),v),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.42 17313[0:SpL:584.0,13272.0] || equal(hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_COMBS(u,v,w,x,y),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.64/300.42 17299[0:SpL:337.0,13272.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.42 17293[0:SpL:540.1,13272.0] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.42 17292[0:SpL:539.1,13272.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.42 17282[0:SpL:299.2,13272.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(v,c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.42 17271[0:SpL:25.1,13272.0] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.42 17363[0:Res:172.2,591.0] class_Orderings_Olinorder(tc_Hoare__Mirabelle_Otriple(t_a)) || c_Finite__Set_Ofinite(v_G,tc_Hoare__Mirabelle_Otriple(t_a)) -> equal(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),c_Finite__Set_Olinorder__class_OMax(v_G,tc_Hoare__Mirabelle_Otriple(t_a)),t_a)*.
% 299.64/300.42 17372[0:SpR:14526.0,415.0] || -> equal(c_Fun_Ofun__upd(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),u),c_Orderings_Obot__class_Obot(tc_bool),x,y),c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)))**.
% 299.64/300.42 17464[0:SpL:584.0,16327.1] || equal(u,c_COMBS(v,w,x,y,z))* equal(hAPP(hAPP(v,v_x),hAPP(w,v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_Procs) -> .
% 299.64/300.42 17450[0:SpL:337.0,16327.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* equal(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_Procs) -> .
% 299.64/300.42 17444[0:SpL:540.1,16327.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),c_Orderings_Obot__class_Obot(tc_bool))** equal(v,v_Procs) -> .
% 299.64/300.42 17443[0:SpL:539.1,16327.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),c_Orderings_Obot__class_Obot(tc_bool))** equal(v,v_Procs) -> .
% 299.64/300.42 17433[0:SpL:299.2,16327.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* equal(v,c_Orderings_Obot__class_Obot(tc_bool)) equal(w,v_Procs) -> .
% 299.64/300.42 17422[0:SpL:25.1,16327.1] class_HOL_Ouminus(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u)))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u),c_Orderings_Obot__class_Obot(tc_bool))** equal(v,v_Procs) -> .
% 299.64/300.42 17481[0:Res:171.2,591.0] class_Orderings_Olinorder(tc_Hoare__Mirabelle_Otriple(t_a)) || c_Finite__Set_Ofinite(v_G,tc_Hoare__Mirabelle_Otriple(t_a)) -> equal(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),c_Finite__Set_Olinorder__class_OMin(v_G,tc_Hoare__Mirabelle_Otriple(t_a)),t_a)*.
% 299.64/300.42 17754[0:Res:8376.2,255.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(v,v_Procs) c_lessequals(v,w,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v_x),w))*.
% 299.64/300.42 17742[0:Res:15262.1,255.0] || equal(c_in(t_a),c_in(u)) c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v_x),v)).
% 299.64/300.42 17741[0:Res:3285.1,255.0] || equal(c_in(tc_Com_Opname),c_in(u)) c_lessequals(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),w,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v_x),w)).
% 299.64/300.42 17740[0:Res:3317.1,255.0] || equal(c_in(u),c_in(v)) c_lessequals(hAPP(c_Set_Oinsert(v_x,u),w),x,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),v_x),x)).
% 299.64/300.42 17724[0:Res:474.0,255.0] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),x,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,y)),x))*.
% 299.64/300.42 18022[0:Res:8376.2,263.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Oinsert(v,u),w),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(u),v_x),w))* equal(v_x,v).
% 299.64/300.42 18163[0:SpR:10463.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.64/300.42 18162[0:SpR:9911.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.64/300.42 18232[0:SSi:18226.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(hAPP(x,v),y),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(z,tc_bool)),y),tc_bool)*.
% 299.64/300.42 18278[0:SpR:15172.0,584.0] || -> equal(hAPP(c_COMBS(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y,z,x1,x2),x3),hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(y,x3)))**.
% 299.64/300.42 18277[0:SpR:15172.0,584.0] || -> equal(hAPP(c_COMBS(u,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)),z,x1,x2),x3),hAPP(hAPP(u,x3),c_Orderings_Obot__class_Obot(tc_bool)))**.
% 299.64/300.42 18363[0:SpR:10463.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),u,x),w)))*.
% 299.64/300.42 18362[0:SpR:9911.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),u,x),w)))*.
% 299.64/300.42 18460[0:Res:8376.2,156.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Ovimage(v,u,w),x),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(w),hAPP(v,v_x)),x))*.
% 299.64/300.42 18531[0:Res:9246.0,454.0] || -> hBOOL(hAPP(u,v)) c_Hoare__Mirabelle_Ohoare__valids(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),v,t_a)*.
% 299.64/300.42 18722[0:SpR:584.0,9568.0] || -> c_lessequals(hAPP(hAPP(u,v),hAPP(w,v)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_COMBS(u,w,y,z,x1)),x2),v),tc_bool)*.
% 299.64/300.42 18713[0:SpR:336.0,9568.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w)),x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_bool)*.
% 299.64/300.42 18699[0:SpR:584.0,9568.0] || -> c_lessequals(hAPP(c_COMBS(u,v,w,x,y),z),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(u,z)),x2),hAPP(v,z)),tc_bool)*.
% 299.64/300.42 18690[0:SpR:337.0,9568.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))),w),x),tc_bool)*.
% 299.64/300.42 18676[0:SpR:540.1,9568.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),y),v),tc_bool)*.
% 299.64/300.42 18675[0:SpR:539.1,9568.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),y),v),tc_bool)*.
% 299.64/300.42 18674[0:SpR:297.2,9568.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(w,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),y),w),tc_bool)*.
% 299.64/300.42 18665[0:SpR:299.2,9568.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(w,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),y),v),tc_bool)*.
% 299.64/300.42 18654[0:SpR:25.1,9568.0] class_HOL_Ouminus(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u))),x),v_x),tc_bool)*.
% 299.64/300.42 19033[0:SpR:584.0,9569.0] || -> c_lessequals(hAPP(hAPP(u,v),hAPP(w,v)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_COMBS(u,w,z,x1,x2)),v),tc_bool)*.
% 299.64/300.42 19024[0:SpR:336.0,9569.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_bool)*.
% 299.64/300.42 19010[0:SpR:584.0,9569.0] || -> c_lessequals(hAPP(c_COMBS(u,v,w,x,y),z),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),x2),hAPP(u,z)),hAPP(v,z)),tc_bool)*.
% 299.64/300.42 19001[0:SpR:337.0,9569.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))),x),tc_bool)*.
% 299.64/300.42 18987[0:SpR:540.1,9569.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),v),tc_bool)*.
% 299.64/300.42 18986[0:SpR:539.1,9569.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),v),tc_bool)*.
% 299.64/300.42 18985[0:SpR:297.2,9569.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(w,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),w),tc_bool)*.
% 299.64/300.42 18976[0:SpR:299.2,9569.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(w,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),v),tc_bool)*.
% 299.64/300.42 18965[0:SpR:25.1,9569.0] class_HOL_Ouminus(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u))),v_x),tc_bool)*.
% 299.64/300.42 19120[0:SpL:196.1,4439.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* equal(x,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),hAPP(u,v_x)))*.
% 299.64/300.42 19111[0:SpR:196.1,7253.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),z))*.
% 299.64/300.42 19341[0:SSi:19329.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(w,v,tc_bool)* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Orderings_Otop__class_Otop(tc_bool),v).
% 299.64/300.42 19387[0:Res:47.2,12719.0] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),c_HOL_Ominus__class_Ominus(u,v,tc_bool),tc_bool) -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),tc_bool),w,tc_bool),u,tc_bool)*.
% 299.64/300.42 19654[0:Res:267.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w))),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w)))* c_Hoare__Mirabelle_Otriple__valid(u,v,t_a).
% 299.64/300.42 19691[0:SpL:9493.1,19641.0] || equal(hAPP(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(v_x,t_a),u),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(v_x,t_a),u)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oinsert(v_x,t_a),u,t_a).
% 299.64/300.42 19689[0:SpL:8498.1,19641.0] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(u,v),w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(u,v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oinsert(u,v),w,t_a)*.
% 299.64/300.42 19892[0:SpL:104.0,347.0] || c_Fun_Oinj__on(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),x,y)* -> c_Fun_Oinj__on(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(x,tc_bool)),x,y).
% 299.64/300.42 19820[0:SpR:104.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))*.
% 299.64/300.42 19803[0:SpR:104.0,335.2] || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v) c_Finite__Set_Ofinite(w,v) -> c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),v)*.
% 299.64/300.42 19761[2:SpR:104.0,4250.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))*.
% 299.64/300.42 19751[0:SpR:104.0,3282.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))*.
% 299.64/300.42 19995[0:SpR:64.0,19744.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)*.
% 299.64/300.42 19980[0:SpR:64.0,15367.0] || -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),v)*.
% 299.64/300.42 19963[0:SpR:64.0,10919.1] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),u),v_x)).
% 299.64/300.42 19961[0:SpR:64.0,9566.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Set_Oinsert(v,w),u),x),tc_bool)*.
% 299.64/300.42 20079[0:SpL:2098.1,215.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,v,t_a) -> c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a) c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,v),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)*.
% 299.64/300.42 20400[0:Rew:20312.1,20343.2] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y)* -> equal(v,u).
% 299.64/300.42 20735[0:Res:313.1,437.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x,w,y),v),y)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x,w,y),u),y)*.
% 299.64/300.42 20724[0:SpR:321.0,313.1] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(w,v,x),u),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.42 20780[0:Res:129.1,437.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(x,y,w),v),y)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(x,y,w),u),y)*.
% 299.64/300.42 20773[0:SpR:105.0,129.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(x,w,u),v),tc_fun(w,tc_bool))*.
% 299.64/300.42 20765[0:SpR:653.0,129.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,v),v,tc_Com_Opname),u),tc_fun(v,tc_bool))*.
% 299.64/300.42 20762[0:SpR:38.0,129.1] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(w,x,v),u),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.42 20790[2:SpL:8415.2,16387.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(c_Com_Ocom_OBODY,v_x) -> c_Com_OWT(c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.42 20811[0:SpR:8415.2,19748.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.64/300.42 20920[0:SpR:321.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),hAPP(c_Set_Oinsert(hAPP(u,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.64/300.42 20903[0:SpR:2097.1,317.0] || hBOOL(hAPP(u,v)) -> equal(hAPP(c_Set_Oinsert(hAPP(w,v),x),hAPP(c_Set_Oimage(w,y,x),u)),hAPP(c_Set_Oimage(w,y,x),u))**.
% 299.64/300.42 20859[0:SpR:317.0,7539.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oinsert(y,w),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(z,v),x))),tc_fun(w,tc_bool))*.
% 299.64/300.42 20830[0:SpR:317.0,16776.0] || -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oinsert(u,v),w),x,v,y),hAPP(c_Set_Oinsert(hAPP(x,u),y),hAPP(c_Set_Oimage(x,v,y),w)),y,v)*.
% 299.64/300.42 21117[0:SpR:584.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,v,w,x,y),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(hAPP(u,x2),hAPP(v,x2))))*.
% 299.64/300.42 21108[0:SpR:336.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w),y)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.42 21094[0:SpR:584.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(u,v),w,x),hAPP(c_Set_Oinsert(hAPP(y,v),w),z)),hAPP(c_COMBS(u,y,x1,x2,x3),v)))*.
% 299.64/300.42 21084[0:SpR:337.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,w),hAPP(c_Set_Oinsert(x,v),y)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.42 21071[0:SpR:540.1,20881.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(y,w),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v)))*.
% 299.64/300.42 21070[0:SpR:539.1,20881.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(y,w),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v)))*.
% 299.64/300.42 21069[0:SpR:297.2,20881.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),hAPP(c_Set_Oinsert(w,x),z)),w))*.
% 299.64/300.42 21060[0:SpR:299.2,20881.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y),hAPP(c_Set_Oinsert(v,x),z)),w))*.
% 299.64/300.42 21049[0:SpR:25.1,20881.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w,x),hAPP(c_Set_Oinsert(v_x,w),y)),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)))*.
% 299.64/300.42 21181[0:SpR:329.1,21130.0] || c_lessequals(u,v_Procs,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w,x),hAPP(c_in(tc_Com_Opname),v_x)),v_Procs))*.
% 299.64/300.42 21180[0:SpR:328.1,21130.0] || c_lessequals(v_Procs,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w,x),hAPP(c_in(tc_Com_Opname),v_x)),u))*.
% 299.64/300.42 21178[0:SpR:538.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_Procs),v)))*.
% 299.64/300.42 21242[0:SpR:329.1,21141.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),v_x))*.
% 299.64/300.42 21241[0:SpR:328.1,21141.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),u))*.
% 299.64/300.42 21239[0:SpR:538.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)))*.
% 299.64/300.42 21264[0:SpL:584.0,469.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(v,w,u),x,y,z),x1))* -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x1,v,x1,w,u)),x1)**.
% 299.64/300.42 21584[0:SpL:21267.0,279.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,w),u),v),v)**.
% 299.64/300.42 21546[0:SpR:9935.1,21267.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.42 21531[0:SpR:297.2,21267.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x,tc_Com_Opname,w)),v_x)**.
% 299.64/300.42 21528[0:SpR:2098.1,21267.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),v_x,tc_Com_Opname,v)),v_x)**.
% 299.64/300.42 21522[0:SpR:299.2,21267.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v,tc_Com_Opname,w)),v)**.
% 299.64/300.42 21336[0:SpR:21267.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,w),u),x))))*.
% 299.64/300.42 21331[0:SpR:21267.0,9071.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,v),u),tc_Com_Opname,tc_fun(u,tc_bool))))*.
% 299.64/300.42 21329[0:SpR:21267.0,9246.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)))) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,w)))*.
% 299.64/300.42 21327[0:SpR:21267.0,1157.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_COMBK(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,v),w,x),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.42 21298[0:SpR:21267.0,212.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),x))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),x)).
% 299.64/300.42 21801[0:SpR:584.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,v,w,x,y),t_a,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(u,v_x),hAPP(v,v_x))))*.
% 299.64/300.42 21786[0:SpR:337.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.42 21779[0:SpR:540.1,21143.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.42 21778[0:SpR:539.1,21143.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.42 21777[0:SpR:297.2,21143.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.42 21768[0:SpR:299.2,21143.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v))*.
% 299.64/300.42 21757[0:SpR:25.1,21143.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)))*.
% 299.64/300.42 21870[0:SpR:584.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,v,w,x,y),tc_Com_Opname,z),hAPP(c_Set_Oinsert(x1,tc_Com_Opname),v_Procs)),hAPP(hAPP(u,v_x),hAPP(v,v_x))))*.
% 299.64/300.42 21848[0:SpR:540.1,21131.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.42 21847[0:SpR:539.1,21131.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)))*.
% 299.64/300.42 21846[0:SpR:297.2,21131.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.42 21837[0:SpR:299.2,21131.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),v))*.
% 299.64/300.42 21826[0:SpR:25.1,21131.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)))*.
% 299.64/300.42 21890[0:SpL:584.0,464.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(v,w,u),x,y,z),x1))* -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(x1,x1,v,w,u)),x1)**.
% 299.64/300.42 22211[0:SpL:21893.0,279.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,w),u),v),v)**.
% 299.64/300.42 22173[0:SpR:9935.1,21893.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.42 22158[0:SpR:297.2,21893.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w)),v_x)**.
% 299.64/300.42 22155[0:SpR:2098.1,21893.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,v)),v_x)**.
% 299.64/300.42 22149[0:SpR:299.2,21893.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w)),v)**.
% 299.64/300.42 21962[0:SpR:21893.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,w),u),x))))*.
% 299.64/300.42 21957[0:SpR:21893.0,9071.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,v),u),tc_Com_Opname,tc_fun(u,tc_bool))))*.
% 299.64/300.42 21955[0:SpR:21893.0,9246.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)))) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,w)))*.
% 299.64/300.42 21953[0:SpR:21893.0,1157.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_COMBK(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,v),w,x),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.42 21924[0:SpR:21893.0,212.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),x))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),x)).
% 299.64/300.42 22392[0:SpR:97.1,16776.0] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,w,x),v),c_Fun_Othe__inv__into(v,u,w,x),x,w),v,w,x)*.
% 299.64/300.42 22437[0:MRR:22402.1,96.1] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,w,x),v),c_Fun_Othe__inv__into(v,u,w,x),x,w),v,w,x)*.
% 299.64/300.42 22502[0:SpR:584.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(v,w,x,y,z),tc_Com_Opname,x1),u),hAPP(hAPP(v,v_x),hAPP(w,v_x))))*.
% 299.64/300.42 22487[0:SpR:337.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),tc_Com_Opname,w),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.42 22480[0:SpR:540.1,21126.1] class_Lattices_Olattice(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),tc_Com_Opname,x),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)))*.
% 299.64/300.42 22479[0:SpR:539.1,21126.1] class_Lattices_Oupper__semilattice(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),tc_Com_Opname,x),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)))*.
% 299.64/300.42 22478[0:SpR:297.2,21126.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(w,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,x),w),v_x))*.
% 299.64/300.42 22469[0:SpR:299.2,21126.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(w,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,x),w),v))*.
% 299.64/300.42 22458[0:SpR:25.1,21126.1] class_HOL_Ouminus(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u)),tc_Com_Opname,x),v),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u)))*.
% 299.64/300.42 22641[0:SpL:158.0,357.1] || c_Finite__Set_Ofinite(u,v) c_lessequals(w,hAPP(c_Set_Oimage(x,y,z),hAPP(c_Set_Oimage(x1,v,y),u)),tc_fun(z,tc_bool))* -> c_Finite__Set_Ofinite(w,z).
% 299.64/300.42 22599[0:SpR:158.0,16776.0] || -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,v,w),x),y,w,z),hAPP(c_Set_Oimage(c_Fun_Ocomp(y,u,w,z,v),v,z),x),z,w)*.
% 299.64/300.42 22537[2:SpR:158.0,4250.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))*.
% 299.64/300.42 22527[0:SpR:158.0,3282.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs)** -> hBOOL(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))*.
% 299.64/300.42 22514[0:SpR:158.0,16776.0] || -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(u,c_Fun_Ocomp(v,w,x,y,z),z,y),hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),u)),y,z)*.
% 299.64/300.42 22681[0:Rew:9.0,22587.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,x))),hAPP(c_Set_Oimage(v,y,u),hAPP(c_Set_Oimage(w,z,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))))*.
% 299.64/300.42 22843[0:SpL:3294.1,298.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) -> c_lessequals(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),u)*.
% 299.64/300.42 22842[0:SpR:15172.0,3294.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_in(t_a))** -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.42 22838[0:SpR:586.0,3294.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_in(t_a))** -> equal(hAPP(hAPP(u,hAPP(y,v_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 22837[0:SpR:585.0,3294.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_in(t_a))** -> equal(hAPP(hAPP(hAPP(u,v_x),y),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 22832[0:SpR:9936.1,3294.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a)) -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 22830[0:SpR:9935.1,3294.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(t_a))** -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 22798[0:SpR:8415.2,3294.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_in(t_a),u) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 22792[0:SpR:445.1,3294.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_in(t_a))** -> equal(v_x,v) equal(hAPP(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 22763[0:SpR:3294.1,510.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_in(u),v),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.42 22750[0:SpR:3294.1,20881.0] || equal(c_in(t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v),x)),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.42 22738[0:SpR:3294.1,297.2] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) c_lessequals(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),u)* -> equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.42 22923[2:SpR:131.0,4250.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)))*.
% 299.64/300.42 22913[0:SpR:131.0,3282.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs)** -> hBOOL(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)))*.
% 299.64/300.42 23223[0:SpL:15172.0,3487.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> .
% 299.64/300.42 23218[0:SpL:586.0,3487.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(y,v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.42 23217[0:SpL:585.0,3487.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),y),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.42 23212[0:SpL:9936.1,3487.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.42 23210[0:SpL:9935.1,3487.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.42 23172[0:SpL:445.1,3487.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> equal(v_x,v).
% 299.64/300.42 23300[0:SpL:15172.0,3489.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_in(tc_Com_Opname))** hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)))) -> .
% 299.64/300.42 23295[0:SpL:586.0,3489.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_in(tc_Com_Opname))** hBOOL(hAPP(hAPP(u,hAPP(y,v_x)),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.42 23294[0:SpL:585.0,3489.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_in(tc_Com_Opname))** hBOOL(hAPP(hAPP(hAPP(u,v_x),y),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.42 23289[0:SpL:9936.1,3489.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname)) hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.42 23287[0:SpL:9935.1,3489.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_in(tc_Com_Opname))** hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.42 23255[0:SpL:8415.2,3489.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u)* equal(c_in(tc_Com_Opname),u) hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.42 23249[0:SpL:445.1,3489.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_in(tc_Com_Opname))** hBOOL(hAPP(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> equal(v_x,v).
% 299.64/300.42 23525[0:SpR:523.1,3279.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v_x,v_x)),hAPP(v_Procs,v_x)))*.
% 299.64/300.42 23607[0:SSi:23546.0,555.1,550.1] class_Lattices_Olattice(u) || c_lessequals(v,w,tc_fun(t_a,u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),hAPP(w,v_x))**.
% 299.64/300.42 23610[0:SSi:23541.0,555.1,550.1] class_Lattices_Olattice(u) || c_lessequals(v,w,tc_fun(t_a,u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(v,v_x)),hAPP(w,v_x))**.
% 299.64/300.42 23778[0:SpR:23682.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,x),w)))*.
% 299.64/300.42 23777[0:SpR:23682.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.42 23871[0:SpR:23840.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) -> hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u,w),v)))*.
% 299.64/300.42 23870[0:SpR:23840.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.42 24207[0:SpR:538.0,542.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v))**.
% 299.64/300.42 24251[0:Rew:99.1,24154.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),y)**.
% 299.64/300.42 24455[0:Res:13385.1,208.0] || equal(hAPP(c_Set_Oinsert(u,v),w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(v),u),x))* c_lessequals(x,w,tc_fun(v,tc_bool))*.
% 299.64/300.42 24980[0:SpR:23902.1,511.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v),c_Orderings_Obot__class_Obot(tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)).
% 299.64/300.42 25273[0:SpR:512.0,158.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),z),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,y,v,w,x),x,w),z))**.
% 299.64/300.42 25677[0:SSi:25577.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),y),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,v,w,x),y),y).
% 299.64/300.42 25727[0:Res:3282.1,455.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Procs)** c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.64/300.42 25719[0:Res:8375.1,455.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)))* c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,x,t_a)*.
% 299.64/300.42 25718[0:Res:19440.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Com_Opname),v_x)),t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,v_Procs,t_a).
% 299.64/300.42 25700[0:Res:648.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(v,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,hAPP(v,v_x),t_a)*.
% 299.64/300.42 25989[0:SpL:339.0,324.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y,tc_fun(v,tc_bool))* -> c_lessequals(x,y,tc_fun(v,tc_bool)).
% 299.64/300.42 25919[0:SpR:339.0,517.1] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),x)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)),x))*.
% 299.64/300.42 26002[0:SSi:25905.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v)),tc_fun(w,tc_bool))*.
% 299.64/300.42 26236[0:SpL:338.0,325.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y,tc_fun(v,tc_bool))* -> c_lessequals(w,y,tc_fun(v,tc_bool)).
% 299.64/300.42 26094[0:SpR:338.0,376.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(x,u),w)),tc_fun(u,tc_bool))*.
% 299.64/300.42 26081[0:SpR:338.0,518.1] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),x)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),w)),x))*.
% 299.64/300.42 26269[0:SSi:26069.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y)),tc_fun(w,tc_bool))*.
% 299.64/300.42 26809[0:SpR:56.1,115.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),x),u)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),u)*.
% 299.64/300.42 27009[0:Res:13238.1,175.0] || equal(hAPP(hAPP(c_Set_Ovimage(u,t_a,v),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(u,v_x),w).
% 299.64/300.42 27008[0:Res:8375.1,175.0] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> equal(hAPP(u,y),x)*.
% 299.64/300.42 27004[0:Res:652.1,175.0] || c_lessequals(v_Procs,hAPP(c_Set_Ovimage(u,tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),tc_fun(tc_Com_Opname,tc_bool))* -> equal(hAPP(u,v_x),w).
% 299.64/300.42 27047[0:Res:23946.1,455.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) c_Hoare__Mirabelle_Otriple__valid(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,v_Procs,t_a).
% 299.64/300.42 27115[0:Res:168.0,280.1] || hBOOL(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,w)),x))* -> c_Hoare__Mirabelle_Ohoare__valids(v,w,t_a) hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,u,tc_Hoare__Mirabelle_Otriple(t_a),tc_fun(y,tc_bool)),x))*.
% 299.64/300.42 27114[0:Res:3282.1,280.1] || equal(hAPP(c_in(u),v),v_Procs)** hBOOL(hAPP(hAPP(w,v),x))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,w,u,tc_fun(y,tc_bool)),x))*.
% 299.64/300.42 27106[0:Res:19451.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,t_a),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),u,t_a,tc_fun(y,tc_bool)),v))*.
% 299.64/300.42 27102[0:Res:13238.1,280.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(hAPP(v,v_x),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,t_a,tc_fun(x,tc_bool)),w))*.
% 299.64/300.42 27095[0:Res:8375.1,280.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(w,x),y))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,w,v,tc_fun(z,tc_bool)),y))*.
% 299.64/300.42 27094[0:Res:19440.0,280.1] || hBOOL(hAPP(hAPP(u,v_Procs),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),hAPP(c_in(tc_Com_Opname),v_x)),u,x,tc_fun(y,tc_bool)),v))*.
% 299.64/300.42 27089[0:Res:3284.1,280.1] || equal(c_in(tc_Com_Opname),u) hBOOL(hAPP(hAPP(v,v_Procs),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(u,v_x),v,x,tc_fun(y,tc_bool)),w))*.
% 299.64/300.42 27076[0:Res:648.0,280.1] || hBOOL(hAPP(hAPP(u,hAPP(v,v_x)),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,tc_Com_Opname,x),v_Procs),u,x,tc_fun(y,tc_bool)),w))*.
% 299.64/300.42 27074[0:Res:652.1,280.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) hBOOL(hAPP(hAPP(v,v_x),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,tc_Com_Opname,tc_fun(x,tc_bool)),w))*.
% 299.64/300.42 27072[0:Res:649.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs),u,tc_Com_Opname,tc_fun(x,tc_bool)),v))*.
% 299.64/300.42 27071[0:Res:650.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w),u,tc_Com_Opname,tc_fun(x,tc_bool)),v))*.
% 299.64/300.42 27191[0:Res:450.0,11894.1] || equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(u),v,w,x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(u)),w),v),t_a)*.
% 299.64/300.42 27289[7:Res:27207.1,455.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)** c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.64/300.42 27280[7:Res:27207.1,280.1] || equal(hAPP(c_in(u),v),v_x)** hBOOL(hAPP(hAPP(w,v),x))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,w,u,tc_fun(y,tc_bool)),x))*.
% 299.64/300.42 27270[7:SpR:131.0,27207.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)** -> hBOOL(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)))*.
% 299.64/300.42 27269[7:SpR:158.0,27207.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)** -> hBOOL(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))*.
% 299.64/300.42 27251[7:SpR:104.0,27207.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))*.
% 299.64/300.42 27300[7:MRR:24306.1,27297.0] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oimage(c_COMBK(v,w,x),x,w),tc_Com_Opname,u),u)*.
% 299.64/300.42 27310[7:MRR:24360.2,27297.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_Procs)** -> .
% 299.64/300.42 27311[7:MRR:24359.2,27297.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.64/300.42 27330[7:MRR:25008.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.42 27389[0:Res:13238.1,470.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,t_a)),w))*.
% 299.64/300.42 27388[0:Res:8375.1,470.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(x,y,u,v,w)),x))*.
% 299.64/300.42 27380[0:Res:652.1,470.0] || c_lessequals(v_Procs,hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(w,v_x,u,v,tc_Com_Opname)),w))*.
% 299.64/300.42 27449[0:Res:13238.1,466.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,t_a)),w))*.
% 299.64/300.42 27448[0:Res:8375.1,466.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,u,y,v,w)),x))*.
% 299.64/300.42 27440[0:Res:652.1,466.0] || c_lessequals(v_Procs,hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(w,u,v_x,v,tc_Com_Opname)),w))*.
% 299.64/300.42 27856[7:SpR:328.1,27219.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)).
% 299.64/300.42 27853[7:SpR:538.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_fun(t_a,tc_bool)),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool))*.
% 299.64/300.42 28033[0:Res:27381.0,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)),x))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(y,tc_bool)),x))*.
% 299.64/300.42 28004[0:SpR:329.1,27381.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.42 28003[0:SpR:328.1,27381.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.42 28000[0:SpR:538.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.42 28051[0:SpR:130.1,28032.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_Com_Opname,x)))*.
% 299.64/300.42 28336[0:Res:27441.0,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)),x))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(y,tc_bool)),x))*.
% 299.64/300.42 28307[0:SpR:329.1,27441.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x,tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.42 28306[0:SpR:328.1,27441.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),u,tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.42 28303[0:SpR:538.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_Com_Opname,w)),v_Procs))*.
% 299.64/300.42 28354[0:SpR:130.1,28335.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_Com_Opname,x)))*.
% 299.64/300.42 28439[0:SpR:770.0,118.0] || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,c_Option_Othe(v),w,x,y),c_Option_Ooption_OSome(z,v),hAPP(u,z),y,x),c_Fun_Ocomp(u,c_Option_Othe(v),w,x,y))**.
% 299.64/300.42 28438[0:SpR:768.0,118.0] || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,c_Set_Oinsert(v_x,tc_Com_Opname),v,w,x),v_Procs,hAPP(u,v_Procs),x,w),c_Fun_Ocomp(u,c_Set_Oinsert(v_x,tc_Com_Opname),v,w,x))**.
% 299.64/300.42 28603[0:SpR:177.1,19747.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.64/300.42 28596[0:SpR:177.1,20186.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.64/300.42 28766[0:SpR:329.1,28031.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 28765[0:SpR:328.1,28031.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 28762[0:SpR:538.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 28701[0:SpR:28031.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w),tc_Com_Opname),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.42 28687[0:SpR:28031.0,446.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w),tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.42 28921[0:SpR:329.1,28334.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x,tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 28920[0:SpR:328.1,28334.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),u,tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 28917[0:SpR:538.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 28856[0:SpR:28334.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w),tc_Com_Opname),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.42 28842[0:SpR:28334.0,446.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w),tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.42 29222[0:SSi:29195.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),c_Orderings_Obot__class_Obot(tc_bool))** -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),x,tc_bool)*.
% 299.64/300.42 29394[7:SpR:27278.1,474.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),x,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.42 29379[7:SpR:27278.1,446.1] || equal(hAPP(c_in(u),v),v_x) c_lessequals(w,v_x,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v,u),w),v_x,tc_fun(u,tc_bool))*.
% 299.64/300.42 29880[0:SpR:27043.1,3294.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(v_Procs,u),c_in(t_a))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 30362[0:SSi:30316.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),c_Orderings_Obot__class_Obot(tc_bool))** -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),x,tc_bool)*.
% 299.64/300.42 31302[0:Res:168.0,356.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a)* equal(hAPP(c_Set_Oimage(c_COMBK(w,x,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Hoare__Mirabelle_Otriple(t_a),x),v),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.64/300.42 31287[0:Res:9258.0,356.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)) equal(hAPP(c_Set_Oimage(c_COMBK(v,w,t_a),t_a,w),u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.64/300.42 31280[0:Res:3283.1,356.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(hAPP(c_Set_Oimage(c_COMBK(v,w,u),u,w),v_Procs),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.64/300.42 31326[0:Res:31315.0,402.0] || c_lessequals(v_Procs,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),tc_fun(tc_Com_Opname,tc_bool))* -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v_Procs).
% 299.64/300.42 31426[0:Res:8375.1,449.0] || equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_in(v),w,x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),w),c_in(v)),t_a)*.
% 299.64/300.42 31504[0:SpL:584.0,24254.1] || equal(c_COMBS(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 31485[0:SpL:337.0,24254.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 31473[0:SpL:540.1,24254.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 31472[0:SpL:539.1,24254.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 31471[0:SpL:297.2,24254.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 31462[0:SpL:299.2,24254.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(v,c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 31450[0:SpL:25.1,24254.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 31542[0:Res:9258.0,473.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),tc_bool)) hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,t_a),v_x)),w))*.
% 299.64/300.42 31873[7:MRR:31788.2,27297.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_x)** -> .
% 299.64/300.42 31884[7:SpL:130.1,31868.0] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_Orderings_Obot__class_Obot(tc_bool))** equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_x) -> .
% 299.64/300.42 32058[0:Res:151.2,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),v),x)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),v))*.
% 299.64/300.42 32656[0:SpR:584.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(u,v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(u,v_x),hAPP(v,v_x)))),v_Procs))*.
% 299.64/300.42 32637[0:SpR:337.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))),v_Procs))*.
% 299.64/300.42 32625[0:SpR:540.1,31533.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))),v_Procs))*.
% 299.64/300.42 32624[0:SpR:539.1,31533.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))),v_Procs))*.
% 299.64/300.42 32623[0:SpR:297.2,31533.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v_x)),v_Procs))*.
% 299.64/300.42 32614[0:SpR:299.2,31533.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v)),v_Procs))*.
% 299.64/300.42 32602[0:SpR:25.1,31533.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_Com_Opname,w),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))),v_Procs))*.
% 299.64/300.42 32812[7:SpL:35.2,27358.0] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(w,tc_bool))* c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),x,tc_fun(w,tc_bool))* equal(u,v_x) -> .
% 299.64/300.42 32810[0:SpL:35.2,17172.0] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(w,tc_bool))* c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),x,tc_fun(w,tc_bool))* equal(u,v_Procs) -> .
% 299.64/300.42 32782[0:SpR:35.2,17173.0] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(w,tc_bool))* c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),x,tc_fun(w,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(y,u,t_a)*.
% 299.64/300.42 32775[0:SpR:35.2,11610.0] || c_lessequals(u,c_Option_Othe(v),tc_fun(w,tc_bool))* c_lessequals(c_Option_Othe(v),x,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(u,c_Option_Ooption_OSome(y,v)),y,tc_bool)*.
% 299.64/300.42 32769[0:SpR:35.2,11580.0] || c_lessequals(u,c_Set_Oinsert(v_x,tc_Com_Opname),tc_fun(v,tc_bool))* c_lessequals(c_Set_Oinsert(v_x,tc_Com_Opname),w,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(u,v_Procs),v_Procs,tc_bool).
% 299.64/300.42 33312[0:SpR:584.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(u,v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(u,v_x),hAPP(v,v_x))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 33293[0:SpR:337.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 33281[0:SpR:540.1,32668.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 33280[0:SpR:539.1,32668.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 33279[0:SpR:297.2,32668.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 33270[0:SpR:299.2,32668.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 33258[0:SpR:25.1,32668.0] class_HOL_Ouminus(u) || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_Com_Opname,w),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 33411[0:Res:526.1,453.0] || hBOOL(hAPP(u,v))* c_Hoare__Mirabelle_Ohoare__valids(w,u,t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x)),w))* c_Hoare__Mirabelle_Otriple__valid(x,v,t_a)*.
% 299.64/300.42 33401[0:Res:267.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,x)),u))* c_Hoare__Mirabelle_Otriple__valid(x,v,t_a)*.
% 299.64/300.42 33598[0:SpR:584.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(v,v_x),hAPP(w,v_x)),c_COMBS(v,w,x,y,z),tc_Com_Opname,x1)))*.
% 299.64/300.42 33579[0:SpR:337.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),tc_Com_Opname,w)))*.
% 299.64/300.42 33567[0:SpR:540.1,28704.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),tc_Com_Opname,x)))*.
% 299.64/300.42 33566[0:SpR:539.1,28704.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),tc_Com_Opname,x)))*.
% 299.64/300.42 33565[0:SpR:297.2,28704.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,x)))*.
% 299.64/300.42 33556[0:SpR:299.2,28704.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,x)))*.
% 299.64/300.42 33544[0:SpR:25.1,28704.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u),c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u)),tc_Com_Opname,x)))*.
% 299.64/300.42 33689[0:SpR:584.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(v,w,x,y,z),hAPP(hAPP(v,v_x),hAPP(w,v_x)),tc_Com_Opname,x1)))*.
% 299.64/300.42 33670[0:SpR:337.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w)))*.
% 299.64/300.42 33658[0:SpR:540.1,28859.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),tc_Com_Opname,x)))*.
% 299.64/300.42 33657[0:SpR:539.1,28859.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),tc_Com_Opname,x)))*.
% 299.64/300.42 33656[0:SpR:297.2,28859.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x,tc_Com_Opname,x)))*.
% 299.64/300.42 33647[0:SpR:299.2,28859.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v,tc_Com_Opname,x)))*.
% 299.64/300.42 33635[0:SpR:25.1,28859.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u)),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u),tc_Com_Opname,x)))*.
% 299.64/300.42 33780[7:SpL:584.0,31886.1] || equal(u,c_COMBS(v,w,x,y,z))* equal(hAPP(hAPP(v,v_x),hAPP(w,v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_x) -> .
% 299.64/300.42 33761[7:SpL:337.0,31886.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* equal(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_x) -> .
% 299.64/300.42 33749[7:SpL:540.1,31886.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),c_Orderings_Obot__class_Obot(tc_bool))** equal(v,v_x) -> .
% 299.64/300.42 33748[7:SpL:539.1,31886.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),c_Orderings_Obot__class_Obot(tc_bool))** equal(v,v_x) -> .
% 299.64/300.42 33738[7:SpL:299.2,31886.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* equal(v,c_Orderings_Obot__class_Obot(tc_bool)) equal(w,v_x) -> .
% 299.64/300.42 33726[7:SpL:25.1,31886.1] class_HOL_Ouminus(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u)))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u),c_Orderings_Obot__class_Obot(tc_bool))** equal(v,v_x) -> .
% 299.64/300.42 34272[0:SpL:24914.0,502.0] || c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x)),u,v) -> c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Obody,tc_Com_Opname,w),hAPP(c_Com_Obody,v_x))),u,v)*.
% 299.64/300.42 34268[0:SpL:24914.0,348.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_x),u,v,w) -> equal(c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Ocom_OBODY,tc_Com_Opname,x),hAPP(c_Com_Ocom_OBODY,v_x)),v,u,w)),v)**.
% 299.64/300.42 34044[0:SpR:24914.0,15367.0] || -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),v_x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),tc_fun(v,tc_bool)),v)*.
% 299.64/300.42 33996[0:SpR:24914.0,87.1] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_HOL_Ouminus__class_Ouminus(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x)),u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.42 33920[0:SpR:24914.0,9566.0] || -> c_lessequals(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),x),hAPP(hAPP(c_Set_Oinsert(u,v),v_x),x),tc_bool)*.
% 299.64/300.42 33910[0:SpR:24914.0,503.1] || c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Obody,tc_Com_Opname,u),hAPP(c_Com_Obody,v_x))),v,w)* -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x)),v,w).
% 299.64/300.42 34652[0:SpL:55.1,3266.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,u),v),w,tc_fun(u,tc_bool)),x)* -> hBOOL(hAPP(hAPP(c_in(u),v_x),w)) hBOOL(hAPP(x,v_x))*.
% 299.64/300.42 34650[0:SpL:55.1,2674.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v)).
% 299.64/300.42 34614[0:SpR:55.1,10813.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_Set_Oinsert(x,u),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool))),v))*.
% 299.64/300.42 34730[0:SpR:34428.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x,v_x,v,w),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u))**.
% 299.64/300.42 34907[0:SpR:584.0,28053.1] || equal(u,c_COMBS(v,w,x,y,z))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(v,v_x),hAPP(w,v_x)),u,tc_Com_Opname,x1)))*.
% 299.64/300.42 34888[0:SpR:337.0,28053.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,tc_Com_Opname,w)))*.
% 299.64/300.42 34876[0:SpR:540.1,28053.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),v,tc_Com_Opname,x)))*.
% 299.64/300.42 34875[0:SpR:539.1,28053.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),v,tc_Com_Opname,x)))*.
% 299.64/300.42 34874[0:SpR:297.2,28053.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,w,tc_Com_Opname,x)))*.
% 299.64/300.42 34865[0:SpR:299.2,28053.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,w,tc_Com_Opname,x)))*.
% 299.64/300.42 34852[0:SpR:25.1,28053.1] class_HOL_Ouminus(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u),v,tc_Com_Opname,x)))*.
% 299.64/300.42 34986[0:SpR:584.0,28356.1] || equal(u,c_COMBS(v,w,x,y,z))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(hAPP(v,v_x),hAPP(w,v_x)),tc_Com_Opname,x1)))*.
% 299.64/300.42 34967[0:SpR:337.0,28356.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w)))*.
% 299.64/300.42 34955[0:SpR:540.1,28356.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),tc_Com_Opname,x)))*.
% 299.64/300.42 34954[0:SpR:539.1,28356.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),tc_Com_Opname,x)))*.
% 299.64/300.42 34953[0:SpR:297.2,28356.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,v_x,tc_Com_Opname,x)))*.
% 299.64/300.42 34944[0:SpR:299.2,28356.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,v,tc_Com_Opname,x)))*.
% 299.64/300.42 34931[0:SpR:25.1,28356.1] class_HOL_Ouminus(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u),tc_Com_Opname,x)))*.
% 299.64/300.42 35241[0:SpR:410.0,9569.0] || -> c_lessequals(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),y),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(z,w),u),v,w,tc_fun(x,tc_bool)),y),tc_bool)*.
% 299.64/300.42 35443[0:SSi:35442.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,v),u),c_COMBK(x,tc_fun(y,tc_bool),v),v,tc_fun(y,tc_bool)),x)**.
% 299.64/300.42 35529[0:SpL:113.0,3863.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))),z))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),z)).
% 299.64/300.42 36187[0:Res:3284.1,516.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),v))* hBOOL(hAPP(hAPP(c_in(u),v_Procs),v_x))*.
% 299.64/300.42 36816[0:SpR:55.1,36588.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),x),u,tc_fun(t_a,tc_bool))),v_x))*.
% 299.64/300.42 37561[0:SpR:328.1,36690.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Set_Oinsert(v_x,t_a))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_bool)).
% 299.64/300.42 37742[0:SpR:538.0,36342.1] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)))*.
% 299.64/300.42 38034[0:MRR:38008.1,418.0] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Oinsert(w,v),u),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))*.
% 299.64/300.42 38327[0:SSi:38302.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),u),v))* c_Finite__Set_Ofinite(v,tc_bool) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool),v,tc_bool,tc_bool),tc_bool)*.
% 299.64/300.42 38328[0:SSi:38283.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u)) c_Finite__Set_Ofinite(u,tc_bool) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,u,tc_bool,tc_bool),tc_bool)*.
% 299.64/300.42 38690[4:SpR:130.1,37987.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),x))*.
% 299.64/300.42 38879[4:SpR:130.1,38042.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),x,t_a)*.
% 299.64/300.42 39014[0:MRR:39002.0,13387.1] || c_Fun_Oinj__on(u,v,w,x)* equal(y,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) -> equal(hAPP(c_Set_Oimage(u,w,x),y),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))**.
% 299.64/300.42 39667[4:SpR:532.0,37987.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),w)))*.
% 299.64/300.42 39934[0:Rew:39932.1,20485.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v),y)**.
% 299.64/300.42 41515[7:MRR:41444.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_Com_Opname,tc_bool))*.
% 299.64/300.42 42196[0:SSi:42138.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v,tc_bool) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,hAPP(c_Set_Oinsert(v,tc_bool),u),tc_bool,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.42 42197[0:SSi:42135.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),tc_bool),u),tc_bool,tc_bool),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,u,tc_bool,tc_bool))**.
% 299.64/300.42 42204[0:MRR:42148.1,379.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),v,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),u,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v))**.
% 299.64/300.42 42731[0:SpL:161.0,333.0] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),u)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool)),u).
% 299.64/300.42 42730[0:SpL:161.0,332.0] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),u)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),u).
% 299.64/300.42 43550[0:SpL:507.0,333.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w).
% 299.64/300.42 43549[0:SpL:507.0,332.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),y),w).
% 299.64/300.42 43772[0:SpL:162.0,333.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),x),v).
% 299.64/300.42 43771[0:SpL:162.0,332.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),y),v).
% 299.64/300.42 44274[0:SSi:44254.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(hAPP(v_Procs,v_x),tc_bool),u),tc_bool,tc_bool))*.
% 299.64/300.42 44360[0:MRR:44320.1,8375.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) equal(hAPP(w,x),hAPP(w,y))* c_Fun_Oinj__on(w,u,v,z)* -> equal(x,y).
% 299.64/300.42 44404[0:Rew:586.0,44383.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(x,v_x)),hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,x,tc_Com_Opname,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.64/300.42 44458[0:Rew:586.0,44437.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(x,v_x)),hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,x,tc_Com_Opname,tc_fun(w,tc_bool))),tc_fun(v,tc_bool))*.
% 299.64/300.42 44641[0:SpR:410.0,35656.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,w),u),v,w,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.42 44675[0:SSi:44624.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,v) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,w,v,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,w,v,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.42 45456[0:Res:45357.1,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),v_x)) -> hBOOL(hAPP(x,hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Set_Ovimage(u,v,w),x),tc_Com_Opname))))*.
% 299.64/300.42 45410[0:SpR:299.2,45357.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname),v,u)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)) -> hBOOL(v).
% 299.64/300.42 45403[0:SpR:2097.1,45357.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname),u))* hBOOL(hAPP(c_Set_Oinsert(u,v),v_x)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname)).
% 299.64/300.42 45715[0:SpR:486.1,44625.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(hAPP(x,v),v_Procs)** -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.42 45913[0:MRR:45912.2,264.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),u,w)))* -> hBOOL(hAPP(u,x))*.
% 299.64/300.42 45970[0:Res:34.1,45899.0] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Set_Ovimage(v,w,x),u),tc_Com_Opname))))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,w,x),u),v_x)).
% 299.64/300.42 45925[0:SpL:299.2,45899.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname),v,u)* hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)).
% 299.64/300.42 45918[0:SpL:2097.1,45899.0] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname),u))* hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname)) -> hBOOL(hAPP(c_Set_Oinsert(u,v),v_x)).
% 299.64/300.42 46420[0:SSi:46419.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) hBOOL(v) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v),tc_bool),u),tc_bool,tc_bool))*.
% 299.64/300.42 46653[4:SpL:328.1,46565.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),u)* -> .
% 299.64/300.42 46649[4:SpL:538.0,46565.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))* -> .
% 299.64/300.42 47166[0:SSi:47078.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_bool)))*.
% 299.64/300.42 47686[4:SSi:47665.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool),tc_bool),u),tc_bool,tc_bool))*.
% 299.64/300.42 47887[0:SSi:47798.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_bool)),y))*.
% 299.64/300.42 48162[4:SpR:584.0,39023.1] || equal(c_COMBS(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(hAPP(u,v_x),hAPP(v,v_x))),x2))*.
% 299.64/300.42 48130[4:SpR:540.1,39023.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),y))*.
% 299.64/300.42 48129[4:SpR:539.1,39023.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),y))*.
% 299.64/300.42 48128[4:SpR:297.2,39023.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),v_x),y))*.
% 299.64/300.42 48119[4:SpR:299.2,39023.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),v),y))*.
% 299.64/300.42 48106[4:SpR:25.1,39023.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)),y))*.
% 299.64/300.42 48277[4:SpR:584.0,39064.1] || equal(c_COMBS(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(z,x1),hAPP(hAPP(u,v_x),hAPP(v,v_x))),x2,t_a)*.
% 299.64/300.42 48245[4:SpR:540.1,39064.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),y,t_a)*.
% 299.64/300.42 48244[4:SpR:539.1,39064.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),y,t_a)*.
% 299.64/300.42 48243[4:SpR:297.2,39064.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),v_x),y,t_a)*.
% 299.64/300.42 48234[4:SpR:299.2,39064.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),v),y,t_a)*.
% 299.64/300.42 48221[4:SpR:25.1,39064.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)),y,t_a)*.
% 299.64/300.42 48588[4:SSi:48549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z,hAPP(c_Set_Oinsert(v_x,tc_bool),u),tc_bool,tc_bool)))*.
% 299.64/300.42 48722[4:SpR:475.1,42357.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,u,y),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y,tc_fun(z,tc_bool)),v_x))*.
% 299.64/300.42 49019[0:Res:48989.1,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,v,tc_Com_Opname)),w))* -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(x,tc_bool)),w))*.
% 299.64/300.42 49076[0:SpR:49017.1,474.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.42 49060[0:SpR:49017.1,446.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(v,v_x)) c_lessequals(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,v,tc_Com_Opname),tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.42 50403[0:SpR:223.1,36605.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,t_a),u,t_a),w),tc_Com_Opname,tc_bool))*.
% 299.64/300.42 50642[0:SSi:50610.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(w,tc_bool),u),tc_bool,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(w) -> hBOOL(x)*.
% 299.64/300.42 50764[0:SSi:50671.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(w,tc_bool),u),tc_bool,tc_bool),x,tc_bool)* hBOOL(w) -> hBOOL(x).
% 299.64/300.42 51085[0:SSi:50984.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(hAPP(x,v))* -> hBOOL(y)*.
% 299.64/300.42 51375[0:SpR:584.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),hAPP(hAPP(c_Set_Oinsert(w,t_a),c_COMBS(u,v,x,y,z)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 51355[0:SpR:337.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 51342[0:SpR:540.1,51231.0] class_Lattices_Olattice(u) || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 51341[0:SpR:539.1,51231.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 51340[0:SpR:297.2,51231.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 51331[0:SpR:299.2,51231.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> equal(c_HOL_Ominus__class_Ominus(v,hAPP(hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 51317[0:SpR:25.1,51231.0] class_HOL_Ouminus(u) || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),hAPP(hAPP(c_Set_Oinsert(w,t_a),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 51434[7:SpL:196.1,27284.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* equal(x,v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),hAPP(u,v_x)))*.
% 299.64/300.42 51977[0:Rew:11176.1,51961.2,11176.1,51961.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x),u)** -> equal(c_List_Ofoldl(y,u,z,x,x1),u)**.
% 299.64/300.42 52159[0:SSi:52093.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_bool),y,tc_bool)* hBOOL(hAPP(x,v))* -> hBOOL(y).
% 299.64/300.42 52827[0:SpR:24019.2,20881.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,u,v),hAPP(c_Set_Oinsert(v_x,u),w)),v_x))*.
% 299.64/300.42 52812[0:SpR:24019.2,9569.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),v_x),tc_bool)*.
% 299.64/300.42 52811[0:SpR:24019.2,9568.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),v_x),tc_bool)*.
% 299.64/300.42 52805[0:SpR:24019.2,3346.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Set_Oinsert(u,v),v_x) -> hBOOL(hAPP(hAPP(c_in(v),u),v_x))*.
% 299.64/300.42 52804[0:SpR:24019.2,28356.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(u,v_x) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,v)))*.
% 299.64/300.42 52803[0:SpR:24019.2,28053.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(u,v_x) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,v)))*.
% 299.64/300.42 52802[0:SpR:24019.2,28859.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_x,v_x,tc_Com_Opname,v)))*.
% 299.64/300.42 52801[0:SpR:24019.2,28704.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,v_x,tc_Com_Opname,v)))*.
% 299.64/300.42 52800[0:SpR:24019.2,21126.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,tc_Com_Opname,v),u),v_x))*.
% 299.64/300.42 52798[0:SpR:24019.2,3305.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(u,v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),v_x))*.
% 299.64/300.42 52791[0:SpR:24019.2,51231.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(u,t_a),v_x),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 52787[0:SpR:24019.2,32668.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_x,tc_Com_Opname,u),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 52785[0:SpR:24019.2,31533.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_x,tc_Com_Opname,u),v_x)),v_Procs))*.
% 299.64/300.42 52778[0:SpR:24019.2,21131.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,tc_Com_Opname,u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.42 52777[0:SpR:24019.2,21143.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v_x,t_a,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.42 52758[0:SpR:24019.2,3279.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.42 52870[0:SpL:8415.2,31349.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(v_x,tc_Com_Opname,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.42 53067[0:SpR:23955.0,11177.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),v_x).
% 299.64/300.42 53057[0:SpR:23955.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w),u),x)),v_x))*.
% 299.64/300.42 53114[0:SSi:53093.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),v_x) -> c_lessequals(v_x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_bool)*.
% 299.64/300.42 53115[0:SSi:53045.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_bool)* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),v_x).
% 299.64/300.42 53119[0:Rew:23884.1,53055.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v)* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 53199[0:SpR:23958.0,11177.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x).
% 299.64/300.42 53189[0:SpR:23958.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),u),x)),v_x))*.
% 299.64/300.42 53246[0:SSi:53225.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x) -> c_lessequals(v_x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_bool)*.
% 299.64/300.42 53247[0:SSi:53177.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_bool)* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x).
% 299.64/300.42 53251[0:Rew:23884.1,53187.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v)* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 53345[0:SpL:8415.2,25019.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x) -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.64/300.42 53447[0:SpR:33303.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,v),x)),v_Procs))*.
% 299.64/300.42 53441[0:SpR:33303.0,353.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))**.
% 299.64/300.42 53418[0:SpR:33303.0,9569.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),v_x),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.42 53417[0:SpR:33303.0,9568.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x),tc_Com_Opname)),w),v_Procs),tc_bool)*.
% 299.64/300.42 53577[0:Rew:10.0,53532.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))).
% 299.64/300.42 53746[0:SpR:8415.2,7226.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(c_Option_Othe(v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.42 53816[0:Rew:20474.1,53806.1] || c_Fun_Oinj__on(c_Option_Othe(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Option_Othe(u),x,z),c_Option_Ooption_OSome(y,u))**.
% 299.64/300.42 53847[0:Rew:20474.1,53837.1] || c_Fun_Oinj__on(c_Option_Othe(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Option_Othe(u),y,x,z),c_Option_Ooption_OSome(y,u))**.
% 299.64/300.42 54167[0:SpL:52997.1,24254.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 54161[0:SpL:52997.1,3484.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,v),v_x)** -> equal(v_x,v).
% 299.64/300.42 54135[0:SpR:52997.1,20881.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),v_x))*.
% 299.64/300.42 54129[0:SpR:52997.1,353.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),hAPP(c_Set_Oinsert(v,u),v_x)),hAPP(c_Set_Oinsert(v,u),v_x))**.
% 299.64/300.42 54105[0:SpR:52997.1,9569.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_Procs,w)),v_x),tc_bool)*.
% 299.64/300.42 54104[0:SpR:52997.1,9568.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_Procs,v)),w),v_x),tc_bool)*.
% 299.64/300.42 54093[0:SpR:52997.1,3346.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(u,v),c_Set_Oinsert(v_Procs,w))* -> hBOOL(hAPP(hAPP(c_in(v),u),v_x))*.
% 299.64/300.42 54092[0:SpR:52997.1,28356.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(u,c_Set_Oinsert(v_Procs,v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,v_x,tc_Com_Opname,w)))*.
% 299.64/300.42 54091[0:SpR:52997.1,28053.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(u,c_Set_Oinsert(v_Procs,v))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,u,tc_Com_Opname,w)))*.
% 299.64/300.42 54090[0:SpR:52997.1,28859.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_Procs,v),v_x,tc_Com_Opname,w)))*.
% 299.64/300.42 54089[0:SpR:52997.1,28704.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_Procs,v),tc_Com_Opname,w)))*.
% 299.64/300.42 54088[0:SpR:52997.1,21126.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,v),tc_Com_Opname,w),u),v_x))*.
% 299.64/300.42 54087[0:SpR:52997.1,3317.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_in(u),c_Set_Oinsert(v_Procs,v))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,u),w)))*.
% 299.64/300.42 54086[0:SpR:52997.1,3305.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(u,c_Set_Oinsert(v_Procs,v))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,w),v_Procs),v_x))*.
% 299.64/300.42 54079[0:SpR:52997.1,51231.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_Procs,v)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 54076[0:SpR:52997.1,24914.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),v_x)),v_x)**.
% 299.64/300.42 54075[0:SpR:52997.1,32668.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 54073[0:SpR:52997.1,31533.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),v_x)),v_Procs))*.
% 299.64/300.42 54066[0:SpR:52997.1,21131.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.42 54065[0:SpR:52997.1,21143.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.42 54059[0:SpR:52997.1,15262.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(v_Procs,u),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.42 54053[4:SpR:52997.1,39064.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),v_x),x,t_a)*.
% 299.64/300.42 54052[4:SpR:52997.1,39023.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(v_Procs,u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),v_x),x))*.
% 299.64/300.42 54046[0:SpR:52997.1,3279.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),c_Set_Oinsert(v_Procs,u))* -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x))*.
% 299.64/300.42 54301[0:Rew:36904.0,54211.0] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),u),tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(w,v),u),tc_fun(v,tc_bool)))**.
% 299.64/300.42 54830[0:SpR:8415.2,13749.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.42 54747[0:SpR:13749.2,20881.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),y)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.42 54721[0:SpR:13749.2,9569.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x)),c_Orderings_Otop__class_Otop(u)),tc_bool)*.
% 299.64/300.42 54720[0:SpR:13749.2,9568.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),x),c_Orderings_Otop__class_Otop(u)),tc_bool)*.
% 299.64/300.42 54927[0:Rew:20479.2,54745.3] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)).
% 299.64/300.42 55305[0:SpR:8415.2,14043.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(v_x,c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.42 55221[0:SpR:14043.2,20881.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),y)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.42 55195[0:SpR:14043.2,9569.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x)),c_Orderings_Otop__class_Otop(u)),tc_bool)*.
% 299.64/300.42 55194[0:SpR:14043.2,9568.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),x),c_Orderings_Otop__class_Otop(u)),tc_bool)*.
% 299.64/300.42 55405[0:Rew:20479.2,55219.3] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_Orderings_Otop__class_Otop(u)).
% 299.64/300.42 55773[0:SpL:538.0,55605.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.42 55828[7:MRR:55827.2,27297.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.42 56006[0:SpL:328.1,55174.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool),u)* -> .
% 299.64/300.42 56002[0:SpL:538.0,55174.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w))* -> .
% 299.64/300.42 55924[0:SpL:328.1,55174.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w)* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(w,v_x))* -> .
% 299.64/300.42 55920[0:SpL:538.0,55174.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool),hAPP(w,v_x))* -> .
% 299.64/300.42 56352[0:SpL:30368.2,3507.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.42 56350[0:SpL:30368.2,16327.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(v,v_Procs) -> .
% 299.64/300.42 56349[7:SpL:30368.2,31886.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(v,v_x) -> .
% 299.64/300.42 56348[0:SpL:30368.2,3499.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.42 56345[0:SpL:30368.2,24254.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 56339[0:SpL:30368.2,13272.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.42 56338[0:SpL:30368.2,3484.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(u),hAPP(c_Com_Ocom_OBODY,v))* -> equal(v_x,v).
% 299.64/300.42 56225[0:SpR:30368.2,20881.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_Set_Oinsert(x,v),y)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.42 56199[0:SpR:30368.2,9569.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),x),tc_bool)*.
% 299.64/300.42 56198[0:SpR:30368.2,9568.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),w),x),tc_bool)*.
% 299.64/300.42 56184[0:SpR:30368.2,3346.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(hAPP(c_in(w),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.42 56183[0:SpR:30368.2,28356.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,c_Orderings_Otop__class_Otop(u),tc_Com_Opname,w)))*.
% 299.64/300.42 56182[0:SpR:30368.2,28053.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),v,tc_Com_Opname,w)))*.
% 299.64/300.42 56181[0:SpR:30368.2,28859.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,w)))*.
% 299.64/300.42 56180[0:SpR:30368.2,28704.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,w)))*.
% 299.64/300.42 56179[0:SpR:30368.2,21126.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,w),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.42 56178[0:SpR:30368.2,3317.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),hAPP(c_Set_Oinsert(v_x,v),w)))*.
% 299.64/300.42 56177[0:SpR:30368.2,3305.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.42 56173[0:SpR:30368.2,2771.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))*.
% 299.64/300.42 56169[0:SpR:30368.2,51231.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 56165[0:SpR:30368.2,32668.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 56163[0:SpR:30368.2,31533.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u))),v_Procs))*.
% 299.64/300.42 56155[0:SpR:30368.2,21143.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.42 56149[0:SpR:30368.2,15262.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.42 56146[0:SpR:30368.2,8376.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v))*.
% 299.64/300.42 56144[0:SpR:30368.2,8415.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(c_Orderings_Otop__class_Otop(u),v_x).
% 299.64/300.42 56143[4:SpR:30368.2,39064.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(u)),x,t_a)*.
% 299.64/300.42 56142[4:SpR:30368.2,39023.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(u)),x))*.
% 299.64/300.42 56141[0:SpR:30368.2,3291.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(u)),v_Procs))*.
% 299.64/300.42 56140[0:SpR:30368.2,3285.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.42 56136[0:SpR:30368.2,3279.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(c_Orderings_Otop__class_Otop(u),v_Procs),v_x))*.
% 299.64/300.42 56794[0:SpL:30928.2,3507.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.64/300.42 56792[0:SpL:30928.2,16327.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(v,v_Procs) -> .
% 299.64/300.42 56791[7:SpL:30928.2,31886.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_bool)) equal(v,v_x) -> .
% 299.64/300.42 56790[0:SpL:30928.2,3499.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.42 56787[0:SpL:30928.2,24254.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 56781[0:SpL:30928.2,13272.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.64/300.42 56780[0:SpL:30928.2,3484.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(u),hAPP(c_Com_Ocom_OBODY,v))* -> equal(v_x,v).
% 299.64/300.42 56667[0:SpR:30928.2,20881.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_Set_Oinsert(x,v),y)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.42 56641[0:SpR:30928.2,9569.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),x),tc_bool)*.
% 299.64/300.42 56640[0:SpR:30928.2,9568.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),w),x),tc_bool)*.
% 299.64/300.42 56625[0:SpR:30928.2,3346.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(hAPP(c_in(w),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.42 56624[0:SpR:30928.2,28356.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,c_Orderings_Otop__class_Otop(u),tc_Com_Opname,w)))*.
% 299.64/300.42 56623[0:SpR:30928.2,28053.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),v,tc_Com_Opname,w)))*.
% 299.64/300.42 56622[0:SpR:30928.2,28859.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,w)))*.
% 299.64/300.42 56621[0:SpR:30928.2,28704.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,w)))*.
% 299.64/300.42 56620[0:SpR:30928.2,21126.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,w),v),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.42 56619[0:SpR:30928.2,3317.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),hAPP(c_Set_Oinsert(v_x,v),w)))*.
% 299.64/300.42 56618[0:SpR:30928.2,3305.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.42 56614[0:SpR:30928.2,2771.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))*.
% 299.64/300.42 56610[0:SpR:30928.2,51231.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 56606[0:SpR:30928.2,32668.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 56604[0:SpR:30928.2,31533.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u))),v_Procs))*.
% 299.64/300.42 56596[0:SpR:30928.2,21143.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.42 56590[0:SpR:30928.2,15262.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(t_a))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.42 56587[0:SpR:30928.2,8376.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** equal(v,v_Procs) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v))*.
% 299.64/300.42 56585[0:SpR:30928.2,8415.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(c_Orderings_Otop__class_Otop(u),v_x).
% 299.64/300.42 56584[4:SpR:30928.2,39064.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(u)),x,t_a)*.
% 299.64/300.42 56583[4:SpR:30928.2,39023.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(u)),x))*.
% 299.64/300.42 56582[0:SpR:30928.2,3291.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(u)),v_Procs))*.
% 299.64/300.42 56581[0:SpR:30928.2,3285.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))*.
% 299.64/300.42 56577[0:SpR:30928.2,3279.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(c_Orderings_Otop__class_Otop(u),v_Procs),v_x))*.
% 299.64/300.42 57012[0:SpR:2771.1,54996.1] || equal(u,v)* equal(w,hAPP(v,v_x))* -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),w,tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))**.
% 299.64/300.42 57731[0:Res:4122.3,427.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) class_Orderings_Opreorder(u) || equal(c_Orderings_Otop__class_Otop(u),v) c_lessequals(v,w,u)* -> c_lessequals(c_Orderings_Obot__class_Obot(u),w,u)*.
% 299.64/300.42 57973[0:SpL:52997.1,55910.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(c_COMBK(u,v,w),c_Set_Oinsert(v_Procs,x))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),v_x) -> .
% 299.64/300.42 57968[0:SpL:584.0,55910.1] || equal(c_COMBK(u,v,w),c_COMBS(x,y,z,x1,x2))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(hAPP(x,v_x),hAPP(y,v_x)))* -> .
% 299.64/300.42 57948[0:SpL:337.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))) -> .
% 299.64/300.42 57935[0:SpL:540.1,55910.1] class_Lattices_Olattice(u) || equal(c_COMBK(v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),y))* -> .
% 299.64/300.42 57934[0:SpL:539.1,55910.1] class_Lattices_Oupper__semilattice(u) || equal(c_COMBK(v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),y))* -> .
% 299.64/300.42 57933[0:SpL:297.2,55910.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(c_COMBK(w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* equal(c_HOL_Ouminus__class_Ouminus(w,tc_bool),v_x) -> .
% 299.64/300.42 57926[0:SpL:30368.2,55910.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_COMBK(v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_Orderings_Otop__class_Otop(u)) -> .
% 299.64/300.42 57925[0:SpL:30928.2,55910.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_COMBK(v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_Orderings_Otop__class_Otop(u)) -> .
% 299.64/300.42 57922[0:SpL:299.2,55910.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_COMBK(w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* equal(c_HOL_Ouminus__class_Ouminus(w,tc_bool),v) -> .
% 299.64/300.42 57907[0:SpL:25.1,55910.1] class_HOL_Ouminus(u) || equal(c_COMBK(v,w,x),c_HOL_Ouminus__class_Ouminus(y,tc_fun(t_a,u)))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(y,v_x),u))* -> .
% 299.64/300.42 58130[0:SpL:52997.1,55992.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname))** equal(c_Set_Oinsert(v_Procs,u),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v) -> .
% 299.64/300.42 58125[0:SpL:584.0,55992.1] || equal(c_COMBS(u,v,w,x,y),c_COMBK(z,x1,x2))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_bool),z)* -> .
% 299.64/300.42 58105[0:SpL:337.0,55992.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool),v) -> .
% 299.64/300.42 58092[0:SpL:540.1,55992.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),w)* -> .
% 299.64/300.42 58091[0:SpL:539.1,55992.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),w)* -> .
% 299.64/300.42 58090[0:SpL:297.2,55992.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w) -> .
% 299.64/300.42 58083[0:SpL:30368.2,55992.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v) -> .
% 299.64/300.42 58082[0:SpL:30928.2,55992.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_COMBK(v,w,x))* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),v) -> .
% 299.64/300.42 58079[0:SpL:299.2,55992.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),w) -> .
% 299.64/300.42 58073[0:SpL:24019.2,55992.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_COMBK(u,v,w),v_x)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),u) -> .
% 299.64/300.42 58064[0:SpL:25.1,55992.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool),w)* -> .
% 299.64/300.42 58168[0:SpL:130.1,58055.0] class_HOL_Ominus(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool),x,y),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)))** -> .
% 299.64/300.42 58388[0:Res:293.2,5005.2] class_Lattices_Oupper__semilattice(u) class_Orderings_Otop(u) class_Orderings_Oorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.42 58385[0:Res:294.2,5005.2] class_Lattices_Oupper__semilattice(u) class_Orderings_Otop(u) class_Orderings_Oorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.42 58510[7:MRR:58437.1,27297.0] || equal(c_COMBK(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w,x),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(c_COMBK(u,v,y),y,v),tc_fun(t_a,tc_bool)))* -> .
% 299.64/300.42 58548[0:SpR:353.0,10771.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x))) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(y,u),x)),v))*.
% 299.64/300.42 58787[0:SpL:303.1,15629.0] class_Lattices_Obounded__lattice(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))*.
% 299.64/300.42 58777[0:SpL:330.0,15629.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w)))*.
% 299.64/300.42 58733[0:SpL:87.1,15629.0] class_Lattices_Oboolean__algebra(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))*.
% 299.64/300.42 58715[0:SpL:414.0,15629.0] || hBOOL(u) -> hBOOL(hAPP(c_Fun_Ofun__upd(v,w,u,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Fun_Ofun__upd(v,w,u,x,y),z)))*.
% 299.64/300.42 58692[0:SpL:365.1,15629.0] class_Orderings_Obot(u) || hBOOL(c_Orderings_Obot__class_Obot(u)) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v)))*.
% 299.64/300.42 58691[0:SpL:397.1,15629.0] class_Orderings_Otop(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v)))*.
% 299.64/300.42 59120[4:MRR:58810.1,6340.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Set_Oinsert(v_Procs,u),v)))*.
% 299.64/300.42 59295[0:SpL:303.1,15857.0] class_Lattices_Obounded__lattice(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))*.
% 299.64/300.42 59285[0:SpL:330.0,15857.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),x)))*.
% 299.64/300.42 59241[0:SpL:87.1,15857.0] class_Lattices_Oboolean__algebra(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))*.
% 299.64/300.42 59223[0:SpL:414.0,15857.0] || hBOOL(u) -> hBOOL(hAPP(c_Fun_Ofun__upd(v,w,u,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Fun_Ofun__upd(v,w,u,x,y),x1)))*.
% 299.64/300.42 59200[0:SpL:365.1,15857.0] class_Orderings_Obot(u) || hBOOL(c_Orderings_Obot__class_Obot(u)) -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),w)))*.
% 299.64/300.42 59199[0:SpL:397.1,15857.0] class_Orderings_Otop(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),w)))*.
% 299.64/300.42 59630[4:MRR:59318.1,6340.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v_Procs,u),w)))*.
% 299.64/300.42 59822[0:SpL:8415.2,4126.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(v_x,v) -> c_lessequals(v_x,v,u).
% 299.64/300.42 59816[0:SpL:8415.2,4126.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) equal(hAPP(v_x,v),v_x) -> c_lessequals(v,v_x,u)*.
% 299.64/300.42 60087[0:Res:4718.2,427.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)* c_lessequals(v,w,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),w,u)*.
% 299.64/300.42 60086[0:Res:4718.2,426.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)* c_lessequals(w,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),u)* -> c_lessequals(w,v,u)*.
% 299.64/300.42 60242[0:SpL:52997.1,58170.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(u,c_Set_Oinsert(v_Procs,v))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w,x),u)* -> .
% 299.64/300.42 60237[0:SpL:584.0,58170.1] || equal(u,c_COMBS(v,w,x,y,z))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(v,v_x),hAPP(w,v_x)),tc_bool),x1,x2),u)* -> .
% 299.64/300.42 60217[0:SpL:337.0,58170.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_bool),w,x),u)* -> .
% 299.64/300.42 60204[0:SpL:540.1,58170.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),tc_bool),x,y),v)* -> .
% 299.64/300.42 60203[0:SpL:539.1,58170.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w),tc_bool),x,y),v)* -> .
% 299.64/300.42 60202[0:SpL:297.2,58170.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),x,y),w)* -> .
% 299.64/300.42 60195[0:SpL:30368.2,58170.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),w,x),v)* -> .
% 299.64/300.42 60194[0:SpL:30928.2,58170.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),w,x),v)* -> .
% 299.64/300.42 60191[0:SpL:299.2,58170.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v,tc_bool),x,y),w)* -> .
% 299.64/300.42 60185[0:SpL:24019.2,58170.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(u,v_x) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),v,w),u)* -> .
% 299.64/300.42 60176[0:SpL:25.1,58170.1] class_HOL_Ouminus(u) || equal(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u))) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u),tc_bool),x,y),v)* -> .
% 299.64/300.42 60327[0:Res:4803.2,427.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)* c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),w,u)* -> c_lessequals(v,w,u)*.
% 299.64/300.42 60326[0:Res:4803.2,426.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)* c_lessequals(w,v,u)* -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),u)*.
% 299.64/300.42 60429[7:Res:58968.1,11894.1] || equal(hAPP(c_in(u),v),v_x) equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.42 60380[7:SpR:300.1,58968.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v))*.
% 299.64/300.42 60472[0:SpR:5882.1,20881.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),z),x2)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.42 60454[0:SpR:5882.1,9569.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1)),c_Orderings_Otop__class_Otop(u)),tc_bool)*.
% 299.64/300.42 60453[0:SpR:5882.1,9568.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z)),x1),c_Orderings_Otop__class_Otop(u)),tc_bool)*.
% 299.64/300.42 60542[0:Res:58969.1,11894.1] || equal(hAPP(c_in(u),v),v_Procs) equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.42 60493[0:SpR:300.1,58969.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v))*.
% 299.64/300.42 60615[7:Res:59476.1,11894.1] || equal(hAPP(c_in(u),v),v_x) equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.42 60566[7:SpR:300.1,59476.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w))*.
% 299.64/300.42 60688[0:Res:59477.1,11894.1] || equal(hAPP(c_in(u),v),v_Procs) equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.42 60639[0:SpR:300.1,59477.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w))*.
% 299.64/300.42 60873[0:Res:59017.1,11894.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(c_in(w),x),u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_in(w),x),t_a)*.
% 299.64/300.42 60824[0:SpR:300.1,59017.1] class_Lattices_Obounded__lattice(u) || -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w))*.
% 299.64/300.42 60946[0:Res:59525.1,11894.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(w),x),v),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_in(w),x),t_a)*.
% 299.64/300.42 60897[0:SpR:300.1,59525.1] class_Lattices_Obounded__lattice(u) || -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x))*.
% 299.64/300.42 61656[0:Res:293.2,8141.2] class_Lattices_Oupper__semilattice(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u) -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),u)*.
% 299.64/300.42 61653[0:Res:294.2,8141.2] class_Lattices_Oupper__semilattice(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || c_lessequals(c_Orderings_Otop__class_Otop(u),v,u) -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v),u)*.
% 299.64/300.42 61794[0:SpR:11167.1,20881.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),v_Procs))*.
% 299.64/300.42 61779[0:SpR:11167.1,9569.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,x),c_Set_Oinsert(v_x,tc_Com_Opname))),v_Procs),tc_bool)*.
% 299.64/300.42 61778[0:SpR:11167.1,9568.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,tc_Com_Opname))),x),v_Procs),tc_bool)*.
% 299.64/300.42 61969[0:SpL:27043.1,15487.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_Procs,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 61962[0:SpL:586.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_COMBB(u,v,w,x),y),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(y,v_x)),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 61961[0:SpL:585.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_COMBC(u,v,w,x),y),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),y),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 61905[0:SpL:8415.2,15487.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 61899[0:SpL:445.1,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Fun_Ofun__upd(u,v,w,x,y),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Com_Ocom_OSKIP) -> equal(v_x,v).
% 299.64/300.42 62128[0:SpR:8415.2,23727.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v),v_x),v_Procs))*.
% 299.64/300.42 62154[0:SpR:8415.2,23754.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.42 62281[0:Res:49.2,4246.1] class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) equal(c_HOL_Ouminus__class_Ouminus(v,u),v) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)*.
% 299.64/300.42 62280[0:Res:45.2,4246.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) equal(c_HOL_Ouminus__class_Ouminus(v,u),v) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)*.
% 299.64/300.42 62255[0:Res:47.2,4246.1] class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) equal(c_HOL_Ouminus__class_Ouminus(v,u),v) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.42 62254[0:Res:43.2,4246.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) equal(c_HOL_Ouminus__class_Ouminus(v,u),v) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.42 62401[0:SSi:62324.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),v_Procs) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),v_Procs,tc_bool)*.
% 299.64/300.42 62402[0:SSi:62322.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),w),x),hAPP(w,x)) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),w),x),hAPP(w,x),tc_bool)*.
% 299.64/300.42 62413[0:SSi:62218.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v_Procs) -> c_lessequals(v_Procs,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.42 62616[0:Res:49.2,4340.1] class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),v).
% 299.64/300.42 62615[0:Res:45.2,4340.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),v,u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),v).
% 299.64/300.42 62590[0:Res:47.2,4340.1] class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),v).
% 299.64/300.42 62589[0:Res:43.2,4340.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),v).
% 299.64/300.42 63111[0:Rew:25.1,62980.3] class_OrderedGroup_Opordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_HOL_Ouminus(u) || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),u),hAPP(v,v_x))**.
% 299.64/300.42 63466[0:Res:4719.2,427.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(v,w,u)* c_lessequals(w,x,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),x,u)*.
% 299.64/300.42 63578[0:Res:62367.1,36528.1] || equal(c_HOL_Ominus__class_Ominus(hAPP(v_Procs,v_x),u,tc_bool),hAPP(v_Procs,v_x)) equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(c_HOL_Ominus__class_Ominus(hAPP(v_Procs,v_x),u,tc_bool))*.
% 299.64/300.42 63891[0:Res:4804.2,427.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(v,w,u)* c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(w,u),u),x,u)* -> c_lessequals(v,x,u)*.
% 299.64/300.42 64014[0:SpL:647.0,148.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v))).
% 299.64/300.42 64105[0:Res:679.1,430.0] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) c_lessequals(v_Procs,v,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.42 64121[0:SSi:64118.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) c_lessequals(v,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),tc_fun(tc_Com_Opname,tc_bool))* -> c_lessequals(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)).
% 299.64/300.42 64239[0:SpR:24020.1,646.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) c_Fun_Oinj__on(hAPP(u,v_x),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(u,v_x),tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.42 64232[0:SpR:9924.0,646.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v_Procs,tc_Com_Opname,u) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_bool)),v_x)**.
% 299.64/300.42 64197[0:SpR:525.1,646.1] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.42 64176[0:SpR:2097.1,646.1] || hBOOL(hAPP(v_x,u)) c_Fun_Oinj__on(c_Set_Oinsert(u,v),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),v_x),v_x)**.
% 299.64/300.42 64153[0:SpR:646.1,415.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(c_Fun_Ofun__upd(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x),v_x,w,x),c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v))**.
% 299.64/300.42 64406[0:SpR:24020.1,645.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) c_Fun_Oinj__on(hAPP(u,v_x),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(u,v_x),tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.42 64399[0:SpR:9924.0,645.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v_Procs,tc_Com_Opname,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_bool)),v_x)**.
% 299.64/300.42 64364[0:SpR:525.1,645.1] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.42 64343[0:SpR:2097.1,645.1] || hBOOL(hAPP(v_x,u)) c_Fun_Oinj__on(c_Set_Oinsert(u,v),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),v_x),v_x)**.
% 299.64/300.42 64320[0:SpR:645.1,415.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(c_Fun_Ofun__upd(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x),v_x,w,x),c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v))**.
% 299.64/300.42 64461[0:SpL:8415.2,24029.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Com_Ocom_OBODY,v_x) equal(hAPP(c_Com_Ocom_OBODY,u),v_x)** -> equal(v_x,u).
% 299.64/300.42 64561[0:SpL:15172.0,24257.1] || equal(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_bool),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.42 64556[0:SpL:586.0,24257.1] || equal(hAPP(c_COMBB(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(u,hAPP(y,v_x)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.42 64555[0:SpL:585.0,24257.1] || equal(hAPP(c_COMBC(u,v,w,x),y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(u,v_x),y),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.42 64549[0:SpL:9936.1,24257.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_in(tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.42 64545[0:SpL:9935.1,24257.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_in(tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.42 64493[0:SpL:445.1,24257.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(u,v_x),c_in(tc_Com_Opname)) -> equal(v_x,v) hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.42 64601[0:SpR:26782.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),y)),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.42 64838[0:SpR:28747.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),v_Procs))*.
% 299.64/300.42 64832[0:SpR:28747.0,353.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))**.
% 299.64/300.42 64808[0:SpR:28747.0,9569.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.42 64807[0:SpR:28747.0,9568.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w),tc_Com_Opname)),x),v_Procs),tc_bool)*.
% 299.64/300.42 64958[0:SpR:28748.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),v_Procs))*.
% 299.64/300.42 64952[0:SpR:28748.0,353.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))**.
% 299.64/300.42 64928[0:SpR:28748.0,9569.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.42 64927[0:SpR:28748.0,9568.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w),tc_Com_Opname)),x),v_Procs),tc_bool)*.
% 299.64/300.42 65078[0:SpR:28902.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),v_Procs))*.
% 299.64/300.42 65072[0:SpR:28902.0,353.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))**.
% 299.64/300.42 65048[0:SpR:28902.0,9569.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.42 65047[0:SpR:28902.0,9568.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w),tc_Com_Opname)),x),v_Procs),tc_bool)*.
% 299.64/300.42 65198[0:SpR:28903.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),v_Procs))*.
% 299.64/300.42 65192[0:SpR:28903.0,353.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))**.
% 299.64/300.42 65168[0:SpR:28903.0,9569.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,x),tc_Com_Opname)),v_Procs),tc_bool)*.
% 299.64/300.42 65167[0:SpR:28903.0,9568.0] || -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w),tc_Com_Opname)),x),v_Procs),tc_bool)*.
% 299.64/300.42 65991[0:SpR:65404.1,646.1] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.42 65985[0:SpR:65404.1,645.1] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.42 66698[0:SpR:1188.2,415.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)))**.
% 299.64/300.42 67453[0:SpR:1189.2,415.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)))**.
% 299.64/300.42 70088[0:Res:45357.1,11883.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_Com_Opname)),u))* -> .
% 299.64/300.42 70365[0:SpL:317.0,12983.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(x,w),y))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(v,x),t_a).
% 299.64/300.42 70436[0:Res:59525.1,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(t_a),v_x),v),v_x),tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(t_a),v_x),t_a)*.
% 299.64/300.42 70435[0:Res:59017.1,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(c_in(t_a),v_x),u),v_x),tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(t_a),v_x),t_a)*.
% 299.64/300.42 70432[7:Res:58968.1,70070.1] || equal(hAPP(c_in(t_a),v_x),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(c_in(t_a),v_x),u),v_x),tc_bool))* -> .
% 299.64/300.42 70431[0:Res:58969.1,70070.1] || equal(hAPP(c_in(t_a),v_x),v_Procs) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(c_in(t_a),v_x),u),v_x),tc_bool))* -> .
% 299.64/300.42 70430[7:Res:59476.1,70070.1] || equal(hAPP(c_in(t_a),v_x),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(t_a),v_x),v),v_x),tc_bool))* -> .
% 299.64/300.42 70429[0:Res:59477.1,70070.1] || equal(hAPP(c_in(t_a),v_x),v_Procs) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(t_a),v_x),v),v_x),tc_bool))* -> .
% 299.64/300.42 70565[0:SpL:141.1,1376.2] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u))** -> equal(c_HOL_Ominus__class_Ominus(w,v,u),c_HOL_Ozero__class_Ozero(u))**.
% 299.64/300.42 70604[7:SpL:55.1,70491.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(t_a,tc_bool)),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.64/300.42 70633[0:SpL:55.1,70492.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(t_a,tc_bool)),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.64/300.42 70896[0:SpL:542.0,6582.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v,tc_fun(u,tc_bool))*.
% 299.64/300.42 71155[0:Rew:533.0,71098.0] || -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y))),tc_fun(w,tc_bool))*.
% 299.64/300.42 71309[0:Res:7538.0,325.0] || -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),y))),tc_fun(v,tc_bool))*.
% 299.64/300.42 71308[0:Res:7538.0,324.0] || -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),u))),tc_fun(v,tc_bool))*.
% 299.64/300.42 71304[0:Res:7538.0,430.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),y,tc_fun(u,tc_bool))* -> c_lessequals(x,y,tc_fun(u,tc_bool)).
% 299.64/300.42 71298[0:SpR:533.0,7538.0] || -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(y,v),u))),tc_fun(v,tc_bool))*.
% 299.64/300.42 71359[0:SSi:71344.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(y,w),v)),tc_fun(w,tc_bool))*.
% 299.64/300.42 71376[7:SpL:130.1,71221.0] class_HOL_Ominus(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool))* equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_x) -> .
% 299.64/300.42 72031[7:Rew:72004.0,72014.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,t_a),v_x,tc_Com_Opname,u),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v_x,t_a),v_x,tc_Com_Opname,u),v_x).
% 299.64/300.42 72032[7:Rew:72004.0,72016.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),v_x).
% 299.64/300.42 72123[0:Res:7830.0,324.0] || -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),u))),tc_fun(w,tc_bool))*.
% 299.64/300.42 72695[0:SpL:21893.0,18903.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_x),u,v,w)* -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Ocom_OBODY,v_x),c_Com_Ocom_OBODY,tc_Com_Opname,x))),u,w)*.
% 299.64/300.42 72694[0:SpL:21267.0,18903.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_x),u,v,w)* -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,v_x),tc_Com_Opname,x))),u,w)*.
% 299.64/300.42 72823[0:Rew:66692.3,72751.5] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || equal(v,w) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)* -> equal(w,c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.42 74287[7:SpL:71835.1,325.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a))** c_lessequals(v_x,w,tc_fun(u,tc_bool))* -> c_lessequals(v,w,tc_fun(u,tc_bool))*.
% 299.64/300.42 74162[7:SpL:71835.1,519.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(hAPP(v_x,v),w))* -> hBOOL(hAPP(v_x,w)) hBOOL(hAPP(v,w)).
% 299.64/300.42 74161[7:SpL:71835.1,325.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) c_lessequals(hAPP(v_x,v),w,tc_fun(u,tc_bool))* -> c_lessequals(v_x,w,tc_fun(u,tc_bool)).
% 299.64/300.42 74160[7:SpL:71835.1,324.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) c_lessequals(hAPP(v_x,v),w,tc_fun(u,tc_bool))* -> c_lessequals(v,w,tc_fun(u,tc_bool)).
% 299.64/300.42 73728[7:SpR:71835.1,229.0] || equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v_x),c_Com_Ocom_OSKIP),c_Set_Oinsert(v_x,t_a)) -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.64/300.42 73664[7:SpR:71835.1,229.0] || equal(c_Set_Oinsert(v_x,t_a),c_Hoare__Mirabelle_Otriple_Otriple(u)) -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,c_Com_Ocom_OSKIP),v_x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.64/300.42 73602[7:SpR:71835.1,96.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_Fun_Oinj__on(u,v_x,v,w) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(v_x,u,v,w),v_x,w,v)*.
% 299.64/300.42 73522[7:SpR:71835.1,338.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(v_x,w)),hAPP(v_x,hAPP(c_Set_Oinsert(v,u),w)))**.
% 299.64/300.42 73352[7:SpR:71835.1,130.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Set_Oinsert(v_x,t_a)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),v_x)**.
% 299.64/300.42 74493[7:MRR:74268.1,6340.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,v_x)),v_x))* c_Hoare__Mirabelle_Otriple__valid(v,u,t_a)*.
% 299.64/300.42 74915[7:SpR:523.1,72297.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(v_x,v_x)))*.
% 299.64/300.42 74834[7:SpR:130.1,72297.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),v_x))*.
% 299.64/300.42 75002[0:Res:341.0,6845.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),w) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),w,tc_fun(u,tc_bool))*.
% 299.64/300.42 75509[0:Res:7820.1,146.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_HOL_Ouminus__class_Ouminus(x,u))),u),x,u)*.
% 299.64/300.42 75499[0:Res:7820.1,8141.2] class_Lattices_Oupper__semilattice(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Orderings_Otop__class_Otop(u))),u)*.
% 299.64/300.42 75963[0:Res:7823.1,146.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),x)),u),w,u)*.
% 299.64/300.42 75953[0:Res:7823.1,8141.2] class_Lattices_Oupper__semilattice(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x)),u)*.
% 299.64/300.42 76078[0:SSi:76077.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.42 76153[0:SpR:9915.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(v,w,x),y,z,x1,x2),x3,u),c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool)))))*.
% 299.64/300.42 76273[0:SpR:10469.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_Set_Oimage(v,w,x),y,z,x1,x2),x3,u),c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool)))))*.
% 299.64/300.42 76403[0:SpR:10470.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(v,w,x),y,z,x1,x2),x3,u),c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool)))))*.
% 299.64/300.42 76640[0:Res:29199.1,146.1] class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_HOL_Ouminus__class_Ouminus(x,u))),u),x,u)*.
% 299.64/300.42 76630[0:Res:29199.1,8141.2] class_Lattices_Olattice(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Orderings_Otop__class_Otop(u))),u)*.
% 299.64/300.42 76995[0:Res:30321.1,146.1] class_Lattices_Olattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),x)),u),w,u)*.
% 299.64/300.42 76985[0:Res:30321.1,8141.2] class_Lattices_Olattice(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x)),u)*.
% 299.64/300.42 77330[0:SpR:1605.2,2399.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,w) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u).
% 299.64/300.42 77329[0:SpR:1628.2,2399.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,w) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u).
% 299.64/300.42 77321[0:SpR:1421.2,2399.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) -> c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.42 77320[0:SpR:1409.2,2399.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) -> c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.42 77522[0:SpR:1605.2,2429.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,w) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u).
% 299.64/300.42 77521[0:SpR:1628.2,2429.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,w) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u).
% 299.64/300.42 77513[0:SpR:1421.2,2429.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) -> c_lessequals(v,c_Orderings_Otop__class_Otop(u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.42 77512[0:SpR:1409.2,2429.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) -> c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.42 77793[0:SpL:9.0,5892.0] || hBOOL(hAPP(hAPP(u,hAPP(v,w)),w))* -> hBOOL(hAPP(c_COMBS(c_in(x),c_Fun_Ocomp(u,v,y,z,x1),x2,x3,x4),w))*.
% 299.64/300.42 78336[7:SpR:78167.0,410.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,v,w,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,v,w,tc_fun(u,tc_bool)))**.
% 299.64/300.42 78539[4:MRR:9476.1,78524.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))**.
% 299.64/300.42 78738[4:Res:78665.1,496.0] || equal(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),v_x)** -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,v)),v))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.64/300.42 78705[4:Res:78665.1,469.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)),v_x)** -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(y,w,v,x,u)),v)**.
% 299.64/300.42 78704[4:Res:78665.1,464.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)),v_x)** -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(y,v,w,x,u)),v)**.
% 299.64/300.42 78945[0:SpR:338.0,15630.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(v,w),y)),z,u,w)))*.
% 299.64/300.42 78942[0:SpR:317.0,15630.1] || hBOOL(hAPP(u,hAPP(v,w))) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oinsert(w,x),z)),x1,u,y)))*.
% 299.64/300.42 79165[0:SpR:338.0,15858.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oinsert(v,x),z)),u,x)))*.
% 299.64/300.42 79162[0:SpR:317.0,15858.1] || hBOOL(hAPP(u,hAPP(v,w))) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oimage(v,y,z),hAPP(c_Set_Oinsert(w,y),x1)),u,z)))*.
% 299.64/300.42 80071[0:SpL:21268.0,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_in(u),hAPP(c_in(u),v),x,y)))*.
% 299.64/300.42 79961[0:SpR:10090.1,21268.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool),v,w)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.42 79952[0:SpR:303.1,21268.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(u),w,x)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.42 79945[0:SpR:3294.1,21268.0] || equal(c_in(t_a),u) -> equal(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_bool),v,w)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 79926[0:SpR:11177.1,21268.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,w,x)),u)**.
% 299.64/300.42 79892[0:SpR:87.1,21268.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(u),w,x)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.42 79861[0:SpR:3586.1,21268.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v,u),v_x,w,x)),v_x)**.
% 299.64/300.42 79860[7:SpR:27278.1,21268.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v,u),v_x,w,x)),v_x)**.
% 299.64/300.42 79853[0:SpR:365.1,21268.0] class_Orderings_Obot(u) || -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Orderings_Obot__class_Obot(u),v,w)),c_Orderings_Obot__class_Obot(u))**.
% 299.64/300.42 79852[0:SpR:397.1,21268.0] class_Orderings_Otop(u) || -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(u),v,w)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.42 79827[0:SpR:9493.1,21268.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),u,v,w)),u)**.
% 299.64/300.42 79824[0:SpR:8498.1,21268.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(hAPP(c_Set_Oinsert(w,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(w,v),u,x,y)),u)**.
% 299.64/300.42 79462[0:SpR:21268.0,526.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_in(w),hAPP(c_in(w),x),v,y)))* -> hBOOL(hAPP(hAPP(c_in(w),x),u)).
% 299.64/300.42 79357[0:SpR:21268.0,376.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool))*.
% 299.64/300.42 80345[0:Rew:25660.1,80251.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Obot__class_Obot(tc_bool)) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x),u)**.
% 299.64/300.42 81266[0:SpL:21894.0,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),c_in(u),x,y)))*.
% 299.64/300.42 81155[0:SpR:10090.1,21894.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),hAPP(u,v_x),v,w)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.42 81146[0:SpR:303.1,21894.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.42 81139[0:SpR:3294.1,21894.0] || equal(c_in(t_a),u) -> equal(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),hAPP(u,v_x),v,w)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 81120[0:SpR:11177.1,21894.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x)),u)**.
% 299.64/300.42 81086[0:SpR:87.1,21894.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.42 81055[0:SpR:3586.1,21894.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_x,c_Set_Oinsert(v,u),w,x)),v_x)**.
% 299.64/300.42 81054[7:SpR:27278.1,21894.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_x,c_Set_Oinsert(v,u),w,x)),v_x)**.
% 299.64/300.42 81047[0:SpR:365.1,21894.0] class_Orderings_Obot(u) || -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,w)),c_Orderings_Obot__class_Obot(u))**.
% 299.64/300.42 81046[0:SpR:397.1,21894.0] class_Orderings_Otop(u) || -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,w)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.42 81021[0:SpR:9493.1,21894.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,c_Set_Oinsert(v_x,t_a),v,w)),u)**.
% 299.64/300.42 81018[0:SpR:8498.1,21894.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(hAPP(c_Set_Oinsert(w,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,c_Set_Oinsert(w,v),x,y)),u)**.
% 299.64/300.42 80655[0:SpR:21894.0,526.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(w),x),c_in(w),v,y)))* -> hBOOL(hAPP(hAPP(c_in(w),x),u)).
% 299.64/300.42 80550[0:SpR:21894.0,376.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool))*.
% 299.64/300.42 81540[0:Rew:25660.1,81446.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Obot__class_Obot(tc_bool)) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,x),u)**.
% 299.64/300.42 81917[0:SpR:9.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(v,hAPP(w,x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Fun_Ocomp(v,w,y,z,x1),x2,x3,x4),x),u)*.
% 299.64/300.42 82389[0:SpR:9.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(v,hAPP(w,x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Fun_Ocomp(v,w,y,z,x1),x2,x3,x4),x),u)*.
% 299.64/300.42 82715[0:Res:111.2,7671.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* c_lessequals(x,c_HOL_Ouminus__class_Ouminus(w,u),u)* -> c_lessequals(x,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.42 82714[0:Res:41.2,7671.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.64/300.42 82712[0:Res:52.2,7671.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(x,c_HOL_Ominus__class_Ominus(v,w,u),u)* -> c_lessequals(x,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.42 82707[0:Res:53.2,7671.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,u),u)* -> c_lessequals(w,c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.42 83114[0:SpL:5924.0,55174.1] || equal(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(hAPP(v,v_x),w))* -> .
% 299.64/300.42 83110[0:SpL:5924.0,3698.2] || equal(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(hAPP(v,v_x),w),c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 83105[4:SpL:5924.0,46565.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool)),hAPP(hAPP(u,v_x),v))* -> .
% 299.64/300.42 83092[0:SpL:5924.0,55174.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool),hAPP(x2,v_x))* -> .
% 299.64/300.42 83053[0:SpR:5924.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,x3),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool))),hAPP(hAPP(u,x4),v)))*.
% 299.64/300.42 83020[0:SpR:5924.0,3339.1] || equal(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2))* -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(hAPP(v,v_x),w),x3,x4),u)**.
% 299.64/300.42 83019[0:SpR:5924.0,3316.1] || equal(c_in(u),c_COMBS(v,c_COMBK(w,x,y),z,x1,x2))* -> hBOOL(hAPP(hAPP(hAPP(v,v_x),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.42 83016[0:SpR:5924.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(v,v_x),w)),hAPP(c_Set_Oimage(c_COMBS(v,c_COMBK(w,x,y),z,x1,x2),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.42 83001[0:SpR:5924.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(u,v_x),v),c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname,x2),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 82999[0:SpR:5924.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(u,v_x),v),c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname,x2)),v_Procs))*.
% 299.64/300.42 82995[0:SpR:5924.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),hAPP(hAPP(u,v_x),v),tc_Com_Opname,x2),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 82993[0:SpR:5924.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),hAPP(hAPP(u,v_x),v),tc_Com_Opname,x2)),v_Procs))*.
% 299.64/300.42 82992[0:SpR:5924.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),t_a,x2),c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool))),hAPP(hAPP(u,v_x),v)))*.
% 299.64/300.42 82990[0:SpR:5924.0,11030.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),v),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool))))*.
% 299.64/300.42 82989[0:SpR:5924.0,10090.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(hAPP(u,v_x),v),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.42 82980[0:SpR:5924.0,3284.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(x2),v_Procs),hAPP(hAPP(u,v_x),v)))*.
% 299.64/300.42 82976[2:SpR:5924.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool)).
% 299.64/300.42 82974[0:SpR:5924.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool)).
% 299.64/300.42 82973[7:SpR:5924.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool)).
% 299.64/300.42 82970[0:SpR:5924.0,651.0] || -> c_lessequals(hAPP(hAPP(u,v_x),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.64/300.42 82962[0:SpR:5924.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,x3),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(hAPP(u,v_Procs),v)))*.
% 299.64/300.42 83147[0:Rew:5924.0,83128.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname)),v))* -> hBOOL(hAPP(hAPP(u,v_x),v)).
% 299.64/300.42 83148[0:Rew:5924.0,83070.0] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname)),v))*.
% 299.64/300.42 83209[7:SpR:130.1,78357.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x,y),v_x),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)))*.
% 299.64/300.42 83434[0:SpL:5961.0,55174.1] || equal(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(v,hAPP(y,v_x)))* -> .
% 299.64/300.42 83430[0:SpL:5961.0,3698.2] || equal(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(v,hAPP(y,v_x)),c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 83425[4:SpL:5961.0,46565.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool)),hAPP(u,hAPP(x,v_x)))* -> .
% 299.64/300.42 83412[0:SpL:5961.0,55174.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(x,v_x)),tc_bool),hAPP(x2,v_x))* -> .
% 299.64/300.42 83378[0:SpR:5961.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2,x3),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool))),hAPP(u,hAPP(x,x4))))*.
% 299.64/300.42 83351[0:SpR:5961.0,3339.1] || equal(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2))* -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(v,hAPP(y,v_x)),x3,x4),u)**.
% 299.64/300.42 83350[0:SpR:5961.0,3316.1] || equal(c_in(u),c_COMBS(c_COMBK(v,w,x),y,z,x1,x2))* -> hBOOL(hAPP(hAPP(v,hAPP(y,v_x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.42 83347[0:SpR:5961.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,v_x))),hAPP(c_Set_Oimage(c_COMBS(c_COMBK(v,x,y),w,z,x1,x2),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.42 83331[0:SpR:5961.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,hAPP(v,v_x)),c_COMBS(c_COMBK(u,w,x),v,y,z,x1),tc_Com_Opname,x2),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 83329[0:SpR:5961.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,hAPP(v,v_x)),c_COMBS(c_COMBK(u,w,x),v,y,z,x1),tc_Com_Opname,x2)),v_Procs))*.
% 299.64/300.42 83325[0:SpR:5961.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(c_COMBK(u,v,w),x,y,z,x1),hAPP(u,hAPP(x,v_x)),tc_Com_Opname,x2),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 83323[0:SpR:5961.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(c_COMBK(u,v,w),x,y,z,x1),hAPP(u,hAPP(x,v_x)),tc_Com_Opname,x2)),v_Procs))*.
% 299.64/300.42 83322[0:SpR:5961.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),t_a,x2),c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool))),hAPP(u,hAPP(x,v_x))))*.
% 299.64/300.42 83320[0:SpR:5961.0,11030.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_in(t_a))** -> hBOOL(hAPP(hAPP(u,hAPP(x,v_x)),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool))))*.
% 299.64/300.42 83319[0:SpR:5961.0,10090.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(u,hAPP(x,v_x)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.64/300.42 83310[0:SpR:5961.0,3284.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(x2),v_Procs),hAPP(u,hAPP(x,v_x))))*.
% 299.64/300.42 83306[2:SpR:5961.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(x,v_x)),tc_bool)).
% 299.64/300.42 83304[0:SpR:5961.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(x,v_x)),tc_bool)).
% 299.64/300.42 83303[7:SpR:5961.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(x,v_x)),tc_bool)).
% 299.64/300.42 83300[0:SpR:5961.0,651.0] || -> c_lessequals(hAPP(u,hAPP(v,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBS(c_COMBK(u,w,x),v,y,z,x1),tc_Com_Opname,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.64/300.42 83297[0:SpR:5961.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2,x3),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(u,hAPP(x,v_Procs))))*.
% 299.64/300.42 83457[0:Rew:5961.0,83447.1] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_COMBS(c_COMBK(u,w,x),v,y,z,x1),tc_Com_Opname))))* -> hBOOL(hAPP(u,hAPP(v,v_x))).
% 299.64/300.42 83458[0:Rew:5961.0,83393.0] || hBOOL(hAPP(u,hAPP(v,v_x))) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_COMBS(c_COMBK(u,w,x),v,y,z,x1),tc_Com_Opname))))*.
% 299.64/300.42 83763[0:SpR:5899.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,v,w,x,y),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),hAPP(c_COMBS(u,v,x2,x3,x4),x5)))*.
% 299.64/300.42 84107[4:SpL:55.1,78769.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(t_a,tc_bool)),v_x),tc_bool),v_x)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.64/300.42 84790[7:SSi:84764.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,w)),v_x),v_x,tc_bool)* -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,w)),v_x),v_x).
% 299.64/300.42 84791[7:SSi:84761.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,w)),v_x),v_x) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,w)),v_x),v_x,tc_bool)*.
% 299.64/300.42 84816[7:SpR:78315.0,118.0] || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,c_Set_Oinsert(v_x,v),w,x,y),v_x,hAPP(u,v_x),y,x),c_Fun_Ocomp(u,c_Set_Oinsert(v_x,v),w,x,y))**.
% 299.64/300.42 84921[4:SpL:9.0,78744.0] || equal(hAPP(u,hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Fun_Ocomp(u,v,w,x,y),z))),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(c_Fun_Ocomp(u,v,w,x,y),z,t_a).
% 299.64/300.42 84892[4:SpL:299.2,78744.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v,u)* equal(v,v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,t_a).
% 299.64/300.42 85059[0:SpR:644.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),w,tc_fun(x,tc_bool)),v_Procs),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool)*.
% 299.64/300.42 85954[0:Res:1103.1,13582.0] || hBOOL(hAPP(hAPP(c_in(u),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)))),x))* -> c_Hoare__Mirabelle_Ohoare__valids(v,c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),t_a).
% 299.64/300.42 86026[0:SpL:130.1,86011.0] class_HOL_Ominus(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool))* equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_Procs) -> .
% 299.64/300.42 87093[0:Rew:6.0,86995.3] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(v,x,tc_fun(w,tc_bool))* c_lessequals(x,u,tc_fun(w,tc_bool))* -> equal(x,v).
% 299.64/300.42 87416[7:MRR:87275.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),x))*.
% 299.64/300.42 87501[7:MRR:87423.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),x,t_a)*.
% 299.64/300.42 87687[7:MRR:87553.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))*.
% 299.64/300.42 88334[0:Res:7227.0,278.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(c_COMBK(v,w,x),y,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),x1,u,z)))*.
% 299.64/300.42 88333[0:Res:7227.0,277.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oimage(c_COMBK(v,x,y),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),u,x1)))*.
% 299.64/300.42 88329[0:Res:7227.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oimage(c_COMBK(v,w,x),y,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,v,t_a).
% 299.64/300.42 88437[0:Res:8176.1,357.1] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool))* c_Finite__Set_Ofinite(y,w) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,z,tc_fun(x,tc_bool)),x)*.
% 299.64/300.42 88985[4:SpR:78507.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,u),v,w),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))*.
% 299.64/300.42 88962[0:SpR:9987.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),u,v),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.42 88960[0:SpR:2095.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.64/300.42 88955[0:SpR:303.1,14196.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.42 88950[0:SpR:23902.1,14196.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.42 88942[0:SpR:330.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))*.
% 299.64/300.42 88936[0:SpR:14216.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,y),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),z))*.
% 299.64/300.42 88933[0:SpR:11176.1,14196.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),x))*.
% 299.64/300.42 88929[0:SpR:11177.1,14196.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),hAPP(c_Set_Oinsert(u,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),u))*.
% 299.64/300.42 88876[0:SpR:331.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),x))*.
% 299.64/300.42 88875[0:SpR:302.1,14196.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),x))*.
% 299.64/300.42 88865[0:SpR:34428.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_x))*.
% 299.64/300.42 88858[0:SpR:15476.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v,w),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_x))*.
% 299.64/300.42 88837[0:SpR:34427.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))*.
% 299.64/300.42 88836[0:SpR:2093.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_Procs,u),v,w),hAPP(c_Set_Oinsert(hAPP(c_in(tc_Com_Opname),v_x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),hAPP(c_in(tc_Com_Opname),v_x)))*.
% 299.64/300.42 88833[0:SpR:3744.1,14196.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,u),v,w),hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_Procs))*.
% 299.64/300.42 89074[7:SpR:35.2,78350.0] || c_lessequals(u,c_Set_Oinsert(v_x,v),tc_fun(w,tc_bool))* c_lessequals(c_Set_Oinsert(v_x,v),x,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(u,v_x),v_x,tc_bool).
% 299.64/300.42 89365[7:SpR:78590.1,14196.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),u))*.
% 299.64/300.42 89710[7:Res:89344.1,473.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),c_Set_Oinsert(v_x,t_a)) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,t_a),v_x)),w))*.
% 299.64/300.42 89697[7:Res:89344.1,356.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(c_Set_Oimage(c_COMBK(v,w,t_a),t_a,w),u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.64/300.42 89949[0:SpL:26183.0,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,w),x),u,w)))* hBOOL(hAPP(hAPP(c_in(w),y),x))* -> hBOOL(hAPP(u,y))*.
% 299.64/300.42 89792[0:SpR:26183.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,u),v)),hAPP(c_Set_Oinsert(y,u),v),tc_bool)*.
% 299.64/300.42 89785[0:SpR:26183.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.64/300.42 89765[0:SpR:26183.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y,z,x1),hAPP(c_Set_Oinsert(u,v),w)))*.
% 299.64/300.42 90155[4:SpR:78660.1,14196.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),u))*.
% 299.64/300.42 90603[4:Rew:104.0,90501.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))*.
% 299.64/300.42 90854[4:Res:90134.1,473.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),v_x) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,t_a),v_x)),w))*.
% 299.64/300.42 90841[4:Res:90134.1,356.0] || equal(hAPP(u,v_x),v_x) -> equal(hAPP(c_Set_Oimage(c_COMBK(v,w,t_a),t_a,w),u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.64/300.42 91406[0:Res:91291.2,251.1] class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,v)) class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,v)),w),hAPP(x,w),v)*.
% 299.64/300.42 91477[0:Res:91292.2,251.1] class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,v)) class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,v)),w),hAPP(x,w),v)*.
% 299.64/300.42 91673[0:SpR:1250.3,91289.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Ogroup__add(u) class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ozero__class_Ozero(u)),v)**.
% 299.64/300.42 91948[0:SpR:79073.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_Procs,u),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.64/300.42 92101[7:SpR:79101.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,u),v,w),hAPP(c_Set_Oinsert(hAPP(c_in(x),v_x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),hAPP(c_in(x),v_x)))*.
% 299.64/300.42 92717[7:MRR:92599.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Set_Oinsert(v_x,x)))*.
% 299.64/300.42 93216[0:SpR:5878.1,9567.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,tc_fun(x1,tc_bool)),c_Orderings_Obot__class_Obot(u)),hAPP(v,c_Orderings_Obot__class_Obot(u)),tc_bool)*.
% 299.64/300.42 93215[0:SpR:5878.1,7253.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),hAPP(v,c_Orderings_Obot__class_Obot(u))))*.
% 299.64/300.42 93438[7:MRR:93259.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),x),tc_bool)*.
% 299.64/300.42 93589[7:MRR:93447.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),x))*.
% 299.64/300.42 93676[7:MRR:93598.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),x,t_a)*.
% 299.64/300.42 93876[7:MRR:93742.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))*.
% 299.64/300.42 93996[7:SpR:78590.1,10791.0] || equal(hAPP(c_Set_Oinsert(u,t_a),v),c_Set_Oinsert(v_x,t_a)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),v),hAPP(c_Set_Oinsert(u,t_a),v),tc_fun(t_a,tc_bool))*.
% 299.64/300.42 93995[4:SpR:78660.1,10791.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),v),v_x),v_x) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),v),hAPP(c_Set_Oinsert(u,t_a),v),tc_fun(t_a,tc_bool))*.
% 299.64/300.42 94191[0:Res:14364.3,12626.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,w,tc_bool),x,tc_bool)))* c_Finite__Set_Ofinite(u,tc_bool) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(u,tc_bool),v,tc_bool).
% 299.64/300.42 94188[0:Res:14364.3,12719.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,c_HOL_Ominus__class_Ominus(v,w,tc_bool)))* c_Finite__Set_Ofinite(u,tc_bool) -> c_lessequals(c_HOL_Ominus__class_Ominus(c_Finite__Set_Olinorder__class_OMin(u,tc_bool),x,tc_bool),v,tc_bool)*.
% 299.64/300.42 94187[0:Res:14364.3,10214.1] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) equal(c_Finite__Set_Olinorder__class_OMin(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(c_Finite__Set_Olinorder__class_OMin(u,tc_bool),v).
% 299.64/300.42 94182[0:Res:14364.3,38189.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) hBOOL(c_Finite__Set_Olinorder__class_OMin(u,tc_bool)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v))*.
% 299.64/300.42 94181[0:Res:14364.3,38190.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) hBOOL(c_Finite__Set_Olinorder__class_OMin(u,tc_bool)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w))*.
% 299.64/300.42 94180[0:Res:14364.3,50575.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) equal(v,c_Orderings_Obot__class_Obot(tc_bool)) hBOOL(c_Finite__Set_Olinorder__class_OMin(u,tc_bool)) -> hBOOL(w)*.
% 299.64/300.42 94179[0:Res:14364.3,50366.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,w,tc_bool)* hBOOL(c_Finite__Set_Olinorder__class_OMin(u,tc_bool)) -> hBOOL(w).
% 299.64/300.42 94330[0:Res:14491.3,36528.1] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,hAPP(v_Procs,v_x)))* c_Finite__Set_Ofinite(u,tc_bool) equal(c_in(tc_Com_Opname),c_in(t_a)) -> hBOOL(c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.64/300.42 94329[0:Res:14491.3,46309.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)))* c_Finite__Set_Ofinite(u,tc_bool) hBOOL(w) -> hBOOL(c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.64/300.42 94328[0:Res:14491.3,46413.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)))* c_Finite__Set_Ofinite(u,tc_bool) hBOOL(v) -> hBOOL(c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.64/300.42 94323[4:Res:14491.3,47549.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool)))* c_Finite__Set_Ofinite(u,tc_bool) -> hBOOL(c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.64/300.42 94319[0:Res:14491.3,24120.1] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) equal(c_Finite__Set_Olinorder__class_OMax(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) -> equal(v,c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.64/300.42 94308[0:Res:14491.3,38189.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),c_Finite__Set_Olinorder__class_OMax(u,tc_bool)))*.
% 299.64/300.42 94307[0:Res:14491.3,38190.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Finite__Set_Olinorder__class_OMax(u,tc_bool)),w))*.
% 299.64/300.42 94306[0:Res:14491.3,50575.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) equal(c_Finite__Set_Olinorder__class_OMax(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) hBOOL(v) -> hBOOL(w)*.
% 299.64/300.42 94305[0:Res:14491.3,50366.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,v))* c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(c_Finite__Set_Olinorder__class_OMax(u,tc_bool),w,tc_bool)* hBOOL(v) -> hBOOL(w).
% 299.64/300.42 94277[7:Res:14491.3,71908.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,v_x)) c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),v_x))*.
% 299.64/300.42 94264[0:Res:14491.3,1051.0] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) || hBOOL(hAPP(u,v_Procs)) c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMax(u,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.42 700[0:Res:589.0,594.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_xa),v_G)) c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(v_Q,v_x)),t_a)*.
% 299.64/300.42 663[0:Res:589.0,268.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))* equal(hAPP(v,u),hAPP(v,v_x))* c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,w)* -> equal(u,v_x).
% 299.64/300.42 681[0:Res:589.0,494.1] || c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(tc_Com_Opname)),v),w),t_a)* c_Natural_Oevaln(v,v_Procs,u,x)* -> hBOOL(hAPP(hAPP(w,v_x),x))*.
% 299.64/300.42 2157[0:SpR:141.1,47.2] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ominus__class_Ominus(v,w,u),u) -> c_lessequals(c_HOL_Ominus__class_Ominus(w,v,u),c_HOL_Ominus__class_Ominus(v,w,u),u)*.
% 299.64/300.42 2178[0:Res:1145.0,2092.0] || -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_Procs,u,v),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_Procs,u,v),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)))**.
% 299.64/300.42 2232[0:SpR:141.1,43.2] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ominus__class_Ominus(v,w,u),u) -> c_lessequals(c_HOL_Ominus__class_Ominus(w,v,u),c_HOL_Ominus__class_Ominus(v,w,u),u)*.
% 299.64/300.42 2392[0:SpL:141.1,48.1] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ominus__class_Ominus(w,v,u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ominus__class_Ominus(w,v,u),u).
% 299.64/300.42 2422[0:SpL:141.1,44.1] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ominus__class_Ominus(w,v,u),u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ominus__class_Ominus(w,v,u),u).
% 299.64/300.42 2452[0:SpR:141.1,49.2] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ominus__class_Ominus(w,v,u),u)*.
% 299.64/300.42 2480[0:SpR:141.1,45.2] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ominus__class_Ominus(w,v,u),u)*.
% 299.64/300.42 2508[0:SpL:141.1,50.1] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ominus__class_Ominus(w,v,u),u)* -> c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.42 2534[0:SpL:141.1,46.1] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ominus__class_Ominus(w,v,u),u)* -> c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u),u).
% 299.64/300.42 3224[0:SpL:2771.1,50.1] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || equal(u,v) c_lessequals(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),tc_bool)* -> c_lessequals(hAPP(u,v_x),c_HOL_Ozero__class_Ozero(tc_bool),tc_bool).
% 299.64/300.42 3155[0:SpR:2771.1,49.2] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || equal(u,v) c_lessequals(hAPP(u,v_x),c_HOL_Ozero__class_Ozero(tc_bool),tc_bool) -> c_lessequals(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),tc_bool)*.
% 299.64/300.42 3153[0:SpR:2771.1,47.2] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || equal(u,v) c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),hAPP(u,v_x),tc_bool) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),hAPP(u,v_x),tc_bool)*.
% 299.64/300.42 4228[0:SpR:299.2,687.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),tc_Com_Opname),w,u)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)) -> hBOOL(w).
% 299.64/300.42 4227[0:SpR:299.2,686.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),tc_Com_Opname),w,u)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)) -> hBOOL(w).
% 299.64/300.42 4441[0:Res:687.1,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),v_x)) -> hBOOL(hAPP(x,hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,v_Procs,hAPP(c_Set_Ovimage(u,v,w),x),tc_Com_Opname))))*.
% 299.64/300.42 4440[0:Res:686.1,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),v_x)) -> hBOOL(hAPP(x,hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,y,hAPP(c_Set_Ovimage(u,v,w),x),tc_Com_Opname))))*.
% 299.64/300.42 5967[0:SpR:330.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y,z),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),hAPP(v,hAPP(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))**.
% 299.64/300.42 5963[0:SpR:87.1,584.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y,z),c_HOL_Ouminus__class_Ouminus(v,u)),hAPP(c_Orderings_Otop__class_Otop(u),hAPP(w,c_HOL_Ouminus__class_Ouminus(v,u))))**.
% 299.64/300.42 5959[0:SpR:540.1,584.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y,z),x1),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),v),hAPP(w,x1)))*.
% 299.64/300.42 5958[0:SpR:539.1,584.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y,z),x1),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),v),hAPP(w,x1)))*.
% 299.64/300.42 5957[0:SpR:297.2,584.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y,z,x1),w),hAPP(w,hAPP(x,w)))*.
% 299.64/300.42 5950[0:SpR:299.2,584.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z,x1),v),hAPP(w,hAPP(x,v)))**.
% 299.64/300.42 5944[0:SpR:2093.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oinsert(v_Procs,u),v,w,x,y),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(v,hAPP(c_in(tc_Com_Opname),v_x))))**.
% 299.64/300.42 5937[0:SpR:2095.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oinsert(v,w),x,y,z),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))**.
% 299.64/300.42 5930[0:SpR:330.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y,z),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w))**.
% 299.64/300.42 5927[0:SpR:337.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w,x,y),z),hAPP(hAPP(u,z),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))**.
% 299.64/300.42 5926[0:SpR:87.1,584.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),c_HOL_Ouminus__class_Ouminus(w,u)),hAPP(hAPP(v,c_HOL_Ouminus__class_Ouminus(w,u)),c_Orderings_Otop__class_Otop(u)))**.
% 299.64/300.42 5922[0:SpR:540.1,584.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),x1),hAPP(hAPP(v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),w)))*.
% 299.64/300.42 5921[0:SpR:539.1,584.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),x1),hAPP(hAPP(v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),w)))*.
% 299.64/300.42 5920[0:SpR:297.2,584.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(c_COMBS(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,z,x1),w),hAPP(hAPP(x,w),w))*.
% 299.64/300.42 5913[0:SpR:299.2,584.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(c_COMBS(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,z,x1),v),hAPP(hAPP(x,v),w))**.
% 299.64/300.42 5907[0:SpR:2093.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oinsert(v_Procs,v),w,x,y),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(hAPP(u,hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_in(tc_Com_Opname),v_x)))**.
% 299.64/300.42 5873[0:SpR:584.0,584.0] || -> equal(hAPP(c_COMBS(c_COMBS(u,v,w,x,y),z,x1,x2,x3),x4),hAPP(hAPP(hAPP(u,x4),hAPP(v,x4)),hAPP(z,x4)))*.
% 299.64/300.42 5872[0:SpR:584.0,584.0] || -> equal(hAPP(c_COMBS(u,c_COMBS(v,w,x,y,z),x1,x2,x3),x4),hAPP(hAPP(u,x4),hAPP(hAPP(v,x4),hAPP(w,x4))))*.
% 299.64/300.42 6196[0:SpR:599.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v))**.
% 299.64/300.42 6435[0:SpR:538.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v),x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v))**.
% 299.64/300.42 6420[0:SpR:538.0,2771.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.42 6415[0:SpR:538.0,3279.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),v_Procs),v_x))*.
% 299.64/300.42 6511[0:SpR:538.0,3285.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.42 6654[0:SpR:329.1,3285.1] || c_lessequals(v_x,hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),tc_fun(v,tc_bool))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs)).
% 299.64/300.42 6634[0:SpR:329.1,415.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v,v,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u))**.
% 299.64/300.42 6616[0:SpR:329.1,3285.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.42 6613[0:SpR:329.1,3279.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(v_x,v_Procs),v_x)).
% 299.64/300.42 6750[0:SpR:329.1,3291.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),v_x),v_Procs))*.
% 299.64/300.42 6749[0:SpR:538.0,3291.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)),v_Procs))*.
% 299.64/300.42 6827[0:SpR:328.1,1103.1] || c_lessequals(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)),w,tc_fun(v,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),t_a) hBOOL(w).
% 299.64/300.42 6796[0:SpR:328.1,415.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),u,v,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v))**.
% 299.64/300.42 6781[0:SpR:328.1,2771.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool))*.
% 299.64/300.42 6778[0:SpR:328.1,3291.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),u),v_Procs))*.
% 299.64/300.42 6777[0:SpR:328.1,3285.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(u,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.64/300.42 6774[0:SpR:328.1,3279.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(u,v_Procs),v_x)).
% 299.64/300.42 6881[0:SpL:329.1,3484.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Com_Ocom_OBODY)** equal(hAPP(c_Com_Ocom_OBODY,w),v_x)** -> equal(v_x,w).
% 299.64/300.42 6880[0:SpL:328.1,3484.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Com_Ocom_OBODY)** equal(u,hAPP(c_Com_Ocom_OBODY,w))* -> equal(v_x,w).
% 299.64/300.42 6879[0:SpL:538.0,3484.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),hAPP(c_Com_Ocom_OBODY,w))* -> equal(v_x,w).
% 299.64/300.42 6915[0:SpL:538.0,3499.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.42 7138[0:SpR:329.1,3305.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,tc_Com_Opname,x),v_Procs),v_x))*.
% 299.64/300.42 7137[0:SpR:328.1,3305.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,tc_Com_Opname,x),v_Procs),u))*.
% 299.64/300.42 7136[0:SpR:538.0,3305.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w)))*.
% 299.64/300.42 7189[0:SpR:329.1,3317.1] || c_lessequals(v_x,hAPP(c_Set_Oinsert(v_x,u),v),tc_fun(w,tc_bool))* equal(c_in(u),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool))) -> hBOOL(hAPP(c_Set_Oinsert(v_x,u),v)).
% 299.64/300.42 7181[0:SpR:329.1,3317.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,w),x)))*.
% 299.64/300.42 7180[0:SpR:328.1,3317.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> hBOOL(hAPP(u,hAPP(c_Set_Oinsert(v_x,w),x)))*.
% 299.64/300.42 7179[0:SpR:538.0,3317.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),hAPP(c_Set_Oinsert(v_x,u),x)))*.
% 299.64/300.42 7252[0:Res:474.0,279.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))),hAPP(c_Set_Oimage(u,x,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))**.
% 299.64/300.42 7250[0:SpR:586.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,x))),hAPP(c_Set_Oimage(hAPP(c_COMBB(v,y,z,x1),w),x2,u),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)))))*.
% 299.64/300.42 7249[0:SpR:585.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(v,w),x)),hAPP(c_Set_Oimage(hAPP(c_COMBC(v,y,z,x1),x),x2,u),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)))))*.
% 299.64/300.42 7198[0:SpR:445.1,474.0] || -> equal(u,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(x,u)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,z,x1),x2,w),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)))))*.
% 299.64/300.42 7342[0:SpL:328.1,3507.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* equal(u,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> .
% 299.64/300.42 7341[0:SpL:538.0,3507.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.42 7455[0:Res:364.1,402.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Oinsert(x,w),v),u,tc_fun(w,tc_bool))* -> equal(u,hAPP(c_Set_Oinsert(x,w),v)).
% 299.64/300.42 7514[0:SpR:329.1,3346.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> hBOOL(hAPP(hAPP(c_in(x),w),v_x))*.
% 299.64/300.42 7513[0:SpR:328.1,3346.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> hBOOL(hAPP(hAPP(c_in(x),w),u))*.
% 299.64/300.42 7512[0:SpR:538.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x)) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),x)))*.
% 299.64/300.42 8148[0:Res:293.2,427.1] class_Lattices_Oupper__semilattice(u) class_Orderings_Opreorder(u) || c_lessequals(v,w,u)* c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),y,u)* -> c_lessequals(v,y,u)*.
% 299.64/300.42 8145[0:Res:294.2,427.1] class_Lattices_Oupper__semilattice(u) class_Orderings_Opreorder(u) || c_lessequals(v,w,u)* c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w),y,u)* -> c_lessequals(v,y,u)*.
% 299.64/300.42 8982[0:SpL:8415.2,295.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** c_lessequals(v_x,w,u)* -> c_lessequals(v,w,u)*.
% 299.64/300.42 8980[0:SpL:8415.2,311.1] class_Lattices_Obounded__lattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_Orderings_Obot__class_Obot(u),v_x) -> equal(v,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.42 8968[0:SpL:8415.2,296.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(hAPP(v_x,v),w,u)* -> c_lessequals(v,w,u).
% 299.64/300.42 8967[0:SpL:8415.2,295.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(hAPP(v_x,v),w,u)* -> c_lessequals(v_x,w,u).
% 299.64/300.42 8965[0:SpL:8415.2,311.1] class_Lattices_Obounded__lattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) equal(hAPP(v_x,v),c_Orderings_Obot__class_Obot(u))* -> equal(c_Orderings_Obot__class_Obot(u),v_x).
% 299.64/300.42 8963[0:SpL:8415.2,327.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(hAPP(v_x,v),v) -> c_lessequals(v_x,v,tc_fun(u,tc_bool))*.
% 299.64/300.42 8897[0:SpR:8415.2,328.1] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname))** c_lessequals(v_x,v,tc_fun(u,tc_bool)) -> equal(v_x,v).
% 299.64/300.42 8895[0:SpR:8415.2,538.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),v_x)**.
% 299.64/300.42 8892[0:SpR:8415.2,293.2] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** c_lessequals(w,v,u)* -> c_lessequals(w,v_x,u)*.
% 299.64/300.42 8877[0:SpR:8415.2,294.2] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v,w,u) -> c_lessequals(v,hAPP(v_x,w),u)*.
% 299.64/300.42 8873[0:SpR:8415.2,474.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(u,w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.42 8872[0:SpR:8415.2,538.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(v_x,v))**.
% 299.64/300.42 8870[0:SpR:8415.2,293.2] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v,v_x,u) -> c_lessequals(v,hAPP(v_x,w),u)*.
% 299.64/300.42 8821[0:SpR:8415.2,328.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(v,v_x,tc_fun(u,tc_bool))* -> equal(hAPP(v_x,v),v_x).
% 299.64/300.42 8820[0:SpR:8415.2,599.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.64/300.42 8754[0:SpR:8415.2,329.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(v_x,v,tc_fun(u,tc_bool))* -> equal(hAPP(v_x,v),v).
% 299.64/300.42 9029[1:MRR:8733.2,589.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),v_P) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_x),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(v_Q,v_x)),t_a)*.
% 299.64/300.42 9030[1:MRR:8731.2,589.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Com_Ocom_OBODY) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),v_x),hAPP(v_Q,v_x)),t_a)*.
% 299.64/300.42 9031[1:MRR:8730.2,589.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),v_Q) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_x),t_a)*.
% 299.64/300.42 9111[0:SSi:9090.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))*.
% 299.64/300.42 9112[0:SSi:9087.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x)))*.
% 299.64/300.42 9172[0:SpR:329.1,8376.2] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(tc_Com_Opname))** equal(w,v_Procs) -> hBOOL(hAPP(v_x,w))*.
% 299.64/300.42 9171[0:SpR:328.1,8376.2] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(tc_Com_Opname))** equal(w,v_Procs) -> hBOOL(hAPP(u,w))*.
% 299.64/300.42 9170[0:SpR:538.0,8376.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) equal(w,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),w))*.
% 299.64/300.42 9477[0:SpR:9.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Fun_Ocomp(u,v,w,x,y)),c_Fun_Ocomp(u,v,w,x,y))**.
% 299.64/300.42 9471[0:SpR:88.1,9268.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)))**.
% 299.64/300.42 9469[0:SpR:540.1,9268.0] class_Lattices_Olattice(u) || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)).
% 299.64/300.42 9468[0:SpR:539.1,9268.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)).
% 299.64/300.42 9460[0:SpR:299.2,9268.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> hBOOL(c_HOL_Ouminus__class_Ouminus(v,tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.64/300.42 9541[0:Res:989.1,251.1] class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(w,y,z),tc_Com_Opname,tc_fun(u,v)),x),v)*.
% 299.64/300.42 10177[0:SSi:10144.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),w,z)* -> c_Fun_Oinj__on(x,u,w,z)*.
% 299.64/300.42 10178[0:SSi:10141.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v),w,z)* -> c_Fun_Oinj__on(x,u,w,z)*.
% 299.64/300.42 10507[0:Res:3285.1,454.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),v),v_x,t_a)*.
% 299.64/300.42 10506[0:Res:3317.1,454.0] || equal(c_in(u),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v_x,u),v),w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oinsert(v_x,u),v),w),v_x,t_a)*.
% 299.64/300.42 10907[0:SpL:353.0,363.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),y,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(u,v),x),y,tc_fun(v,tc_bool)).
% 299.64/300.42 10851[0:SpR:353.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),y))),hAPP(c_Set_Oimage(c_Set_Oinsert(x,w),z,u),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.64/300.42 10845[0:SpR:353.0,364.1] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(y,w),x)),tc_fun(w,tc_bool))*.
% 299.64/300.42 10842[0:SpR:353.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),y),c_Set_Oinsert(w,v),z,x1,x2),hAPP(c_Set_Oinsert(u,v),x)))*.
% 299.64/300.42 11039[0:SpR:9987.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oinsert(v_x,t_a),v,w,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),hAPP(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))))*.
% 299.64/300.42 11440[0:SpL:584.0,344.0] || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> equal(hAPP(v,z),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.64/300.42 11587[0:SpR:353.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(u,v),w,tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,v),z)),hAPP(c_Set_Oinsert(y,v),hAPP(c_Set_Oinsert(u,v),z)),tc_bool)*.
% 299.64/300.42 11750[0:SpL:130.1,3506.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(x,y),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))* -> .
% 299.64/300.42 11732[0:SpR:130.1,9566.0] class_HOL_Ominus(u) || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),hAPP(hAPP(c_Set_Oinsert(x,y),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u))),v_x),tc_bool)*.
% 299.64/300.42 11892[0:Rew:8415.2,11877.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,v)) hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))))* -> .
% 299.64/300.42 12390[0:SpL:584.0,324.0] || c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),x1,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(v,z),x1,tc_fun(u,tc_bool)).
% 299.64/300.42 12559[0:Rew:8415.2,12549.3] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))))* -> hBOOL(hAPP(v_x,v)).
% 299.64/300.42 12655[0:SpL:584.0,519.0] || hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),x1))* -> hBOOL(hAPP(z,x1)) hBOOL(hAPP(hAPP(v,z),x1)).
% 299.64/300.42 12690[4:MRR:12662.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(w,v_x)).
% 299.64/300.42 12986[0:Res:149.1,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),w),v))* c_Hoare__Mirabelle_Otriple__valid(u,w,t_a)*.
% 299.64/300.42 12977[0:SpL:3229.1,501.0] || equal(u,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v))* hBOOL(hAPP(u,v_x))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,v_x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,v,t_a)*.
% 299.64/300.42 12974[0:SpL:3229.1,501.0] || equal(u,c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(hAPP(u,v_x),v))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.64/300.42 13162[0:SpR:2267.1,108.1] || equal(u,v)* c_lessequals(w,u,tc_fun(x,tc_bool))* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.42 13141[0:SpR:2267.1,108.1] || equal(u,v)* c_lessequals(u,w,tc_fun(x,tc_bool))* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.42 13374[0:Res:448.1,109.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* c_lessequals(v,w,tc_fun(u,tc_bool)).
% 299.64/300.42 13357[0:SpL:2267.1,109.0] || equal(u,v)* c_lessequals(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> c_lessequals(x,u,tc_fun(w,tc_bool))*.
% 299.64/300.42 13336[0:SpL:2267.1,109.0] || equal(u,v)* c_lessequals(c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* -> c_lessequals(u,w,tc_fun(x,tc_bool))*.
% 299.64/300.42 13579[0:SpL:3229.1,147.1] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) hBOOL(hAPP(hAPP(u,v_x),c_HOL_Ominus__class_Ominus(x,w,tc_fun(v,tc_bool))))* -> .
% 299.64/300.42 13627[0:SpR:11473.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,c_Orderings_Otop__class_Otop(tc_bool),x,y),hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))**.
% 299.64/300.42 13728[0:SpR:544.1,8376.2] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))*.
% 299.64/300.42 14022[0:SpR:543.1,8376.2] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))*.
% 299.64/300.42 14101[0:Res:13015.2,251.1] class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(hAPP(v_x,w),hAPP(c_Orderings_Otop__class_Otop(tc_bool),w),v)*.
% 299.64/300.42 14111[0:Res:13016.2,251.1] class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(hAPP(v_x,w),hAPP(c_Orderings_Otop__class_Otop(tc_bool),w),v)*.
% 299.64/300.42 14193[0:SpR:3229.1,176.0] || equal(u,c_in(v)) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Ovimage(w,v,x),hAPP(c_Set_Oinsert(hAPP(w,v_x),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.64/300.42 14139[0:SpR:525.1,176.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.64/300.42 14136[0:SpR:3229.1,176.0] || equal(u,v) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Ovimage(v,w,x),hAPP(c_Set_Oinsert(hAPP(u,v_x),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.64/300.42 14119[0:SpR:8385.1,176.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.64/300.42 14372[0:Res:11030.1,170.1] class_Orderings_Olinorder(u) || equal(c_in(t_a),c_in(u)) c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u),v_x,u)*.
% 299.64/300.42 14369[0:Res:3316.1,170.1] class_Orderings_Olinorder(u) || equal(c_in(v),c_in(u)) c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u),v_x,u)*.
% 299.64/300.42 14355[0:Res:648.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,tc_Com_Opname,u),v_Procs),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,tc_Com_Opname,u),v_Procs),u),hAPP(v,v_x),u)*.
% 299.64/300.42 14344[0:SpL:3229.1,170.1] class_Orderings_Olinorder(u) || equal(v,hAPP(c_in(u),w))* hBOOL(hAPP(v,v_x))* c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_x,u),w,u)*.
% 299.64/300.42 14341[0:SpL:3229.1,170.1] class_Orderings_Olinorder(u) || equal(v,c_in(u))* hBOOL(hAPP(hAPP(v,v_x),w))* c_Finite__Set_Ofinite(w,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(w,u),v_x,u)*.
% 299.64/300.42 14424[0:SpR:12944.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y,c_Orderings_Otop__class_Otop(tc_bool),z,x1),hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)))**.
% 299.64/300.42 14499[0:Res:11030.1,169.1] class_Orderings_Olinorder(u) || equal(c_in(t_a),c_in(u)) c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u),u)*.
% 299.64/300.42 14496[0:Res:3316.1,169.1] class_Orderings_Olinorder(u) || equal(c_in(v),c_in(u)) c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u),u)*.
% 299.64/300.42 14482[0:Res:648.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,tc_Com_Opname,u),v_Procs),u) -> c_lessequals(hAPP(v,v_x),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,tc_Com_Opname,u),v_Procs),u),u)*.
% 299.64/300.42 14471[0:SpL:3229.1,169.1] class_Orderings_Olinorder(u) || equal(v,hAPP(c_in(u),w))* hBOOL(hAPP(v,v_x))* c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(w,c_Finite__Set_Olinorder__class_OMax(v_x,u),u)*.
% 299.64/300.42 14468[0:SpL:3229.1,169.1] class_Orderings_Olinorder(u) || equal(v,c_in(u))* hBOOL(hAPP(hAPP(v,v_x),w))* c_Finite__Set_Ofinite(w,u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(w,u),u)*.
% 299.64/300.42 14793[0:SpL:128.0,2063.0] || equal(u,hAPP(c_Set_Ovimage(v,w,x),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))))* -> equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),y))*.
% 299.64/300.42 14790[0:SpL:128.0,16.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(w,v,x),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))))* -> equal(u,hAPP(c_Set_Ovimage(w,v,x),y)).
% 299.64/300.42 14760[0:SpR:3229.1,128.0] || equal(u,c_Set_Ovimage(v,w,x)) -> equal(hAPP(c_Set_Ovimage(v,w,x),c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(x,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_fun(w,tc_bool)))*.
% 299.64/300.42 14756[0:SpR:2267.1,128.0] || equal(u,v) -> equal(hAPP(c_Set_Ovimage(w,x,y),c_HOL_Ouminus__class_Ouminus(v,tc_fun(y,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(w,x,y),u),tc_fun(x,tc_bool)))*.
% 299.64/300.42 14732[0:SpR:128.0,2267.1] || equal(hAPP(c_Set_Ovimage(u,v,w),x),y) -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(y,tc_fun(v,tc_bool)))*.
% 299.64/300.42 14729[0:SpR:128.0,8369.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y)))* hBOOL(hAPP(hAPP(c_Set_Ovimage(w,u,x),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))),v))*.
% 299.64/300.42 15100[0:SpR:181.1,3229.1] || equal(u,c_Set_Ovimage(c_COMBK(v,w,x),x,w))* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)) equal(hAPP(u,v_x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))*.
% 299.64/300.42 15083[0:SpR:181.1,1158.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),v_Procs),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.64/300.42 15146[0:Rew:81.0,15113.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))**.
% 299.64/300.42 15151[0:Rew:10463.0,15088.2] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_x)).
% 299.64/300.42 15224[0:SpR:3229.1,446.1] || equal(u,c_Set_Oinsert(v,w)) c_lessequals(v_x,x,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(u,v_x),hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool))*.
% 299.64/300.42 15206[0:SpR:3229.1,446.1] || equal(u,c_Set_Oinsert(v,w)) c_lessequals(x,v_x,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v,w),x),hAPP(u,v_x),tc_fun(w,tc_bool))*.
% 299.64/300.42 15201[0:SpR:369.0,446.1] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v,w),u),hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool))*.
% 299.64/300.42 15200[0:SpR:2089.0,446.1] || c_lessequals(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.42 15258[0:SpR:10063.0,446.1] || c_lessequals(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(t_a,tc_bool))*.
% 299.64/300.42 15312[0:SpR:3229.1,63.1] || equal(u,c_Set_Oinsert(v,w))* c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,v_x,tc_fun(w,tc_bool)),w) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,hAPP(u,v_x),tc_fun(w,tc_bool)),w)*.
% 299.64/300.42 15350[0:SpL:3229.1,62.0] || equal(u,c_Set_Oinsert(v,w))* c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,hAPP(u,v_x),tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,v_x,tc_fun(w,tc_bool)),w).
% 299.64/300.42 15656[0:Res:1103.1,278.1] || hBOOL(hAPP(u,v)) -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(x),v),t_a) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,hAPP(c_in(x),v)),y,u,x)))*.
% 299.64/300.42 15631[0:Res:254.1,278.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(y,u),w),z,x,u)))*.
% 299.64/300.42 15616[0:SpL:3229.1,278.1] || equal(u,hAPP(c_in(v),w))* hBOOL(hAPP(x,w))* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,y,x,v)))*.
% 299.64/300.42 15613[0:SpL:3229.1,278.1] || equal(u,c_in(v))* hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(u,v_x),x))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,y,w,v)))*.
% 299.64/300.42 15884[0:Res:1103.1,277.1] || hBOOL(hAPP(u,v)) -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(x),v),t_a) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,hAPP(c_in(x),v)),u,x)))*.
% 299.64/300.42 15859[0:Res:254.1,277.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(z,u),w),x,u)))*.
% 299.64/300.42 15844[0:SpL:3229.1,277.1] || equal(u,hAPP(c_in(v),w))* hBOOL(hAPP(x,w))* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,v_x,x,v)))*.
% 299.64/300.42 15841[0:SpL:3229.1,277.1] || equal(u,c_in(v))* hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(u,v_x),x))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,x,w,v)))*.
% 299.64/300.42 16009[0:SpL:3229.1,515.0] || equal(u,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x))* equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),y),z),x1),hAPP(u,v_x))* -> equal(y,w)*.
% 299.64/300.42 16004[0:SpL:3229.1,515.0] || equal(u,hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w))* equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),x),y),z),hAPP(hAPP(u,v_x),x1))* -> equal(x,w)*.
% 299.64/300.42 16001[0:SpL:3229.1,515.0] || equal(u,c_Hoare__Mirabelle_Otriple_Otriple(v)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),y),hAPP(hAPP(hAPP(u,v_x),z),x1))* -> equal(w,v_x).
% 299.64/300.42 16117[0:SpL:3229.1,514.0] || equal(u,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x))* equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),y),z),x1),hAPP(u,v_x))* -> equal(z,x)*.
% 299.64/300.42 16112[0:SpL:3229.1,514.0] || equal(u,hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w))* equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),x),y),z),hAPP(hAPP(u,v_x),x1))* -> equal(y,v_x).
% 299.64/300.42 16109[0:SpL:3229.1,514.0] || equal(u,c_Hoare__Mirabelle_Otriple_Otriple(v)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),y),hAPP(hAPP(hAPP(u,v_x),z),x1))* -> equal(x,z).
% 299.64/300.42 16177[0:SpR:329.1,15262.1] || c_lessequals(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),tc_fun(u,tc_bool))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) -> hBOOL(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))).
% 299.64/300.42 16163[0:SpR:329.1,15262.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(t_a))** -> hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.42 16162[0:SpR:328.1,15262.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(t_a))** -> hBOOL(hAPP(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.42 16161[0:SpR:538.0,15262.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.42 16313[0:SpL:3229.1,513.0] || equal(u,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x))* equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),y),z),x1),hAPP(u,v_x))* -> equal(x1,v_x).
% 299.64/300.42 16308[0:SpL:3229.1,513.0] || equal(u,hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w))* equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),x),y),z),hAPP(hAPP(u,v_x),x1))* -> equal(z,x1).
% 299.64/300.42 16305[0:SpL:3229.1,513.0] || equal(u,c_Hoare__Mirabelle_Otriple_Otriple(v)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),y),hAPP(hAPP(hAPP(u,v_x),z),x1))* -> equal(y,x1).
% 299.64/300.42 16346[0:SpL:181.1,16286.0] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Set_Ovimage(c_COMBK(v,w,u),u,w),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)).
% 299.64/300.42 16599[0:Res:361.2,296.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,u),u)*.
% 299.64/300.42 16598[0:Res:361.2,295.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,u),u)*.
% 299.64/300.42 16526[0:SpR:525.1,361.2] class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),x),y)) -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,v),v)*.
% 299.64/300.42 16522[0:SpR:3229.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(v,w) hBOOL(hAPP(hAPP(c_in(x),v_x),y)) -> c_lessequals(hAPP(v,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,x,u),u)*.
% 299.64/300.42 16504[0:SpR:8385.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(v,v_Procs) hBOOL(hAPP(hAPP(c_in(w),v),x)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v_x,tc_Com_Opname),w,u),u)*.
% 299.64/300.42 16607[0:SSi:16589.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),x),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.64/300.42 16608[0:SSi:16588.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.42 16740[0:SpL:3229.1,202.1] || equal(u,c_Set_Oimage(v,w,w))* c_Finite__Set_Ofinite(v_x,w) c_lessequals(v_x,hAPP(u,v_x),tc_fun(w,tc_bool))* -> c_Fun_Oinj__on(v,v_x,w,w)*.
% 299.64/300.42 16803[0:Res:448.1,390.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(hAPP(c_Set_Oimage(v,w,u),x),y,tc_fun(u,tc_bool))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(x,v,w,u),y,u,w)*.
% 299.64/300.42 16774[0:SpL:3229.1,390.0] || equal(u,c_Set_Oimage(v,w,x))* c_lessequals(y,hAPP(u,v_x),tc_fun(x,tc_bool))* -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_x,v,w,x),y,x,w)*.
% 299.64/300.42 16977[0:SpL:600.0,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x))* -> hBOOL(hAPP(w,x)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),x)).
% 299.64/300.42 16975[0:SpL:600.0,324.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool)).
% 299.64/300.42 16973[0:SpL:600.0,344.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.64/300.42 16985[0:Rew:8872.2,16960.2] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(v_x,c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool))),hAPP(v_x,v))**.
% 299.64/300.42 16986[0:SSi:16938.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),w),tc_fun(x,tc_bool))*.
% 299.64/300.42 17136[0:SpR:17045.0,415.0] || -> equal(c_Fun_Ofun__upd(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x,c_Orderings_Obot__class_Obot(tc_bool),y,z),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)))**.
% 299.64/300.42 17242[0:SpR:584.0,510.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x,y,z,x1),w)))*.
% 299.64/300.42 17301[0:SpL:328.1,13272.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(u,c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.42 17300[0:SpL:538.0,13272.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.64/300.42 17452[0:SpL:328.1,16327.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(w,v_Procs) -> .
% 299.64/300.42 17451[0:SpL:538.0,16327.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_Procs) -> .
% 299.64/300.42 17732[0:Res:149.1,255.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),x),u))* hBOOL(hAPP(hAPP(c_in(v),x),w))*.
% 299.64/300.42 17889[0:SpL:188.1,3483.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 17919[0:Rew:9911.0,17886.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_COMBS(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z,x1,x2),w),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.42 18205[0:SpR:9925.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),v)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.42 18184[0:SpR:9924.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.42 18160[0:SpR:414.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ofun__upd(y,v,x,z,x1),u,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.64/300.42 18151[0:SpR:524.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.64/300.42 18269[0:SpR:15172.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)),z,u),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.64/300.42 18417[0:SpR:584.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(w,v)))* -> hBOOL(hAPP(c_COMBS(c_in(x),c_Set_Oimage(w,u,x),y,z,x1),hAPP(w,v)))*.
% 299.64/300.42 18405[0:SpR:9925.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),v)) -> hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u,w),v)))*.
% 299.64/300.42 18384[0:SpR:9924.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,x),w)))*.
% 299.64/300.42 18360[0:SpR:414.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,y,x1,x2),u,x),w)))*.
% 299.64/300.42 18351[0:SpR:524.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),u,x),w)))*.
% 299.64/300.42 18525[0:Res:9246.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u) -> hBOOL(hAPP(v,w)) c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u),w,u)*.
% 299.64/300.42 18524[0:Res:9246.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u) -> hBOOL(hAPP(v,w)) c_lessequals(w,c_Finite__Set_Olinorder__class_OMax(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u),u)*.
% 299.64/300.42 18512[0:SpR:128.0,9246.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool)))))* hBOOL(hAPP(hAPP(c_Set_Ovimage(w,u,x),y),v)).
% 299.64/300.42 18693[0:SpR:329.1,9568.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u)),y),v),tc_bool)*.
% 299.64/300.42 18692[0:SpR:328.1,9568.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v)),y),u),tc_bool)*.
% 299.64/300.42 18691[0:SpR:538.0,9568.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w)),y),v),tc_bool)*.
% 299.64/300.42 18688[0:SpR:599.0,9568.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w)),x),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))),tc_bool)*.
% 299.64/300.42 19004[0:SpR:329.1,9569.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u)),v),tc_bool)*.
% 299.64/300.42 19003[0:SpR:328.1,9569.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v)),u),tc_bool)*.
% 299.64/300.42 19002[0:SpR:538.0,9569.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w)),v),tc_bool)*.
% 299.64/300.42 18999[0:SpR:599.0,9569.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(u,tc_bool))),tc_bool)*.
% 299.64/300.42 19091[0:SSi:19075.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),u))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),u)),tc_bool)*.
% 299.64/300.42 19092[0:SSi:19074.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),y))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),y)),tc_bool)*.
% 299.64/300.42 19094[0:SpR:196.1,34.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),hAPP(u,y)))* -> hBOOL(hAPP(x,y)).
% 299.64/300.42 19258[0:SSi:19237.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) c_lessequals(v,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool),tc_bool)* -> equal(v,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool)).
% 299.64/300.42 19344[0:SSi:19331.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_bool),tc_bool)* c_lessequals(x,c_HOL_Ominus__class_Ominus(v,w,tc_bool),tc_bool)* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x),v,tc_bool)*.
% 299.64/300.42 19560[0:SpL:132.1,36.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ouminus__class_Ouminus(x,u))* c_lessequals(w,v,u) -> c_lessequals(x,c_HOL_Ozero__class_Ozero(u),u)*.
% 299.64/300.42 19544[0:SpL:132.1,36.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ominus__class_Ominus(w,x,u))* c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(x,w,u).
% 299.64/300.42 19628[0:Res:19436.1,170.1] class_Orderings_Olinorder(tc_Com_Opname) || equal(u,v_Procs) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,tc_Com_Opname),u),tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(v,tc_Com_Opname),u),tc_Com_Opname),v_x,tc_Com_Opname)*.
% 299.64/300.42 19627[0:Res:19436.1,169.1] class_Orderings_Olinorder(tc_Com_Opname) || equal(u,v_Procs) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,tc_Com_Opname),u),tc_Com_Opname) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(v,tc_Com_Opname),u),tc_Com_Opname),tc_Com_Opname)*.
% 299.64/300.42 19682[0:Res:8376.2,496.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u)),u))* c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.64/300.42 19665[0:Res:3346.1,496.0] || equal(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,hAPP(v,v_x))),hAPP(v,v_x)))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.64/300.42 19729[0:Res:517.1,19641.0] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),x)))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),x,t_a).
% 299.64/300.42 19728[0:Res:518.1,19641.0] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),x)))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),x,t_a).
% 299.64/300.42 19716[0:SpL:586.0,19641.0] || hBOOL(hAPP(u,hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_COMBB(u,w,x,y),v),z))))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_COMBB(u,w,x,y),v),z,t_a).
% 299.64/300.42 19715[0:SpL:585.0,19641.0] || hBOOL(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_COMBC(u,v,w,x),y),z)),y))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_COMBC(u,v,w,x),y),z,t_a).
% 299.64/300.42 19696[0:SpL:331.0,19641.0] || hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,t_a)*.
% 299.64/300.42 19906[0:Rew:104.0,19860.1] || equal(u,v) -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)))*.
% 299.64/300.42 19960[0:SpR:64.0,212.1] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),x))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),x)).
% 299.64/300.42 20070[0:SpL:3744.1,215.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(u)),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__derivs(v,v_Procs,u) -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.64/300.42 20187[0:SpR:128.0,20152.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Ovimage(v,w,x),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))),tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool))*.
% 299.64/300.42 20240[0:SpR:128.0,20186.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))),tc_fun(w,tc_bool))*.
% 299.64/300.42 20330[0:SpR:456.0,438.1] || c_Fun_Oinj__on(c_Option_Othe(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(u),v,w),x),c_Option_Ooption_OSome(x,u))**.
% 299.64/300.42 20294[0:SpR:659.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),u,v),v_Procs),v_Procs)**.
% 299.64/300.42 20474[0:SpR:456.0,99.1] || c_Fun_Oinj__on(c_Option_Othe(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(u),v,w),x),c_Option_Ooption_OSome(x,u))**.
% 299.64/300.42 20437[0:SpR:659.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),u,v),v_Procs),v_Procs)**.
% 299.64/300.42 20729[0:Res:313.1,18625.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Set_Oimage(x,w,y),u),z),hAPP(hAPP(c_Set_Oimage(x,w,y),v),z),tc_bool)*.
% 299.64/300.42 20775[0:Res:129.1,18625.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Set_Ovimage(x,y,w),u),z),hAPP(hAPP(c_Set_Ovimage(x,y,w),v),z),tc_bool)*.
% 299.64/300.42 21028[0:SpL:317.0,7600.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oimage(w,x,v),hAPP(c_Set_Oinsert(y,x),z))),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(w,x,v),z),v).
% 299.64/300.42 21026[0:SpL:317.0,360.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(y,w),z)),x,x1)* -> c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(v,w,x),z),x,x1).
% 299.64/300.42 21025[0:SpL:317.0,442.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(x)),hAPP(c_Set_Oinsert(y,w),z)),x)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(x)),z),x).
% 299.64/300.42 21022[0:SpL:317.0,214.0] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),z,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,x)),z)).
% 299.64/300.42 20964[0:SpR:456.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Option_Othe(u),v,w),hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(x,u),v),y)),hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oimage(c_Option_Othe(u),v,w),y)))*.
% 299.64/300.42 20926[0:SpR:659.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),hAPP(c_Set_Oinsert(v_Procs,u),w)),hAPP(c_Set_Oinsert(v_Procs,v),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),w)))*.
% 299.64/300.42 20906[0:SpR:2093.0,317.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v_Procs),v),hAPP(c_Set_Oimage(u,w,v),hAPP(c_in(tc_Com_Opname),v_x))),hAPP(c_Set_Oimage(u,w,v),hAPP(c_in(tc_Com_Opname),v_x)))**.
% 299.64/300.42 20905[0:SpR:3744.1,317.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(hAPP(c_Set_Oinsert(hAPP(v,v_x),w),hAPP(c_Set_Oimage(v,u,w),v_Procs)),hAPP(c_Set_Oimage(v,u,w),v_Procs))**.
% 299.64/300.42 20891[0:SpR:317.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(u,v),w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(c_Set_Oimage(u,z,w),hAPP(c_Set_Oinsert(v,z),x1))))*.
% 299.64/300.42 20868[0:SpR:317.0,19436.1] || equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),v_Procs) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(c_Set_Oimage(u,v,tc_Com_Opname),hAPP(c_Set_Oinsert(x,v),w))))*.
% 299.64/300.42 20867[0:SpR:317.0,7460.1] || c_lessequals(v_Procs,hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),hAPP(c_Set_Oinsert(x,v),w)),v_x))*.
% 299.64/300.42 21088[0:SpR:329.1,20881.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y),hAPP(c_Set_Oinsert(v,x),z)),v))*.
% 299.64/300.42 21087[0:SpR:328.1,20881.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,y),hAPP(c_Set_Oinsert(u,x),z)),v))*.
% 299.64/300.42 21085[0:SpR:538.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(y,w),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v)))*.
% 299.64/300.42 21280[0:Res:8376.2,469.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Oimage(v,w,u),x),v_Procs) -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,v_x,w,u)),v_x)**.
% 299.64/300.42 21647[0:SpL:21267.0,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,w),v))*.
% 299.64/300.42 21558[0:SpL:21267.0,591.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),v_G)) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),tc_Com_Opname,u),t_a)*.
% 299.64/300.42 21538[0:SpR:88.1,21267.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_Orderings_Otop__class_Otop(u),tc_Com_Opname,v)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.42 21446[0:SpR:21267.0,526.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,w),v))* -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)).
% 299.64/300.42 21363[0:SpR:21267.0,309.1] class_Lattices_Olattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),u)*.
% 299.64/300.42 21362[0:SpR:21267.0,306.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),u)*.
% 299.64/300.42 21305[0:SpR:21267.0,318.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),v_x),w).
% 299.64/300.42 21293[0:SpR:21267.0,7539.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(u,v),v_x)),tc_fun(v,tc_bool))*.
% 299.64/300.42 21698[0:Rew:9.0,21552.0] || -> equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ocomp(u,v,w,x,y),hAPP(u,hAPP(v,v_x)),tc_Com_Opname,z))),hAPP(u,hAPP(v,v_x)))**.
% 299.64/300.42 21740[0:Rew:196.1,21444.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v_x)**.
% 299.64/300.42 21790[0:SpR:329.1,21143.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_x))*.
% 299.64/300.42 21789[0:SpR:328.1,21143.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u))*.
% 299.64/300.42 21787[0:SpR:538.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)))*.
% 299.64/300.42 21859[0:SpR:329.1,21131.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),v_x))*.
% 299.64/300.42 21858[0:SpR:328.1,21131.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),u))*.
% 299.64/300.42 21856[0:SpR:538.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)))*.
% 299.64/300.42 21906[0:Res:8376.2,464.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Oimage(v,w,u),x),v_Procs) -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(x,v_x,v,w,u)),v_x)**.
% 299.64/300.42 22275[0:SpL:21893.0,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,w),v))*.
% 299.64/300.42 22185[0:SpL:21893.0,591.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),v_G)) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,u),t_a)*.
% 299.64/300.42 22165[0:SpR:88.1,21893.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,v)),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.42 22072[0:SpR:21893.0,526.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,w),v))* -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)).
% 299.64/300.42 21989[0:SpR:21893.0,309.1] class_Lattices_Olattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),u)*.
% 299.64/300.42 21988[0:SpR:21893.0,306.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),u)*.
% 299.64/300.42 21931[0:SpR:21893.0,318.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),v_x),w).
% 299.64/300.42 21919[0:SpR:21893.0,7539.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(u,v),v_x)),tc_fun(v,tc_bool))*.
% 299.64/300.42 22327[0:Rew:9.0,22179.0] || -> equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,hAPP(v,v_x)),c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname,z))),hAPP(u,hAPP(v,v_x)))**.
% 299.64/300.42 22369[0:Rew:196.1,22070.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v_x)**.
% 299.64/300.42 22430[0:SpL:97.1,357.1] || c_Fun_Oinj__on(u,v,w,x) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,w,x),v),x)* c_lessequals(y,v,tc_fun(w,tc_bool))* -> c_Finite__Set_Ofinite(y,w).
% 299.64/300.42 22410[0:SpR:97.1,7253.0] || c_Fun_Oinj__on(u,v,w,x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),v))*.
% 299.64/300.42 22505[0:SpR:97.1,21126.1] || c_Fun_Oinj__on(u,v,w,tc_Com_Opname) equal(hAPP(c_Set_Oimage(u,w,tc_Com_Opname),v),v_Procs) -> hBOOL(hAPP(v,hAPP(c_Fun_Othe__inv__into(v,u,w,tc_Com_Opname),v_x)))*.
% 299.64/300.42 22491[0:SpR:329.1,21126.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(w,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,x),w),v_x))*.
% 299.64/300.42 22490[0:SpR:328.1,21126.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(w,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,x),w),u))*.
% 299.64/300.42 22488[0:SpR:538.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname,x),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w)))*.
% 299.64/300.42 22618[0:SpR:158.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(u,v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,z,v,w,x1),x1,w),x2)))*.
% 299.64/300.42 22520[0:SpR:158.0,3305.1] || equal(c_Fun_Ocomp(u,v,w,x,tc_Com_Opname),y) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs)),hAPP(y,v_x)))*.
% 299.64/300.42 22873[0:SpL:3294.1,324.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v,tc_fun(u,tc_bool)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v,tc_fun(u,tc_bool))*.
% 299.64/300.42 22870[0:SpL:3294.1,327.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) -> c_lessequals(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),tc_fun(u,tc_bool))*.
% 299.64/300.42 22839[0:SpR:584.0,3294.1] || equal(c_COMBS(u,v,w,x,y),c_in(t_a))** -> equal(hAPP(hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 22817[0:SpR:540.1,3294.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 22816[0:SpR:539.1,3294.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 22815[0:SpR:297.2,3294.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 22806[0:SpR:299.2,3294.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(t_a))** -> equal(hAPP(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 22795[0:SpR:25.1,3294.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_in(t_a)) -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.42 22769[0:SpR:3294.1,329.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_lessequals(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),tc_fun(u,tc_bool))* -> equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.42 23039[0:SpL:131.0,4439.0] || equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,w,x),z),hAPP(v,v_x))).
% 299.64/300.42 22999[0:SpR:131.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(c_Set_Ovimage(c_Fun_Ocomp(z,u,w,x1,v),v,x1),x2)))*.
% 299.64/300.42 23060[0:Res:22736.2,251.1] class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),c_in(t_a))** -> c_lessequals(hAPP(v_x,w),hAPP(c_Orderings_Obot__class_Obot(tc_bool),w),v)*.
% 299.64/300.42 23148[0:Res:22737.2,251.1] class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),c_in(t_a))** -> c_lessequals(hAPP(v_x,w),hAPP(c_Orderings_Obot__class_Obot(tc_bool),w),v)*.
% 299.64/300.42 23219[0:SpL:584.0,3487.1] || equal(c_COMBS(u,v,w,x,y),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.42 23204[0:SpL:337.0,3487.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> .
% 299.64/300.42 23197[0:SpL:540.1,3487.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.42 23196[0:SpL:539.1,3487.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.42 23186[0:SpL:299.2,3487.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.42 23175[0:SpL:25.1,3487.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.42 23302[0:SpL:297.2,3489.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),u)* equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) hBOOL(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))) -> .
% 299.64/300.42 23296[0:SpL:584.0,3489.1] || equal(c_COMBS(u,v,w,x,y),c_in(tc_Com_Opname))** hBOOL(hAPP(hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.42 23274[0:SpL:540.1,3489.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.42 23273[0:SpL:539.1,3489.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.42 23272[0:SpL:297.2,3489.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname))** hBOOL(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.42 23263[0:SpL:299.2,3489.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_in(tc_Com_Opname))** hBOOL(hAPP(v,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.42 23252[0:SpL:25.1,3489.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_in(tc_Com_Opname)) hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.42 23349[2:SpR:460.1,4250.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Com_Ocom_OBODY) -> c_Com_OWT(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))*.
% 299.64/300.42 23339[0:SpR:460.1,3282.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))*.
% 299.64/300.42 23561[0:SpR:301.1,523.1] class_Lattices_Obounded__lattice(tc_fun(t_a,u)) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x)),hAPP(v,v_x))**.
% 299.64/300.42 23540[0:SpR:300.1,523.1] class_Lattices_Obounded__lattice(tc_fun(t_a,u)) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x)),hAPP(v,v_x)),hAPP(v,v_x))**.
% 299.64/300.42 23480[2:SpR:523.1,4250.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Com_Ocom_OBODY) -> c_Com_OWT(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)))*.
% 299.64/300.42 23470[0:SpR:523.1,3282.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)))*.
% 299.64/300.42 23601[0:Rew:540.1,23564.2,10463.0,23564.2] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),c_in(t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(v_x,v_x)),hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_x))**.
% 299.64/300.42 24397[0:AED:24.0,24331.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(u,v,w),w,v),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))*.
% 299.64/300.42 24398[0:MRR:24268.0,3591.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(u,v,w),w,v),x,y),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))*.
% 299.64/300.42 24622[0:SpR:130.1,24020.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),v_x),v_x)**.
% 299.64/300.42 24579[0:SpR:24020.1,523.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(v_x,v_x)),v_x)**.
% 299.64/300.42 24911[0:SpL:584.0,467.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(v,w,u),x,y,z),x1))* -> equal(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(x1,v,w,u),x1)),x1)**.
% 299.64/300.42 25133[0:Res:252.1,12956.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),x),t_a) c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(v,x,w,u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,x,w,u))*.
% 299.64/300.42 25330[2:SpR:512.0,4250.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)))*.
% 299.64/300.42 25320[0:SpR:512.0,3282.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),v_Procs)** -> hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)))*.
% 299.64/300.42 25306[0:SpR:512.0,16776.0] || -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(u,hAPP(c_COMBB(v,w,x,y),z),y,x),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(z,y,w),u)),x,y)*.
% 299.64/300.42 25714[0:Res:3346.1,455.0] || equal(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v)* c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(v,v_x),t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.64/300.42 25709[0:Res:9246.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w),t_a)* -> hBOOL(hAPP(v,x))* c_Hoare__Mirabelle_Otriple__valid(w,x,t_a)*.
% 299.64/300.42 25705[0:Res:1157.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(c_COMBK(v,w,x),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,y),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(y,v,t_a)*.
% 299.64/300.42 25986[0:SpL:339.0,327.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),x)** -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)).
% 299.64/300.42 25937[0:SpR:8385.1,339.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v))**.
% 299.64/300.42 25921[0:SpR:339.0,329.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)) -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),x)**.
% 299.64/300.42 25912[0:SpR:339.0,538.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v)))*.
% 299.64/300.42 26244[0:SpL:338.0,214.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),y,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),w),y)).
% 299.64/300.42 26241[0:SpL:338.0,377.0] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),u)* -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),u).
% 299.64/300.42 26208[0:SpR:329.1,338.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),hAPP(c_Set_Oinsert(x,w),v)),hAPP(c_Set_Oinsert(x,w),v))**.
% 299.64/300.42 26207[0:SpR:328.1,338.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(c_Set_Oinsert(x,w),u)),hAPP(c_Set_Oinsert(x,w),v))**.
% 299.64/300.42 26147[0:SpR:8385.1,338.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u))**.
% 299.64/300.42 26144[0:SpR:338.0,19744.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),u),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),u),w),t_a)*.
% 299.64/300.42 26130[0:SpR:338.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),hAPP(c_Set_Oinsert(u,v),z))))*.
% 299.64/300.42 26106[0:SpR:338.0,3291.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),v_x)),v_Procs))*.
% 299.64/300.42 26098[0:SpR:338.0,378.1] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(x,u),w)),u)*.
% 299.64/300.42 26083[0:SpR:338.0,328.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)) -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),w)),x)**.
% 299.64/300.42 26259[0:Rew:339.0,26074.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),w)))*.
% 299.64/300.42 26310[0:Res:23960.1,251.1] class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(v_x,w),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(u,v)),w),v)*.
% 299.64/300.42 26380[0:Res:13385.1,85.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))) -> c_lessequals(c_HOL_Ominus__class_Ominus(x,v,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))*.
% 299.64/300.42 26357[0:SpL:538.0,85.0] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,x,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool)).
% 299.64/300.42 26430[0:Res:24940.2,251.1] class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_bool),w),hAPP(v_x,w),v)*.
% 299.64/300.42 26445[0:Res:24941.2,251.1] class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_bool),w),hAPP(v_x,w),v)*.
% 299.64/300.42 26506[0:SpR:329.1,84.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool))* -> c_lessequals(x,v,tc_fun(w,tc_bool)).
% 299.64/300.42 26505[0:SpR:328.1,84.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(c_HOL_Ominus__class_Ominus(x,v,tc_fun(w,tc_bool)),u,tc_fun(w,tc_bool))* -> c_lessequals(x,v,tc_fun(w,tc_bool)).
% 299.64/300.42 26502[0:SpR:538.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v),tc_fun(w,tc_bool))*.
% 299.64/300.42 26859[0:SpL:56.1,4964.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),x),v_x))*.
% 299.64/300.42 26812[0:SpR:56.1,9567.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),y),hAPP(hAPP(c_Set_Oinsert(v,u),x),y),tc_bool)*.
% 299.64/300.42 27111[0:Res:23946.1,280.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(u,v_Procs),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,u,w,tc_fun(x,tc_bool)),v))*.
% 299.64/300.42 27109[0:Res:19436.1,280.1] || equal(u,v_Procs) hBOOL(hAPP(hAPP(v,v_x),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,tc_Com_Opname),u),v,tc_Com_Opname,tc_fun(y,tc_bool)),w))*.
% 299.64/300.42 27108[0:Res:19441.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,tc_Com_Opname),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),u,tc_Com_Opname,tc_fun(y,tc_bool)),v))*.
% 299.64/300.42 27107[0:Res:19452.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u,t_a,tc_fun(x,tc_bool)),v))*.
% 299.64/300.42 27093[0:Res:9067.0,280.1] || hBOOL(hAPP(hAPP(u,v),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oinsert(v,y),z)),u,y,tc_fun(x1,tc_bool)),w))*.
% 299.64/300.42 27090[0:Res:3346.1,280.1] || equal(c_Set_Oinsert(u,v),w)* hBOOL(hAPP(hAPP(x,u),y))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(w,v_x),x,v,tc_fun(z,tc_bool)),y))*.
% 299.64/300.42 27087[0:Res:9071.0,280.1] || hBOOL(hAPP(hAPP(u,v),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,x),tc_Com_Opname,tc_fun(x,tc_bool)),u,x,tc_fun(y,tc_bool)),w))*.
% 299.64/300.42 27085[0:Res:9246.0,280.1] || hBOOL(hAPP(hAPP(u,v),w))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_HOL_Ouminus__class_Ouminus(x,tc_fun(y,tc_bool)),u,y,tc_fun(z,tc_bool)),w))*.
% 299.64/300.42 27081[0:Res:1157.0,280.1] || hBOOL(hAPP(hAPP(u,v),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(c_COMBK(v,x,y),tc_Com_Opname,z),v_Procs),u,z,tc_fun(x1,tc_bool)),w))*.
% 299.64/300.42 27147[0:SpR:351.0,450.0] || -> hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_COMBK(u,v,w),x,y,z)))* c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBK(u,v,w)),y),x),t_a)*.
% 299.64/300.42 27246[7:SpR:523.1,27207.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)))*.
% 299.64/300.42 27245[7:SpR:460.1,27207.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))*.
% 299.64/300.42 27312[7:MRR:24363.2,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_in(tc_Com_Opname))** equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> .
% 299.64/300.42 27313[7:MRR:24298.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.64/300.42 27314[7:MRR:24297.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.42 27315[7:MRR:24292.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))*.
% 299.64/300.42 27316[7:MRR:24287.1,27297.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool)).
% 299.64/300.42 27317[7:MRR:24285.1,27297.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool)).
% 299.64/300.42 27337[7:MRR:24307.0,27297.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(v,w,x),x,w),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.42 27338[7:MRR:24300.0,27297.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(u,v,w),w,v),t_a,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))*.
% 299.64/300.42 27339[7:MRR:24282.0,27297.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_Com_Opname,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.42 27346[7:MRR:24369.3,27297.0] || equal(u,c_Set_Oimage(c_COMBK(v,w,x),x,w))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.42 27347[7:MRR:24311.1,27297.0] || equal(u,c_Set_Oimage(c_COMBK(v,w,x),x,w))* -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),y,z),u)**.
% 299.64/300.42 27348[7:MRR:24310.1,27297.0] || equal(c_in(u),c_Set_Oimage(c_COMBK(v,w,x),x,w))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.64/300.42 27664[7:SpL:56.1,27293.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),v_x)** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),x),v_x))*.
% 299.64/300.42 27907[7:MRR:27817.1,27297.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool)).
% 299.64/300.42 27928[0:Res:468.0,279.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(y,v,w),x)) equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(x,u,y,v,w),v),x),x)**.
% 299.64/300.42 28040[7:MRR:27964.0,27297.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_Com_Opname,x)),v_Procs))*.
% 299.64/300.42 28073[0:SpR:181.1,28032.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x)))*.
% 299.64/300.42 28343[7:MRR:28266.0,27297.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_Com_Opname,x)),v_Procs))*.
% 299.64/300.42 28376[0:SpR:181.1,28335.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x)))*.
% 299.64/300.42 28815[7:MRR:28725.0,27297.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 28970[7:MRR:28880.0,27297.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 29179[0:SpL:537.1,312.1] class_Lattices_Olattice(u) class_Lattices_Obounded__lattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),c_Orderings_Obot__class_Obot(u))** -> equal(x,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.42 29233[0:SSi:29087.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.42 29244[0:SSi:29191.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),v,z)* -> c_Fun_Oinj__on(u,y,v,z).
% 299.64/300.42 29704[0:SpL:534.1,312.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),c_Orderings_Obot__class_Obot(u))** -> equal(x,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.42 29917[0:SpR:27043.1,474.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.42 29903[0:SpR:27043.1,446.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_Procs,v),u),v_x,tc_fun(v,tc_bool))*.
% 299.64/300.42 30301[0:SpL:536.1,311.1] class_Lattices_Olattice(u) class_Lattices_Obounded__lattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),c_Orderings_Obot__class_Obot(u))** -> equal(w,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.42 30385[0:SSi:30138.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),tc_bool) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.42 30407[0:SSi:30314.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),v,z)* -> c_Fun_Oinj__on(u,x,v,z).
% 299.64/300.42 30509[0:Res:28009.0,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)),w))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(x,tc_bool)),w))*.
% 299.64/300.42 30521[0:Res:28312.0,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)),w))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(x,tc_bool)),w))*.
% 299.64/300.42 30865[0:SpL:535.1,311.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),c_Orderings_Obot__class_Obot(u))** -> equal(w,c_Orderings_Obot__class_Obot(u)).
% 299.64/300.42 31088[0:SpR:28771.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),tc_Com_Opname),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.42 31074[0:SpR:28771.0,446.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.42 31174[0:SpR:28926.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v),tc_Com_Opname),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.42 31160[0:SpR:28926.0,446.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v),tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.42 31286[0:Res:13238.1,356.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(c_Set_Oimage(c_COMBK(v,w,t_a),t_a,w),u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.64/300.42 31279[0:Res:8375.1,356.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,v),v,x),u),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.64/300.42 31273[0:Res:3284.1,356.0] || equal(c_in(tc_Com_Opname),u) -> equal(hAPP(c_Set_Oimage(c_COMBK(v,w,x),x,w),hAPP(u,v_x)),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.64/300.42 31258[0:Res:652.1,356.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> equal(hAPP(c_Set_Oimage(c_COMBK(v,w,tc_Com_Opname),tc_Com_Opname,w),u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.64/300.42 31256[0:Res:649.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.64/300.42 31255[0:Res:650.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.64/300.42 31363[0:Res:23961.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),t_a)* c_Hoare__Mirabelle_Otriple__valid(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.64/300.42 31361[0:Res:23961.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),v_Procs),u,w,tc_fun(x,tc_bool)),v))*.
% 299.64/300.42 31490[0:SpL:329.1,24254.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Com_Ocom_OBODY,v_x) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 31489[0:SpL:328.1,24254.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(u,c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 31486[0:SpL:538.0,24254.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.42 31541[0:Res:13238.1,473.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,t_a),v_x)),w))*.
% 299.64/300.42 31540[0:Res:8375.1,473.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(x,u,v,w),y)),x))*.
% 299.64/300.42 31532[0:Res:652.1,473.0] || c_lessequals(v_Procs,hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,tc_Com_Opname),v_x)),w))*.
% 299.64/300.42 31907[7:SpL:181.1,31868.0] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Set_Ovimage(c_COMBK(v,w,u),u,w),v_x)** -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)).
% 299.64/300.42 31993[0:SpR:768.0,383.1] || -> equal(u,v_Procs) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,tc_Com_Opname),u,v,w,x),v_Procs,v_Procs,w,x),c_Fun_Ofun__upd(c_Set_Oinsert(v_x,tc_Com_Opname),u,v,w,x))**.
% 299.64/300.42 32670[0:Res:31533.0,280.1] || hBOOL(hAPP(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))),x))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(y,tc_bool)),x))*.
% 299.64/300.42 32642[0:SpR:329.1,31533.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),v_x)),v_Procs))*.
% 299.64/300.42 32641[0:SpR:328.1,31533.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),u)),v_Procs))*.
% 299.64/300.42 32638[0:SpR:538.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))),v_Procs))*.
% 299.64/300.42 32685[0:SpR:130.1,32669.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_Com_Opname,x),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))))*.
% 299.64/300.42 32776[0:SpR:35.2,14526.0] || c_lessequals(u,c_Option_Othe(v),tc_fun(w,tc_bool))* c_lessequals(c_Option_Othe(v),x,tc_fun(w,tc_bool))* -> equal(hAPP(u,c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v)),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.64/300.42 32822[0:Rew:32817.1,32797.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(v,c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),u).
% 299.64/300.42 32845[0:SpR:475.1,3291.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x))* equal(c_Set_Oimage(w,u,x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,u,x),v_x),v_Procs))*.
% 299.64/300.42 33298[0:SpR:329.1,32668.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),v_x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 33297[0:SpR:328.1,32668.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),u),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 33294[0:SpR:538.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.42 33230[0:SpR:32668.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x)),tc_Com_Opname),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.42 33215[0:SpR:32668.0,446.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x)),tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.42 33432[0:Res:168.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a)* -> c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,x)),u))* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,v),t_a)*.
% 299.64/300.42 33584[0:SpR:329.1,28704.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,x)))*.
% 299.64/300.42 33583[0:SpR:328.1,28704.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,x)))*.
% 299.64/300.42 33580[0:SpR:538.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname,x)))*.
% 299.64/300.42 33675[0:SpR:329.1,28859.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x,tc_Com_Opname,x)))*.
% 299.64/300.42 33674[0:SpR:328.1,28859.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),u,tc_Com_Opname,x)))*.
% 299.64/300.42 33671[0:SpR:538.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),tc_Com_Opname,x)))*.
% 299.64/300.42 33765[7:SpL:328.1,31886.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(w,v_x) -> .
% 299.64/300.42 33762[7:SpL:538.0,31886.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_x) -> .
% 299.64/300.42 33845[0:SpR:23965.1,395.0] || equal(c_Fun_Ofun__upd(u,v_x,v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> equal(c_Fun_Ofun__upd(u,v_x,v,w,x),c_Fun_Ofun__upd(u,v_x,v_x,w,x))*.
% 299.64/300.42 34292[0:SpL:24914.0,279.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,w),hAPP(c_in(u),v_x)),u),v),v)**.
% 299.64/300.42 34240[0:SpR:9935.1,24914.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.42 34219[0:SpR:297.2,24914.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v_x)),v_x)**.
% 299.64/300.42 34216[0:SpR:2098.1,24914.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,v),v_x)),v_x)**.
% 299.64/300.42 34210[0:SpR:299.2,24914.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v)),v)**.
% 299.64/300.42 33974[0:SpR:24914.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,w),hAPP(c_in(u),v_x)),u),x))))*.
% 299.64/300.42 33968[0:SpR:24914.0,9071.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),hAPP(c_in(u),v_x)),u),tc_Com_Opname,tc_fun(u,tc_bool))))*.
% 299.64/300.42 33966[0:SpR:24914.0,9246.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)))) hBOOL(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,w),hAPP(c_in(u),v_x))))*.
% 299.64/300.42 33963[0:SpR:24914.0,1157.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_COMBK(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),hAPP(c_in(u),v_x)),w,x),tc_Com_Opname,u),v_Procs)))*.
% 299.64/300.42 33919[0:SpR:24914.0,212.1] || hBOOL(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),x))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),x)).
% 299.64/300.42 34568[0:SpR:34427.0,584.0] || -> equal(hAPP(c_COMBS(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v,w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(v_x,hAPP(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))))**.
% 299.64/300.42 34567[0:SpR:34427.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,v),w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(hAPP(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v_x))**.
% 299.64/300.42 34825[0:Res:27383.0,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y)),z))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(x1,tc_bool)),z))*.
% 299.64/300.42 34835[0:Res:27443.0,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y)),z))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(x1,tc_bool)),z))*.
% 299.64/300.42 34893[0:SpR:329.1,28053.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,w,tc_Com_Opname,x)))*.
% 299.64/300.42 34892[0:SpR:328.1,28053.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,w,tc_Com_Opname,x)))*.
% 299.64/300.42 34889[0:SpR:538.0,28053.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),u,tc_Com_Opname,x)))*.
% 299.64/300.42 34972[0:SpR:329.1,28356.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,v_x,tc_Com_Opname,x)))*.
% 299.64/300.42 34971[0:SpR:328.1,28356.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,u,tc_Com_Opname,x)))*.
% 299.64/300.42 34968[0:SpR:538.0,28356.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),tc_Com_Opname,x)))*.
% 299.64/300.42 35046[0:SpR:28755.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y),tc_Com_Opname),z,u),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.64/300.42 35031[0:SpR:28755.0,446.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y),tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.42 35135[0:SpR:28910.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y),tc_Com_Opname),z,u),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.64/300.42 35120[0:SpR:28910.0,446.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y),tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.42 35431[0:SpL:410.0,325.0] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),z,tc_fun(y,tc_bool))* -> c_lessequals(hAPP(x,u),z,tc_fun(y,tc_bool)).
% 299.64/300.42 35429[0:SpL:410.0,345.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))** -> equal(hAPP(x,u),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))).
% 299.64/300.42 35240[0:SpR:410.0,518.1] || hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),y)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(z,w),u),v,w,tc_fun(x,tc_bool)),y))*.
% 299.64/300.42 35439[0:SSi:35228.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(v,w),tc_fun(x,tc_bool)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,y),z),v,y,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.42 35490[0:SpR:113.0,19747.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(y,x,tc_fun(w,tc_bool))),tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.42 35484[0:SpR:113.0,20186.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.64/300.42 36188[0:Res:3346.1,516.0] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) -> hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(v),u),v_x))*.
% 299.64/300.42 36182[0:Res:8366.1,516.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),u)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v)).
% 299.64/300.42 36357[0:SpR:55.1,36264.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),w),u,tc_fun(t_a,tc_bool)),v_x)))*.
% 299.64/300.42 36424[0:SpR:55.1,36407.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),v),u,tc_fun(t_a,tc_bool)),v_x)),w))*.
% 299.64/300.42 36498[0:SpR:55.1,36471.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),v),u,tc_fun(t_a,tc_bool)),v_x)),w,t_a)*.
% 299.64/300.43 36594[0:Res:10697.0,36406.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(hAPP(c_Set_Oinsert(v_x,t_a),x),v_x))),hAPP(hAPP(c_Set_Oinsert(v_x,t_a),x),v_x)))*.
% 299.64/300.43 36540[0:SpL:55.1,36406.0] || c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(t_a,tc_bool)),v_x),w,tc_bool)* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)) hBOOL(w).
% 299.64/300.43 36775[0:SpL:67.0,147.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,u),w),tc_fun(u,tc_bool))))* -> .
% 299.64/300.43 36855[0:SpR:66.0,114.1] || c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),x,y) -> c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(z,x),w),tc_fun(x,tc_bool)),x,y)*.
% 299.64/300.43 36853[0:SpR:66.0,64.0] || -> equal(hAPP(c_Set_Oinsert(u,v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),x),tc_fun(v,tc_bool))),hAPP(c_Set_Oinsert(u,v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool))))**.
% 299.64/300.43 38329[0:Obv:38319.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Finite__Set_Ofinite(w,u) -> c_lessequals(x,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,w,u,u),u)*.
% 299.64/300.43 38330[0:Obv:38318.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(v,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,w,u,u),u)*.
% 299.64/300.43 38488[0:Res:13385.1,385.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) c_Finite__Set_Ofinite(u,v) c_Fun_Oinj__on(w,u,v,v) -> equal(hAPP(c_Set_Oimage(w,v,v),u),u)**.
% 299.64/300.43 38660[0:Res:3284.1,184.0] || equal(c_Set_Oimage(u,v,w),c_in(tc_Com_Opname)) c_Fun_Oinj__on(u,v_x,v,w) -> equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(v_x,u,v,w),v_Procs)),v_Procs)**.
% 299.64/300.43 38939[0:SpR:354.2,318.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,v,w,y)* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x,w,y),u),y)* -> c_Finite__Set_Ofinite(u,w).
% 299.64/300.43 39015[0:MRR:38955.2,20734.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,v,w,y)* -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(x,w,y),u),y),c_Finite__Set_Ocard(u,w))**.
% 299.64/300.43 39865[0:Rew:524.0,39666.0] || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z))**.
% 299.64/300.43 42143[4:SpR:180.2,37987.1] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(v_x,u),v),u,u))*.
% 299.64/300.43 42059[0:SpR:180.2,302.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),u),v),u,u),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.43 42198[0:SSi:42134.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,u,tc_bool,tc_bool)) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(w,tc_bool),u),tc_bool,tc_bool))*.
% 299.64/300.43 42302[0:SpL:35.2,38144.0] || c_lessequals(u,c_Set_Oinsert(v_x,tc_Com_Opname),tc_fun(v,tc_bool))* c_lessequals(c_Set_Oinsert(v_x,tc_Com_Opname),w,tc_fun(v,tc_bool))* hBOOL(hAPP(u,v_Procs)) -> hBOOL(v_Procs).
% 299.64/300.43 42686[0:SpR:161.0,9568.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),v,tc_fun(w,tc_bool)),x),tc_bool)*.
% 299.64/300.43 42683[0:SpR:161.0,9569.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),u),v,tc_fun(w,tc_bool)),x),tc_bool)*.
% 299.64/300.43 43247[0:Obv:43230.1] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))* -> equal(u,x).
% 299.64/300.43 43354[0:Obv:43350.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> equal(u,x).
% 299.64/300.43 43504[0:SpR:507.0,9568.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oimage(u,v,w),x),y),hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z)),y),tc_bool)*.
% 299.64/300.43 43501[0:SpR:507.0,9569.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oimage(u,v,w),x),y),hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),x)),y),tc_bool)*.
% 299.64/300.43 43726[0:SpR:162.0,9568.0] || -> c_lessequals(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y),hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)),y),tc_bool)*.
% 299.64/300.43 43723[0:SpR:162.0,9569.0] || -> c_lessequals(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y),hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x)),y),tc_bool)*.
% 299.64/300.43 44405[0:Rew:586.0,44400.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,x,tc_Com_Opname,tc_fun(v,tc_bool))),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),hAPP(x,v_x)),w).
% 299.64/300.43 44459[0:Rew:586.0,44454.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,x,tc_Com_Opname,tc_fun(w,tc_bool))),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),hAPP(x,v_x)),v).
% 299.64/300.43 44638[0:SpR:161.0,35656.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),u),v,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.43 44637[0:SpR:162.0,35656.1] || equal(hAPP(c_Set_Ovimage(u,tc_Com_Opname,v),w),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,tc_Com_Opname,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),w)),v_x))*.
% 299.64/300.43 44636[0:SpR:507.0,35656.1] || equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),w)),v_x))*.
% 299.64/300.43 45257[0:SpR:317.0,37394.1] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oimage(u,v,t_a),hAPP(c_Set_Oinsert(x,v),w)),tc_Com_Opname,tc_bool))*.
% 299.64/300.43 45455[0:Res:45357.1,8513.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x)) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_Com_Opname),u)**.
% 299.64/300.43 45550[0:SpR:323.0,342.0] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.43 45519[0:SpR:323.0,341.0] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),u),v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.64/300.43 45710[0:SpR:161.0,44625.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),w),v,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.64/300.43 45709[0:SpR:162.0,44625.1] || equal(hAPP(c_Set_Ovimage(u,tc_Com_Opname,v),w),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,tc_Com_Opname,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),v_x))*.
% 299.64/300.43 45708[0:SpR:507.0,44625.1] || equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),v_x))*.
% 299.64/300.43 46077[0:SpR:317.0,36802.1] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(y,v),x)),v_x))*.
% 299.64/300.43 46315[0:SSi:46240.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v))))*.
% 299.64/300.43 46421[0:SSi:46346.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),x))))*.
% 299.64/300.43 46536[4:SpR:317.0,42029.1] || equal(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(y,v),x)),v_x))*.
% 299.64/300.43 46675[7:MRR:46608.2,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.64/300.43 46711[0:Res:129.1,44639.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* equal(hAPP(c_Set_Ovimage(x,tc_Com_Opname,w),u),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Ovimage(x,tc_Com_Opname,w),v),v_x))*.
% 299.64/300.43 46710[0:Res:313.1,44639.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* equal(hAPP(c_Set_Oimage(x,w,tc_Com_Opname),u),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oimage(x,w,tc_Com_Opname),v),v_x))*.
% 299.64/300.43 47167[0:SSi:47079.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(w,v,tc_bool)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v))*.
% 299.64/300.43 47888[0:SSi:47799.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(w,v,tc_bool)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),x))*.
% 299.64/300.43 48179[4:SpR:338.0,39023.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),v_x)),x))*.
% 299.64/300.43 48178[4:SpR:475.1,39023.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x))* equal(c_Set_Oimage(w,u,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,u,x),v_x),y))*.
% 299.64/300.43 48148[4:SpR:329.1,39023.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),v_x),y))*.
% 299.64/300.43 48147[4:SpR:328.1,39023.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),u),y))*.
% 299.64/300.43 48143[4:SpR:538.0,39023.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)),y))*.
% 299.64/300.43 48294[4:SpR:338.0,39064.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),v_x)),x,t_a)*.
% 299.64/300.43 48293[4:SpR:475.1,39064.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x))* equal(c_Set_Oimage(w,u,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oimage(w,u,x),v_x),y,t_a)*.
% 299.64/300.43 48263[4:SpR:329.1,39064.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),v_x),y,t_a)*.
% 299.64/300.43 48262[4:SpR:328.1,39064.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),u),y,t_a)*.
% 299.64/300.43 48258[4:SpR:538.0,39064.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)),y,t_a)*.
% 299.64/300.43 49344[0:Res:49314.1,280.1] || hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)),w))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,tc_fun(x,tc_bool)),w))*.
% 299.64/300.43 49399[0:SpR:49342.1,474.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.64/300.43 49383[0:SpR:49342.1,446.1] || hBOOL(hAPP(u,v_x)) c_lessequals(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.43 50382[0:SSi:50287.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),x,tc_bool)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w)) -> hBOOL(x).
% 299.64/300.43 50581[0:SSi:50545.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w)) -> hBOOL(x)*.
% 299.64/300.43 50643[0:SSi:50612.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)) -> hBOOL(x)*.
% 299.64/300.43 50765[0:SSi:50673.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),x,tc_bool)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)) -> hBOOL(x).
% 299.64/300.43 51086[0:SSi:50985.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(w,v,tc_bool)* equal(v,c_Orderings_Obot__class_Obot(tc_bool)) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w))* -> hBOOL(x)*.
% 299.64/300.43 51174[0:SpR:317.0,26873.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(y,v),x)),tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.64/300.43 51361[0:SpR:329.1,51231.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.43 51360[0:SpR:328.1,51231.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(u,hAPP(hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.43 51356[0:SpR:538.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),hAPP(hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.43 51294[0:SpR:317.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),hAPP(hAPP(c_Set_Oimage(u,v,t_a),hAPP(c_Set_Oinsert(x,v),w)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.43 51435[7:SpL:131.0,27284.0] || equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),v_x)** -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,w,x),z),hAPP(v,v_x))).
% 299.64/300.43 51488[0:SpL:317.0,33513.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(y,v),x)),w),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.64/300.43 51676[0:SpL:35.2,38146.0] || c_lessequals(u,c_Option_Othe(v),tc_fun(w,tc_bool))* c_lessequals(c_Option_Othe(v),x,tc_fun(w,tc_bool))* hBOOL(hAPP(u,c_Option_Ooption_OSome(y,v)))* -> hBOOL(y).
% 299.64/300.43 51817[4:SpR:317.0,40792.1] || c_lessequals(v_x,hAPP(hAPP(c_Set_Oimage(u,v,w),x),y),tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(z,v),x)),y))*.
% 299.64/300.43 52160[0:SSi:52094.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(w,v,tc_bool)* c_lessequals(v,x,tc_bool)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w))* -> hBOOL(x).
% 299.64/300.43 53003[0:Res:23739.1,455.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) c_Hoare__Mirabelle_Otriple__valid(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,v_Procs,t_a).
% 299.64/300.43 53762[0:Res:7226.0,279.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oimage(c_Option_Othe(w),x,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))),hAPP(c_Set_Oimage(c_Option_Othe(w),x,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))**.
% 299.64/300.43 54071[0:SpR:52997.1,3294.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_Set_Oinsert(v_Procs,u),c_in(t_a))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.43 56110[7:MRR:55959.2,27297.0] || equal(u,c_Set_Oimage(c_COMBK(v,w,x),x,w))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))* -> .
% 299.64/300.43 56111[7:MRR:55876.2,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),x)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool),hAPP(x,v_x))* -> .
% 299.64/300.43 56344[0:SpL:30368.2,3489.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.43 56343[0:SpL:30368.2,3487.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.43 56323[0:SpR:30368.2,584.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w,x,y),z),hAPP(c_Orderings_Otop__class_Otop(u),hAPP(v,z)))**.
% 299.64/300.43 56322[0:SpR:30368.2,584.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,x,y),z),hAPP(hAPP(v,z),c_Orderings_Otop__class_Otop(u)))**.
% 299.64/300.43 56161[0:SpR:30368.2,3294.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(t_a))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.43 56786[0:SpL:30928.2,3489.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(tc_Com_Opname))** hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.64/300.43 56785[0:SpL:30928.2,3487.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.43 56765[0:SpR:30928.2,584.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w,x,y),z),hAPP(c_Orderings_Otop__class_Otop(u),hAPP(v,z)))**.
% 299.64/300.43 56764[0:SpR:30928.2,584.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,x,y),z),hAPP(hAPP(v,z),c_Orderings_Otop__class_Otop(u)))**.
% 299.64/300.43 56602[0:SpR:30928.2,3294.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_in(t_a))** -> equal(hAPP(c_Orderings_Otop__class_Otop(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.43 56899[0:Obv:56684.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),u),v),u,u),c_Orderings_Otop__class_Otop(u))**.
% 299.64/300.43 57954[0:SpL:329.1,55910.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(c_COMBK(w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* equal(c_HOL_Ouminus__class_Ouminus(w,tc_bool),v_x) -> .
% 299.64/300.43 57953[0:SpL:328.1,55910.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(c_COMBK(w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* equal(c_HOL_Ouminus__class_Ouminus(w,tc_bool),u) -> .
% 299.64/300.43 57949[0:SpL:538.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),y))* -> .
% 299.64/300.43 58111[0:SpL:329.1,55992.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),w) -> .
% 299.64/300.43 58110[0:SpL:328.1,55992.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),w) -> .
% 299.64/300.43 58106[0:SpL:538.0,55992.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool),w)* -> .
% 299.64/300.43 58196[0:SpL:181.1,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_bool),v,w),c_Set_Ovimage(c_COMBK(x,y,u),u,y))* -> hBOOL(hAPP(hAPP(c_in(y),x),v_x)).
% 299.64/300.43 59031[4:Res:39450.0,15629.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),x1)))*.
% 299.64/300.43 58992[0:Res:710.0,15629.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(u,tc_bool)),v)))*.
% 299.64/300.43 58935[0:Res:1042.0,15629.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),v)))*.
% 299.64/300.43 58932[0:Res:1020.0,15629.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u),v)))*.
% 299.64/300.43 58931[0:Res:23944.1,15629.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(v_x,v_Procs),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(v_x,v_Procs),u)))*.
% 299.64/300.43 58875[0:Res:21126.1,15629.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Set_Oimage(v,tc_Com_Opname,w),u),x)))*.
% 299.64/300.43 58770[0:SpL:584.0,15629.0] || hBOOL(hAPP(c_COMBS(u,v,w,x,y),z))* -> hBOOL(hAPP(hAPP(u,z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,hAPP(u,z),x1)))*.
% 299.64/300.43 58666[0:SpL:8498.1,15629.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* hBOOL(u)* -> hBOOL(hAPP(c_Set_Oinsert(w,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Set_Oinsert(w,v),x)))*.
% 299.64/300.43 59121[0:Rew:9.0,58797.1] || hBOOL(hAPP(u,hAPP(v,w)))* -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Fun_Ocomp(u,v,z,x1,x2),x))))*.
% 299.64/300.43 59539[4:Res:39450.0,15857.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),x2)))*.
% 299.64/300.43 59500[0:Res:710.0,15857.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(u,tc_bool)),w)))*.
% 299.64/300.43 59443[0:Res:1042.0,15857.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),w)))*.
% 299.64/300.43 59440[0:Res:1020.0,15857.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u),w)))*.
% 299.64/300.43 59439[0:Res:23944.1,15857.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(v_x,v_Procs),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(v_x,v_Procs),v)))*.
% 299.64/300.43 59383[0:Res:21126.1,15857.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(v,tc_Com_Opname,w),u),y)))*.
% 299.64/300.43 59278[0:SpL:584.0,15857.0] || hBOOL(hAPP(c_COMBS(u,v,w,x,y),z))* -> hBOOL(hAPP(hAPP(u,z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(u,z),x2)))*.
% 299.64/300.43 59174[0:SpL:8498.1,15857.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* hBOOL(u)* -> hBOOL(hAPP(c_Set_Oinsert(w,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(w,v),y)))*.
% 299.64/300.43 59631[0:Rew:9.0,59305.1] || hBOOL(hAPP(u,hAPP(v,w)))* -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Fun_Ocomp(u,v,z,x1,x2),y))))*.
% 299.64/300.43 59753[0:SpL:475.1,21018.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(hAPP(c_Set_Oimage(x,y,z),hAPP(c_Set_Oimage(x1,u,y),w)),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))** -> .
% 299.64/300.43 59924[0:SSi:59854.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),w)** -> c_lessequals(hAPP(c_Set_Oinsert(u,v),x),w,tc_fun(v,tc_bool)).
% 299.64/300.43 60223[0:SpL:329.1,58170.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),x,y),w)* -> .
% 299.64/300.43 60222[0:SpL:328.1,58170.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(u,tc_bool),x,y),w)* -> .
% 299.64/300.43 60218[0:SpL:538.0,58170.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),tc_bool),x,y),u)* -> .
% 299.64/300.43 60440[7:Res:58968.1,3863.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)))*.
% 299.64/300.43 60417[7:Res:58968.1,2629.1] || equal(hAPP(c_in(tc_Com_Opname),v_x),v_x) equal(c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(c_in(tc_Com_Opname),v_x),u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.43 60465[0:SpR:5882.1,474.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1,v),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.64/300.43 60450[0:SpR:5882.1,415.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Fun_Ofun__upd(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_Orderings_Otop__class_Otop(u),c_Orderings_Otop__class_Otop(u),z,x1),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y))**.
% 299.64/300.43 60553[0:Res:58969.1,3863.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_Procs) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)))*.
% 299.64/300.43 60530[0:Res:58969.1,2629.1] || equal(hAPP(c_in(tc_Com_Opname),v_x),v_Procs) equal(c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(c_in(tc_Com_Opname),v_x),u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.43 60626[7:Res:59476.1,3863.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),y)))*.
% 299.64/300.43 60603[7:Res:59476.1,2629.1] || equal(hAPP(c_in(tc_Com_Opname),v_x),v_x) equal(c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x),v),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.43 60699[0:Res:59477.1,3863.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_Procs) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),y)))*.
% 299.64/300.43 60676[0:Res:59477.1,2629.1] || equal(hAPP(c_in(tc_Com_Opname),v_x),v_Procs) equal(c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x),v),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.64/300.43 60718[0:SpL:113.0,59706.0] || equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),y),v)*.
% 299.64/300.43 60884[0:Res:59017.1,3863.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),t_a)* hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),y)))*.
% 299.64/300.43 60861[0:Res:59017.1,2629.1] || equal(c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(c_in(tc_Com_Opname),v_x),u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(tc_Com_Opname),v_x),t_a)*.
% 299.64/300.43 60957[0:Res:59525.1,3863.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),t_a)* hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),z)))*.
% 299.64/300.43 60934[0:Res:59525.1,2629.1] || equal(c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x),v),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(tc_Com_Opname),v_x),t_a)*.
% 299.64/300.43 61775[0:SpR:11167.1,415.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> equal(c_Fun_Ofun__upd(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs,v_Procs,w,x),hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)))**.
% 299.64/300.43 61968[0:SpL:52997.1,15487.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_Procs,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.43 61963[0:SpL:584.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBS(u,v,w,x,y),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.43 61943[0:SpL:337.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.43 61930[0:SpL:540.1,15487.1] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.43 61929[0:SpL:539.1,15487.1] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.64/300.43 61928[0:SpL:297.2,15487.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.43 61921[0:SpL:30368.2,15487.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.43 61920[0:SpL:30928.2,15487.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.43 61917[0:SpL:299.2,15487.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.43 61911[0:SpL:24019.2,15487.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.43 61902[0:SpL:25.1,15487.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.64/300.43 62166[0:Res:23754.0,279.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs))**.
% 299.64/300.43 62403[0:SSi:62342.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool) equal(v,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool)) -> c_lessequals(v,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_bool),x,tc_bool),tc_bool)*.
% 299.64/300.43 62415[0:SSi:62206.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) equal(hAPP(c_Set_Oinsert(x,w),v),u) -> c_lessequals(hAPP(c_Set_Oinsert(x,w),v),u,tc_fun(w,tc_bool))*.
% 299.64/300.43 63670[0:Res:62368.3,251.1] class_Orderings_Olinorder(tc_fun(u,v)) class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || equal(w,x) -> c_lessequals(hAPP(w,y),hAPP(x,y),v)*.
% 299.64/300.43 63982[0:SpR:353.0,647.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v)),v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v),v_Procs,tc_fun(tc_Com_Opname,tc_bool)))**.
% 299.64/300.43 64023[0:Rew:66.0,63957.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)))**.
% 299.64/300.43 64107[0:Res:679.1,402.0] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) c_lessequals(v_Procs,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),tc_fun(tc_Com_Opname,tc_bool))* -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v_Procs).
% 299.64/300.43 64091[0:SpR:353.0,679.1] || c_lessequals(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v),v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v)),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.43 64122[0:SSi:64117.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v_Procs) -> c_lessequals(v_Procs,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),tc_fun(tc_Com_Opname,tc_bool))*.
% 299.64/300.43 64206[0:SpR:414.0,646.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v_x,v,w,x),v_Procs,tc_Com_Opname,y) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Fun_Ofun__upd(u,v_x,v,w,x),tc_Com_Opname,y),v),v_x)**.
% 299.64/300.43 64195[0:SpR:524.0,646.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.43 64187[0:SpR:8415.2,646.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.43 64183[0:SpR:365.1,646.1] class_Orderings_Obot(u) || c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,v),c_Orderings_Obot__class_Obot(u)),v_x)**.
% 299.64/300.43 64182[0:SpR:397.1,646.1] class_Orderings_Otop(u) || c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u)),v_x)**.
% 299.64/300.43 64172[0:SpR:646.1,20881.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,x),hAPP(c_Set_Oinsert(hAPP(u,v_x),w),y)),v_x))*.
% 299.64/300.43 64165[0:SpR:646.1,474.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),x,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.43 64157[0:SpR:646.1,9569.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v)),hAPP(u,v_x)),tc_bool)*.
% 299.64/300.43 64156[0:SpR:646.1,9568.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v)),x),hAPP(u,v_x)),tc_bool)*.
% 299.64/300.43 64260[4:MRR:64253.1,6340.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> hBOOL(hAPP(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w)))*.
% 299.64/300.43 64261[4:MRR:64252.1,6340.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> hBOOL(hAPP(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),x)))*.
% 299.64/300.43 64373[0:SpR:414.0,645.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v_x,v,w,x),v_Procs,tc_Com_Opname,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ofun__upd(u,v_x,v,w,x),tc_Com_Opname,y),v),v_x)**.
% 299.64/300.43 64362[0:SpR:524.0,645.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.43 64354[0:SpR:8415.2,645.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),v_x),v_x)**.
% 299.64/300.43 64350[0:SpR:365.1,645.1] class_Orderings_Obot(u) || c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),tc_Com_Opname,v),c_Orderings_Obot__class_Obot(u)),v_x)**.
% 299.64/300.43 64349[0:SpR:397.1,645.1] class_Orderings_Otop(u) || c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u)),v_x)**.
% 299.64/300.43 64339[0:SpR:645.1,20881.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,x),hAPP(c_Set_Oinsert(hAPP(u,v_x),w),y)),v_x))*.
% 299.64/300.43 64332[0:SpR:645.1,474.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),x,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.43 64324[0:SpR:645.1,9569.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v)),hAPP(u,v_x)),tc_bool)*.
% 299.64/300.43 64323[0:SpR:645.1,9568.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v)),x),hAPP(u,v_x)),tc_bool)*.
% 299.64/300.43 64426[4:MRR:64420.1,6340.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w)))*.
% 299.64/300.43 64427[4:MRR:64419.1,6340.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),x)))*.
% 299.64/300.43 64480[0:Res:662.1,19641.0] || hBOOL(hAPP(hAPP(u,v_x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),w)))* -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),w,t_a).
% 299.64/300.43 64557[0:SpL:584.0,24257.1] || equal(c_COMBS(u,v,w,x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.43 64537[0:SpL:337.0,24257.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.43 64524[0:SpL:540.1,24257.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.43 64523[0:SpL:539.1,24257.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.43 64515[0:SpL:30368.2,24257.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.43 64514[0:SpL:30928.2,24257.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Otop__class_Otop(u),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.43 64511[0:SpL:299.2,24257.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(v,c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.43 64496[0:SpL:25.1,24257.1] class_HOL_Ouminus(u) || equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.64/300.43 64592[0:SpR:26782.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,tc_fun(w,tc_bool)),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.64/300.43 66044[0:SpR:65404.1,361.2] class_Lattices_Olattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),x),y)) -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,v),v)*.
% 299.64/300.43 66025[0:SpR:65404.1,176.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.64/300.43 66476[0:Rew:130.1,66328.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),v_Procs) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),v_x))*.
% 299.64/300.43 66728[0:SpR:1188.2,20881.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,w),hAPP(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(u),v),x)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.43 66702[0:SpR:1188.2,9569.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u))),c_HOL_Ozero__class_Ozero(u)),tc_bool)*.
% 299.64/300.43 66701[0:SpR:1188.2,9568.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u))),w),c_HOL_Ozero__class_Ozero(u)),tc_bool)*.
% 299.64/300.43 67483[0:SpR:1189.2,20881.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,w),hAPP(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(u),v),x)),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.43 67457[0:SpR:1189.2,9569.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u))),c_HOL_Ozero__class_Ozero(u)),tc_bool)*.
% 299.64/300.43 67456[0:SpR:1189.2,9568.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> c_lessequals(c_Orderings_Otop__class_Otop(u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u))),w),c_HOL_Ozero__class_Ozero(u)),tc_bool)*.
% 299.64/300.43 68452[0:Rew:1250.3,68254.4] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Ogroup__add(u) class_Orderings_Obot(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) equal(c_HOL_Ozero__class_Ozero(u),v_Procs) -> hBOOL(hAPP(c_HOL_Ozero__class_Ozero(u),v_x))*.
% 299.64/300.43 69690[0:Res:364.1,6239.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),w),tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Oinsert(u,v),w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))).
% 299.64/300.43 70083[0:Res:687.1,11883.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_Com_Opname)),u))* -> .
% 299.64/300.43 70082[0:Res:686.1,11883.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_Com_Opname)),u))* -> .
% 299.64/300.43 70367[0:SpL:338.0,12983.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,w,t_a).
% 299.64/300.43 70356[0:SpL:8415.2,12983.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),c_Set_Oinsert(v_x,tc_Com_Opname))** c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,v_x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a)*.
% 299.64/300.43 70470[0:SpL:223.1,70390.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,t_a),u,t_a),w),v_x),tc_bool))* -> .
% 299.64/300.43 70523[0:SpL:223.1,70504.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,t_a),u,t_a),w),v_x),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.64/300.43 70863[0:SpL:8415.2,6582.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(v_x,v) -> c_lessequals(v_x,v,tc_fun(u,tc_bool)).
% 299.64/300.43 70857[0:SpL:8415.2,6582.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(hAPP(v_x,v),v_x) -> c_lessequals(v,v_x,tc_fun(u,tc_bool))*.
% 299.64/300.43 71059[0:SpR:339.0,7568.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y))),tc_fun(v,tc_bool))*.
% 299.64/300.43 71020[0:SpR:8415.2,7568.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> c_lessequals(v,hAPP(c_Set_Oinsert(w,u),v_x),tc_fun(u,tc_bool))*.
% 299.64/300.43 71269[0:SpR:8415.2,7538.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> c_lessequals(v,hAPP(v_x,hAPP(c_Set_Oinsert(w,u),v)),tc_fun(u,tc_bool))*.
% 299.64/300.43 71235[0:SpR:353.0,7538.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(y,v),w))),tc_fun(v,tc_bool))*.
% 299.64/300.43 71404[7:SpL:181.1,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_bool)) equal(c_Set_Ovimage(c_COMBK(v,w,u),u,w),v_x)** -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)).
% 299.64/300.43 71686[7:SpR:71455.1,338.0] || equal(u,v_x) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u))**.
% 299.64/300.43 71615[7:SpR:71455.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(v,v_x) hBOOL(hAPP(hAPP(c_in(w),v),x)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v_x,t_a),w,u),u)*.
% 299.64/300.43 71609[7:SpR:71455.1,339.0] || equal(u,v_x) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))**.
% 299.64/300.43 71591[7:SpR:71455.1,176.0] || equal(u,v_x) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.64/300.43 72078[0:SpR:338.0,7830.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),w))),tc_fun(v,tc_bool))*.
% 299.64/300.43 72492[0:Res:45357.1,12554.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname)),u))*.
% 299.64/300.43 72693[0:SpL:24914.0,18903.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_x),u,v,w)* -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Ocom_OBODY,tc_Com_Opname,x),hAPP(c_Com_Ocom_OBODY,v_x)))),u,w)*.
% 299.64/300.43 72690[0:SpL:8415.2,18903.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Com_Ocom_OBODY) c_Natural_Oevaln(v_x,u,v,w)* -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x)),u,w)*.
% 299.64/300.43 73042[7:Res:71608.1,516.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.64/300.43 74346[7:SpL:71835.1,390.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_lessequals(x,v_x,tc_fun(w,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_x,u,v,w),x,w,v)*.
% 299.64/300.43 74344[7:SpL:71835.1,515.0] || equal(c_Set_Oinsert(v_x,t_a),c_Hoare__Mirabelle_Otriple_Otriple(u)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(v_x,y),z))* -> equal(v,v_x).
% 299.64/300.43 74343[7:SpL:71835.1,514.0] || equal(c_Set_Oinsert(v_x,t_a),c_Hoare__Mirabelle_Otriple_Otriple(u)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(v_x,y),z))* -> equal(w,y).
% 299.64/300.43 74342[7:SpL:71835.1,513.0] || equal(c_Set_Oinsert(v_x,t_a),c_Hoare__Mirabelle_Otriple_Otriple(u)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(v_x,y),z))* -> equal(x,z).
% 299.64/300.43 74326[7:SpL:71835.1,515.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Set_Oinsert(v_x,t_a))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),hAPP(v_x,z))* -> equal(w,v)*.
% 299.64/300.43 74325[7:SpL:71835.1,514.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Set_Oinsert(v_x,t_a))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),hAPP(v_x,z))* -> equal(x,v_x).
% 299.64/300.43 74324[7:SpL:71835.1,513.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Set_Oinsert(v_x,t_a))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),hAPP(v_x,z))* -> equal(y,z).
% 299.64/300.43 74278[7:SpL:71835.1,515.0] || equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),c_Set_Oinsert(v_x,t_a))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),x),y),z),v_x)** -> equal(v,x)*.
% 299.64/300.43 74277[7:SpL:71835.1,514.0] || equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),c_Set_Oinsert(v_x,t_a))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),x),y),z),v_x)** -> equal(w,y)*.
% 299.64/300.43 74276[7:SpL:71835.1,513.0] || equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),c_Set_Oinsert(v_x,t_a))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),x),y),z),v_x)** -> equal(v_x,z).
% 299.64/300.43 74150[7:SpL:71835.1,278.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,w)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,x,v,u)))*.
% 299.64/300.43 74149[7:SpL:71835.1,277.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,w)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,w,v,u)))*.
% 299.64/300.43 74122[7:SpL:71835.1,170.1] class_Orderings_Olinorder(u) || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,v)) c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),v_x,u)*.
% 299.64/300.43 74121[7:SpL:71835.1,169.1] class_Orderings_Olinorder(u) || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,v)) c_Finite__Set_Ofinite(v,u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.64/300.43 73956[7:SpL:71835.1,501.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(v_x,u)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.64/300.43 73691[7:SpR:71835.1,128.0] || equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(v,tc_bool)))**.
% 299.64/300.43 73668[7:SpR:71835.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Set_Oinsert(v_x,t_a),v) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,w,u),u)*.
% 299.64/300.43 73592[7:SpR:71835.1,446.1] || equal(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(u,v)) c_lessequals(w,v_x,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),v_x,tc_fun(v,tc_bool))*.
% 299.64/300.43 73585[7:SpR:71835.1,176.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.64/300.43 73508[7:SpR:71835.1,176.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(hAPP(v,v_x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.64/300.43 74511[7:Rew:71835.1,73507.2,71835.1,73507.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(v_x,w)) hBOOL(hAPP(v_x,c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))))*.
% 299.64/300.43 74659[7:Res:71906.0,15629.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),w)))*.
% 299.64/300.43 74658[7:Res:71906.0,15857.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),x)))*.
% 299.64/300.43 74715[7:Res:71907.0,15629.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),w)))*.
% 299.64/300.43 74714[7:Res:71907.0,15857.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),x)))*.
% 299.64/300.43 74814[0:SpR:8415.2,5893.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(u)) -> c_Hoare__Mirabelle_Otriple__valid(c_HOL_Ozero__class_Ozero(tc_nat),hAPP(c_COMBS(v_x,v,w,x,y),hAPP(c_Com_Ocom_OBODY,z)),u)*.
% 299.64/300.43 75414[0:SpR:8415.2,7820.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v,hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v)),u)*.
% 299.64/300.43 75604[0:SSi:75485.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(c_Set_Oinsert(v,u),y)))))*.
% 299.64/300.43 75605[0:SSi:75368.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v)),tc_fun(w,tc_bool))*.
% 299.64/300.43 75868[0:SpR:8415.2,7823.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v,hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),u)*.
% 299.64/300.43 75790[0:SpR:8415.2,7823.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x),u)*.
% 299.64/300.43 76073[0:SSi:75838.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,y),z),u,y,tc_fun(w,tc_bool))),tc_fun(w,tc_bool))*.
% 299.64/300.43 76160[0:SpR:9915.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x2),x4)),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.43 76145[0:SpR:9915.0,9569.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_COMBS(c_Set_Ovimage(w,x,y),z,x1,x2,x3)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),tc_bool)*.
% 299.64/300.43 76144[0:SpR:9915.0,9568.0] || -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_COMBS(c_Set_Ovimage(v,w,x),y,z,x1,x2)),x3),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),tc_bool)*.
% 299.64/300.43 76280[0:SpR:10469.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),x2,x3),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),x2),x4)),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.43 76410[0:SpR:10470.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x2),x4)),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.64/300.43 76638[0:Res:29199.1,427.1] class_Lattices_Olattice(u) class_Orderings_Opreorder(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y,u)* -> c_lessequals(x,y,u).
% 299.64/300.43 76637[0:Res:29199.1,426.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(v,w,u) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w)),u)*.
% 299.64/300.43 76545[0:SpR:8415.2,29199.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v,hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v)),u)*.
% 299.64/300.43 76993[0:Res:30321.1,427.1] class_Lattices_Olattice(u) class_Orderings_Opreorder(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y,u)* -> c_lessequals(w,y,u).
% 299.64/300.43 76992[0:Res:30321.1,426.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(v,w,u) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),u)*.
% 299.64/300.43 76900[0:SpR:8415.2,30321.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v,hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),u)*.
% 299.64/300.43 76822[0:SpR:8415.2,30321.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x),u)*.
% 299.64/300.43 77142[7:SpL:130.1,74788.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_x) equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),x)* -> hBOOL(x)*.
% 299.64/300.43 77393[0:Res:2399.2,427.1] class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(v,w,u).
% 299.64/300.43 77392[0:Res:2399.2,426.1] class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,w,u) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,u),u)*.
% 299.64/300.43 77374[0:Res:2399.2,70.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.64/300.43 77585[0:Res:2429.2,427.1] class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(v,w,u).
% 299.64/300.43 77584[0:Res:2429.2,426.1] class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,w,u) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,u),u)*.
% 299.64/300.43 77795[0:SpL:586.0,5892.0] || hBOOL(hAPP(hAPP(u,hAPP(v,w)),w))* -> hBOOL(hAPP(c_COMBS(c_in(x),hAPP(c_COMBB(u,y,z,x1),v),x2,x3,x4),w))*.
% 299.64/300.43 77794[0:SpL:585.0,5892.0] || hBOOL(hAPP(hAPP(hAPP(u,v),w),v))* -> hBOOL(hAPP(c_COMBS(c_in(x),hAPP(c_COMBC(u,y,z,x1),w),x2,x3,x4),v))*.
% 299.64/300.43 77653[0:SpL:445.1,5892.0] || hBOOL(hAPP(hAPP(u,v),v))* -> equal(v,w) hBOOL(hAPP(c_COMBS(c_in(x),c_Fun_Ofun__upd(u,w,y,z,x1),x2,x3,x4),v))*.
% 299.64/300.43 78162[7:Res:77996.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x))* equal(hAPP(w,v_x),hAPP(w,v))* c_Fun_Oinj__on(w,v_x,u,x)* -> equal(v_x,v).
% 299.64/300.43 78353[7:SpR:78167.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),x)))*.
% 299.64/300.43 78352[7:SpR:78167.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,u),v,w),v_x),v_x)**.
% 299.64/300.43 78351[7:SpR:78167.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,u),v,w),v_x),v_x)**.
% 299.64/300.43 78703[4:Res:78665.1,467.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)),v_x)** -> equal(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v)),v)**.
% 299.64/300.43 78861[0:SpR:393.1,11064.1] || c_Finite__Set_Ofinite(u,v)* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),y,tc_fun(x,tc_bool)),x)*.
% 299.64/300.43 80143[0:SpL:21268.0,377.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v) -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),w),x,y),v)*.
% 299.64/300.43 80125[0:SpL:21268.0,3484.1] || equal(c_Com_Ocom_OBODY,u) equal(hAPP(u,v_x),hAPP(c_Com_Ocom_OBODY,v))* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,v),w,x),v_x)**.
% 299.64/300.43 79978[0:SpR:27043.1,21268.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_Procs,u),v_x,v,w)),v_x)**.
% 299.64/300.43 79975[0:SpR:10063.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,v)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.64/300.43 79955[0:SpR:105.0,21268.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x,y)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.64/300.43 79942[0:SpR:38.0,21268.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),x,y)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.64/300.43 79940[0:SpR:321.0,21268.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(u,v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x,y)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.64/300.43 79935[0:SpR:11695.0,21268.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Orderings_Otop__class_Otop(tc_bool),x,y)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.43 79835[0:SpR:2089.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),u,w)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))**.
% 299.64/300.43 79812[0:SpR:21268.0,19744.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v),w,x),t_a)*.
% 299.64/300.43 79652[0:SpR:21268.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,hAPP(u,y),x,z),v),x1)),hAPP(u,y)))*.
% 299.64/300.43 79531[0:SpR:21268.0,9569.0] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),u,hAPP(u,v),y,z)),tc_bool)*.
% 299.64/300.43 79530[0:SpR:21268.0,9568.0] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),u,hAPP(u,v),y,z)),tc_bool)*.
% 299.64/300.43 79440[0:SpR:21268.0,31323.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_Procs,hAPP(v_Procs,v),u,w)),hAPP(v_Procs,v),tc_bool)*.
% 299.64/300.43 79365[0:SpR:21268.0,378.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,w),x),w).
% 299.64/300.43 81338[0:SpL:21894.0,377.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v) -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(u,v),x,y),v)*.
% 299.64/300.43 81320[0:SpL:21894.0,3484.1] || equal(c_Com_Ocom_OBODY,u) equal(hAPP(u,v_x),hAPP(c_Com_Ocom_OBODY,v))* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Com_Ocom_OBODY,v),c_Com_Ocom_OBODY,w,x),v_x)**.
% 299.64/300.43 81172[0:SpR:27043.1,21894.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v_x,c_Set_Oinsert(v_Procs,u),v,w)),v_x)**.
% 299.64/300.43 81169[0:SpR:10063.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Set_Oinsert(v_x,t_a),u,v)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.64/300.43 81149[0:SpR:105.0,21894.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Ovimage(u,v,w),x,y)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.64/300.43 81136[0:SpR:38.0,21894.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Set_Ovimage(u,v,w),x,y)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.64/300.43 81134[0:SpR:321.0,21894.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Set_Oimage(u,v,w),x,y)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.64/300.43 81129[0:SpR:11695.0,21894.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),x,y)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.64/300.43 81029[0:SpR:2089.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_Set_Oinsert(v_x,tc_Com_Opname),u,w)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))**.
% 299.64/300.43 81006[0:SpR:21894.0,19744.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v),c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),w,x),t_a)*.
% 299.64/300.43 80846[0:SpR:21894.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(u,y),u,x,z),v),x1)),hAPP(u,y)))*.
% 299.64/300.43 80724[0:SpR:21894.0,9569.0] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(u,v),u,y,z)),tc_bool)*.
% 299.64/300.43 80723[0:SpR:21894.0,9568.0] || -> c_lessequals(hAPP(u,v),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(u,v),u,y,z)),tc_bool)*.
% 299.64/300.43 80633[0:SpR:21894.0,31323.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(v_Procs,v),v_Procs,u,w)),hAPP(v_Procs,v),tc_bool)*.
% 299.64/300.43 80558[0:SpR:21894.0,378.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,w),x),w).
% 299.64/300.43 81748[0:SpR:128.0,5075.1] || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(w,x,v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(w,x,v),u),tc_fun(x,tc_bool))),v)*.
% 299.64/300.43 81954[0:SpR:53771.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Option_Othe(w),x,y,z),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),v,c_Option_Othe(w),x1,x2)),u)*.
% 299.64/300.43 81950[0:SpR:53772.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Option_Othe(w),x,y,z),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Option_Othe(w),v,x1,x2)),u)*.
% 299.64/300.43 81919[0:SpR:586.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(v,hAPP(w,x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_COMBB(v,y,z,x1),w),x2,x3,x4),x),u)*.
% 299.64/300.43 81918[0:SpR:585.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(v,w),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_COMBC(v,y,z,x1),x),x2,x3,x4),w),u)*.
% 299.64/300.43 81782[0:SpR:445.1,5879.1] class_Lattices_Oupper__semilattice(u) || -> equal(v,w) c_lessequals(hAPP(x,v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Fun_Ofun__upd(x,w,y,z,x1),x2,x3,x4),v),u)*.
% 299.64/300.43 82103[7:Res:78321.0,15629.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,c_in(tc_Com_Opname),u,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,c_in(tc_Com_Opname),u,tc_fun(v,tc_bool)),w)))*.
% 299.64/300.43 82102[7:Res:78321.0,15857.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,c_in(tc_Com_Opname),u,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,c_in(tc_Com_Opname),u,tc_fun(v,tc_bool)),x)))*.
% 299.64/300.43 82189[7:SpR:78597.0,338.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),c_Set_Oinsert(v_x,v))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),c_Set_Oinsert(v_x,v)))**.
% 299.64/300.43 82158[7:SpR:78597.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Set_Oinsert(v_x,w)),x)) -> c_lessequals(c_Set_Oinsert(v_x,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v_x,t_a),v,u),u)*.
% 299.64/300.43 82149[7:SpR:78597.0,339.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,u)),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,u)),v))**.
% 299.64/300.43 82131[7:SpR:78597.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Set_Oinsert(v_x,v)),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),u,w),hAPP(c_Set_Oinsert(c_Set_Oinsert(v_x,v),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.64/300.43 82455[0:Res:5880.1,427.1] class_Lattices_Olattice(u) class_Orderings_Opreorder(u) || c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),x1,u)* -> c_lessequals(hAPP(v,z),x1,u).
% 299.64/300.43 82454[0:Res:5880.1,426.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(v,hAPP(w,x),u) -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,y,z,x1),x),u)*.
% 299.64/300.43 82427[0:SpR:53771.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Option_Othe(w),x,y,z),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),v,c_Option_Othe(w),x1,x2)),u)*.
% 299.64/300.43 82423[0:SpR:53772.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Option_Othe(w),x,y,z),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Option_Othe(w),v,x1,x2)),u)*.
% 299.64/300.43 82391[0:SpR:586.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(v,hAPP(w,x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_COMBB(v,y,z,x1),w),x2,x3,x4),x),u)*.
% 299.64/300.43 82390[0:SpR:585.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(v,w),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_COMBC(v,y,z,x1),x),x2,x3,x4),w),u)*.
% 299.64/300.43 82254[0:SpR:445.1,5880.1] class_Lattices_Olattice(u) || -> equal(v,w) c_lessequals(hAPP(x,v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Fun_Ofun__upd(x,w,y,z,x1),x2,x3,x4),v),u)*.
% 299.64/300.43 82700[0:Res:2399.2,7671.1] class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,u),u)*.
% 299.64/300.43 82699[0:Res:2429.2,7671.1] class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,u),u)*.
% 299.64/300.43 82914[0:SpR:393.1,22513.1] || c_Finite__Set_Ofinite(u,v)* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(w,x,y),hAPP(c_Set_Oinsert(z,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),y)*.
% 299.64/300.43 83116[0:SpL:5924.0,55910.1] || equal(c_COMBK(u,v,w),c_COMBS(x,c_COMBK(y,z,x1),x2,x3,x4))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(hAPP(x,v_x),y)) -> .
% 299.64/300.43 83115[0:SpL:5924.0,3507.1] || equal(c_Set_Oinsert(u,v),c_COMBS(w,c_COMBK(x,y,z),x1,x2,x3))* equal(hAPP(hAPP(w,v_x),x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.64/300.43 83113[0:SpL:5924.0,16327.1] || equal(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2))* equal(hAPP(hAPP(v,v_x),w),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_Procs) -> .
% 299.64/300.43 83112[7:SpL:5924.0,31886.1] || equal(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2))* equal(hAPP(hAPP(v,v_x),w),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_x) -> .
% 299.64/300.43 83111[0:SpL:5924.0,3499.1] || equal(c_in(u),c_COMBS(v,c_COMBK(w,x,y),z,x1,x2))* hBOOL(hAPP(hAPP(hAPP(v,v_x),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.43 83109[0:SpL:5924.0,58170.1] || equal(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(v,v_x),w),tc_bool),x3,x4),u)* -> .
% 299.64/300.43 83104[0:SpL:5924.0,24254.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(u,v_x),v),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.43 83099[0:SpL:5924.0,13272.0] || equal(hAPP(hAPP(u,v_x),v),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2)* -> hBOOL(hAPP(x2,v_x))*.
% 299.64/300.43 83098[0:SpL:5924.0,3484.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Com_Ocom_OBODY)** equal(hAPP(hAPP(u,v_x),v),hAPP(c_Com_Ocom_OBODY,x2))* -> equal(v_x,x2).
% 299.64/300.43 83093[0:SpL:5924.0,55992.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_COMBK(x2,x3,x4))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool),x2) -> .
% 299.64/300.43 83058[0:SpR:5924.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,x3),hAPP(c_Set_Oinsert(x4,x2),x5)),hAPP(hAPP(u,x4),v)))*.
% 299.64/300.43 83033[0:SpR:5924.0,9569.0] || -> c_lessequals(hAPP(hAPP(u,v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_COMBS(u,c_COMBK(w,z,x1),x2,x3,x4)),v),tc_bool)*.
% 299.64/300.43 83032[0:SpR:5924.0,9568.0] || -> c_lessequals(hAPP(hAPP(u,v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_COMBS(u,c_COMBK(w,y,z),x1,x2,x3)),x4),v),tc_bool)*.
% 299.64/300.43 83028[0:SpR:5924.0,3346.1] || equal(c_Set_Oinsert(u,v),c_COMBS(w,c_COMBK(x,y,z),x1,x2,x3))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(hAPP(w,v_x),x)))*.
% 299.64/300.43 83027[0:SpR:5924.0,28356.1] || equal(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(hAPP(v,v_x),w),tc_Com_Opname,x3)))*.
% 299.64/300.43 83026[0:SpR:5924.0,28053.1] || equal(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(v,v_x),w),u,tc_Com_Opname,x3)))*.
% 299.64/300.43 83025[0:SpR:5924.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2),hAPP(hAPP(v,v_x),w),tc_Com_Opname,x3)))*.
% 299.64/300.43 83024[0:SpR:5924.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(v,v_x),w),c_COMBS(v,c_COMBK(w,x,y),z,x1,x2),tc_Com_Opname,x3)))*.
% 299.64/300.43 83023[0:SpR:5924.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(v,c_COMBK(w,x,y),z,x1,x2),tc_Com_Opname,x3),u),hAPP(hAPP(v,v_x),w)))*.
% 299.64/300.43 83022[0:SpR:5924.0,3317.1] || equal(c_in(u),c_COMBS(v,c_COMBK(w,x,y),z,x1,x2))* -> hBOOL(hAPP(hAPP(hAPP(v,v_x),w),hAPP(c_Set_Oinsert(v_x,u),x3)))*.
% 299.64/300.43 83021[0:SpR:5924.0,3305.1] || equal(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x3),v_Procs),hAPP(hAPP(v,v_x),w)))*.
% 299.64/300.43 83017[0:SpR:5924.0,2771.1] || equal(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2))* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(v,v_x),w),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.43 83012[0:SpR:5924.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(u,v_x),v),hAPP(hAPP(c_Set_Oinsert(w,t_a),c_COMBS(u,c_COMBK(v,x,y),z,x1,x2)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.43 83007[0:SpR:5924.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname,x2),hAPP(hAPP(u,v_x),v)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.43 83005[0:SpR:5924.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname,x2),hAPP(hAPP(u,v_x),v))),v_Procs))*.
% 299.64/300.43 82998[0:SpR:5924.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname,x2),hAPP(c_Set_Oinsert(x3,tc_Com_Opname),v_Procs)),hAPP(hAPP(u,v_x),v)))*.
% 299.64/300.43 82997[0:SpR:5924.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),t_a,x2),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(u,v_x),v)))*.
% 299.64/300.43 82991[0:SpR:5924.0,15262.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.43 82988[0:SpR:5924.0,8376.2] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_in(tc_Com_Opname))** equal(x2,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(u,v_x),v),x2))*.
% 299.64/300.43 82986[4:SpR:5924.0,39064.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(x2,x3),hAPP(hAPP(u,v_x),v)),x4,t_a)*.
% 299.64/300.43 82985[4:SpR:5924.0,39023.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x2,x3),hAPP(hAPP(u,v_x),v)),x4))*.
% 299.64/300.43 82984[0:SpR:5924.0,3291.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x2,x3),hAPP(hAPP(u,v_x),v)),v_Procs))*.
% 299.64/300.43 82983[0:SpR:5924.0,3285.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(hAPP(u,v_x),v),hAPP(c_Set_Oinsert(x2,tc_Com_Opname),v_Procs)))*.
% 299.64/300.43 83149[0:Rew:5924.0,83063.0] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,c_COMBS(u,c_COMBK(v,x,y),z,x1,x2),tc_Com_Opname)),v))*.
% 299.64/300.43 83150[0:Rew:5924.0,83062.0] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,c_COMBS(u,c_COMBK(v,x,y),z,x1,x2),tc_Com_Opname)),v))*.
% 299.64/300.43 83235[7:SpR:181.1,78357.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,w),w,u),x,y),v_x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.64/300.43 83435[0:SpL:5961.0,55910.1] || equal(c_COMBK(u,v,w),c_COMBS(c_COMBK(x,y,z),x1,x2,x3,x4))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(x,hAPP(x1,v_x))) -> .
% 299.64/300.43 83433[0:SpL:5961.0,16327.1] || equal(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2))* equal(hAPP(v,hAPP(y,v_x)),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_Procs) -> .
% 299.64/300.43 83432[7:SpL:5961.0,31886.1] || equal(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2))* equal(hAPP(v,hAPP(y,v_x)),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_x) -> .
% 299.64/300.43 83431[0:SpL:5961.0,3499.1] || equal(c_in(u),c_COMBS(c_COMBK(v,w,x),y,z,x1,x2))* hBOOL(hAPP(hAPP(v,hAPP(y,v_x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.64/300.43 83429[0:SpL:5961.0,58170.1] || equal(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(v,hAPP(y,v_x)),tc_bool),x3,x4),u)* -> .
% 299.64/300.43 83424[0:SpL:5961.0,24254.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(u,hAPP(x,v_x)),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.64/300.43 83419[0:SpL:5961.0,13272.0] || equal(hAPP(u,hAPP(v,v_x)),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),x2)* -> hBOOL(hAPP(x2,v_x))*.
% 299.64/300.43 83418[0:SpL:5961.0,3484.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Com_Ocom_OBODY)** equal(hAPP(u,hAPP(x,v_x)),hAPP(c_Com_Ocom_OBODY,x2))* -> equal(v_x,x2).
% 299.64/300.43 83413[0:SpL:5961.0,55992.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_COMBK(x2,x3,x4))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(x,v_x)),tc_bool),x2) -> .
% 299.64/300.43 83383[0:SpR:5961.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2,x3),hAPP(c_Set_Oinsert(x4,x2),x5)),hAPP(u,hAPP(x,x4))))*.
% 299.64/300.43 83364[0:SpR:5961.0,9569.0] || -> c_lessequals(hAPP(u,hAPP(v,w)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_COMBS(c_COMBK(u,z,x1),v,x2,x3,x4)),w),tc_bool)*.
% 299.64/300.43 83363[0:SpR:5961.0,9568.0] || -> c_lessequals(hAPP(u,hAPP(v,w)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_COMBS(c_COMBK(u,y,z),v,x1,x2,x3)),x4),w),tc_bool)*.
% 299.64/300.43 83359[0:SpR:5961.0,3346.1] || equal(c_Set_Oinsert(u,v),c_COMBS(c_COMBK(w,x,y),z,x1,x2,x3))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(w,hAPP(z,v_x))))*.
% 299.64/300.43 83358[0:SpR:5961.0,28356.1] || equal(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(v,hAPP(y,v_x)),tc_Com_Opname,x3)))*.
% 299.64/300.43 83357[0:SpR:5961.0,28053.1] || equal(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,hAPP(y,v_x)),u,tc_Com_Opname,x3)))*.
% 299.64/300.43 83356[0:SpR:5961.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2),hAPP(v,hAPP(y,v_x)),tc_Com_Opname,x3)))*.
% 299.64/300.43 83355[0:SpR:5961.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,hAPP(w,v_x)),c_COMBS(c_COMBK(v,x,y),w,z,x1,x2),tc_Com_Opname,x3)))*.
% 299.64/300.43 83354[0:SpR:5961.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_COMBK(v,w,x),y,z,x1,x2),tc_Com_Opname,x3),u),hAPP(v,hAPP(y,v_x))))*.
% 299.64/300.43 83353[0:SpR:5961.0,3317.1] || equal(c_in(u),c_COMBS(c_COMBK(v,w,x),y,z,x1,x2))* -> hBOOL(hAPP(hAPP(v,hAPP(y,v_x)),hAPP(c_Set_Oinsert(v_x,u),x3)))*.
% 299.64/300.43 83352[0:SpR:5961.0,3305.1] || equal(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x3),v_Procs),hAPP(v,hAPP(y,v_x))))*.
% 299.64/300.43 83348[0:SpR:5961.0,2771.1] || equal(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2))* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,hAPP(y,v_x)),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.64/300.43 83342[0:SpR:5961.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(u,hAPP(v,v_x)),hAPP(hAPP(c_Set_Oinsert(w,t_a),c_COMBS(c_COMBK(u,x,y),v,z,x1,x2)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.64/300.43 83337[0:SpR:5961.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(c_COMBK(u,v,w),x,y,z,x1),tc_Com_Opname,x2),hAPP(u,hAPP(x,v_x))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.64/300.43 83335[0:SpR:5961.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(c_COMBK(u,v,w),x,y,z,x1),tc_Com_Opname,x2),hAPP(u,hAPP(x,v_x)))),v_Procs))*.
% 299.64/300.43 83328[0:SpR:5961.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),tc_Com_Opname,x2),hAPP(c_Set_Oinsert(x3,tc_Com_Opname),v_Procs)),hAPP(u,hAPP(x,v_x))))*.
% 299.64/300.43 83327[0:SpR:5961.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),t_a,x2),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(u,hAPP(x,v_x))))*.
% 299.64/300.43 83321[0:SpR:5961.0,15262.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_in(t_a))** -> hBOOL(hAPP(hAPP(u,hAPP(x,v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.64/300.43 83318[0:SpR:5961.0,8376.2] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_in(tc_Com_Opname))** equal(x2,v_Procs) -> hBOOL(hAPP(hAPP(u,hAPP(x,v_x)),x2))*.
% 299.64/300.43 83316[4:SpR:5961.0,39064.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(x2,x3),hAPP(u,hAPP(x,v_x))),x4,t_a)*.
% 299.64/300.43 83315[4:SpR:5961.0,39023.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x2,x3),hAPP(u,hAPP(x,v_x))),x4))*.
% 299.64/300.43 83314[0:SpR:5961.0,3291.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x2,x3),hAPP(u,hAPP(x,v_x))),v_Procs))*.
% 299.64/300.43 83313[0:SpR:5961.0,3285.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(u,hAPP(x,v_x)),hAPP(c_Set_Oinsert(x2,tc_Com_Opname),v_Procs)))*.
% 299.64/300.43 83459[0:Rew:5961.0,83386.0] || hBOOL(hAPP(u,hAPP(v,v_x))) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,c_COMBS(c_COMBK(u,x,y),v,z,x1,x2),tc_Com_Opname))))*.
% 299.64/300.43 83460[0:Rew:5961.0,83385.0] || hBOOL(hAPP(u,hAPP(v,v_x))) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,c_COMBS(c_COMBK(u,x,y),v,z,x1,x2),tc_Com_Opname))))*.
% 299.64/300.43 83785[0:SpR:5899.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_COMBS(v,w,x,y,z),t_a) hBOOL(hAPP(c_COMBS(v,w,x1,x2,x3),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_COMBS(v,w,x,y,z))))*.
% 299.64/300.43 83768[0:SpR:5899.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(u,v,w,x,y),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(c_COMBS(u,v,x4,x5,x6),x2)))*.
% 299.64/300.43 83742[0:SpR:5899.0,9569.0] || -> c_lessequals(hAPP(c_COMBS(u,v,w,x,y),z),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),x2),c_COMBS(u,v,x3,x4,x5)),z),tc_bool)*.
% 299.64/300.43 83741[0:SpR:5899.0,9568.0] || -> c_lessequals(hAPP(c_COMBS(u,v,w,x,y),z),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_COMBS(u,v,x2,x3,x4)),x5),z),tc_bool)*.
% 299.64/300.43 83738[0:SpR:5899.0,415.0] || -> equal(c_Fun_Ofun__upd(c_COMBS(u,v,w,x,y),z,hAPP(c_COMBS(u,v,x1,x2,x3),z),x4,x5),c_COMBS(u,v,w,x,y))**.
% 299.64/300.43 84160[7:SpL:130.1,78767.0] class_HOL_Ominus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool),v_x)** equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_x) -> .
% 299.64/300.43 84818[7:SpR:78315.0,383.1] || -> equal(u,v_x) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(c_Set_Oinsert(v_x,v),u,w,x,y),v_x,v_x,x,y),c_Fun_Ofun__upd(c_Set_Oinsert(v_x,v),u,w,x,y))**.
% 299.64/300.43 84885[4:SpL:8498.1,78744.0] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(u,v),w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oinsert(u,v),w),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oinsert(u,v),w,t_a)*.
% 299.64/300.43 85160[0:SpL:338.0,85001.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u),w)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> .
% 299.64/300.43 85374[0:SpL:533.0,26240.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(x,u),y))),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.64/300.43 85477[4:SpR:78507.0,317.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v_x),v),hAPP(c_Set_Oimage(u,w,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))),hAPP(c_Set_Oimage(u,w,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))**.
% 299.64/300.43 85474[4:SpR:78507.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oinsert(v_x,u),v,w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),hAPP(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))))**.
% 299.64/300.43 85473[4:SpR:78507.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oinsert(v_x,v),w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(hAPP(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))**.
% 299.64/300.43 85667[4:SpR:21894.0,85425.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v),tc_bool)*.
% 299.64/300.43 85664[4:SpR:21268.0,85425.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v),u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v),tc_bool)*.
% 299.64/300.43 85747[0:SpR:317.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(c_Set_Oimage(v,y,u),hAPP(c_Set_Oinsert(w,y),z)))))*.
% 299.64/300.43 86052[0:SpL:181.1,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_bool)) equal(c_Set_Ovimage(c_COMBK(v,w,u),u,w),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)).
% 299.64/300.43 86350[0:SpR:86109.1,338.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u))**.
% 299.64/300.43 86272[0:SpR:86109.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(v,v_Procs) hBOOL(hAPP(hAPP(c_in(w),v),x)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v_x,t_a),w,u),u)*.
% 299.64/300.43 86262[0:SpR:86109.1,339.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))**.
% 299.64/300.43 86244[0:SpR:86109.1,176.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.64/300.43 86636[0:Res:86261.1,516.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.64/300.43 86705[4:SpL:130.1,86106.0] class_HOL_Ominus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool),v_x)** equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_Procs) -> .
% 299.64/300.43 87154[7:Res:82177.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Set_Oinsert(v_x,v)),w))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(x,t_a),u,tc_fun(t_a,tc_bool))))*.
% 299.64/300.43 87151[7:Res:82177.0,170.1] class_Orderings_Olinorder(t_a) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v)),t_a) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v)),t_a),v_x,t_a)*.
% 299.64/300.43 87150[7:Res:82177.0,169.1] class_Orderings_Olinorder(t_a) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v)),t_a) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(u,t_a),c_Set_Oinsert(v_x,v)),t_a),t_a)*.
% 299.64/300.43 87746[7:SpL:21894.0,74399.0] || equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,t_a)) -> hBOOL(hAPP(v_x,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(u),v),c_in(u),w,x)))*.
% 299.64/300.43 87744[7:SpL:21268.0,74399.0] || equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,t_a)) -> hBOOL(hAPP(v_x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(u),hAPP(c_in(u),v),w,x)))*.
% 299.64/300.43 88306[0:Res:7227.0,255.0] || c_lessequals(hAPP(c_Set_Oimage(c_COMBK(u,v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),z,tc_fun(y,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(y),u),z)).
% 299.64/300.43 88423[0:Res:8176.1,430.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(v,x,tc_fun(w,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))*.
% 299.64/300.43 88459[0:SSi:88444.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> c_lessequals(x,v,tc_fun(w,tc_bool))*.
% 299.64/300.43 88612[7:SpL:130.1,88086.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_x) hBOOL(c_HOL_Ominus__class_Ominus(x,c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool))* -> .
% 299.64/300.43 89005[0:SpR:21893.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(u,v_x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,x)))*.
% 299.64/300.43 89001[0:SpR:21267.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(u,v_x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,x)))*.
% 299.64/300.43 88998[0:SpR:49017.1,14196.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_Procs))*.
% 299.64/300.43 88991[0:SpR:28334.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_Procs))*.
% 299.64/300.43 88986[0:SpR:28031.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_Procs))*.
% 299.64/300.43 88974[0:SpR:12944.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y,z),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))),x1))*.
% 299.64/300.43 88967[0:SpR:9.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),z,x1),hAPP(c_Set_Oinsert(hAPP(u,hAPP(v,x2)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),x2))*.
% 299.64/300.43 88965[0:SpR:11499.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x,y),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.43 88964[0:SpR:10090.1,14196.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_Orderings_Otop__class_Otop(tc_bool)))*.
% 299.64/300.43 88958[0:SpR:105.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.64/300.43 88956[0:SpR:1196.1,14196.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_Orderings_Otop__class_Otop(u)))*.
% 299.64/300.43 88945[0:SpR:38.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.64/300.43 88943[0:SpR:321.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oimage(u,v,w),x,y),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))*.
% 299.64/300.43 88941[0:SpR:1195.1,14196.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_Orderings_Obot__class_Obot(u)))*.
% 299.64/300.43 88938[0:SpR:11695.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),x,y),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),w)))*.
% 299.64/300.43 88937[0:SpR:11473.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),y))*.
% 299.64/300.43 88895[0:SpR:87.1,14196.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),c_HOL_Ouminus__class_Ouminus(v,u)))*.
% 299.64/300.43 88894[0:SpR:88.1,14196.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v))*.
% 299.64/300.43 88890[0:SpR:17045.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x,y),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),z))*.
% 299.64/300.43 88878[0:SpR:2098.1,14196.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,x),hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v))*.
% 299.64/300.43 88864[0:SpR:3586.1,14196.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v,u),w,x),hAPP(c_Set_Oinsert(v_x,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_x))*.
% 299.64/300.43 88863[7:SpR:27278.1,14196.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v,u),w,x),hAPP(c_Set_Oinsert(v_x,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_x))*.
% 299.64/300.43 88834[0:SpR:653.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_Procs))*.
% 299.64/300.43 88829[0:SpR:9493.1,14196.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),u))*.
% 299.64/300.43 88825[0:SpR:8498.1,14196.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(w,v),x,y),hAPP(c_Set_Oinsert(u,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),u))*.
% 299.64/300.43 89025[0:Rew:9.0,89016.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),hAPP(c_Set_Oinsert(hAPP(x,hAPP(u,z)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))),z))*.
% 299.64/300.43 89054[0:Res:78099.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w)),u))* c_Hoare__Mirabelle_Otriple__valid(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),t_a)*.
% 299.64/300.43 89162[0:SpL:533.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))),v)* -> c_Finite__Set_Ofinite(y,v).
% 299.64/300.43 89243[7:SpR:78590.1,353.0] || equal(hAPP(c_Set_Oinsert(u,t_a),v),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),hAPP(c_Set_Oinsert(u,t_a),v))**.
% 299.64/300.43 89665[7:Rew:78167.0,89381.1,78167.0,89381.0] || equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),v_x),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),v_x),v_x).
% 299.64/300.43 90033[4:SpR:78660.1,353.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),v),v_x),v_x) -> equal(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),hAPP(c_Set_Oinsert(u,t_a),v))**.
% 299.64/300.43 90443[7:Rew:78167.0,90171.1,78167.0,90171.0] || equal(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),v_x),v_x),v_x)** -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),v_x),v_x).
% 299.64/300.43 90662[0:SpL:532.0,26231.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))),v)* -> c_Finite__Set_Ofinite(x,v).
% 299.64/300.43 91327[0:Rew:91288.1,91155.2] class_Complete__Lattice_Ocomplete__lattice(tc_fun(t_a,u)) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x)),hAPP(v,v_x))**.
% 299.64/300.43 91821[4:SpL:299.2,78747.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname),v,u)* equal(v,v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)).
% 299.64/300.43 91810[4:SpL:2097.1,78747.0] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname),u))* equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname),v_x) -> hBOOL(hAPP(c_Set_Oinsert(u,v),v_x)).
% 299.64/300.43 91882[4:Rew:5961.0,91859.1] || equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_COMBS(c_COMBK(u,w,x),v,y,z,x1),tc_Com_Opname))),v_x)** -> hBOOL(hAPP(u,hAPP(v,v_x))).
% 299.64/300.43 91883[4:Rew:5924.0,91858.1] || equal(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname)),v),v_x)** -> hBOOL(hAPP(hAPP(u,v_x),v)).
% 299.64/300.43 91956[0:SpR:79073.0,317.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v_Procs),v),hAPP(c_Set_Oimage(u,w,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))),hAPP(c_Set_Oimage(u,w,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))**.
% 299.64/300.43 91952[0:SpR:79073.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oinsert(v_Procs,v),w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),hAPP(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))*.
% 299.64/300.43 92106[7:SpR:79101.0,317.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v_x),v),hAPP(c_Set_Oimage(u,w,v),hAPP(c_in(x),v_x))),hAPP(c_Set_Oimage(u,w,v),hAPP(c_in(x),v_x)))**.
% 299.64/300.43 92105[7:SpR:79101.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oinsert(v_x,u),v,w,x,y),hAPP(c_in(z),v_x)),hAPP(hAPP(c_in(z),v_x),hAPP(v,hAPP(c_in(z),v_x))))*.
% 299.64/300.43 92104[7:SpR:79101.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oinsert(v_x,v),w,x,y),hAPP(c_in(z),v_x)),hAPP(hAPP(u,hAPP(c_in(z),v_x)),hAPP(c_in(z),v_x)))*.
% 299.64/300.43 92189[0:SpR:141.1,4019.2] class_OrderedGroup_Oab__group__add(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ominus__class_Ominus(v,w,u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ominus__class_Ominus(w,v,u),u)*.
% 299.64/300.43 92188[0:SpR:1605.2,4019.2] class_OrderedGroup_Ogroup__add(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u)*.
% 299.64/300.43 92187[0:SpR:1628.2,4019.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,w)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u)*.
% 299.64/300.43 92179[0:SpR:1421.2,4019.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Obot__class_Obot(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Otop__class_Otop(u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.43 92178[0:SpR:1409.2,4019.2] class_Lattices_Oboolean__algebra(u) class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(v,c_Orderings_Otop__class_Otop(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Orderings_Obot__class_Obot(u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u)*.
% 299.64/300.43 92420[0:Rew:92419.1,71096.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),w,tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Oinsert(u,v),w),w).
% 299.64/300.43 92423[0:Rew:92422.1,72121.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),x,tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Oinsert(u,v),x),x).
% 299.64/300.43 92576[0:SpR:5227.1,288.1] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x) c_Natural_Oevaln(y,z,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),x1)* -> c_Natural_Oevaln(y,z,c_Suc(w),x1).
% 299.64/300.43 92703[7:Res:82151.1,496.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_Set_Oinsert(v_x,v))),c_Set_Oinsert(v_x,v)))* c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.64/300.43 92702[7:Res:82151.1,455.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a)) c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Oinsert(v_x,v),t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.64/300.43 92694[7:Res:82151.1,280.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(hAPP(v,v_x),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(v_x,x),v,u,tc_fun(y,tc_bool)),w))*.
% 299.64/300.43 92946[0:SpR:9.0,5876.0] || -> c_lessequals(hAPP(u,hAPP(v,w)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Fun_Ocomp(u,v,y,z,x1),x2,x3,x4),w),tc_fun(x,tc_bool))*.
% 299.64/300.43 93087[0:SSi:93018.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(v,w),tc_fun(x,tc_bool)) -> c_lessequals(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v,y,z,x1),w),tc_fun(x,tc_bool))*.
% 299.64/300.43 93999[0:SpR:9493.1,10791.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),v),v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,t_a),v),hAPP(c_Set_Oinsert(u,t_a),v),tc_fun(t_a,tc_bool))*.
% 299.64/300.43 94175[0:Res:14364.3,4203.2] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(v,c_Orderings_Obot__class_Obot(u)))* c_Finite__Set_Ofinite(v,u) -> equal(c_Finite__Set_Olinorder__class_OMin(v,u),c_Orderings_Obot__class_Obot(u)).
% 299.64/300.43 94174[0:Res:14364.3,4996.2] class_Orderings_Olinorder(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || hBOOL(hAPP(v,c_Orderings_Obot__class_Obot(u)))* c_Finite__Set_Ofinite(v,u) -> equal(c_Finite__Set_Olinorder__class_OMin(v,u),c_Orderings_Obot__class_Obot(u)).
% 299.64/300.43 94171[0:Res:14364.3,144.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || hBOOL(hAPP(v,c_HOL_Ouminus__class_Ouminus(w,u))) c_Finite__Set_Ofinite(v,u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(c_Finite__Set_Olinorder__class_OMin(v,u),u),u)*.
% 299.64/300.43 94302[0:Res:14491.3,146.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) || hBOOL(hAPP(v,c_HOL_Ouminus__class_Ouminus(w,u))) c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_Finite__Set_Olinorder__class_OMax(v,u),u),w,u)*.
% 299.64/300.43 94295[0:Res:14491.3,4229.2] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(v,c_Orderings_Otop__class_Otop(u)))* c_Finite__Set_Ofinite(v,u) -> equal(c_Finite__Set_Olinorder__class_OMax(v,u),c_Orderings_Otop__class_Otop(u)).
% 299.64/300.43 94294[0:Res:14491.3,5005.2] class_Orderings_Olinorder(u) class_Orderings_Otop(u) class_Orderings_Oorder(u) || hBOOL(hAPP(v,c_Orderings_Otop__class_Otop(u)))* c_Finite__Set_Ofinite(v,u) -> equal(c_Finite__Set_Olinorder__class_OMax(v,u),c_Orderings_Otop__class_Otop(u)).
% 299.64/300.43 94292[0:Res:14491.3,7766.2] class_Orderings_Olinorder(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(v,c_Orderings_Otop__class_Otop(u))) c_Finite__Set_Ofinite(v,u) -> c_lessequals(w,c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.64/300.43 94291[0:Res:14491.3,8141.2] class_Orderings_Olinorder(u) class_Orderings_Otop(u) class_Orderings_Opreorder(u) || hBOOL(hAPP(v,c_Orderings_Otop__class_Otop(u))) c_Finite__Set_Ofinite(v,u) -> c_lessequals(w,c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.64/300.43 701[0:Res:589.0,593.0] || c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),hAPP(v_Q,v_x)),t_a)*.
% 299.64/300.43 2124[0:SpR:2097.1,687.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname),v))* hBOOL(hAPP(c_Set_Oinsert(v,w),v_x)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname)).
% 299.64/300.43 2123[0:SpR:2097.1,686.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,c_Set_Oinsert(v,w),tc_Com_Opname),v))* hBOOL(hAPP(c_Set_Oinsert(v,w),v_x)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,c_Set_Oinsert(v,w),tc_Com_Opname)).
% 299.64/300.43 2161[0:Res:47.2,437.1] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* c_Finite__Set_Ofinite(v,u) -> c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u).
% 299.64/300.43 2462[0:Res:49.2,437.1] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(v,c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u) -> c_Finite__Set_Ofinite(v,u).
% 299.64/300.43 5020[0:Res:41.2,405.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.43 5018[0:Res:53.2,405.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)).
% 299.64/300.43 5015[0:Res:683.1,405.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Oorder(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,u),hAPP(v,v_x),u)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,u),hAPP(v,v_x)).
% 299.64/300.43 5026[0:SSi:4988.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),hAPP(u,v_x),tc_fun(v,tc_bool))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),hAPP(u,v_x)).
% 299.64/300.43 5936[0:SpR:105.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Ovimage(v,w,x),y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))**.
% 299.64/300.43 5932[0:SpR:38.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Ovimage(v,w,x),y,z,x1),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),hAPP(hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.64/300.43 5931[0:SpR:321.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oimage(v,w,x),y,z,x1),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),hAPP(hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.64/300.43 6455[0:SpR:538.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y,z),x1),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x1),v),hAPP(w,x1)))*.
% 299.64/300.43 6454[0:SpR:538.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y,z),x1),hAPP(hAPP(u,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),w)))*.
% 299.64/300.43 6666[0:SpR:329.1,584.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y,z,x1),v),hAPP(v,hAPP(x,v)))*.
% 299.64/300.43 6665[0:SpR:329.1,584.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(c_COMBS(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y,z,x1),v),hAPP(hAPP(x,v),v))*.
% 299.64/300.43 6829[0:SpR:328.1,584.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,y,z,x1),u),hAPP(v,hAPP(x,u)))**.
% 299.79/300.43 6828[0:SpR:328.1,584.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(c_COMBS(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y,z,x1),u),hAPP(hAPP(x,u),v))**.
% 299.79/300.43 7251[0:SpR:584.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(v,w),hAPP(x,w))),hAPP(c_Set_Oimage(c_COMBS(v,x,y,z,x1),x2,u),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)))))*.
% 299.79/300.43 7225[0:SpR:540.1,474.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y,v),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.79/300.43 7224[0:SpR:539.1,474.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y,v),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.79/300.43 7223[0:SpR:297.2,474.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> hBOOL(hAPP(hAPP(c_in(x),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.79/300.43 7209[0:SpR:25.1,474.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u)),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u)),x,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.79/300.43 7574[0:Res:7542.0,402.0] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),v_x,tc_fun(v,tc_bool))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),v_x).
% 299.79/300.43 8960[0:SpL:8415.2,355.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> equal(v_x,v).
% 299.79/300.43 8750[0:SpR:8415.2,335.2] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Finite__Set_Ofinite(v_x,u) c_Finite__Set_Ofinite(v,u) -> c_Finite__Set_Ofinite(hAPP(v_x,v),u)*.
% 299.79/300.43 9057[0:SpL:8415.2,214.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Set_Oinsert(u,v)) c_lessequals(v_x,w,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),u),w))*.
% 299.79/300.43 9354[0:SpL:8415.2,347.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname))** c_Fun_Oinj__on(w,v_x,u,x)* -> c_Fun_Oinj__on(w,v,u,x)*.
% 299.79/300.43 9351[0:SpL:8415.2,347.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Fun_Oinj__on(v,hAPP(v_x,w),u,x)* -> c_Fun_Oinj__on(v,v_x,u,x).
% 299.79/300.43 9410[0:SpL:8415.2,346.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Fun_Oinj__on(v,hAPP(v_x,w),u,x)* -> c_Fun_Oinj__on(v,w,u,x).
% 299.79/300.43 9452[0:SpR:25.1,9268.0] class_HOL_Ouminus(u) || -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u))),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)))**.
% 299.79/300.43 9447[0:SpR:445.1,9268.0] || -> equal(v_x,u) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Fun_Ofun__upd(v,u,w,x,y)),c_Fun_Ofun__upd(v,u,w,x,y))**.
% 299.79/300.43 9540[0:Res:5887.1,251.1] class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),y,z,x1,x2),w),x),v)*.
% 299.79/300.43 9539[0:Res:5888.1,251.1] class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),y,z,x1,x2),w),x),v)*.
% 299.79/300.43 9841[0:SpR:8415.2,98.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Fun_Oinj__on(u,v_x,v,w)* -> equal(c_Finite__Set_Ocard(v_x,w),c_Finite__Set_Ocard(v_x,v)).
% 299.79/300.43 9873[0:SpL:8415.2,447.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Finite__Set_Ofinite(v_x,w) c_Fun_Oinj__on(u,v_x,v,w)* -> c_Finite__Set_Ofinite(v_x,v).
% 299.79/300.43 10491[0:SpL:584.0,454.0] || hBOOL(hAPP(c_COMBS(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u,v,w,x),y))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(u,y),z,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(u,y),z),y,t_a)*.
% 299.79/300.43 10583[0:SpL:1605.2,57.1] class_OrderedGroup_Ogroup__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(v,w) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_HOL_Ouminus__class_Ouminus(v,u)),c_HOL_Ozero__class_Ozero(u))** -> equal(w,c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.43 10828[0:SpR:353.0,8498.1] || equal(hAPP(c_Set_Oinsert(u,v),w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(x,v),w)),hAPP(c_Set_Oinsert(u,v),w))**.
% 299.79/300.43 11479[0:SSi:11467.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),w,tc_bool)* -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),w).
% 299.79/300.43 11505[0:SSi:11493.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),x,tc_bool)* -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),x).
% 299.79/300.43 11664[0:SSi:11657.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(u,v),hAPP(c_HOL_Ominus__class_Ominus(u,w,tc_fun(x,tc_bool)),v),tc_bool)* -> equal(hAPP(c_HOL_Ominus__class_Ominus(u,w,tc_fun(x,tc_bool)),v),hAPP(u,v)).
% 299.79/300.43 11682[0:SSi:11674.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_Procs,hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs),tc_bool)* -> equal(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs),v_Procs).
% 299.79/300.43 11705[0:SSi:11689.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(x,w)),x,tc_bool)* -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(x,w)),x).
% 299.79/300.43 11748[0:SpL:130.1,3929.0] class_HOL_Ominus(u) || hBOOL(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))* equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.79/300.43 11736[0:SpR:130.1,9567.0] class_HOL_Ominus(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x,tc_fun(y,tc_bool)),v_x),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool)*.
% 299.79/300.43 11721[0:SpR:130.1,683.1] class_HOL_Ominus(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u)),tc_Com_Opname,v),v)*.
% 299.79/300.43 12671[0:Res:3285.1,519.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))* hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.79/300.43 12670[0:Res:3317.1,519.0] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* -> hBOOL(hAPP(w,hAPP(c_Set_Oinsert(v_x,u),x)))* hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v_x,u),x)))*.
% 299.79/300.43 12954[0:SSi:12938.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(w,x,y)),z),w,tc_bool)* -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(w,x,y)),z),w).
% 299.79/300.43 13002[0:Res:1103.1,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),w))),t_a)* -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),w),t_a) c_Hoare__Mirabelle_Otriple__valid(u,w,t_a).
% 299.79/300.43 12984[0:Res:254.1,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(t_a)),v)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.43 12978[0:SpL:584.0,501.0] || hBOOL(hAPP(c_COMBS(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u,v,w,x),y))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(z),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(z,hAPP(u,y)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(z,y,t_a).
% 299.79/300.43 13003[4:MRR:12975.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_Set_Oinsert(v_x,tc_Com_Opname))** c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,v_x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a)*.
% 299.79/300.43 13164[0:Res:108.1,431.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),w,y)* -> c_Fun_Oinj__on(x,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),w,y)*.
% 299.79/300.43 13202[0:SpR:9493.1,353.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),v),v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v)),hAPP(c_Set_Oinsert(u,t_a),v))**.
% 299.79/300.43 13594[0:Rew:8415.2,13577.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,v)) hBOOL(hAPP(v_x,c_HOL_Ominus__class_Ominus(w,v,tc_fun(u,tc_bool))))* -> .
% 299.79/300.43 13706[0:SpR:544.1,9566.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_bool)*.
% 299.79/300.43 13998[0:SpR:543.1,9566.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_bool)*.
% 299.79/300.43 14175[0:SpR:2935.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),hAPP(c_Set_Ovimage(hAPP(c_in(t_a),v_x),u,v),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))))*.
% 299.79/300.43 14170[0:SpR:301.1,176.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.43 14140[0:SpR:300.1,176.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,x),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.43 14131[0:SpR:365.1,176.0] class_Orderings_Obot(u) || -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Ovimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.43 14130[0:SpR:397.1,176.0] class_Orderings_Otop(u) || -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Ovimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.43 14117[0:SpR:2097.1,176.0] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),u),hAPP(c_Set_Ovimage(c_Set_Oinsert(v,x),w,y),hAPP(c_Set_Oinsert(u,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.43 14329[0:SpR:11695.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),x,y,z,x1),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),w)),hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(x,c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),w))))**.
% 299.79/300.43 14328[0:SpR:11695.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),y,z,x1),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),x)),hAPP(hAPP(u,c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),x)),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.79/300.43 14385[4:MRR:14342.3,6340.0] class_Orderings_Olinorder(u) || equal(v_Procs,v_x) equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_x,u),v,u)*.
% 299.79/300.43 14512[4:MRR:14469.3,6340.0] class_Orderings_Olinorder(u) || equal(v_Procs,v_x) equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Finite__Set_Ofinite(v_x,u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(v_x,u),u)*.
% 299.79/300.43 14689[0:SpR:128.0,9566.0] || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)),hAPP(hAPP(c_Set_Oinsert(y,z),c_Set_Ovimage(u,v,w)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),tc_bool)*.
% 299.79/300.43 15126[0:SpL:181.1,3506.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(x,y),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)).
% 299.79/300.43 15108[0:SpR:181.1,9566.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),hAPP(hAPP(c_Set_Oinsert(y,z),c_Set_Ovimage(c_COMBK(v,u,x),x,u)),w),tc_bool)*.
% 299.79/300.43 15230[0:Res:446.1,431.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,hAPP(c_Set_Oinsert(y,w),v),w,z)* -> c_Fun_Oinj__on(x,hAPP(c_Set_Oinsert(y,w),u),w,z)*.
% 299.79/300.43 15208[0:SpR:2098.1,446.1] || c_lessequals(u,v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a) c_lessequals(hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,v),tc_Hoare__Mirabelle_Otriple(t_a)),u),v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))*.
% 299.79/300.43 15617[0:SpL:584.0,278.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(c_COMBS(c_in(w),x,y,z,x1),v))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(x,v),x2,u,w)))*.
% 299.79/300.43 15658[4:MRR:15614.3,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,x,w,u)))*.
% 299.79/300.43 15845[0:SpL:584.0,277.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(c_COMBS(c_in(w),x,y,z,x1),v))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x2,hAPP(x,v),u,w)))*.
% 299.79/300.43 15886[4:MRR:15842.3,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_x,w,u)))*.
% 299.79/300.43 16113[0:SpL:584.0,514.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),y,z,x1,x2),x3),x4))* -> equal(w,hAPP(y,x3)).
% 299.79/300.43 16193[0:Res:15262.1,519.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(t_a))** -> hBOOL(hAPP(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* hBOOL(hAPP(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.79/300.43 16232[0:SpL:130.1,16217.0] class_HOL_Ominus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_Procs) -> .
% 299.79/300.43 16314[0:SpL:584.0,513.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(c_COMBS(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),z,x1,x2,x3),x4))* -> equal(x,hAPP(z,x4)).
% 299.79/300.43 16566[0:SpR:2935.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),w)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_in(t_a),v_x),v,u),u)*.
% 299.79/300.43 16561[0:SpR:301.1,361.2] class_Lattices_Obounded__lattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Obot__class_Obot(u)),x)) -> c_lessequals(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w,v),v)*.
% 299.79/300.43 16527[0:SpR:300.1,361.2] class_Lattices_Obounded__lattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),x),y)) -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,v),v)*.
% 299.79/300.43 16516[0:SpR:365.1,361.2] class_Orderings_Obot(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),w,v),v)*.
% 299.79/300.43 16515[0:SpR:397.1,361.2] class_Orderings_Otop(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),w,v),v)*.
% 299.79/300.43 16502[0:SpR:2097.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(v,w)) hBOOL(hAPP(hAPP(c_in(x),v),y)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(w,z),x,u),u)*.
% 299.79/300.43 16851[0:Res:114.1,95.0] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),z,y,x)* -> c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(v,y,w),c_HOL_Ominus__class_Ominus(z,x1,tc_fun(y,tc_bool))),w,x)*.
% 299.79/300.43 16962[0:SpR:3229.1,600.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) -> equal(hAPP(hAPP(u,v_x),c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x))**.
% 299.79/300.43 16993[0:Res:9952.1,251.1] class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_Orderings_Otop__class_Otop(tc_bool),w),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),tc_Com_Opname,tc_fun(u,v)),w),v)*.
% 299.79/300.43 17018[0:Res:10531.1,251.1] class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_bool),w),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),tc_Com_Opname,tc_fun(u,v)),w),v)*.
% 299.79/300.43 17095[0:SpR:3229.1,511.1] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),w)))*.
% 299.79/300.43 17061[0:SpR:3229.1,511.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(hAPP(c_in(v),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),x),hAPP(u,v_x)))*.
% 299.79/300.43 17058[0:SpR:3229.1,511.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_in(v),w),x)) -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(hAPP(u,v_x),x)))*.
% 299.79/300.43 17252[0:SpR:3229.1,510.1] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))*.
% 299.79/300.43 17218[0:SpR:3229.1,510.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(hAPP(c_in(v),x),w))* -> hBOOL(hAPP(hAPP(c_in(v),x),hAPP(u,v_x)))*.
% 299.79/300.43 17215[0:SpR:3229.1,510.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_in(v),w),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(hAPP(u,v_x),x)))*.
% 299.79/300.43 17757[0:Res:1103.1,255.0] || c_lessequals(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(v),w)),x,tc_fun(v,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a) hBOOL(hAPP(hAPP(c_in(v),w),x)).
% 299.79/300.43 17727[0:Res:254.1,255.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(hAPP(c_Set_Oinsert(x,u),w),y,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),y))*.
% 299.79/300.43 17712[0:SpL:3229.1,255.0] || equal(u,hAPP(c_in(v),w))* hBOOL(hAPP(u,v_x))* c_lessequals(v_x,x,tc_fun(v,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),w),x))*.
% 299.79/300.43 17709[0:SpL:3229.1,255.0] || equal(u,c_in(v))* hBOOL(hAPP(hAPP(u,v_x),w))* c_lessequals(w,x,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),v_x),x))*.
% 299.79/300.43 17894[0:SpL:188.1,16286.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_Procs)** -> .
% 299.79/300.43 17861[0:SpR:188.1,3229.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u))* -> equal(hAPP(w,v_x),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))*.
% 299.79/300.43 17841[0:SpR:188.1,1158.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),v_Procs),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.79/300.43 17913[0:Rew:79.0,17876.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))**.
% 299.79/300.43 17918[0:Rew:9911.0,17848.2] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x)).
% 299.79/300.43 18004[0:SpL:3229.1,263.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oinsert(w,v),x)))* -> hBOOL(hAPP(hAPP(c_in(v),v_x),x)) equal(v_x,w).
% 299.79/300.43 17995[0:SpL:3229.1,263.0] || equal(u,c_Set_Oinsert(v,w))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(u,v_x)))* -> hBOOL(hAPP(hAPP(c_in(w),x),v_x)) equal(x,v)*.
% 299.79/300.43 18153[0:SpR:525.1,362.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.43 18149[0:SpR:3229.1,362.1] || equal(u,v) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> c_lessequals(hAPP(u,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,w,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.43 18131[0:SpR:8385.1,362.1] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,tc_Com_Opname),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.43 18353[0:SpR:525.1,545.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> hBOOL(hAPP(hAPP(c_in(y),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),x)))*.
% 299.79/300.43 18349[0:SpR:3229.1,545.1] || equal(u,v) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(u,v_x)),hAPP(c_Set_Oimage(v,w,y),x)))*.
% 299.79/300.43 18331[0:SpR:8385.1,545.1] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> hBOOL(hAPP(hAPP(c_in(x),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,x),w)))*.
% 299.79/300.43 18327[0:SpR:3229.1,545.1] || equal(u,c_Set_Oimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(w),y),v_x))* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(v,y)),hAPP(u,v_x)))*.
% 299.79/300.43 18446[0:SpL:3229.1,156.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Ovimage(w,v,x),y)))* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,v_x)),y)).
% 299.79/300.43 18438[0:SpL:3229.1,156.0] || equal(u,c_Set_Ovimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(w),y),hAPP(u,v_x)))* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(v,y)),v_x))*.
% 299.79/300.43 18478[0:Res:687.1,8513.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x)) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_Com_Opname),u)**.
% 299.79/300.43 18477[0:Res:686.1,8513.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x)) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_Com_Opname),u)**.
% 299.79/300.43 18582[0:SpR:3229.1,153.1] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(c_in(w),hAPP(x,v_x)),y)) -> hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Ovimage(x,v,w),y)))*.
% 299.79/300.43 18574[0:SpR:3229.1,153.1] || equal(u,c_Set_Ovimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(x),hAPP(v,y)),v_x))* -> hBOOL(hAPP(hAPP(c_in(w),y),hAPP(u,v_x)))*.
% 299.79/300.43 18899[0:SpR:3229.1,463.1] || equal(u,c_Com_Obody) c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_x),v,w,x) -> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(u,v_x)),v,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_x,w,v,x),x)*.
% 299.79/300.43 19117[0:SpR:3229.1,196.1] || equal(u,c_Set_Oimage(v,w,x)) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> equal(hAPP(c_Set_Ovimage(v,w,x),hAPP(u,v_x)),v_x)**.
% 299.79/300.43 19266[0:SpR:3229.1,304.3] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* c_lessequals(w,x,u)* c_lessequals(v_x,x,u) -> c_lessequals(hAPP(v,v_x),x,u)*.
% 299.79/300.43 19263[0:SpR:3229.1,304.3] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v_x,w,u) c_lessequals(x,w,u) -> c_lessequals(hAPP(hAPP(v,v_x),x),w,u)*.
% 299.79/300.43 19430[0:SpL:3229.1,193.1] || equal(u,c_Set_Oimage(v,w,x))* c_Finite__Set_Ofinite(v_x,w) equal(c_Finite__Set_Ocard(hAPP(u,v_x),x),c_Finite__Set_Ocard(v_x,w))* -> c_Fun_Oinj__on(v,v_x,w,x)*.
% 299.79/300.43 19517[0:Res:19440.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Com_Opname),v_x)),v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Com_Opname),v_x)),v),v_Procs,t_a)*.
% 299.79/300.43 19557[0:SpL:5.2,36.1] class_Int_Onumber__ring(u) class_Ring__and__Field_Oidom(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u))** c_lessequals(w,v,u) -> c_lessequals(x,x,u)*.
% 299.79/300.43 19541[0:SpL:5.2,36.1] class_Int_Onumber__ring(u) class_Ring__and__Field_Oidom(u) class_OrderedGroup_Opordered__ab__group__add(u) || equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u))** c_lessequals(x,x,u)* -> c_lessequals(w,v,u).
% 299.79/300.43 19705[0:SpL:328.1,19641.0] || c_lessequals(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v,tc_fun(u,tc_bool))* hBOOL(v) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,t_a).
% 299.79/300.43 19890[0:SpL:104.0,519.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),x))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),x)) hBOOL(hAPP(v,x)).
% 299.79/300.43 19889[0:SpL:104.0,325.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)).
% 299.79/300.43 19887[0:SpL:104.0,345.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.43 19866[0:SpL:104.0,3483.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_Com_Ocom_OSKIP) -> .
% 299.79/300.43 19912[0:SSi:19814.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)) -> c_lessequals(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.43 19956[0:SpR:64.0,7539.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oinsert(v,w),u)),tc_fun(w,tc_bool))*.
% 299.79/300.43 20078[0:SpL:3586.1,215.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(u)),v),v_Procs) c_Hoare__Mirabelle_Ohoare__derivs(w,v_x,u) -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.79/300.43 20069[0:SpL:8498.1,215.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)))* c_Hoare__Mirabelle_Ohoare__derivs(w,u,v)* -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.79/300.43 20733[0:Res:313.1,436.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_Set_Oimage(x,w,y),u),z))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(x,w,y),v),z))*.
% 299.79/300.43 20779[0:Res:129.1,436.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_Set_Ovimage(x,y,w),u),z))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(x,y,w),v),z))*.
% 299.79/300.43 20913[0:SpR:3586.1,317.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(hAPP(w,v),x),hAPP(c_Set_Oimage(w,u,x),v_x)),hAPP(c_Set_Oimage(w,u,x),v_x))**.
% 299.79/300.43 20904[0:SpR:8498.1,317.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(hAPP(c_Set_Oinsert(hAPP(w,x),y),hAPP(c_Set_Oimage(w,v,y),u)),hAPP(c_Set_Oimage(w,v,y),u))**.
% 299.79/300.43 20847[0:SpR:317.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(u,v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(c_Set_Oinsert(hAPP(u,z),w),hAPP(c_Set_Oimage(u,v,w),x1))))*.
% 299.79/300.43 21637[0:SpL:21267.0,7600.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),v)* -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(w,v),v_x),tc_Com_Opname,x),v)*.
% 299.79/300.43 21635[0:SpL:21267.0,360.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),v_x),w,x) -> c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),v_x),tc_Com_Opname,y),w,x)*.
% 299.79/300.43 21622[0:SpL:21267.0,4382.0] || equal(hAPP(c_Set_Oinsert(u,v),v_x),v_Procs) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),v_x))* equal(u,v_x).
% 299.79/300.43 21569[0:SpL:21267.0,505.0] || c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x)),u,v,w) -> c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Obody,hAPP(c_Com_Obody,v_x),tc_Com_Opname,x)),u,c_Suc(v),w)*.
% 299.79/300.43 21512[0:SpR:15476.0,21267.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),tc_Com_Opname,v)),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))**.
% 299.79/300.43 21714[0:Rew:586.0,21554.0] || -> equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_COMBB(u,w,x,y),v),hAPP(u,hAPP(v,v_x)),tc_Com_Opname,z))),hAPP(u,hAPP(v,v_x)))**.
% 299.79/300.43 21715[0:Rew:585.0,21553.0] || -> equal(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_COMBC(u,v,w,x),y),hAPP(hAPP(u,v_x),y),tc_Com_Opname,z)),y),hAPP(hAPP(u,v_x),y))**.
% 299.79/300.43 21716[0:Rew:586.0,21493.0] || -> equal(hAPP(u,hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBB(u,v,w,x),hAPP(c_COMBB(u,v,w,x),v_x),tc_Com_Opname,y),z)),hAPP(u,hAPP(v_x,z)))**.
% 299.79/300.43 21717[0:Rew:585.0,21492.0] || -> equal(hAPP(hAPP(u,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBC(u,w,x,y),hAPP(c_COMBC(u,w,x,y),v_x),tc_Com_Opname,z)),hAPP(hAPP(u,v),v_x))**.
% 299.79/300.43 22265[0:SpL:21893.0,7600.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),v)* -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(w,v),v_x),c_Set_Oinsert(w,v),tc_Com_Opname,x),v)*.
% 299.79/300.43 22263[0:SpL:21893.0,360.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),v_x),w,x) -> c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),v_x),c_Set_Oinsert(v,w),tc_Com_Opname,y),w,x)*.
% 299.79/300.43 22250[0:SpL:21893.0,4382.0] || equal(hAPP(c_Set_Oinsert(u,v),v_x),v_Procs) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),v_x))* equal(u,v_x).
% 299.79/300.43 22196[0:SpL:21893.0,505.0] || c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x)),u,v,w) -> c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Obody,v_x),c_Com_Obody,tc_Com_Opname,x)),u,c_Suc(v),w)*.
% 299.79/300.43 22139[0:SpR:15476.0,21893.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),tc_Com_Opname,v)),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))**.
% 299.79/300.43 22343[0:Rew:586.0,22181.0] || -> equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,hAPP(v,v_x)),hAPP(c_COMBB(u,w,x,y),v),tc_Com_Opname,z))),hAPP(u,hAPP(v,v_x)))**.
% 299.79/300.43 22344[0:Rew:585.0,22180.0] || -> equal(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(u,v_x),v),hAPP(c_COMBC(u,w,x,y),v),tc_Com_Opname,z)),v),hAPP(hAPP(u,v_x),v))**.
% 299.79/300.43 22345[0:Rew:586.0,22119.0] || -> equal(hAPP(u,hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBB(u,v,w,x),v_x),c_COMBB(u,v,w,x),tc_Com_Opname,y),z)),hAPP(u,hAPP(v_x,z)))**.
% 299.79/300.43 22346[0:Rew:585.0,22118.0] || -> equal(hAPP(hAPP(u,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBC(u,w,x,y),v_x),c_COMBC(u,w,x,y),tc_Com_Opname,z)),hAPP(hAPP(u,v),v_x))**.
% 299.79/300.43 22645[0:SpL:158.0,3483.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Com_Ocom_OBODY)** equal(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.43 22524[0:SpR:158.0,83.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z))),z,tc_fun(w,tc_bool))*.
% 299.79/300.43 22884[0:SpL:3294.1,514.0] || equal(c_Hoare__Mirabelle_Otriple_Otriple(u),c_in(t_a)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(c_Orderings_Obot__class_Obot(tc_bool),y))* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))).
% 299.79/300.43 22864[0:SpL:3294.1,513.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_in(t_a))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),y).
% 299.79/300.43 22828[0:SpR:329.1,3294.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(t_a))** -> equal(hAPP(v_x,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.79/300.43 22827[0:SpR:328.1,3294.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_in(t_a))** -> equal(hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.43 22825[0:SpR:538.0,3294.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(t_a)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.43 23038[0:SpL:131.0,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),x1))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,w,x),z),hAPP(v,x1))).
% 299.79/300.43 23023[0:SpL:131.0,3483.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Com_Ocom_OBODY)** equal(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.43 22996[0:SpR:131.0,83.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z)),hAPP(c_Set_Ovimage(x,w,y),z),tc_fun(w,tc_bool))*.
% 299.79/300.43 22980[0:SpR:131.0,34.1] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(y,z))) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,y,v,w,x1),x1,w),x),z))*.
% 299.79/300.43 22959[0:SpR:131.0,83.0] || -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),z))),z,tc_fun(x,tc_bool))*.
% 299.79/300.43 23049[0:Rew:38.0,23015.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(c_COMBK(v,u,x),y,x,u,z),z,u),w),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))**.
% 299.79/300.43 23207[0:SpL:328.1,3487.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> .
% 299.79/300.43 23205[0:SpL:538.0,3487.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.43 23304[0:SpL:329.1,3489.1] || c_lessequals(v_x,c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(u,tc_bool))* equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(tc_Com_Opname)) hBOOL(c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))) -> .
% 299.79/300.43 23282[0:SpL:538.0,3489.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.79/300.43 23603[0:SSi:23602.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(u,v_x)),hAPP(c_HOL_Ominus__class_Ominus(v,u,tc_fun(t_a,tc_bool)),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v,v_x)),hAPP(u,v_x)))**.
% 299.79/300.43 24399[0:MRR:24355.2,16753.0] || c_Finite__Set_Ofinite(u,v) c_lessequals(u,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))* -> c_Fun_Oinj__on(c_COMBK(w,v,v),u,v,v)*.
% 299.79/300.43 24400[0:Rew:610.0,24354.1] || c_Finite__Set_Ofinite(u,v) equal(c_Finite__Set_Ocard(u,v),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))) -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) c_Fun_Oinj__on(c_COMBK(w,x,v),u,v,x)*.
% 299.79/300.43 24563[0:SpR:24020.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(v,v_x),w,u),u)*.
% 299.79/300.43 24550[0:SpR:24020.1,176.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Ovimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.43 24927[0:Res:8376.2,467.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Oimage(v,w,u),x),v_Procs) -> equal(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),v_x)),v_x)**.
% 299.79/300.43 25014[0:SpR:130.1,23902.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.43 24988[0:SpR:23902.1,523.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v_x,v_x)),hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_x)),hAPP(v_x,v_x))**.
% 299.79/300.43 25312[0:SpR:512.0,3305.1] || equal(hAPP(c_COMBB(u,v,w,tc_Com_Opname),x),y) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,tc_Com_Opname,v),v_Procs)),hAPP(y,v_x)))*.
% 299.79/300.43 25679[0:SSi:25603.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) -> equal(hAPP(x,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_bool))*.
% 299.79/300.43 25725[0:Res:11030.1,455.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a)) c_Hoare__Mirabelle_Ohoare__valids(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.79/300.43 25721[0:Res:3316.1,455.0] || equal(c_in(u),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) c_Hoare__Mirabelle_Ohoare__valids(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.79/300.43 25717[0:Res:9067.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x)),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,y),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(y,w,t_a)*.
% 299.79/300.43 25711[0:Res:9071.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,v,t_a)*.
% 299.79/300.43 25993[0:SpL:339.0,347.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),w,z)* -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),x),w,z).
% 299.79/300.43 25935[0:SpR:2097.1,339.0] || hBOOL(hAPP(u,v)) -> equal(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x))**.
% 299.79/300.43 25913[0:SpR:339.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w))))*.
% 299.79/300.43 25892[0:SpR:339.0,335.2] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v) c_Finite__Set_Ofinite(x,v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),v)*.
% 299.79/300.43 25841[2:SpR:339.0,4250.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Com_Ocom_OBODY) -> c_Com_OWT(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))*.
% 299.79/300.43 25831[0:SpR:339.0,3282.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))*.
% 299.79/300.43 26238[0:SpL:338.0,346.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),w,z)* -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),y),w,z).
% 299.79/300.43 26177[0:SpR:3229.1,338.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) -> equal(hAPP(hAPP(u,v_x),hAPP(c_Set_Oinsert(w,v),x)),hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(u,v_x),x)))*.
% 299.79/300.43 26145[0:SpR:2097.1,338.0] || hBOOL(hAPP(u,v)) -> equal(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u))**.
% 299.79/300.43 26121[0:SpR:338.0,15367.0] || -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),tc_fun(u,tc_bool)),u)*.
% 299.79/300.43 26102[0:SpR:338.0,9566.0] || -> c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(y,u),w)),x),tc_bool)*.
% 299.79/300.43 26078[0:SpR:338.0,510.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y))))*.
% 299.79/300.43 26057[0:SpR:338.0,335.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(w,v),x),v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),x)),v)*.
% 299.79/300.43 26533[0:Res:84.1,437.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),w) -> c_Finite__Set_Ofinite(u,w).
% 299.79/300.43 26532[0:Res:84.1,682.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_in(tc_Com_Opname),v_x),u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_Procs)).
% 299.79/300.43 26527[0:Res:84.1,17941.0] || c_lessequals(c_HOL_Ominus__class_Ominus(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)),v,tc_fun(tc_Com_Opname,tc_bool))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))) -> .
% 299.79/300.43 26787[0:Res:23997.0,12626.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool)),x,tc_fun(y,tc_bool)),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool)),u,tc_bool)*.
% 299.79/300.43 26858[0:SpL:56.1,3863.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),y))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),x),y))*.
% 299.79/300.43 26955[0:Res:424.2,437.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(x,w,tc_fun(u,tc_bool))* c_Finite__Set_Ofinite(w,u) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),x),u)*.
% 299.79/300.43 27110[0:Res:19748.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),u,tc_Com_Opname,tc_fun(x,tc_bool)),v))*.
% 299.79/300.43 27101[0:Res:11030.1,280.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(hAPP(v,v_x),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),v,u,tc_fun(y,tc_bool)),w))*.
% 299.79/300.43 27097[0:Res:3316.1,280.1] || equal(c_in(u),c_in(v)) hBOOL(hAPP(hAPP(w,v_x),x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w,v,tc_fun(y,tc_bool)),x))*.
% 299.79/300.43 27189[0:Res:450.0,527.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(v)),w),x),t_a) hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),x,w,u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(v),x,w,u)))*.
% 299.79/300.43 27143[0:SpR:10463.0,450.0] || -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w,x))) c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),w),v),t_a)*.
% 299.79/300.43 27142[0:SpR:9911.0,450.0] || -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w,x))) c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),w),v),t_a)*.
% 299.79/300.43 27252[7:SpR:339.0,27207.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_x) -> hBOOL(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))*.
% 299.79/300.43 27301[7:MRR:24314.1,27297.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(v,w,x),x,w),tc_Com_Opname,y),u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))))*.
% 299.79/300.43 27318[7:MRR:24365.2,27297.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.79/300.43 27319[7:MRR:24364.2,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Com_Ocom_OBODY)** equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Com_Ocom_OBODY,x))* -> equal(v_x,x).
% 299.79/300.43 27320[7:MRR:24299.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.79/300.43 27321[7:MRR:24296.2,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_in(tc_Com_Opname))** equal(x,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),x))*.
% 299.79/300.43 27322[7:MRR:24295.2,27297.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x)**.
% 299.79/300.43 27323[7:MRR:24294.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),v_Procs))*.
% 299.79/300.43 27324[7:MRR:24293.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)))*.
% 299.79/300.43 27325[7:MRR:24290.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_Procs),v_x))*.
% 299.79/300.43 27340[7:MRR:24303.0,27297.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_Com_Opname,x),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))*.
% 299.79/300.43 27341[7:MRR:24302.0,27297.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(u,v,w),w,v),t_a,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))*.
% 299.79/300.43 27349[7:MRR:24372.3,27297.0] || equal(u,c_Set_Oimage(c_COMBK(v,w,x),x,w))* equal(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_Procs) -> .
% 299.79/300.43 27350[7:MRR:24371.2,27297.0] || equal(c_in(u),c_Set_Oimage(c_COMBK(v,w,x),x,w))* hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.79/300.43 27351[7:MRR:24313.1,27297.0] || equal(c_in(u),c_Set_Oimage(c_COMBK(v,w,x),x,w))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),hAPP(c_Set_Oinsert(v_x,u),y)))*.
% 299.79/300.43 27352[7:MRR:24312.1,27297.0] || equal(u,c_Set_Oimage(c_COMBK(v,w,x),x,w))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,y),v_Procs),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))))*.
% 299.79/300.43 27353[7:MRR:24308.1,27297.0] || equal(u,c_Set_Oimage(c_COMBK(v,w,x),x,w))* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.79/300.43 27356[7:MRR:24373.2,27297.0] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(c_COMBK(w,x,y),y,x))* equal(hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.79/300.43 27357[7:MRR:24315.1,27297.0] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(c_COMBK(w,x,y),y,x))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))))*.
% 299.79/300.43 27378[0:SpL:584.0,470.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(v,w,u),x,y,z),x1))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(x1,x1,v,w,u)),x1))*.
% 299.79/300.43 27438[0:SpL:584.0,466.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(v,w,u),x,y,z),x1))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x1,v,x1,w,u)),x1))*.
% 299.79/300.43 27933[0:Res:468.0,591.0] || -> equal(hAPP(c_Set_Oimage(u,tc_Hoare__Mirabelle_Otriple(t_a),v),v_G),hAPP(c_Set_Oimage(w,tc_Hoare__Mirabelle_Otriple(t_a),v),v_G)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v_G,u,w,tc_Hoare__Mirabelle_Otriple(t_a),v),t_a)*.
% 299.79/300.43 28072[0:SpR:188.1,28032.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x)))*.
% 299.79/300.43 28143[2:SpR:465.1,4250.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Com_Ocom_OBODY)** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) c_Com_OWT(hAPP(c_Set_Oimage(u,x,y),v_x)).
% 299.79/300.43 28132[0:SpR:465.1,3282.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(c_Set_Oimage(u,x,y),v_x)).
% 299.79/300.43 28131[7:SpR:465.1,27207.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_x)** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(c_Set_Oimage(u,x,y),v_x)).
% 299.79/300.43 28121[0:SpR:465.1,648.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs)) hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Fun_Ofun__upd(w,u,x,tc_Com_Opname,v),v_x)),hAPP(c_Set_Oimage(w,tc_Com_Opname,v),v_Procs)))*.
% 299.79/300.43 28117[0:SpR:465.1,16776.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(w,c_Fun_Ofun__upd(x,v,y,u,z),u,z),hAPP(c_Set_Oimage(x,u,z),w),z,u)*.
% 299.79/300.43 28375[0:SpR:188.1,28335.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x)))*.
% 299.79/300.43 28444[0:SpR:23979.0,118.0] || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x,y),v,hAPP(u,v),y,x),c_Fun_Ocomp(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x,y))**.
% 299.79/300.43 28443[0:SpR:771.0,118.0] || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,c_COMBK(v,w,x),y,z,x1),x2,hAPP(u,v),x1,z),c_Fun_Ocomp(u,c_COMBK(v,w,x),y,z,x1))**.
% 299.79/300.43 28440[0:SpR:3339.1,118.0] || equal(u,v) -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(w,u,x,y,z),v_x,hAPP(w,hAPP(v,v_x)),z,y),c_Fun_Ocomp(w,u,x,y,z))**.
% 299.79/300.43 28420[0:SpR:118.0,9.0] || -> equal(hAPP(c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,w,x,y),z,hAPP(u,x1),y,x),x2),hAPP(u,hAPP(c_Fun_Ofun__upd(v,z,x1,y,w),x2)))**.
% 299.79/300.43 28680[0:SpR:28031.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),v_Procs,v_Procs,w,x),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname))**.
% 299.79/300.43 28835[0:SpR:28334.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),v_Procs,v_Procs,w,x),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname))**.
% 299.79/300.43 29241[0:Obv:29042.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))*.
% 299.79/300.43 29440[7:SpL:27278.1,215.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(u)),v),v_x) c_Hoare__Mirabelle_Ohoare__derivs(w,v_x,u) -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.79/300.43 29406[7:SpR:27278.1,317.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(hAPP(w,v),x),hAPP(c_Set_Oimage(w,u,x),v_x)),hAPP(c_Set_Oimage(w,u,x),v_x))**.
% 299.79/300.43 29748[0:Obv:29702.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),x)** -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,u).
% 299.79/300.43 29752[0:Obv:29644.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))**.
% 299.79/300.43 29756[0:Obv:29639.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))**.
% 299.79/300.43 29757[0:Obv:29565.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),x)**.
% 299.79/300.43 29758[0:Obv:29563.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))*.
% 299.79/300.43 29960[0:SpL:27043.1,215.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__derivs(u,v_x,v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v_Procs,tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.79/300.43 30394[0:Rew:537.1,30393.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w)))*.
% 299.79/300.43 30946[0:Obv:30790.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w))**.
% 299.79/300.43 30948[0:Obv:30785.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w))**.
% 299.79/300.43 30955[0:Rew:534.1,30954.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w)))*.
% 299.79/300.43 30956[0:Obv:30627.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w)),x)**.
% 299.79/300.43 31274[0:Res:3346.1,356.0] || equal(c_Set_Oinsert(u,v),w)* -> equal(hAPP(c_Set_Oimage(c_COMBK(x,y,v),v,y),hAPP(w,v_x)),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.43 31271[0:Res:9071.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(x,w),tc_Com_Opname,tc_fun(w,tc_bool))),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.79/300.43 31269[0:Res:9246.0,356.0] || -> hBOOL(hAPP(u,v))* equal(hAPP(c_Set_Oimage(c_COMBK(w,x,y),y,x),c_HOL_Ouminus__class_Ouminus(u,tc_fun(y,tc_bool))),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.79/300.43 31261[0:Res:474.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(c_Set_Oimage(x,y,w),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.79/300.43 31385[0:SpL:351.0,449.0] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,c_COMBK(u,w,x),y,z)))* -> c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),y),c_COMBK(u,w,x)),t_a)*.
% 299.79/300.43 31512[7:MRR:31446.3,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.79/300.43 31794[7:SpL:130.1,31778.0] class_HOL_Ominus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_x) -> .
% 299.79/300.43 31906[7:SpL:188.1,31868.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x)** -> .
% 299.79/300.43 32262[0:Res:23753.1,251.1] class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(v_x,w),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_fun(u,v)),w),v)*.
% 299.79/300.43 32674[7:MRR:32598.0,27297.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_Com_Opname,x),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))),v_Procs))*.
% 299.79/300.43 32708[0:SpR:181.1,32669.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))))*.
% 299.79/300.43 32814[7:SpL:35.2,27359.0] || c_lessequals(u,c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),tc_fun(x,tc_bool))* c_lessequals(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),y,tc_fun(x,tc_bool))* equal(u,v_x) -> .
% 299.79/300.43 32813[0:SpL:35.2,18303.0] || c_lessequals(u,c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),tc_fun(x,tc_bool))* c_lessequals(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),y,tc_fun(x,tc_bool))* equal(u,v_Procs) -> .
% 299.79/300.43 32781[0:SpR:35.2,18304.0] || c_lessequals(u,c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),tc_fun(x,tc_bool))* c_lessequals(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),y,tc_fun(x,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(z,u,t_a)*.
% 299.79/300.43 32780[0:SpR:35.2,11611.0] || c_lessequals(u,c_COMBK(v,w,x),tc_fun(y,tc_bool))* c_lessequals(c_COMBK(v,w,x),z,tc_fun(y,tc_bool))* -> c_lessequals(hAPP(u,x1),v,tc_bool)*.
% 299.79/300.43 32778[0:SpR:35.2,23997.0] || c_lessequals(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),tc_fun(w,tc_bool))* c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),x,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(u,v),v,tc_bool)*.
% 299.79/300.43 32777[0:SpR:35.2,17045.0] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(w,tc_bool))* c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),x,tc_fun(w,tc_bool))* -> equal(hAPP(u,y),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.43 32884[0:SpR:475.1,9067.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,v)),hAPP(c_Set_Oinsert(z,x),hAPP(c_Set_Oimage(y,u,x),w))))*.
% 299.79/300.43 32883[0:SpR:475.1,20881.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(x,y,z),hAPP(c_Set_Oimage(x1,u,y),w)),hAPP(x,hAPP(x1,v))))*.
% 299.79/300.43 33344[7:MRR:33254.0,27297.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_Com_Opname,x),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.43 33419[0:Res:3283.1,453.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__valids(u,v_Procs,t_a) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v)),u))* c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.79/300.43 33412[0:Res:3284.1,453.0] || equal(c_in(tc_Com_Opname),u) c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(u,v_x),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,v_Procs,t_a).
% 299.79/300.43 33626[7:MRR:33540.0,27297.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),c_Set_Oimage(c_COMBK(v,w,x),x,w),tc_Com_Opname,y)))*.
% 299.79/300.43 33717[7:MRR:33631.0,27297.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBK(v,w,x),x,w),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_Com_Opname,y)))*.
% 299.79/300.43 33790[7:MRR:33722.3,27297.0] || equal(u,c_Set_Oimage(c_COMBK(v,w,x),x,w))* equal(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_x) -> .
% 299.79/300.43 34370[0:SpL:24914.0,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,w),hAPP(hAPP(c_in(u),v),v_x)),v))*.
% 299.79/300.43 34260[0:SpL:24914.0,591.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),v_G)) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,u),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x)),t_a)*.
% 299.79/300.43 34229[0:SpR:88.1,24914.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u))),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.43 34106[0:SpR:24914.0,526.1] || hBOOL(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,w),hAPP(hAPP(c_in(u),v),v_x)),v))* -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)).
% 299.79/300.43 34008[0:SpR:24914.0,309.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),u)*.
% 299.79/300.43 34007[0:SpR:24914.0,306.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),u)*.
% 299.79/300.43 33926[0:SpR:24914.0,318.1] || c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),v_x),w).
% 299.79/300.43 33914[0:SpR:24914.0,7539.0] || -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(u,v),v_x)),tc_fun(v,tc_bool))*.
% 299.79/300.43 34462[0:Rew:9.0,34249.0] || -> equal(hAPP(u,hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname,z),hAPP(u,hAPP(v,v_x))))),hAPP(u,hAPP(v,v_x)))**.
% 299.79/300.43 34507[0:Rew:196.1,34104.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v_x)**.
% 299.79/300.43 34642[0:SpR:7.0,55.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),w),w,tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))**.
% 299.79/300.43 34669[0:MRR:34582.1,56.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v,tc_fun(tc_Com_Opname,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(tc_Com_Opname,tc_bool)))**.
% 299.79/300.43 34710[0:SpR:34428.0,21893.0] || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_Com_Opname,v)),v_x)**.
% 299.79/300.43 34704[0:SpR:34428.0,21267.0] || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x,tc_Com_Opname,v)),v_x)**.
% 299.79/300.43 34811[7:SpL:21893.0,27282.0] || equal(hAPP(c_Set_Oinsert(u,v),v_x),v_x) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),v_x))* equal(u,v_x).
% 299.79/300.43 34810[7:SpL:21267.0,27282.0] || equal(hAPP(c_Set_Oinsert(u,v),v_x),v_x) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),v_x))* equal(u,v_x).
% 299.79/300.43 34922[7:MRR:34848.1,27297.0] || equal(u,c_Set_Oimage(c_COMBK(v,w,x),x,w))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),u,tc_Com_Opname,y)))*.
% 299.79/300.43 35001[7:MRR:34927.1,27297.0] || equal(u,c_Set_Oimage(c_COMBK(v,w,x),x,w))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_Com_Opname,y)))*.
% 299.79/300.43 35489[0:SpR:113.0,114.1] || c_Fun_Oinj__on(u,hAPP(c_Set_Ovimage(v,w,x),y),w,z) -> c_Fun_Oinj__on(u,hAPP(c_Set_Ovimage(v,w,x),c_HOL_Ominus__class_Ominus(y,x1,tc_fun(x,tc_bool))),w,z)*.
% 299.79/300.43 35544[0:Rew:11.0,35515.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))**.
% 299.79/300.43 35676[0:SpR:475.1,26119.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(z,u,x),w)),hAPP(z,v)))*.
% 299.79/300.43 36186[0:Res:526.1,516.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x))* -> hBOOL(hAPP(hAPP(c_in(u),x),v)) hBOOL(hAPP(hAPP(c_in(u),x),w)).
% 299.79/300.43 36856[0:SpR:66.0,19747.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),x),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.79/300.43 36848[0:SpR:66.0,20186.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.43 36907[0:Rew:36859.0,36720.0] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),v),tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(x,w),v),tc_fun(w,tc_bool)))**.
% 299.79/300.43 36975[0:Res:376.0,375.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,v),hAPP(c_Set_Oinsert(y,z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(z,tc_bool))),tc_fun(z,tc_bool))*.
% 299.79/300.43 37146[0:Res:651.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(x,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oimage(x,u,w),tc_Com_Opname,tc_fun(w,tc_bool))))*.
% 299.79/300.43 37409[0:SpR:55.1,36687.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(v,t_a),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),w),u,tc_fun(t_a,tc_bool))),tc_Com_Opname,tc_bool))*.
% 299.79/300.43 38661[0:Res:3346.1,184.0] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(w,x,v)) c_Fun_Oinj__on(w,v_x,x,v) -> equal(hAPP(w,hAPP(c_Fun_Othe__inv__into(v_x,w,x,v),u)),u)**.
% 299.79/300.43 38654[0:Res:8366.1,184.0] || equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),v_Procs) c_Fun_Oinj__on(u,w,v,tc_Com_Opname) -> equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(w,u,v,tc_Com_Opname),v_x)),v_x)**.
% 299.79/300.43 41425[0:Res:19451.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(x,t_a),u,tc_fun(t_a,tc_bool))))*.
% 299.79/300.43 41417[0:Res:19440.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(tc_Com_Opname),v_x)),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(x,w),u,tc_fun(w,tc_bool))))*.
% 299.79/300.43 41412[0:Res:3284.1,275.1] || equal(c_in(tc_Com_Opname),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,u,v,tc_fun(x,tc_bool))))*.
% 299.79/300.43 41403[0:Res:648.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(x,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oimage(x,tc_Com_Opname,w),u,tc_fun(w,tc_bool))))*.
% 299.79/300.43 41399[0:Res:649.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),u,tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.79/300.43 41398[0:Res:650.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u,tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.79/300.43 41450[4:SpR:130.1,38236.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_Com_Opname,tc_bool))*.
% 299.79/300.43 42199[0:Obv:42162.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u),y,u)* -> c_lessequals(x,y,u).
% 299.79/300.43 42200[0:Obv:42099.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,x,u) -> c_lessequals(w,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),y,hAPP(c_Set_Oinsert(x,u),v),u,u),u)*.
% 299.79/300.43 42685[0:SpR:161.0,517.1] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),v,tc_fun(w,tc_bool)),x))*.
% 299.79/300.43 42682[0:SpR:161.0,518.1] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),u),v,tc_fun(w,tc_bool)),x))*.
% 299.79/300.43 43273[4:Res:84.1,42356.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),v_x)).
% 299.79/300.43 43379[4:Res:84.1,42582.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),x))*.
% 299.79/300.43 43503[0:SpR:507.0,517.1] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),y)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z)),y))*.
% 299.79/300.43 43500[0:SpR:507.0,518.1] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),y)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),x)),y))*.
% 299.79/300.43 43615[4:Res:84.1,43176.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),x,t_a)*.
% 299.79/300.43 43725[0:SpR:162.0,517.1] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y)) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)),y))*.
% 299.79/300.43 43722[0:SpR:162.0,518.1] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y)) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x)),y))*.
% 299.79/300.43 44932[0:Res:84.1,44833.0] || c_lessequals(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),v_x)).
% 299.79/300.43 45404[0:SpR:8498.1,45357.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) hBOOL(hAPP(c_Set_Oinsert(u,v),v_x)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname))*.
% 299.79/300.43 45615[0:SpL:323.0,333.0] || c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),y)* -> c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool)),y).
% 299.79/300.43 45614[0:SpL:323.0,332.0] || c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),y)* -> c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),y).
% 299.79/300.43 45980[0:Res:517.1,45899.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),tc_Com_Opname)))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x)).
% 299.79/300.43 45977[0:Res:518.1,45899.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),tc_Com_Opname)))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x)).
% 299.79/300.43 45919[0:SpL:8498.1,45899.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname))* -> hBOOL(hAPP(c_Set_Oinsert(u,v),v_x)).
% 299.79/300.43 47413[0:MRR:47412.1,264.0] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool)),u,x)))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,u,x)),w))*.
% 299.79/300.43 47982[0:MRR:47981.1,264.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),u,w)))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)),v))*.
% 299.79/300.43 48199[7:MRR:48102.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),z))*.
% 299.79/300.43 48295[7:MRR:48217.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),z,t_a)*.
% 299.79/300.43 50354[0:Res:10697.0,46309.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),u))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),u)))*.
% 299.79/300.43 50491[0:SpL:223.1,3266.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,y),u,y),w),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.79/300.43 50485[0:SpL:223.1,2674.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,tc_Com_Opname),u,tc_Com_Opname),w),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.43 50459[0:SpR:223.1,36588.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,v_x,u,t_a),u,t_a),w)),v_x))*.
% 299.79/300.43 50437[0:SpR:223.1,10813.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,x1,u,y),u,y),w)),x1))*.
% 299.79/300.43 50737[0:Res:10697.0,46413.0] || hBOOL(u) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),y))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),y)))*.
% 299.79/300.43 51190[0:SpR:21893.0,26873.0] || -> equal(c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.43 51189[0:SpR:21267.0,26873.0] || -> equal(c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.43 51301[0:SpR:21893.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,t_a),v_x),c_Set_Oinsert(u,t_a),tc_Com_Opname,v),v_x),hAPP(hAPP(c_Set_Oinsert(u,t_a),v_x),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.43 51300[0:SpR:21267.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,t_a),hAPP(c_Set_Oinsert(u,t_a),v_x),tc_Com_Opname,v),v_x),hAPP(hAPP(c_Set_Oinsert(u,t_a),v_x),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.43 51430[7:MRR:51313.0,27297.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(hAPP(c_Set_Oinsert(w,t_a),c_Set_Oimage(c_COMBK(u,v,x),x,v)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.43 51504[0:SpL:21893.0,33513.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),v)* equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(u,v),v_x),v),c_HOL_Ozero__class_Ozero(tc_nat)) -> .
% 299.79/300.43 51503[0:SpL:21267.0,33513.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),v)* equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(u,v),v_x),v),c_HOL_Ozero__class_Ozero(tc_nat)) -> .
% 299.79/300.43 51833[4:SpR:21893.0,40792.1] || c_lessequals(v_x,hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),x),tc_bool)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),x)).
% 299.79/300.43 51832[4:SpR:21267.0,40792.1] || c_lessequals(v_x,hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),x),tc_bool)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),x)).
% 299.79/300.43 51980[0:Rew:302.1,51926.2,302.1,51926.2] class_Lattices_Obounded__lattice(u) || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w,x),c_Orderings_Otop__class_Otop(u))** -> equal(c_List_Ofoldl(y,c_Orderings_Otop__class_Otop(u),z,x,x1),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.43 51982[0:Rew:14216.0,51962.1,14216.0,51962.1] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,y,z),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_List_Ofoldl(x1,c_Orderings_Otop__class_Otop(tc_bool),x2,z,x3),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.43 52269[0:SpL:475.1,35720.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(hAPP(c_Set_Oimage(x,u,y),w),z,tc_fun(y,tc_bool))* -> hBOOL(hAPP(z,hAPP(x,v)))*.
% 299.79/300.43 52523[7:SpL:35.2,52504.0] || c_lessequals(u,c_COMBK(v,w,x),tc_fun(y,tc_bool))* c_lessequals(c_COMBK(v,w,x),z,tc_fun(y,tc_bool))* equal(u,v_x) -> hBOOL(v).
% 299.79/300.43 52593[0:SpL:35.2,52505.0] || c_lessequals(u,c_COMBK(v,w,x),tc_fun(y,tc_bool))* c_lessequals(c_COMBK(v,w,x),z,tc_fun(y,tc_bool))* equal(u,v_Procs) -> hBOOL(v).
% 299.79/300.43 52602[0:SpR:35.2,52509.0] || c_lessequals(u,c_COMBK(v,w,x),tc_fun(y,tc_bool))* c_lessequals(c_COMBK(v,w,x),z,tc_fun(y,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(x1,u,t_a)* hBOOL(v).
% 299.79/300.43 52820[0:SpR:24019.2,474.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v_x,v,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))))*.
% 299.79/300.43 52999[0:Res:23739.1,280.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(u,v_Procs),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,u,w,tc_fun(x,tc_bool)),v))*.
% 299.79/300.43 53116[0:SSi:53066.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x))**.
% 299.79/300.43 53117[0:SSi:53049.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u)),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v))**.
% 299.79/300.43 53248[0:SSi:53198.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x))**.
% 299.79/300.43 53249[0:SSi:53181.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u)),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v))**.
% 299.79/300.43 53366[0:Res:31543.0,280.1] || hBOOL(hAPP(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x)),w))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(x,tc_bool)),w))*.
% 299.79/300.43 53437[0:SpR:33303.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x),tc_Com_Opname),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.79/300.43 53421[0:SpR:33303.0,446.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x),tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.79/300.43 53778[0:Res:7226.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(c_Option_Othe(v),w,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,y,t_a)*.
% 299.79/300.43 53774[0:Res:7226.0,280.1] || hBOOL(hAPP(hAPP(u,v),w))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(c_Option_Othe(x),y,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u,z,tc_fun(x1,tc_bool)),w))*.
% 299.79/300.43 53787[0:MRR:53757.0,7226.0] || equal(hAPP(u,v),hAPP(u,w))* c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(c_Option_Othe(x),y,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),z,x1)* -> equal(v,w).
% 299.79/300.43 54125[0:SpR:52997.1,474.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.79/300.43 54108[0:SpR:52997.1,446.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v_Procs,v),u),v_x,tc_fun(v,tc_bool))*.
% 299.79/300.43 54827[0:SpR:13749.2,584.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y,z),c_Orderings_Otop__class_Otop(u)),hAPP(c_Orderings_Otop__class_Otop(u),hAPP(w,c_Orderings_Otop__class_Otop(u))))**.
% 299.79/300.43 54826[0:SpR:13749.2,584.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),c_Orderings_Otop__class_Otop(u)),hAPP(hAPP(v,c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u)))**.
% 299.79/300.43 55302[0:SpR:14043.2,584.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y,z),c_Orderings_Otop__class_Otop(u)),hAPP(c_Orderings_Otop__class_Otop(u),hAPP(w,c_Orderings_Otop__class_Otop(u))))**.
% 299.79/300.43 55301[0:SpR:14043.2,584.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),c_Orderings_Otop__class_Otop(u)),hAPP(hAPP(v,c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u)))**.
% 299.79/300.43 55632[0:Rew:130.1,55489.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(x,c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool)*.
% 299.79/300.43 56132[0:SpR:30368.2,9268.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))**.
% 299.79/300.43 56573[0:SpR:30928.2,9268.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(u),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)))**.
% 299.79/300.43 57976[7:MRR:57903.2,27297.0] || equal(c_COMBK(u,v,w),c_Set_Oimage(c_COMBK(x,y,z),z,y))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))* -> .
% 299.79/300.43 58157[7:MRR:58060.2,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_COMBK(x,y,z))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool),x)* -> .
% 299.79/300.43 58195[0:SpL:188.1,58055.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool),x,y),c_Set_Ovimage(c_COMBK(v,u,w),w,u))* -> .
% 299.79/300.43 58443[0:SpL:130.1,58248.0] class_HOL_Ominus(u) || equal(c_COMBK(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),x,y),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_fun(t_a,tc_bool)))** -> .
% 299.79/300.43 58559[0:SpR:317.0,10771.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oinsert(z,x),y)),v))*.
% 299.79/300.43 58990[0:Res:8369.1,15629.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),x)))*.
% 299.79/300.43 58928[0:Res:3279.1,15629.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u) -> hBOOL(hAPP(hAPP(hAPP(u,v_x),v_Procs),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(hAPP(u,v_x),v_Procs),v)))*.
% 299.79/300.43 58694[0:SpL:15476.0,15629.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v)))*.
% 299.79/300.43 58679[0:SpL:353.0,15629.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)))* -> hBOOL(hAPP(c_Set_Oinsert(w,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_Set_Oinsert(w,v),y)))*.
% 299.79/300.43 59122[0:Rew:586.0,58799.1] || hBOOL(hAPP(u,hAPP(v,w)))* -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_COMBB(u,z,x1,x2),v),x))))*.
% 299.79/300.43 59123[0:Rew:585.0,58798.1] || hBOOL(hAPP(hAPP(u,v),w))* -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_COMBC(u,z,x1,x2),w),x)),w))*.
% 299.79/300.43 59498[0:Res:8369.1,15857.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),y)))*.
% 299.79/300.43 59436[0:Res:3279.1,15857.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u) -> hBOOL(hAPP(hAPP(hAPP(u,v_x),v_Procs),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(u,v_x),v_Procs),w)))*.
% 299.79/300.43 59202[0:SpL:15476.0,15857.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),w)))*.
% 299.79/300.43 59187[0:SpL:353.0,15857.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)))* -> hBOOL(hAPP(c_Set_Oinsert(w,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oinsert(w,v),z)))*.
% 299.79/300.43 59632[0:Rew:586.0,59307.1] || hBOOL(hAPP(u,hAPP(v,w)))* -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_COMBB(u,z,x1,x2),v),y))))*.
% 299.79/300.43 59633[0:Rew:585.0,59306.1] || hBOOL(hAPP(hAPP(u,v),w))* -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_COMBC(u,z,x1,x2),w),y)),w))*.
% 299.79/300.43 59681[0:SpL:113.0,19883.0] || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))),tc_fun(v,tc_bool)),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),y),v).
% 299.79/300.43 59922[0:Obv:59845.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),w)** -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),w,u).
% 299.79/300.43 60088[0:Res:4718.2,405.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),u)* -> equal(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u)).
% 299.79/300.43 60269[7:MRR:60172.2,27297.0] || equal(u,c_Set_Oimage(c_COMBK(v,w,x),x,w))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_bool),y,z),u)* -> .
% 299.79/300.43 60328[0:Res:4803.2,405.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),v,u)* -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(u),u),v).
% 299.79/300.43 60477[0:SpR:5882.1,584.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1,x2,x3),c_Orderings_Otop__class_Otop(u)),hAPP(c_Orderings_Otop__class_Otop(u),hAPP(z,c_Orderings_Otop__class_Otop(u))))**.
% 299.79/300.43 60476[0:SpR:5882.1,584.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(v,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1,x2,x3),c_Orderings_Otop__class_Otop(u)),hAPP(hAPP(v,c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u)))**.
% 299.79/300.43 61787[0:SpR:11167.1,474.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,tc_Com_Opname)),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.79/300.43 61949[0:SpL:329.1,15487.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(v_x,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.79/300.43 61948[0:SpL:328.1,15487.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.79/300.43 61944[0:SpL:538.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.43 62182[0:Res:23754.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),t_a)* c_Hoare__Mirabelle_Otriple__valid(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.79/300.43 62177[0:Res:23754.0,280.1] || hBOOL(hAPP(hAPP(u,v_x),v)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,w),v_Procs),u,w,tc_fun(x,tc_bool)),v))*.
% 299.79/300.43 62294[0:Res:41.2,4246.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.79/300.43 62286[0:Res:53.2,4246.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)*.
% 299.79/300.43 62283[0:Res:683.1,4246.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,u),hAPP(v,v_x)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,u),hAPP(v,v_x),u)*.
% 299.79/300.43 62404[0:SSi:62343.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs),v_Procs) -> c_lessequals(v_Procs,hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)),v_Procs),tc_bool)*.
% 299.79/300.43 62405[0:SSi:62340.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,tc_bool),u) -> c_lessequals(u,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),x,tc_bool),tc_bool)*.
% 299.79/300.43 62406[0:SSi:62334.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(w,x,y)),z),w) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_COMBK(w,x,y)),z),w,tc_bool)*.
% 299.79/300.43 62407[0:SSi:62333.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(x,w)),x) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Option_Ooption_OSome(x,w)),x,tc_bool)*.
% 299.79/300.43 62408[0:SSi:62331.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),x) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),x,tc_bool)*.
% 299.79/300.43 62409[0:SSi:62330.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),w) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x),w,tc_bool)*.
% 299.79/300.43 62410[0:SSi:62323.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),hAPP(u,x)) -> c_lessequals(hAPP(u,x),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),tc_bool)*.
% 299.79/300.43 62411[0:Obv:62276.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),v) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),v,u)*.
% 299.79/300.43 62412[0:Obv:62273.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w),v) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w),v,u)*.
% 299.79/300.43 62419[0:SSi:62220.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),v_x) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),v_x,tc_fun(v,tc_bool))*.
% 299.79/300.43 62420[0:SSi:62219.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),hAPP(u,v_x)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),hAPP(u,v_x),tc_fun(v,tc_bool))*.
% 299.79/300.43 62421[0:SSi:62205.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),x) -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),x,tc_fun(v,tc_bool))*.
% 299.79/300.43 62629[0:Res:41.2,4340.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.43 62621[0:Res:53.2,4340.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.43 62618[0:Res:683.1,4340.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,u),hAPP(v,v_x),u)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,u),hAPP(v,v_x)).
% 299.79/300.43 62747[0:Obv:62611.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),v,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),v).
% 299.79/300.43 62748[0:Obv:62608.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w),v,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w),v).
% 299.79/300.43 63469[0:Res:4719.2,50.1] class_OrderedGroup_Opordered__ab__group__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),c_HOL_Ozero__class_Ozero(u),u).
% 299.79/300.43 63468[0:Res:4719.2,46.1] class_OrderedGroup_Opordered__ab__group__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),c_HOL_Ozero__class_Ozero(u),u).
% 299.79/300.43 63882[0:Res:4804.2,48.1] class_OrderedGroup_Opordered__ab__group__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),v,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u).
% 299.79/300.43 63881[0:Res:4804.2,44.1] class_OrderedGroup_Opordered__ab__group__add(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),v,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u).
% 299.79/300.43 64238[0:SpR:11176.1,646.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),u),v_x)**.
% 299.79/300.43 64234[0:SpR:11177.1,646.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),v_x),v_x)**.
% 299.79/300.43 64198[0:SpR:300.1,646.1] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),tc_Com_Opname,v),v_x),v_x)**.
% 299.79/300.43 64193[0:SpR:24019.2,646.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Fun_Oinj__on(v_x,v_Procs,tc_Com_Opname,u) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,v_x,tc_Com_Opname,u),v_x),v_x)**.
% 299.79/300.43 64192[0:SpR:3586.1,646.1] || equal(hAPP(c_in(u),v),v_Procs) c_Fun_Oinj__on(c_Set_Oinsert(v,u),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x),v_x)**.
% 299.79/300.43 64191[7:SpR:27278.1,646.1] || equal(hAPP(c_in(u),v),v_x) c_Fun_Oinj__on(c_Set_Oinsert(v,u),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x),v_x)**.
% 299.79/300.43 64177[0:SpR:8498.1,646.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) c_Fun_Oinj__on(c_Set_Oinsert(v,u),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x),v_x)**.
% 299.79/300.43 64405[0:SpR:11176.1,645.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),u),v_x)**.
% 299.79/300.43 64401[0:SpR:11177.1,645.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_x) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),v_x),v_x)**.
% 299.79/300.43 64360[0:SpR:24019.2,645.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Fun_Oinj__on(v_x,v_Procs,tc_Com_Opname,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_x,tc_Com_Opname,u),v_x),v_x)**.
% 299.79/300.43 64359[0:SpR:3586.1,645.1] || equal(hAPP(c_in(u),v),v_Procs) c_Fun_Oinj__on(c_Set_Oinsert(v,u),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x),v_x)**.
% 299.79/300.43 64358[7:SpR:27278.1,645.1] || equal(hAPP(c_in(u),v),v_x) c_Fun_Oinj__on(c_Set_Oinsert(v,u),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x),v_x)**.
% 299.79/300.43 64344[0:SpR:8498.1,645.1] || equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x) c_Fun_Oinj__on(c_Set_Oinsert(v,u),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),v_x),v_x)**.
% 299.79/300.43 64483[0:Res:662.1,45899.0] || hBOOL(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),tc_Com_Opname)))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),v_x)).
% 299.79/300.43 64542[0:SpL:328.1,24257.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(u,c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.43 64538[0:SpL:538.0,24257.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.43 64702[0:Res:27986.0,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w)),x))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(y,tc_bool)),x))*.
% 299.79/300.43 64722[0:Res:27987.0,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w)),x))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(y,tc_bool)),x))*.
% 299.79/300.43 64742[0:Res:28288.0,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)),x))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(y,tc_bool)),x))*.
% 299.79/300.43 64762[0:Res:28289.0,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w)),x))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(y,tc_bool)),x))*.
% 299.79/300.43 64828[0:SpR:28747.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w),tc_Com_Opname),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.79/300.43 64811[0:SpR:28747.0,446.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w),tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.79/300.43 64948[0:SpR:28748.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w),tc_Com_Opname),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.79/300.43 64931[0:SpR:28748.0,446.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w),tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.79/300.43 65068[0:SpR:28902.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w),tc_Com_Opname),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.79/300.43 65051[0:SpR:28902.0,446.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w),tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.79/300.43 65188[0:SpR:28903.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w),tc_Com_Opname),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.79/300.43 65171[0:SpR:28903.0,446.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w),tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.79/300.43 66030[0:SpR:65404.1,545.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> hBOOL(hAPP(hAPP(c_in(y),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),x)))*.
% 299.79/300.43 66026[0:SpR:65404.1,362.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.43 66833[0:Rew:65404.1,66759.3] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(u) || -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x))**.
% 299.79/300.43 67597[0:Rew:65404.1,67515.3] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(u) || -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x))**.
% 299.79/300.43 70606[7:SpL:223.1,70491.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,t_a),u,t_a),w),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.79/300.43 70635[0:SpL:223.1,70492.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,t_a),u,t_a),w),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.79/300.43 71403[7:SpL:188.1,71221.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x)** -> .
% 299.79/300.43 71602[7:SpR:71455.1,545.1] || equal(u,v_x) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> hBOOL(hAPP(hAPP(c_in(x),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,x),w)))*.
% 299.79/300.43 71598[7:SpR:71455.1,362.1] || equal(u,v_x) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.43 71986[7:MRR:71675.1,56.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)),v_x) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(t_a,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)))**.
% 299.79/300.43 72033[7:Rew:72004.0,72018.1] || equal(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),v_x),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,u),v_x),v_x).
% 299.79/300.43 72092[0:SpR:410.0,7830.0] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(z,w),u),v,w,tc_fun(x,tc_bool))),tc_fun(x,tc_bool))*.
% 299.79/300.43 72487[0:Res:687.1,12554.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname)),u))*.
% 299.79/300.43 72486[0:Res:686.1,12554.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname)),u))*.
% 299.79/300.43 72469[0:SpL:66.0,12554.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),y))* -> hBOOL(hAPP(hAPP(c_in(w),y),c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)))).
% 299.79/300.43 73059[7:Res:71608.1,184.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_x) c_Fun_Oinj__on(u,w,v,t_a) -> equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(w,u,v,t_a),v_x)),v_x)**.
% 299.79/300.43 74360[7:SpL:71835.1,156.0] || equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(hAPP(c_in(v),x),v_x))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,x)),v_x))*.
% 299.79/300.43 74133[7:SpL:71835.1,156.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Ovimage(v,u,w),x)))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(v,v_x)),x))*.
% 299.79/300.43 73976[7:SpL:71835.1,193.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_Finite__Set_Ofinite(v_x,v) equal(c_Finite__Set_Ocard(v_x,w),c_Finite__Set_Ocard(v_x,v)) -> c_Fun_Oinj__on(u,v_x,v,w)*.
% 299.79/300.43 73773[7:SpR:71835.1,510.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(u),w),v))* -> hBOOL(hAPP(hAPP(c_in(u),w),v_x))*.
% 299.79/300.43 73704[7:SpR:71835.1,196.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(hAPP(c_Set_Ovimage(u,v,w),v_x),v_x).
% 299.79/300.43 73693[7:SpR:71835.1,153.1] || equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(hAPP(c_in(w),hAPP(u,x)),v_x))* -> hBOOL(hAPP(hAPP(c_in(v),x),v_x))*.
% 299.79/300.43 73685[7:SpR:71835.1,511.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(v_x,w)))*.
% 299.79/300.43 73671[7:SpR:71835.1,475.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(hAPP(c_in(v),x),v_x))* -> equal(hAPP(c_Set_Oinsert(hAPP(u,x),w),v_x),v_x)**.
% 299.79/300.43 73669[7:SpR:71835.1,545.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(hAPP(c_in(v),x),v_x))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,x)),v_x))*.
% 299.79/300.43 73663[7:SpR:71835.1,153.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(hAPP(c_in(v),hAPP(w,v_x)),x))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Ovimage(w,u,v),x)))*.
% 299.79/300.43 73655[7:SpR:71835.1,510.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(v_x,w)))*.
% 299.79/300.43 73611[7:SpR:71835.1,545.1] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> hBOOL(hAPP(hAPP(c_in(x),v_x),hAPP(c_Set_Oimage(u,v,x),w)))*.
% 299.79/300.43 73607[7:SpR:71835.1,362.1] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,u,v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.43 73548[7:SpR:71835.1,304.3] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v_x,v,u) c_lessequals(w,v,u) -> c_lessequals(hAPP(v_x,w),v,u)*.
% 299.79/300.43 73201[7:SpR:71835.1,463.1] || equal(c_Set_Oinsert(v_x,t_a),c_Com_Obody) c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_x),u,v,w) -> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),v_x),u,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_x,v,u,w),w)*.
% 299.79/300.43 74501[7:MRR:74337.2,6340.0] || equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(hAPP(w,v),x))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,w,u,tc_fun(y,tc_bool)),x))*.
% 299.79/300.43 74502[7:MRR:74267.1,6340.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_Set_Oinsert(v_x,t_a))** c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.43 75720[7:SpR:71883.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,v_x,v,u),u)*.
% 299.79/300.43 75712[7:SpR:71883.1,176.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(v_x,u,v),hAPP(c_Set_Oinsert(v_x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))))*.
% 299.79/300.43 76071[0:Rew:42241.2,76070.2] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> c_lessequals(w,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w),u),v),u,u),u)*.
% 299.79/300.43 76764[7:SpR:338.0,71682.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(x,u),w)),v_x))*.
% 299.79/300.43 76761[7:SpR:475.1,71682.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(hAPP(c_Set_Oimage(x,u,y),w),v_x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(x,u,y),w),v_x))*.
% 299.79/300.43 77172[7:SpL:181.1,74788.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_x)** equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x)* -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) hBOOL(x)*.
% 299.79/300.43 77399[0:Res:2399.2,146.1] class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u) c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),v,u)*.
% 299.79/300.43 77591[0:Res:2429.2,146.1] class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) class_OrderedGroup_Opordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ouminus__class_Ouminus(v,u),u) c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(v,u),u),u),v,u)*.
% 299.79/300.43 77901[0:Res:149.1,5892.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v))* hBOOL(hAPP(c_COMBS(c_in(w),c_in(u),x,y,z),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))))*.
% 299.79/300.43 77796[0:SpL:584.0,5892.0] || hBOOL(hAPP(hAPP(hAPP(u,v),hAPP(w,v)),v))* -> hBOOL(hAPP(c_COMBS(c_in(x),c_COMBS(u,w,y,z,x1),x2,x3,x4),v))*.
% 299.79/300.43 77708[0:SpL:540.1,5892.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v))* -> hBOOL(hAPP(c_COMBS(c_in(x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,z,x1),v))*.
% 299.79/300.43 77707[0:SpL:539.1,5892.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v))* -> hBOOL(hAPP(c_COMBS(c_in(x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,z,x1),v))*.
% 299.79/300.43 77706[0:SpL:297.2,5892.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) hBOOL(hAPP(w,w))* -> hBOOL(hAPP(c_COMBS(c_in(x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,z,x1),w))*.
% 299.79/300.43 78737[4:Res:78665.1,455.0] || equal(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),v_x)** c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.79/300.43 78712[4:Res:78665.1,280.1] || equal(hAPP(hAPP(c_in(u),v),w),v_x)** hBOOL(hAPP(hAPP(x,v),y))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(z,tc_bool)),y))*.
% 299.79/300.43 78706[4:Res:78665.1,175.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),hAPP(c_Set_Oinsert(y,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))),v_x)** -> equal(hAPP(w,v),y).
% 299.79/300.43 78702[4:Res:78665.1,470.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)),v_x)** -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__XimageE__1__1(y,v,w,x,u)),y))*.
% 299.79/300.43 78701[4:Res:78665.1,466.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)),v_x)** -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(y,w,v,x,u)),y))*.
% 299.79/300.43 78885[0:SpR:197.1,11064.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Finite__Set_Ofinite(x,v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),w)*.
% 299.79/300.43 78866[0:SpR:205.1,11064.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)),v)*.
% 299.79/300.43 79025[0:Res:15630.1,70070.1] || hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,hAPP(c_in(t_a),v_x),v),v_x),tc_bool))* -> .
% 299.79/300.43 79021[0:Res:15630.1,11894.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,hAPP(c_in(u),v),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.79/300.43 79052[0:Rew:9.0,79003.0] || hBOOL(hAPP(u,hAPP(v,w))) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,c_Fun_Ocomp(u,v,x1,x2,x3),x))))*.
% 299.79/300.43 79245[0:Res:15858.1,70070.1] || hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(u,w),x),hAPP(c_in(t_a),v_x),w),v_x),tc_bool))* -> .
% 299.79/300.43 79241[0:Res:15858.1,11894.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(w,y),z),hAPP(c_in(u),v),y),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> .
% 299.79/300.43 79272[0:Rew:9.0,79223.0] || hBOOL(hAPP(u,hAPP(v,w))) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(w,y),z),c_Fun_Ocomp(u,v,x1,x2,x3),y))))*.
% 299.79/300.43 80020[0:SpL:21268.0,502.0] || c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u)),v,w) -> c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Com_Obody,hAPP(c_Com_Obody,u),x,y)),v,w)*.
% 299.79/300.43 80016[0:SpL:21268.0,348.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x) -> equal(c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,u),y,z),w,v,x)),w)**.
% 299.79/300.43 79977[0:SpR:52997.1,21268.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_Procs,u),v_x,v,w)),v_x)**.
% 299.79/300.43 79726[0:SpR:21268.0,37799.1] || hBOOL(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),u,x))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)).
% 299.79/300.43 79567[0:SpR:21268.0,15367.0] || -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),w),x,y),tc_fun(v,tc_bool)),v)*.
% 299.79/300.43 79495[0:SpR:21268.0,87.1] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.43 79370[0:SpR:21268.0,9566.0] || -> c_lessequals(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),z),hAPP(hAPP(c_Set_Oinsert(v,w),x),z),tc_bool)*.
% 299.79/300.43 79359[7:SpR:21268.0,71682.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),v_x)** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),x),v_x)).
% 299.79/300.43 79355[0:SpR:21268.0,503.1] || c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Com_Obody,hAPP(c_Com_Obody,v),u,w)),x,y)* -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v)),x,y).
% 299.79/300.43 81215[0:SpL:21894.0,502.0] || c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u)),v,w) -> c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Com_Obody,u),c_Com_Obody,x,y)),v,w)*.
% 299.79/300.43 81211[0:SpL:21894.0,348.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x) -> equal(c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Com_Ocom_OBODY,u),c_Com_Ocom_OBODY,y,z),w,v,x)),w)**.
% 299.79/300.43 81171[0:SpR:52997.1,21894.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v_x,c_Set_Oinsert(v_Procs,u),v,w)),v_x)**.
% 299.79/300.43 80920[0:SpR:21894.0,37799.1] || hBOOL(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,x))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)).
% 299.79/300.43 80760[0:SpR:21894.0,15367.0] || -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(u,v),x,y),tc_fun(v,tc_bool)),v)*.
% 299.79/300.43 80688[0:SpR:21894.0,87.1] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(u),w,x),u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.43 80563[0:SpR:21894.0,9566.0] || -> c_lessequals(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),z),hAPP(hAPP(c_Set_Oinsert(v,w),x),z),tc_bool)*.
% 299.79/300.43 80552[7:SpR:21894.0,71682.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),v_x)** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),x),v_x)).
% 299.79/300.43 80548[0:SpR:21894.0,503.1] || c_Natural_Oevalc(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Com_Obody,v),c_Com_Obody,u,w)),x,y)* -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v)),x,y).
% 299.79/300.43 81920[0:SpR:584.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(v,w),hAPP(x,w)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_COMBS(v,x,y,z,x1),x2,x3,x4),w),u)*.
% 299.79/300.43 81884[0:SpR:584.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_COMBS(v,w,x,y,z),x1),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,x1),x2,x3,x4),hAPP(w,x1)),u)*.
% 299.79/300.43 81833[0:SpR:540.1,5879.1] class_Lattices_Olattice(u) class_Lattices_Oupper__semilattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y,z,x1),w),v)*.
% 299.79/300.43 81832[0:SpR:539.1,5879.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Oupper__semilattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y,z,x1),w),v)*.
% 299.79/300.43 82142[7:SpR:78597.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Set_Oinsert(v_x,v)),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Set_Oinsert(v_x,v)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,x),w)))*.
% 299.79/300.43 82138[7:SpR:78597.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Set_Oinsert(v_x,v)),w)) -> c_lessequals(c_Set_Oinsert(v_x,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.43 82392[0:SpR:584.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(v,w),hAPP(x,w)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_COMBS(v,x,y,z,x1),x2,x3,x4),w),u)*.
% 299.79/300.43 82356[0:SpR:584.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_COMBS(v,w,x,y,z),x1),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,x1),x2,x3,x4),hAPP(w,x1)),u)*.
% 299.79/300.43 82305[0:SpR:540.1,5880.1] class_Lattices_Olattice(u) class_Lattices_Olattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y,z,x1),w),v)*.
% 299.79/300.43 82304[0:SpR:539.1,5880.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Olattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y,z,x1),w),v)*.
% 299.79/300.43 82919[0:SpR:205.1,22513.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(y,v,z),x),z)*.
% 299.79/300.43 83107[0:SpL:5924.0,24257.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(u,v_x),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.43 83103[0:SpL:5924.0,3489.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_in(tc_Com_Opname))** hBOOL(hAPP(hAPP(hAPP(u,v_x),v),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.79/300.43 83095[0:SpL:5924.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.79/300.43 83076[0:SpR:5924.0,584.0] || -> equal(hAPP(c_COMBS(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,x3,x4,x5),x6),hAPP(hAPP(hAPP(u,x6),v),hAPP(x2,x6)))*.
% 299.79/300.43 83075[0:SpR:5924.0,584.0] || -> equal(hAPP(c_COMBS(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2),x3,x4,x5),x6),hAPP(hAPP(u,x6),hAPP(hAPP(v,x6),w)))*.
% 299.79/300.43 83003[0:SpR:5924.0,3294.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_in(t_a))** -> equal(hAPP(hAPP(hAPP(u,v_x),v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.43 83234[7:SpR:188.1,78357.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,w),w,u),x,y),v_x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.79/300.43 83427[0:SpL:5961.0,24257.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(u,hAPP(x,v_x)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.43 83423[0:SpL:5961.0,3489.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_in(tc_Com_Opname))** hBOOL(hAPP(hAPP(u,hAPP(x,v_x)),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.79/300.43 83415[0:SpL:5961.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(x,v_x)),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.79/300.43 83396[0:SpR:5961.0,584.0] || -> equal(hAPP(c_COMBS(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2,x3,x4,x5),x6),hAPP(hAPP(u,hAPP(x,x6)),hAPP(x2,x6)))*.
% 299.79/300.43 83395[0:SpR:5961.0,584.0] || -> equal(hAPP(c_COMBS(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2),x3,x4,x5),x6),hAPP(hAPP(u,x6),hAPP(v,hAPP(y,x6))))*.
% 299.79/300.43 83333[0:SpR:5961.0,3294.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_in(t_a))** -> equal(hAPP(hAPP(u,hAPP(x,v_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.43 83891[0:SpL:5899.0,19641.0] || hBOOL(hAPP(c_COMBS(u,v,w,x,y),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_COMBS(u,v,z,x1,x2),x3)))* -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBS(u,v,z,x1,x2),x3,t_a).
% 299.79/300.43 83787[0:SpR:5899.0,584.0] || -> equal(hAPP(c_COMBS(c_COMBS(u,v,w,x,y),z,x1,x2,x3),x4),hAPP(hAPP(c_COMBS(u,v,x5,x6,x7),x4),hAPP(z,x4)))*.
% 299.79/300.43 83786[0:SpR:5899.0,584.0] || -> equal(hAPP(c_COMBS(u,c_COMBS(v,w,x,y,z),x1,x2,x3),x4),hAPP(hAPP(u,x4),hAPP(c_COMBS(v,w,x5,x6,x7),x4)))*.
% 299.79/300.43 84066[0:Rew:584.0,83889.1] || hBOOL(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_COMBS(u,v,z,x1,x2),tc_Com_Opname)))* -> hBOOL(hAPP(hAPP(u,v_x),hAPP(v,v_x))).
% 299.79/300.43 84068[0:Rew:584.0,83781.0] || hBOOL(hAPP(hAPP(u,v_x),hAPP(v,v_x))) -> hBOOL(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_COMBS(u,v,z,x1,x2),tc_Com_Opname)))*.
% 299.79/300.43 84111[4:SpL:223.1,78769.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,t_a),u,t_a),w),v_x),tc_bool),v_x)** -> .
% 299.79/300.43 84186[7:SpL:181.1,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_bool),v_x) equal(c_Set_Ovimage(c_COMBK(v,w,u),u,w),v_x)** -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)).
% 299.79/300.43 84923[4:SpL:586.0,78744.0] || equal(hAPP(u,hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_COMBB(u,w,x,y),v),z))),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_COMBB(u,w,x,y),v),z,t_a).
% 299.79/300.43 84922[4:SpL:585.0,78744.0] || equal(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_COMBC(u,v,w,x),y),z)),y),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_COMBC(u,v,w,x),y),z,t_a).
% 299.79/300.43 84896[4:SpL:331.0,78744.0] || equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,t_a)*.
% 299.79/300.43 85097[0:SpL:644.0,390.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))* -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBK(v,w,tc_Com_Opname),tc_Com_Opname,w),u,w,tc_Com_Opname).
% 299.79/300.43 85063[0:SpR:644.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))*.
% 299.79/300.43 85038[0:SpR:644.0,9569.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v)),v_Procs),tc_bool)*.
% 299.79/300.43 85037[0:SpR:644.0,9568.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v)),x),v_Procs),tc_bool)*.
% 299.79/300.43 85953[0:Res:45357.1,13582.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname)),v))* -> .
% 299.79/300.43 85982[4:Res:85725.0,10214.1] || equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),v_x).
% 299.79/300.43 85986[4:SSi:85973.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_bool)* -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),v_x).
% 299.79/300.43 85987[4:SSi:85970.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),v_x) -> c_lessequals(v_x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_bool)*.
% 299.79/300.43 86051[0:SpL:188.1,86011.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_Procs)** -> .
% 299.79/300.43 86255[0:SpR:86109.1,545.1] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> hBOOL(hAPP(hAPP(c_in(x),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,x),w)))*.
% 299.79/300.43 86251[0:SpR:86109.1,362.1] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.43 86550[0:MRR:86337.1,56.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)),v_Procs) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(t_a,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)))**.
% 299.79/300.43 86653[0:Res:86261.1,184.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_Procs) c_Fun_Oinj__on(u,w,v,t_a) -> equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(w,u,v,t_a),v_x)),v_x)**.
% 299.79/300.43 86731[4:SpL:181.1,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_bool),v_x) equal(c_Set_Ovimage(c_COMBK(v,w,u),u,w),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)).
% 299.79/300.43 86890[0:SpR:21894.0,86345.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),x),v_x)).
% 299.79/300.43 86888[0:SpR:21268.0,86345.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),x),v_x)).
% 299.79/300.43 86867[0:SpR:338.0,86345.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(x,u),w)),v_x))*.
% 299.79/300.43 86864[0:SpR:475.1,86345.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(hAPP(c_Set_Oimage(x,u,y),w),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(x,u,y),w),v_x))*.
% 299.79/300.43 87281[7:SpR:130.1,71492.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)),x))*.
% 299.79/300.43 87429[7:SpR:130.1,71493.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)),x,t_a)*.
% 299.79/300.43 87559[7:SpR:130.1,71679.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)))*.
% 299.79/300.43 88428[0:Res:8176.1,390.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(y,v,w,x),c_HOL_Ominus__class_Ominus(u,z,tc_fun(x,tc_bool)),x,w)*.
% 299.79/300.43 88638[7:SpL:181.1,88086.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(x,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)).
% 299.79/300.43 89007[0:SpR:53771.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Option_Othe(u),v,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),x,c_Option_Othe(u),y,z)))*.
% 299.79/300.43 89003[0:SpR:53772.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Option_Othe(u),v,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Option_Othe(u),x,y,z)))*.
% 299.79/300.43 88999[0:SpR:49342.1,14196.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_Procs))*.
% 299.79/300.43 88996[0:SpR:32668.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_Procs))*.
% 299.79/300.43 88995[0:SpR:28910.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),y,z),hAPP(c_Set_Oinsert(v_Procs,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))),v_Procs))*.
% 299.79/300.43 88994[0:SpR:28926.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_Procs))*.
% 299.79/300.43 88990[0:SpR:28755.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),y,z),hAPP(c_Set_Oinsert(v_Procs,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))),v_Procs))*.
% 299.79/300.43 88989[0:SpR:28771.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_Procs))*.
% 299.79/300.43 88983[0:SpR:27043.1,14196.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_Procs,u),v,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_x))*.
% 299.79/300.43 88979[0:SpR:10063.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),u,v),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.79/300.43 88975[0:SpR:15172.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y,z),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))),x1))*.
% 299.79/300.43 88969[0:SpR:586.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_COMBB(u,v,w,x),y),z,x1),hAPP(c_Set_Oinsert(hAPP(u,hAPP(y,x2)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),x2))*.
% 299.79/300.43 88968[0:SpR:585.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_COMBC(u,v,w,x),y),z,x1),hAPP(c_Set_Oinsert(hAPP(hAPP(u,x2),y),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),x2))*.
% 299.79/300.43 88952[0:SpR:24914.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(u,v_x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,x),hAPP(u,v_x))))*.
% 299.79/300.43 88932[0:SpR:9936.1,14196.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),x))*.
% 299.79/300.43 88928[0:SpR:9935.1,14196.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),u))*.
% 299.79/300.43 88888[0:SpR:14526.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),x,y),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),u)))*.
% 299.79/300.43 88839[0:SpR:369.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),y),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),hAPP(c_Set_Oinsert(u,v),y)))*.
% 299.79/300.43 88838[0:SpR:2089.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.79/300.43 88831[0:SpR:445.1,14196.0] || -> equal(u,v) hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Fun_Ofun__upd(w,v,x,y,z),x1,x2),hAPP(c_Set_Oinsert(hAPP(w,u),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool)))),u))*.
% 299.79/300.43 89093[7:Res:78350.0,10214.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,u),v,tc_fun(w,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,u),v,tc_fun(w,tc_bool)),v_x),v_x).
% 299.79/300.43 89104[7:SSi:89084.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(v_x,hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,u),v,tc_fun(w,tc_bool)),v_x),tc_bool)* -> equal(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,u),v,tc_fun(w,tc_bool)),v_x),v_x).
% 299.79/300.43 89105[7:SSi:89081.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,u),v,tc_fun(w,tc_bool)),v_x),v_x) -> c_lessequals(v_x,hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,u),v,tc_fun(w,tc_bool)),v_x),tc_bool)*.
% 299.79/300.43 89156[0:SpL:338.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(w,v),y),v).
% 299.79/300.43 89843[0:SpR:26183.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),v),tc_fun(w,tc_bool))* -> c_lessequals(u,hAPP(c_Set_Oinsert(x,w),v),tc_fun(w,tc_bool)).
% 299.79/300.43 89830[0:SpR:26183.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(x,u),v))),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(x,u),v)))**.
% 299.79/300.43 89797[0:SpR:26183.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(y,u),v),w),z)),hAPP(c_Set_Oinsert(y,u),v)))*.
% 299.79/300.43 89768[0:SpR:26183.0,9569.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)),hAPP(c_Set_Oinsert(u,v),w)),tc_bool)*.
% 299.79/300.43 89767[0:SpR:26183.0,9568.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)),y),hAPP(c_Set_Oinsert(u,v),w)),tc_bool)*.
% 299.79/300.43 89764[0:SpR:26183.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),v),hAPP(c_Set_Oinsert(w,u),v),x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v))**.
% 299.79/300.43 90522[4:SpR:131.0,90130.1] || equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x),v_x)** -> hBOOL(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)))*.
% 299.79/300.43 90521[4:SpR:158.0,90130.1] || equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x),v_x)** -> hBOOL(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))*.
% 299.79/300.43 90660[0:SpL:339.0,26231.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(w,v),x),v).
% 299.79/300.43 90773[0:Res:364.1,26480.0] || c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)).
% 299.79/300.43 91035[4:Rew:130.1,90910.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool))* -> .
% 299.79/300.43 91340[0:Rew:91288.1,91096.2] class_Complete__Lattice_Ocomplete__lattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Obot__class_Obot(u)),x)) -> c_lessequals(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w,v),v)*.
% 299.79/300.43 91341[0:Rew:91288.1,91073.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.43 92217[0:Res:4019.2,427.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Opreorder(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),w,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),v,u) c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u).
% 299.79/300.43 92216[0:Res:4019.2,426.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,u),u)*.
% 299.79/300.43 92213[0:Res:4019.2,7671.1] class_Orderings_Olinorder(u) class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),w,u) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,u),u)*.
% 299.79/300.43 92688[7:Res:82151.1,356.0] || equal(c_in(t_a),c_in(u)) -> equal(hAPP(c_Set_Oimage(c_COMBK(v,w,u),u,w),c_Set_Oinsert(v_x,x)),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.79/300.43 92605[7:SpR:130.1,82151.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_Set_Oinsert(v_x,x)))*.
% 299.79/300.43 92988[0:SpR:53771.0,5876.0] || -> c_lessequals(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Option_Othe(w),x,y,z),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),u,c_Option_Othe(w),x1,x2)),tc_fun(v,tc_bool))*.
% 299.79/300.43 92984[0:SpR:53772.0,5876.0] || -> c_lessequals(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Option_Othe(w),x,y,z),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Option_Othe(w),u,x1,x2)),tc_fun(v,tc_bool))*.
% 299.79/300.43 92948[0:SpR:586.0,5876.0] || -> c_lessequals(hAPP(u,hAPP(v,w)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_COMBB(u,y,z,x1),v),x2,x3,x4),w),tc_fun(x,tc_bool))*.
% 299.79/300.43 92947[0:SpR:585.0,5876.0] || -> c_lessequals(hAPP(hAPP(u,v),w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_COMBC(u,y,z,x1),w),x2,x3,x4),v),tc_fun(x,tc_bool))*.
% 299.79/300.43 92808[0:SpR:445.1,5876.0] || -> equal(u,v) c_lessequals(hAPP(w,u),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Fun_Ofun__upd(w,v,y,z,x1),x2,x3,x4),u),tc_fun(x,tc_bool))*.
% 299.79/300.43 93221[0:SpR:5878.1,20881.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),z),x2)),hAPP(v,c_Orderings_Obot__class_Obot(u))))*.
% 299.79/300.43 93195[0:SpR:5878.1,9569.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(hAPP(v,c_Orderings_Obot__class_Obot(u)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,y,z,x1)),c_Orderings_Obot__class_Obot(u)),tc_bool)*.
% 299.79/300.43 93194[0:SpR:5878.1,9568.0] class_Lattices_Obounded__lattice(u) || -> c_lessequals(hAPP(v,c_Orderings_Obot__class_Obot(u)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z)),x1),c_Orderings_Obot__class_Obot(u)),tc_bool)*.
% 299.79/300.43 93360[4:SpR:532.0,85556.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),w)),tc_bool)*.
% 299.79/300.43 93265[4:SpR:130.1,85556.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),x),tc_bool)*.
% 299.79/300.43 93453[0:SpR:130.1,86147.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)),x))*.
% 299.79/300.43 93604[0:SpR:130.1,86148.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)),x,t_a)*.
% 299.79/300.43 93691[0:SpL:353.0,7462.1] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(y,w),x)),w)* -> c_Finite__Set_Ofinite(u,w).
% 299.79/300.43 93748[0:SpR:130.1,86342.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)))*.
% 299.79/300.43 94019[0:SpR:353.0,10791.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(y,v),hAPP(c_Set_Oinsert(u,v),x))),tc_fun(v,tc_bool))*.
% 299.79/300.43 93952[0:SpR:353.0,10791.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(y,v),x))),tc_fun(v,tc_bool))*.
% 299.79/300.43 94170[0:Res:14364.3,50.1] class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) || hBOOL(hAPP(v,c_HOL_Ouminus__class_Ouminus(c_Finite__Set_Olinorder__class_OMin(v,u),u)))* c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.79/300.43 94169[0:Res:14364.3,46.1] class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) || hBOOL(hAPP(v,c_HOL_Ouminus__class_Ouminus(c_Finite__Set_Olinorder__class_OMin(v,u),u)))* c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),c_HOL_Ozero__class_Ozero(u),u)*.
% 299.79/300.43 94167[0:Res:14364.3,427.1] class_Orderings_Olinorder(u) class_Orderings_Opreorder(u) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,u) c_lessequals(w,x,u)* -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),x,u)*.
% 299.79/300.43 94166[0:Res:14364.3,426.1] class_Orderings_Olinorder(u) class_Orderings_Oorder(u) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,u) c_lessequals(x,c_Finite__Set_Olinorder__class_OMin(v,u),u)* -> c_lessequals(x,w,u)*.
% 299.79/300.43 94163[0:Res:14364.3,7671.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,u) c_lessequals(x,c_Finite__Set_Olinorder__class_OMin(v,u),u)* -> c_lessequals(x,w,u)*.
% 299.79/300.43 94304[0:Res:14491.3,296.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* c_Finite__Set_Ofinite(v,u) -> c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.79/300.43 94303[0:Res:14491.3,295.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* c_Finite__Set_Ofinite(v,u) -> c_lessequals(w,c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.79/300.43 94300[0:Res:14491.3,427.1] class_Orderings_Olinorder(u) class_Orderings_Opreorder(u) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,u) c_lessequals(c_Finite__Set_Olinorder__class_OMax(v,u),x,u)* -> c_lessequals(w,x,u)*.
% 299.79/300.43 94299[0:Res:14491.3,426.1] class_Orderings_Olinorder(u) class_Orderings_Oorder(u) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,u) c_lessequals(x,w,u)* -> c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.79/300.43 94296[0:Res:14491.3,7671.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,u) c_lessequals(x,w,u)* -> c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.79/300.43 94290[0:Res:14491.3,48.1] class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) || hBOOL(hAPP(v,c_HOL_Ouminus__class_Ouminus(c_Finite__Set_Olinorder__class_OMax(v,u),u)))* c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.79/300.43 94289[0:Res:14491.3,44.1] class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) || hBOOL(hAPP(v,c_HOL_Ouminus__class_Ouminus(c_Finite__Set_Olinorder__class_OMax(v,u),u)))* c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.79/300.43 2649[0:SpR:337.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))**.
% 299.79/300.43 2760[0:SpR:141.1,25.1] class_OrderedGroup_Oab__group__add(tc_fun(t_a,u)) class_HOL_Ouminus(u) || -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_x),u),hAPP(c_HOL_Ominus__class_Ominus(w,v,tc_fun(t_a,u)),v_x))**.
% 299.79/300.43 2755[0:SpR:1259.2,25.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_HOL_Ouminus(u) || equal(v,c_HOL_Ozero__class_Ozero(tc_fun(t_a,u))) -> equal(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))*.
% 299.79/300.43 2752[0:SpR:1421.2,25.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_HOL_Ouminus(u) || equal(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,u))) -> equal(hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))*.
% 299.79/300.43 2751[0:SpR:1409.2,25.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_HOL_Ouminus(u) || equal(v,c_Orderings_Otop__class_Otop(tc_fun(t_a,u))) -> equal(hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))*.
% 299.79/300.43 4327[0:SpR:297.2,1103.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),u)* -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),t_a) hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))).
% 299.79/300.43 4386[0:Res:1103.1,371.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,w),x),t_a) hBOOL(hAPP(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oinsert(v,w),x))))* equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oinsert(v,w),x)),v).
% 299.79/300.43 5021[0:Res:111.2,405.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,w,u) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u)).
% 299.79/300.43 5019[0:Res:52.2,405.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) || c_lessequals(v,w,u) c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ominus__class_Ominus(v,w,u),u)* -> equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.43 5902[0:SpR:584.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(u,v),w,x,y,z),hAPP(x1,v)),hAPP(hAPP(c_COMBS(u,x1,x2,x3,x4),v),hAPP(w,hAPP(x1,v))))*.
% 299.79/300.43 5901[0:SpR:584.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(v,w),x,y,z),hAPP(x1,w)),hAPP(hAPP(u,hAPP(x1,w)),hAPP(c_COMBS(v,x1,x2,x3,x4),w)))*.
% 299.79/300.43 7235[0:SpR:329.1,474.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(x),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.79/300.43 7233[0:SpR:538.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.79/300.43 9480[0:SpR:584.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_COMBS(u,v,w,x,y)),c_COMBS(u,v,w,x,y))**.
% 299.79/300.43 9479[0:SpR:586.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_COMBB(u,w,x,y),v)),hAPP(c_COMBB(u,w,x,y),v))**.
% 299.79/300.43 9478[0:SpR:585.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_COMBC(u,w,x,y),v)),hAPP(c_COMBC(u,w,x,y),v))**.
% 299.79/300.43 10417[0:SpL:8415.2,590.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),v_P) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_x),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(v_Q,v_x)),t_a)* -> .
% 299.79/300.43 10414[0:SpL:8415.2,590.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Com_Ocom_OBODY) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),v_x),hAPP(v_Q,v_x)),t_a)* -> .
% 299.79/300.43 10411[0:SpL:8415.2,590.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),v_Q) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),v_x),t_a)* -> .
% 299.79/300.43 10485[0:SpL:8415.2,454.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(v_x,u)) -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(u,v),v_x,t_a)*.
% 299.79/300.43 10595[0:SpL:8415.2,57.1] class_OrderedGroup_Olordered__ab__group__add(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) equal(hAPP(v_x,c_HOL_Ouminus__class_Ouminus(v_x,u)),c_HOL_Ozero__class_Ozero(u))** -> equal(c_HOL_Ozero__class_Ozero(u),v_x).
% 299.79/300.43 10579[0:SpL:5390.2,57.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Orderings_Oorder(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),v),c_HOL_Ozero__class_Ozero(u))** -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.43 10655[0:SpL:8415.2,505.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Com_Obody) c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),v_x),u,v,w)* -> c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_x),u,c_Suc(v),w).
% 299.79/300.43 10879[0:SpR:8415.2,353.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Set_Oinsert(u,v)) -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),hAPP(c_Set_Oinsert(w,v),v_x))**.
% 299.79/300.43 10853[0:SpR:353.0,353.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(x,v),y))),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(u,v),y))))*.
% 299.79/300.43 10850[0:SpR:353.0,254.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(y,u),x))))*.
% 299.79/300.43 11058[0:SpL:8415.2,357.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname))** c_Finite__Set_Ofinite(v_x,v) c_lessequals(x,v_x,tc_fun(w,tc_bool))* -> c_Finite__Set_Ofinite(x,w).
% 299.79/300.43 11753[0:SpL:130.1,3698.2] class_HOL_Ominus(u) || equal(v,c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u)))* equal(c_Com_Ocom_OBODY,v) equal(c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.43 11751[0:SpL:130.1,3493.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_in(tc_Com_Opname)) equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> .
% 299.79/300.43 11741[0:SpR:132.1,130.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_HOL_Ominus(u) || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),hAPP(v,v_x),u),hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_x))**.
% 299.79/300.43 11735[0:SpR:130.1,7253.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)))*.
% 299.79/300.43 11726[0:SpR:130.1,3339.1] class_HOL_Ominus(u) || equal(v,c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u))) -> equal(c_Fun_Ofun__upd(v,v_x,c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u),y,z),v)**.
% 299.79/300.43 11725[0:SpR:130.1,3316.1] class_HOL_Ominus(u) || equal(c_in(v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u))) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.79/300.43 11722[0:SpR:130.1,648.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u)),tc_Com_Opname,v),v_Procs)))*.
% 299.79/300.43 11716[0:SpR:130.1,3284.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)))*.
% 299.79/300.43 11708[0:SpR:130.1,651.0] class_HOL_Ominus(u) || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_Com_Opname,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.43 12665[0:SpL:584.0,519.0] || hBOOL(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y,z),x1))* -> hBOOL(hAPP(v,hAPP(w,x1))) hBOOL(hAPP(x1,hAPP(w,x1)))*.
% 299.79/300.43 12832[0:SSi:12806.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),y,tc_fun(w,tc_bool))* -> c_lessequals(u,y,tc_fun(w,tc_bool))*.
% 299.79/300.43 12833[0:SSi:12803.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v),y,tc_fun(w,tc_bool))* -> c_lessequals(u,y,tc_fun(w,tc_bool))*.
% 299.79/300.43 13053[0:SpR:130.1,10090.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.43 13183[0:SSi:13148.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) c_lessequals(w,u,tc_fun(v,tc_bool))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.79/300.43 13184[0:SSi:13126.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) c_lessequals(u,w,tc_fun(v,tc_bool))* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.79/300.43 13383[0:SSi:13343.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> c_lessequals(w,u,tc_fun(v,tc_bool))*.
% 299.79/300.43 13388[0:SSi:13321.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) c_lessequals(c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> c_lessequals(u,w,tc_fun(v,tc_bool))*.
% 299.79/300.43 13512[0:SpR:130.1,11030.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.79/300.43 13759[0:SpR:584.0,544.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),v)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),v))**.
% 299.79/300.43 13715[0:SpR:544.1,9567.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),tc_bool)*.
% 299.79/300.43 13705[0:SpR:544.1,5875.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,z,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))*.
% 299.79/300.43 13704[0:SpR:544.1,415.0] class_Lattices_Olattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.79/300.43 14054[0:SpR:584.0,543.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),v)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),v))**.
% 299.79/300.43 14008[0:SpR:543.1,9567.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),tc_bool)*.
% 299.79/300.43 13997[0:SpR:543.1,5875.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,z,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))*.
% 299.79/300.43 13996[0:SpR:543.1,415.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.79/300.43 14197[0:Res:176.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),w),hAPP(c_Set_Oinsert(hAPP(v,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,x,t_a).
% 299.79/300.43 14181[0:SpR:9987.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),u,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.43 14179[0:SpR:2095.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Ovimage(c_Set_Oinsert(w,v),u,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.43 14176[0:SpR:303.1,176.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.43 14172[0:SpR:330.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,x),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.43 14167[0:SpR:11176.1,176.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,x),hAPP(c_Set_Oinsert(u,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.43 14166[0:SpR:11177.1,176.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v,x),hAPP(c_Set_Oinsert(u,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.43 14145[0:SpR:331.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),u,x),hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.43 14144[0:SpR:302.1,176.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.43 14125[0:SpR:2093.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_Procs,v),u,w),hAPP(c_Set_Oinsert(hAPP(c_in(tc_Com_Opname),v_x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.43 14123[0:SpR:3744.1,176.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,u),v,w),hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.43 14262[0:SpR:14216.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(hAPP(c_Set_Oinsert(w,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u,z),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.43 14371[0:Res:3285.1,170.1] class_Orderings_Olinorder(u) || equal(c_in(tc_Com_Opname),c_in(u)) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),u),v_x,u)*.
% 299.79/300.43 14370[0:Res:3317.1,170.1] class_Orderings_Olinorder(u) || equal(c_in(v),c_in(u)) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v_x,v),w),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(v_x,v),w),u),v_x,u)*.
% 299.79/300.43 14351[0:Res:649.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),tc_Com_Opname),v_x,tc_Com_Opname)*.
% 299.79/300.43 14350[0:Res:650.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u),tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u),tc_Com_Opname),v_x,tc_Com_Opname)*.
% 299.79/300.43 14498[0:Res:3285.1,169.1] class_Orderings_Olinorder(u) || equal(c_in(tc_Com_Opname),c_in(u)) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),u),u)*.
% 299.79/300.43 14497[0:Res:3317.1,169.1] class_Orderings_Olinorder(u) || equal(c_in(v),c_in(u)) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v_x,v),w),u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(v_x,v),w),u),u)*.
% 299.79/300.43 14478[0:Res:649.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),tc_Com_Opname) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v_Procs),tc_Com_Opname),tc_Com_Opname)*.
% 299.79/300.43 14477[0:Res:650.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u),tc_Com_Opname) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),u),tc_Com_Opname),tc_Com_Opname)*.
% 299.79/300.43 14695[0:SpR:128.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Ovimage(u,v,w),x,tc_fun(y,tc_bool)),c_HOL_Ouminus__class_Ouminus(z,tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),z),tc_fun(v,tc_bool)),tc_bool)*.
% 299.79/300.43 14691[0:SpR:128.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(v,w,x),z,u),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.43 14688[0:SpR:128.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)),y),c_Set_Ovimage(u,v,w),z,x1,x2),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))))*.
% 299.79/300.43 14687[0:SpR:128.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)),y,z),c_Set_Ovimage(u,v,w))**.
% 299.79/300.43 14804[0:SSi:14771.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> equal(hAPP(c_Set_Ovimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))).
% 299.79/300.43 14805[0:SSi:14770.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> equal(hAPP(c_Set_Ovimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.79/300.43 14810[0:SSi:14714.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Ovimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.43 14811[0:SSi:14713.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Ovimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.79/300.43 15124[0:SpL:181.1,3929.0] || hBOOL(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(c_Set_Ovimage(c_COMBK(v,w,u),u,w),x)* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)) hBOOL(hAPP(x,v_x))*.
% 299.79/300.43 15115[0:SpR:181.1,9567.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,tc_fun(z,tc_bool)),w),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),tc_bool)*.
% 299.79/300.43 15097[0:SpR:181.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),v_x)) c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Ovimage(c_COMBK(w,v,x),x,v),tc_Com_Opname,u),u)*.
% 299.79/300.43 15539[0:Rew:15475.0,15438.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),u,w),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.43 15633[0:Res:176.0,278.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Ovimage(w,x,y),hAPP(c_Set_Oinsert(hAPP(w,v),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),z,u,x)))*.
% 299.79/300.43 15776[0:SpR:130.1,15482.1] class_HOL_Ominus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool))*.
% 299.79/300.43 15861[0:Res:176.0,277.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Ovimage(x,y,z),hAPP(c_Set_Oinsert(hAPP(x,v),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))),u,y)))*.
% 299.79/300.43 15916[2:SpR:130.1,15483.1] class_HOL_Ominus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool))*.
% 299.79/300.43 16184[0:Res:15262.1,170.1] class_Orderings_Olinorder(u) || equal(c_in(t_a),c_in(u)) c_Finite__Set_Ofinite(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u),v_x,u)*.
% 299.79/300.43 16183[0:Res:15262.1,169.1] class_Orderings_Olinorder(u) || equal(c_in(t_a),c_in(u)) c_Finite__Set_Ofinite(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u),u)*.
% 299.79/300.43 16253[0:SpL:181.1,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Ovimage(c_COMBK(v,w,u),u,w),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)).
% 299.79/300.43 16572[0:SpR:9987.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v_x,t_a),v,u),u)*.
% 299.79/300.43 16570[0:SpR:2095.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(y,w),v,u),u)*.
% 299.79/300.43 16567[0:SpR:303.1,361.2] class_Lattices_Obounded__lattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Otop__class_Otop(u)),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w,v),v)*.
% 299.79/300.43 16563[0:SpR:330.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x)) -> c_lessequals(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v,u),u)*.
% 299.79/300.43 16558[0:SpR:14216.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Set_Oinsert(y,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),v,u),u)*.
% 299.79/300.43 16556[0:SpR:11176.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Orderings_Otop__class_Otop(tc_bool),v) hBOOL(hAPP(hAPP(c_in(w),x),y))* -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,u),u)*.
% 299.79/300.43 16555[0:SpR:11177.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Orderings_Otop__class_Otop(tc_bool),v) hBOOL(hAPP(hAPP(c_in(w),v),x)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),w,u),u)*.
% 299.79/300.43 16532[0:SpR:331.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),v,u),u)*.
% 299.79/300.43 16531[0:SpR:302.1,361.2] class_Lattices_Obounded__lattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),x),y))* -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,v),v)*.
% 299.79/300.43 16518[0:SpR:15476.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(x,v_x),tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,tc_bool)),v,u),u)*.
% 299.79/300.43 16510[0:SpR:2093.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_in(tc_Com_Opname),v_x)),w)) -> c_lessequals(hAPP(c_in(tc_Com_Opname),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_Procs,x),v,u),u)*.
% 299.79/300.43 16508[0:SpR:3744.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_in(tc_Com_Opname),c_in(v)) hBOOL(hAPP(hAPP(c_in(w),v_Procs),x)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v_x,v),w,u),u)*.
% 299.79/300.43 16609[0:SSi:16585.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)),z,x1)* -> c_Fun_Oinj__on(x,hAPP(y,v),z,x1)*.
% 299.79/300.43 16972[0:SpL:600.0,327.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))) -> c_lessequals(w,c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.43 16945[0:SpR:600.0,329.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),u),c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool))).
% 299.79/300.43 16925[0:SpR:600.0,9566.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),tc_bool)*.
% 299.79/300.43 17085[0:SpR:584.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(w,x))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w,y,z,x1),x)))*.
% 299.79/300.43 17080[0:SpR:600.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))*.
% 299.79/300.43 17106[0:Rew:8415.2,17093.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v)))*.
% 299.79/300.43 17263[0:Rew:8415.2,17250.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))*.
% 299.79/300.43 17384[0:SpR:14526.0,584.0] || -> equal(hAPP(c_COMBS(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),x,y,z,x1),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),u)),hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(x,c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),u))))**.
% 299.79/300.43 17383[0:SpR:14526.0,584.0] || -> equal(hAPP(c_COMBS(u,c_HOL_Ominus__class_Ominus(c_Option_Othe(v),w,tc_fun(x,tc_bool)),y,z,x1),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v)),hAPP(hAPP(u,c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v)),c_Orderings_Obot__class_Obot(tc_bool)))**.
% 299.79/300.43 17713[0:SpL:584.0,255.0] || hBOOL(hAPP(c_COMBS(c_in(u),v,w,x,y),z))* c_lessequals(hAPP(v,z),x1,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),z),x1)).
% 299.79/300.43 17758[4:MRR:17710.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(v_x,w,tc_fun(u,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),v),w))*.
% 299.79/300.43 17759[0:Rew:8415.2,17707.4] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,v)) c_lessequals(v,w,tc_fun(u,tc_bool))* -> hBOOL(hAPP(v_x,w)).
% 299.79/300.43 17890[0:SpL:188.1,3506.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(x,y),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))* -> .
% 299.79/300.43 17869[0:SpR:188.1,9566.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Set_Oinsert(y,z),c_Set_Ovimage(c_COMBK(v,u,x),x,u)),w),tc_bool)*.
% 299.79/300.43 18026[0:Rew:8415.2,18002.3] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oinsert(v,u),w)))* -> hBOOL(hAPP(v_x,w)) equal(v_x,v).
% 299.79/300.43 18198[0:SpR:2935.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_in(t_a),v_x),u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.43 18193[0:SpR:301.1,362.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.43 18154[0:SpR:300.1,362.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.43 18143[0:SpR:365.1,362.1] class_Orderings_Obot(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(c_Orderings_Obot__class_Obot(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.43 18142[0:SpR:397.1,362.1] class_Orderings_Otop(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.43 18129[0:SpR:2097.1,362.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),u),x)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v,y),w,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.43 18264[0:SpR:15172.0,415.0] || -> equal(c_Fun_Ofun__upd(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y,c_Orderings_Obot__class_Obot(tc_bool),z,x1),c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)))**.
% 299.79/300.43 18398[0:SpR:2935.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v)) -> hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_in(t_a),v_x),u,w),v)))*.
% 299.79/300.43 18393[0:SpR:301.1,545.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,x),w)))*.
% 299.79/300.43 18354[0:SpR:300.1,545.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> hBOOL(hAPP(hAPP(c_in(y),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,y),x)))*.
% 299.79/300.43 18343[0:SpR:365.1,545.1] class_Orderings_Obot(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,x),w)))*.
% 299.79/300.43 18342[0:SpR:397.1,545.1] class_Orderings_Otop(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,x),w)))*.
% 299.79/300.43 18329[0:SpR:2097.1,545.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),u),x)) -> hBOOL(hAPP(hAPP(c_in(y),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v,z),w,y),x)))*.
% 299.79/300.43 18457[0:Res:168.0,156.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),w),x),t_a) hBOOL(hAPP(hAPP(c_in(w),hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),w),x)))),x))*.
% 299.79/300.43 18588[0:Res:153.1,279.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x)) -> equal(hAPP(c_Set_Oinsert(w,y),hAPP(c_Set_Ovimage(v,y,u),x)),hAPP(c_Set_Ovimage(v,y,u),x))**.
% 299.79/300.43 18651[0:SpR:353.0,9568.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Oinsert(w,v)),z),hAPP(c_Set_Oinsert(u,v),x)),tc_bool)*.
% 299.79/300.43 18962[0:SpR:353.0,9569.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),c_Set_Oinsert(w,v)),hAPP(c_Set_Oinsert(u,v),x)),tc_bool)*.
% 299.79/300.43 19104[0:SpR:196.1,474.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),z,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.43 19098[0:SpR:196.1,9566.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(hAPP(c_Set_Oinsert(y,z),c_Set_Ovimage(u,v,w)),hAPP(c_Set_Oimage(u,v,w),x)),tc_bool)*.
% 299.79/300.43 19176[0:Res:47.2,12626.0] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),tc_bool) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),tc_bool),u,tc_bool)*.
% 299.79/300.43 19239[0:Res:12627.1,50.1] class_OrderedGroup_Olordered__ab__group__add(tc_bool) || c_lessequals(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),tc_bool),tc_bool)* -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_bool),w,tc_bool),c_HOL_Ozero__class_Ozero(tc_bool),tc_bool).
% 299.79/300.43 19295[0:SpR:584.0,304.3] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(hAPP(x,v),w,u) -> c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v),w,u)*.
% 299.79/300.43 19346[0:SSi:19284.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool)).
% 299.79/300.43 19492[0:Res:19451.0,170.1] class_Orderings_Olinorder(t_a) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),t_a) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),t_a),v_x,t_a)*.
% 299.79/300.43 19491[0:Res:19451.0,169.1] class_Orderings_Olinorder(t_a) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),t_a) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),t_a),t_a)*.
% 299.79/300.43 19512[0:Res:19440.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),hAPP(c_in(tc_Com_Opname),v_x)),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(v,u),hAPP(c_in(tc_Com_Opname),v_x)),u),v_Procs,u)*.
% 299.79/300.43 19511[0:Res:19440.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),hAPP(c_in(tc_Com_Opname),v_x)),u) -> c_lessequals(v_Procs,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(v,u),hAPP(c_in(tc_Com_Opname),v_x)),u),u)*.
% 299.79/300.43 19676[0:Res:11030.1,496.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.79/300.43 19672[0:Res:3316.1,496.0] || equal(c_in(u),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))* c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.79/300.43 19647[0:SpL:3229.1,496.0] || equal(u,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v))* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,v_x)),v_x))* c_Hoare__Mirabelle_Otriple__valid(w,v,t_a)*.
% 299.79/300.43 19644[0:SpL:3229.1,496.0] || equal(u,c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(hAPP(u,v_x),v))* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,v)),v))* c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.79/300.43 19871[0:SpL:104.0,16286.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),v_Procs)** -> .
% 299.79/300.43 19825[0:SpR:104.0,328.1] || c_lessequals(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)) -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)))**.
% 299.79/300.43 19773[0:SpR:104.0,3229.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))))* -> equal(hAPP(u,v_x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))*.
% 299.79/300.43 19759[0:SpR:104.0,3283.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),v_Procs))*.
% 299.79/300.43 19753[0:SpR:104.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),tc_Com_Opname,w),v_Procs),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))*.
% 299.79/300.43 20022[0:SpL:64.0,7600.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),v)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v)*.
% 299.79/300.43 20020[0:SpL:64.0,360.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),x),w,y) -> c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),w,y)*.
% 299.79/300.43 20016[0:SpL:64.0,4382.0] || equal(hAPP(c_Set_Oinsert(u,v),w),v_Procs) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v_x))* equal(u,v_x).
% 299.79/300.43 19965[0:SpR:64.0,19436.1] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(c_Set_Oinsert(v,tc_Com_Opname),u))).
% 299.79/300.43 19964[0:SpR:64.0,7460.1] || c_lessequals(v_Procs,c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),u),v_x)).
% 299.79/300.43 20077[0:SpL:3229.1,215.0] || equal(u,c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)))* c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(u,v_x),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.79/300.43 20104[0:SpR:3229.1,246.2] || equal(u,c_Set_Oinsert(v,w))* c_Finite__Set_Ofinite(v_x,w) -> hBOOL(hAPP(hAPP(c_in(w),v),v_x))* equal(c_Finite__Set_Ocard(hAPP(u,v_x),w),c_Suc(c_Finite__Set_Ocard(v_x,w)))**.
% 299.79/300.43 20310[0:SpR:3229.1,438.1] || equal(u,v) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,x),hAPP(u,v_x)),v_x)**.
% 299.79/300.43 20454[0:SpR:3229.1,99.1] || equal(u,v) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,x),hAPP(u,v_x)),v_x)**.
% 299.79/300.43 20615[0:Res:49.2,18625.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(v,c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> c_lessequals(hAPP(v,w),hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),w),tc_bool)*.
% 299.79/300.43 20591[0:Res:47.2,18625.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),w),hAPP(v,w),tc_bool)*.
% 299.79/300.43 20727[0:SpR:3229.1,313.1] || equal(u,c_Set_Oimage(v,w,x)) c_lessequals(v_x,y,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(u,v_x),hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool))*.
% 299.79/300.43 20723[0:SpR:3229.1,313.1] || equal(u,c_Set_Oimage(v,w,x)) c_lessequals(y,v_x,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),y),hAPP(u,v_x),tc_fun(x,tc_bool))*.
% 299.79/300.43 20769[0:SpR:3229.1,129.1] || equal(u,c_Set_Ovimage(v,w,x)) c_lessequals(v_x,y,tc_fun(x,tc_bool)) -> c_lessequals(hAPP(u,v_x),hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool))*.
% 299.79/300.43 20759[0:SpR:3229.1,129.1] || equal(u,c_Set_Ovimage(v,w,x)) c_lessequals(y,v_x,tc_fun(x,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),y),hAPP(u,v_x),tc_fun(w,tc_bool))*.
% 299.79/300.43 21023[0:SpL:317.0,363.0] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),z,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),y),z,tc_fun(w,tc_bool)).
% 299.79/300.43 21021[0:SpL:317.0,4382.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),y),v_x)) equal(hAPP(u,x),v_x).
% 299.79/300.43 20966[0:SpR:351.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),x,y),hAPP(c_Set_Oinsert(z,x),x1)),hAPP(c_Set_Oinsert(u,y),hAPP(c_Set_Oimage(c_COMBK(u,v,w),x,y),x1)))*.
% 299.79/300.43 20944[0:SpR:3229.1,317.0] || equal(u,v) -> equal(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(v_x,w),y)),hAPP(c_Set_Oinsert(hAPP(u,v_x),x),hAPP(c_Set_Oimage(v,w,x),y)))*.
% 299.79/300.43 20919[0:SpR:3229.1,317.0] || equal(u,c_Set_Oimage(v,w,x)) -> equal(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(y,w),v_x)),hAPP(c_Set_Oinsert(hAPP(v,y),x),hAPP(u,v_x)))*.
% 299.79/300.43 20912[0:SpR:3229.1,317.0] || equal(u,c_Set_Oinsert(v,w)) -> equal(hAPP(c_Set_Oimage(x,w,y),hAPP(u,v_x)),hAPP(c_Set_Oinsert(hAPP(x,v),y),hAPP(c_Set_Oimage(x,w,y),v_x)))*.
% 299.79/300.43 20907[0:SpR:369.0,317.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),hAPP(c_Set_Oinsert(v,x),y))),hAPP(c_Set_Oimage(u,x,w),hAPP(c_Set_Oinsert(v,x),y)))**.
% 299.79/300.43 20876[0:SpR:317.0,364.1] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) -> c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(z,w),y)),tc_fun(x,tc_bool))*.
% 299.79/300.43 21042[0:SpR:353.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(y,v),z),w),x1)),hAPP(c_Set_Oinsert(y,v),hAPP(c_Set_Oinsert(u,v),z))))*.
% 299.79/300.43 21211[0:SpR:130.1,21141.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),t_a,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)))*.
% 299.79/300.43 21263[0:SpL:3229.1,469.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(w,x,v),y)))* -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(y,w,v_x,x,v)),v_x)**.
% 299.79/300.43 21259[0:SpL:3229.1,469.0] || equal(u,c_Set_Oimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(u,v_x)))* -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_x,v,y,w,x)),y)**.
% 299.79/300.43 21634[0:SpL:21267.0,442.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),v_x),w) -> c_Hoare__Mirabelle_Ohoare__derivs(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),v_x),tc_Com_Opname,x),w)*.
% 299.79/300.43 21621[0:SpL:21267.0,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),w)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,x),w))* equal(u,w).
% 299.79/300.43 21589[0:SpL:21267.0,355.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,w),v)*.
% 299.79/300.43 21544[0:SpR:329.1,21267.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x,tc_Com_Opname,w)),v_x)**.
% 299.79/300.43 21543[0:SpR:328.1,21267.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),u,tc_Com_Opname,w)),u)**.
% 299.79/300.43 21508[0:SpR:445.1,21267.0] || -> equal(v_x,u) equal(hAPP(c_Fun_Ofun__upd(v,u,w,x,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ofun__upd(v,u,w,x,y),hAPP(v,v_x),tc_Com_Opname,z)),hAPP(v,v_x))**.
% 299.79/300.43 21449[0:SpR:21267.0,8375.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)).
% 299.79/300.43 21383[0:SpR:21267.0,12687.1] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x),tc_Com_Opname,w)))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x)).
% 299.79/300.43 21369[0:SpR:21267.0,9566.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),u),hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x),tc_Com_Opname,x)),hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x),tc_bool)*.
% 299.79/300.43 21306[0:SpR:21267.0,16776.0] || -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),w,v)*.
% 299.79/300.43 21888[0:SpL:3229.1,464.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(w,x,v),y)))* -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(y,v_x,w,x,v)),v_x)**.
% 299.79/300.43 21883[0:SpL:3229.1,464.0] || equal(u,c_Set_Oimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(u,v_x)))* -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_x,y,v,w,x)),y)**.
% 299.79/300.43 22262[0:SpL:21893.0,442.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),v_x),w) -> c_Hoare__Mirabelle_Ohoare__derivs(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),v_x),c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,x),w)*.
% 299.79/300.43 22249[0:SpL:21893.0,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),w)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,x),w))* equal(u,w).
% 299.79/300.43 22216[0:SpL:21893.0,355.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,w),v)*.
% 299.79/300.43 22171[0:SpR:329.1,21893.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w)),v_x)**.
% 299.79/300.43 22170[0:SpR:328.1,21893.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w)),u)**.
% 299.79/300.43 22135[0:SpR:445.1,21893.0] || -> equal(v_x,u) equal(hAPP(c_Fun_Ofun__upd(v,u,w,x,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),c_Fun_Ofun__upd(v,u,w,x,y),tc_Com_Opname,z)),hAPP(v,v_x))**.
% 299.79/300.43 22075[0:SpR:21893.0,8375.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)).
% 299.79/300.43 22009[0:SpR:21893.0,12687.1] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_Com_Opname,w)))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x)).
% 299.79/300.43 21995[0:SpR:21893.0,9566.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x),hAPP(c_Set_Oinsert(v,w),u),tc_Com_Opname,x)),hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x),tc_bool)*.
% 299.79/300.43 21932[0:SpR:21893.0,16776.0] || -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),w,v)*.
% 299.79/300.43 22424[0:SpR:3229.1,97.1] || equal(u,c_Set_Oimage(v,w,x)) c_Fun_Oinj__on(v,v_x,w,x) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v_x,v,w,x),x,w),hAPP(u,v_x)),v_x)**.
% 299.79/300.43 22650[0:SpL:158.0,16286.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_Procs)** -> .
% 299.79/300.43 22635[0:SpR:3229.1,158.0] || equal(u,c_Set_Oimage(v,w,x)) -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(y,v,x,z,w),w,z),v_x),hAPP(c_Set_Oimage(y,x,z),hAPP(u,v_x)))*.
% 299.79/300.43 22554[0:SpR:158.0,3229.1] || equal(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> equal(hAPP(u,v_x),hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x)))*.
% 299.79/300.43 22535[0:SpR:158.0,3283.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),v_Procs))*.
% 299.79/300.43 22529[0:SpR:158.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),v_Procs),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))))*.
% 299.79/300.43 22762[0:SpR:3294.1,511.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) hBOOL(hAPP(hAPP(c_in(u),v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(u),v),c_Orderings_Obot__class_Obot(tc_bool))).
% 299.79/300.43 22759[0:SpR:3294.1,304.3] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) c_lessequals(v_x,v,u) c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v,u)* -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v,u).
% 299.79/300.43 23028[0:SpL:131.0,16286.0] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_Procs)** -> .
% 299.79/300.43 23013[0:SpR:3229.1,131.0] || equal(u,c_Set_Ovimage(v,w,x)) -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,y,w,x,z),z,x),v_x),hAPP(c_Set_Ovimage(y,z,w),hAPP(u,v_x)))*.
% 299.79/300.43 22941[0:SpR:131.0,3229.1] || equal(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> equal(hAPP(u,v_x),hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x)))*.
% 299.79/300.43 22921[0:SpR:131.0,3283.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),v_Procs))*.
% 299.79/300.43 22915[0:SpR:131.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),v_Procs),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))))*.
% 299.79/300.43 23052[0:Rew:105.0,23014.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(c_COMBK(v,u,x),y,x,u,z),z,u),w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))**.
% 299.79/300.43 23395[0:SpL:460.1,3483.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.43 23573[0:SpL:523.1,3483.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.43 23568[0:SpR:10090.1,523.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v_x,v_x)),hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x)),hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_x))**.
% 299.79/300.43 24000[0:SpR:23912.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_Set_Oinsert(u,v),x)),hAPP(c_Set_Oinsert(u,w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),x)))*.
% 299.79/300.43 24356[0:SpL:393.1,357.1] || c_Finite__Set_Ofinite(u,v)* c_lessequals(w,hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool))* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* c_Finite__Set_Ofinite(w,y).
% 299.79/300.43 24277[0:SpR:393.1,83.0] || -> equal(hAPP(c_Set_Ovimage(c_COMBK(u,v,w),w,v),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** c_lessequals(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),x,tc_fun(v,tc_bool))*.
% 299.79/300.43 24552[0:SpR:24020.1,545.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> hBOOL(hAPP(hAPP(c_in(x),v_x),hAPP(c_Set_Oimage(hAPP(u,v_x),v,x),w)))*.
% 299.79/300.43 24551[0:SpR:24020.1,362.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.43 24783[0:SpR:614.2,7253.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u)))*.
% 299.79/300.43 24961[0:SpR:23902.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v) hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Obot__class_Obot(tc_bool)),x)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(v,v_x),w,u),u)*.
% 299.79/300.43 24950[0:SpR:23902.1,176.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Ovimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.43 25132[0:Res:252.1,12959.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),x),t_a) c_Natural_Oevalc(c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,w)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(v,x,w,u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,x,w,u))*.
% 299.79/300.43 25425[0:SpL:512.0,3483.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_Com_Ocom_OBODY)** equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.43 25316[0:SpR:512.0,83.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),hAPP(c_Set_Ovimage(hAPP(c_COMBB(u,v,w,y),x),y,w),z))),z,tc_fun(w,tc_bool))*.
% 299.79/300.43 25731[0:Res:8376.2,455.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) equal(u,v_Procs) c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.79/300.43 25724[0:Res:15262.1,455.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a)) c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),t_a)* c_Hoare__Mirabelle_Otriple__valid(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.79/300.43 25723[0:Res:3285.1,455.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.79/300.43 25722[0:Res:3317.1,455.0] || equal(c_in(u),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Set_Oinsert(v_x,u),w),t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,v_x,t_a).
% 299.79/300.43 25701[0:Res:474.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(v,y),t_a)*.
% 299.79/300.43 25952[0:SpR:9987.0,339.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v))**.
% 299.79/300.43 25941[0:SpR:2093.0,339.0] || -> equal(hAPP(c_Set_Oinsert(v_Procs,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),v))**.
% 299.79/300.43 25940[0:SpR:3744.1,339.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_Procs),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_Procs),v))**.
% 299.79/300.43 26215[0:SpR:23902.1,338.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_bool))),hAPP(c_Set_Oinsert(v,u),v_x))**.
% 299.79/300.43 26162[0:SpR:9987.0,338.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))**.
% 299.79/300.43 26151[0:SpR:2093.0,338.0] || -> equal(hAPP(c_Set_Oinsert(v_Procs,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_in(tc_Com_Opname),v_x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_in(tc_Com_Opname),v_x)))**.
% 299.79/300.43 26150[0:SpR:3744.1,338.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs))**.
% 299.79/300.43 26101[0:SpR:338.0,212.1] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(y,u),w)),x))*.
% 299.79/300.43 26383[0:Res:20152.0,85.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool)),x,tc_fun(v,tc_bool))*.
% 299.79/300.43 26537[0:Res:84.1,18768.0] || c_lessequals(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> c_lessequals(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_Procs),tc_bool).
% 299.79/300.43 26530[0:Res:84.1,1937.1] || c_lessequals(c_HOL_Ominus__class_Ominus(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)),v,tc_fun(tc_Com_Opname,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.43 26528[0:Res:84.1,6546.0] || c_lessequals(c_HOL_Ominus__class_Ominus(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)),v,tc_fun(tc_Com_Opname,tc_bool))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.79/300.43 26520[0:Res:84.1,18625.0] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(u,y),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),y),tc_bool)*.
% 299.79/300.43 26513[0:SpR:23902.1,84.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_fun(u,tc_bool))* -> c_lessequals(v,v_x,tc_fun(u,tc_bool)).
% 299.79/300.43 26949[0:Res:424.2,18625.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(x,w,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v,u),x),y),hAPP(w,y),tc_bool)*.
% 299.79/300.43 27014[0:Res:8376.2,175.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_Procs)** -> equal(hAPP(v,v_x),x).
% 299.79/300.43 27118[0:Res:8376.2,280.1] || equal(c_in(tc_Com_Opname),c_in(u)) equal(v,v_Procs) hBOOL(hAPP(hAPP(w,v_x),x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,u,tc_fun(y,tc_bool)),x))*.
% 299.79/300.43 27100[0:Res:15262.1,280.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(hAPP(v,v_x),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v,u,tc_fun(x,tc_bool)),w))*.
% 299.79/300.43 27099[0:Res:3285.1,280.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(v,v_x),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs),v,u,tc_fun(y,tc_bool)),w))*.
% 299.79/300.43 27098[0:Res:3317.1,280.1] || equal(c_in(u),c_in(v)) hBOOL(hAPP(hAPP(w,v_x),x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),y),w,v,tc_fun(z,tc_bool)),x))*.
% 299.79/300.43 27077[0:Res:474.0,280.1] || hBOOL(hAPP(hAPP(u,hAPP(v,w)),x))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,y,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u,z,tc_fun(x1,tc_bool)),x))*.
% 299.79/300.43 27326[7:MRR:24368.2,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_in(tc_Com_Opname))** hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.79/300.43 27327[7:MRR:24367.2,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.43 27328[7:MRR:24305.1,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_in(t_a))** -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.43 27394[0:Res:8376.2,470.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Oimage(v,w,u),x),v_Procs) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(x,v_x,v,w,u)),x))*.
% 299.79/300.43 27454[0:Res:8376.2,466.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Oimage(v,w,u),x),v_Procs) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,v_x,w,u)),x))*.
% 299.79/300.43 27543[0:SpR:659.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),v,u,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(v_x,tc_Com_Opname),u,w),v_Procs),v_Procs)**.
% 299.79/300.43 27695[0:SpR:659.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),v,u,w) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(v_x,tc_Com_Opname),u,w),v_Procs),v_Procs)**.
% 299.79/300.43 27823[7:SpR:130.1,27219.1] class_HOL_Ominus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool))*.
% 299.79/300.43 27970[0:SpR:130.1,27381.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.43 28101[0:SpR:131.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),tc_Com_Opname,z)))*.
% 299.79/300.43 28100[0:SpR:158.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),tc_Com_Opname,z)))*.
% 299.79/300.43 28082[0:SpR:104.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),tc_Com_Opname,w)))*.
% 299.79/300.43 28124[0:SpR:465.1,3305.1] || equal(c_Fun_Ofun__upd(u,v,w,tc_Com_Opname,x),y)* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v),v_Procs))* hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x),v_Procs),hAPP(y,v_x)))*.
% 299.79/300.43 28119[0:SpR:465.1,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v),u)) hBOOL(hAPP(hAPP(c_Set_Oimage(w,tc_Com_Opname,x),u),hAPP(c_Fun_Ofun__upd(w,v,y,tc_Com_Opname,x),v_x)))*.
% 299.79/300.43 28272[0:SpR:130.1,27441.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.43 28405[0:SpR:131.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_Com_Opname,z)))*.
% 299.79/300.43 28404[0:SpR:158.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_Com_Opname,z)))*.
% 299.79/300.43 28386[0:SpR:104.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),tc_Com_Opname,w)))*.
% 299.79/300.43 28567[2:SpL:118.0,4275.0] || equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,w,x,y),z,hAPP(u,x1),y,x),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(u,hAPP(c_Fun_Ofun__upd(v,z,x1,y,w),v_x))).
% 299.79/300.43 28566[0:SpL:118.0,3582.0] || equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,w,x,y),z,hAPP(u,x1),y,x),v_Procs)** -> hBOOL(hAPP(u,hAPP(c_Fun_Ofun__upd(v,z,x1,y,w),v_x))).
% 299.79/300.43 28496[0:SpR:456.0,118.0] || -> equal(c_Fun_Ocomp(c_Option_Othe(u),c_Fun_Ofun__upd(v,w,c_Option_Ooption_OSome(x,u),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Option_Othe(u),v,z,x1,y),w,x,y,x1))*.
% 299.79/300.43 28451[0:SpR:659.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_x,tc_Com_Opname),c_Fun_Ofun__upd(u,v,v_Procs,w,x),x,y,w),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_x,tc_Com_Opname),u,x,y,w),v,v_Procs,w,y))*.
% 299.79/300.43 28442[0:SpR:10540.0,118.0] || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,x,y),z,hAPP(u,c_Orderings_Obot__class_Obot(tc_bool)),y,x),c_Fun_Ocomp(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,x,y))**.
% 299.79/300.43 28441[0:SpR:9961.0,118.0] || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,x,y),z,hAPP(u,c_Orderings_Otop__class_Otop(tc_bool)),y,x),c_Fun_Ocomp(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,x,y))**.
% 299.79/300.43 28431[0:SpR:118.0,3339.1] || equal(c_Fun_Ocomp(u,v,w,x,y),u) -> equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,v_x,v_x,y,w),w,x,y),c_Fun_Ocomp(u,v,w,x,y))**.
% 299.79/300.43 28731[0:SpR:130.1,28031.0] class_HOL_Ominus(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.43 28886[0:SpR:130.1,28334.0] class_HOL_Ominus(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.43 29058[0:SpR:537.1,87.1] class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u))),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.43 28988[2:SpR:537.1,4250.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Com_Ocom_OBODY) -> c_Com_OWT(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))*.
% 299.79/300.43 28977[0:SpR:537.1,3282.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))*.
% 299.79/300.43 28976[7:SpR:537.1,27207.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))*.
% 299.79/300.43 29246[0:SSi:29188.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),y,tc_fun(u,tc_bool))* -> c_lessequals(x,y,tc_fun(u,tc_bool)).
% 299.79/300.43 29247[0:SSi:29186.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> equal(x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.79/300.43 29581[0:SpR:534.1,87.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u))),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.43 29510[2:SpR:534.1,4250.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Com_Ocom_OBODY) -> c_Com_OWT(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))*.
% 299.79/300.43 29499[0:SpR:534.1,3282.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))*.
% 299.79/300.43 29498[7:SpR:534.1,27207.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))*.
% 299.79/300.43 29762[0:Obv:29705.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y,u)* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),y,u).
% 299.79/300.43 29763[0:Obv:29586.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),u) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),u)*.
% 299.79/300.43 29929[0:SpR:27043.1,317.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(hAPP(u,v_Procs),v),hAPP(c_Set_Oimage(u,w,v),v_x)),hAPP(c_Set_Oimage(u,w,v),v_x))**.
% 299.79/300.43 30409[0:SSi:30311.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),y,tc_fun(u,tc_bool))* -> c_lessequals(w,y,tc_fun(u,tc_bool)).
% 299.79/300.43 30410[0:SSi:30309.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.79/300.43 30971[0:Obv:30868.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y,u)* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),y,u).
% 299.79/300.43 30973[0:Obv:30669.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),u) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),x)),u)*.
% 299.79/300.43 31294[0:Res:19748.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.79/300.43 31425[0:Res:526.1,449.0] || hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_in(v),w,x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,c_in(v),w,x)))* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),w),c_in(v)),t_a).
% 299.79/300.43 31380[0:SpL:10463.0,449.0] || hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,x))) -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),w),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),t_a)*.
% 299.79/300.43 31379[0:SpL:9911.0,449.0] || hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,x))) -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),t_a)*.
% 299.79/300.43 31530[0:SpL:584.0,473.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(v,w,u),x,y,z),x1))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(x1,v,w,u),x1)),x1))*.
% 299.79/300.43 31817[7:SpL:181.1,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Ovimage(c_COMBK(v,w,u),u,w),v_x)** -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)).
% 299.79/300.43 31938[7:SpL:131.0,31868.0] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_x)** -> .
% 299.79/300.43 31937[7:SpL:158.0,31868.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x)** -> .
% 299.79/300.43 31919[7:SpL:104.0,31868.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),v_x)** -> .
% 299.79/300.43 32000[0:SpR:23979.0,383.1] || -> equal(u,v) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,w,x,y),v,v,x,y),c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,w,x,y))**.
% 299.79/300.43 31998[0:SpR:771.0,383.1] || -> equal(u,v) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(c_COMBK(w,x,y),u,z,x1,x2),v,w,x1,x2),c_Fun_Ofun__upd(c_COMBK(w,x,y),u,z,x1,x2))**.
% 299.79/300.43 31995[0:SpR:3339.1,383.1] || equal(u,v) -> equal(w,v_x) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,w,x,y,z),v_x,hAPP(v,v_x),y,z),c_Fun_Ofun__upd(u,w,x,y,z))**.
% 299.79/300.43 31994[0:SpR:770.0,383.1] || -> equal(u,c_Option_Ooption_OSome(v,w)) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(c_Option_Othe(w),u,x,y,z),c_Option_Ooption_OSome(v,w),v,y,z),c_Fun_Ofun__upd(c_Option_Othe(w),u,x,y,z))**.
% 299.79/300.43 32023[0:Rew:445.1,32010.2] || equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v,w,x,y),z,x1,x,y),c_Fun_Ofun__upd(u,z,x1,x,y))** -> equal(v,z) equal(hAPP(u,v),w).
% 299.79/300.43 32062[0:Res:151.2,11894.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(u),v),x))*.
% 299.79/300.43 32318[0:SpL:329.1,477.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,w)))* hBOOL(hAPP(hAPP(c_in(w),y),u))* -> hBOOL(hAPP(x,y))*.
% 299.79/300.43 32397[0:Rew:23682.0,32360.2] || hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u))* hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(x).
% 299.79/300.43 32577[0:Rew:23682.0,32540.2] || hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u))* hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(x).
% 299.79/300.43 32707[0:SpR:188.1,32669.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.79/300.43 32811[2:SpL:35.2,17118.0] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(w,tc_bool))* c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),x,tc_fun(w,tc_bool))* equal(u,c_Com_Ocom_OBODY) -> c_Com_OWT(c_Orderings_Obot__class_Obot(tc_bool)).
% 299.79/300.43 32762[0:SpR:35.2,117.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(v,x,tc_fun(w,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),u)**.
% 299.79/300.43 33111[0:Res:84.1,32232.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),v,tc_fun(tc_Com_Opname,tc_bool)),w,tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),w),v_x)).
% 299.79/300.43 33431[0:Res:3282.1,453.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Procs)** c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.43 33430[7:Res:27207.1,453.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)** c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.43 33427[0:Res:23946.1,453.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v)),u))* c_Hoare__Mirabelle_Otriple__valid(v,v_Procs,t_a).
% 299.79/300.43 33418[0:Res:8375.1,453.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)))* c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,x,t_a)*.
% 299.79/300.43 33417[0:Res:19440.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Com_Opname),v_x)),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w)),u))* c_Hoare__Mirabelle_Otriple__valid(w,v_Procs,t_a).
% 299.79/300.43 33398[0:Res:648.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(v,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w)),u))* c_Hoare__Mirabelle_Otriple__valid(w,hAPP(v,v_x),t_a)*.
% 299.79/300.43 33456[0:SpR:35.2,23882.0] || c_lessequals(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),tc_fun(w,tc_bool))* c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),x,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(u,c_Orderings_Obot__class_Obot(tc_bool)),v,tc_bool).
% 299.79/300.43 33519[0:Rew:369.0,33509.2] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v) -> hBOOL(hAPP(hAPP(c_in(v),u),w)) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(u,v),w),v),c_Suc(c_Finite__Set_Ocard(w,v)))**.
% 299.79/300.43 33810[0:MRR:33809.3,418.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,tc_fun(u,tc_bool))* -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),w,u).
% 299.79/300.43 33816[0:SpR:23864.0,118.0] || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x,y),c_Orderings_Obot__class_Obot(tc_bool),hAPP(u,v),y,x),c_Fun_Ocomp(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x,y))**.
% 299.79/300.43 33852[0:SpR:23965.1,118.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(v,u,w,x,y),v_x,hAPP(v,v_x),y,x),c_Fun_Ocomp(v,u,w,x,y))**.
% 299.79/300.43 33888[0:MRR:33887.3,418.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,tc_fun(u,tc_bool))* -> c_lessequals(w,c_Finite__Set_Olinorder__class_OMax(v,u),u).
% 299.79/300.43 34358[0:SpL:24914.0,7600.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),v)* -> c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(w,v),tc_Com_Opname,x),hAPP(c_Set_Oinsert(w,v),v_x)),v)*.
% 299.79/300.43 34355[0:SpL:24914.0,360.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),v_x),w,x) -> c_Fun_Oinj__on(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,y),hAPP(c_Set_Oinsert(v,w),v_x)),w,x)*.
% 299.79/300.43 34338[0:SpL:24914.0,4382.0] || equal(hAPP(c_Set_Oinsert(u,v),v_x),v_Procs) -> hBOOL(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),v_x))* equal(u,v_x).
% 299.79/300.43 34273[0:SpL:24914.0,505.0] || c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x)),u,v,w) -> c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Obody,tc_Com_Opname,x),hAPP(c_Com_Obody,v_x))),u,c_Suc(v),w)*.
% 299.79/300.43 34199[0:SpR:15476.0,24914.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),tc_Com_Opname,v),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))**.
% 299.79/300.43 34470[0:Rew:586.0,34251.0] || -> equal(hAPP(u,hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_COMBB(u,w,x,y),v),tc_Com_Opname,z),hAPP(u,hAPP(v,v_x))))),hAPP(u,hAPP(v,v_x)))**.
% 299.79/300.43 34471[0:Rew:585.0,34250.0] || -> equal(hAPP(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_COMBC(u,v,w,x),y),tc_Com_Opname,z),hAPP(hAPP(u,v_x),y))),y),hAPP(hAPP(u,v_x),y))**.
% 299.79/300.43 34472[0:Rew:586.0,34173.0] || -> equal(hAPP(u,hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBB(u,v,w,x),tc_Com_Opname,y),hAPP(c_COMBB(u,v,w,x),v_x)),z)),hAPP(u,hAPP(v_x,z)))**.
% 299.79/300.43 34473[0:Rew:585.0,34172.0] || -> equal(hAPP(hAPP(u,v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBC(u,w,x,y),tc_Com_Opname,z),hAPP(c_COMBC(u,w,x,y),v_x))),hAPP(hAPP(u,v),v_x))**.
% 299.79/300.43 34559[0:SpR:34427.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,x),v,u),u)*.
% 299.79/300.43 34552[0:SpR:34427.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(c_Set_Ovimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,v),u,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.43 34635[0:SpR:55.1,21035.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,w),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_Procs,u),x),v,tc_fun(u,tc_bool))),v_Procs))*.
% 299.79/300.43 34627[0:SpR:55.1,9067.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(x,u),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool)))))*.
% 299.79/300.43 34626[0:SpR:55.1,20881.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),z),w,tc_fun(u,tc_bool))),hAPP(x,v)))*.
% 299.79/300.43 34609[0:SpR:55.1,3317.1] || equal(c_in(u),v) -> hBOOL(hAPP(hAPP(c_in(u),v_x),w)) hBOOL(hAPP(hAPP(v,v_x),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,u),x),w,tc_fun(u,tc_bool))))*.
% 299.79/300.43 34573[0:SpR:55.1,376.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.43 34670[0:MRR:34574.1,56.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,w),u),v,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)))**.
% 299.79/300.43 34742[0:SpR:34428.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,x),v,u),u)*.
% 299.79/300.43 34735[0:SpR:34428.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),u,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.43 34716[0:SpR:34428.0,24914.0] || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_Com_Opname,v),v_x)),v_x)**.
% 299.79/300.43 34803[7:SpL:64.0,27282.0] || equal(hAPP(c_Set_Oinsert(u,v),w),v_x) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v_x))* equal(u,v_x).
% 299.79/300.43 34796[7:SpL:317.0,27282.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),v_x)** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),y),v_x)) equal(hAPP(u,x),v_x).
% 299.79/300.43 34792[7:SpL:24914.0,27282.0] || equal(hAPP(c_Set_Oinsert(u,v),v_x),v_x) -> hBOOL(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),v_x))* equal(u,v_x).
% 299.79/300.43 35433[0:SpL:410.0,346.0] || c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),y,w,tc_fun(z,tc_bool)),z,x1)* -> c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,w,tc_fun(z,tc_bool)),z,x1).
% 299.79/300.43 35237[0:SpR:410.0,510.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(w,x))) -> hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,y),z),w,y,tc_fun(u,tc_bool))))*.
% 299.79/300.43 35465[0:SpR:55.1,35192.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),v)) hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,u),w),v,tc_fun(u,tc_bool)),c_in(tc_Com_Opname),u,tc_fun(x,tc_bool)),v_Procs))*.
% 299.79/300.43 35547[0:Rew:80.0,35499.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))**.
% 299.79/300.43 35674[0:SpR:55.1,26119.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool))),v))*.
% 299.79/300.43 36191[0:Res:9258.0,516.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),tc_bool))* hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.79/300.43 36718[0:SpR:67.0,124.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.43 36784[0:Rew:10.0,36752.0] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),w),tc_fun(v,tc_bool)))**.
% 299.79/300.43 36904[0:Rew:10.0,36878.0] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(w,v),u),tc_fun(v,tc_bool)))**.
% 299.79/300.43 37694[0:Rew:438.1,37690.2,9.0,37690.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* equal(c_Fun_Ocomp(x,y,z,x1,v),x2)* -> equal(hAPP(x,hAPP(y,x3)),hAPP(x2,x3))*.
% 299.79/300.43 38659[0:Res:526.1,184.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),y)) c_Fun_Oinj__on(u,x,v,w) -> equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(x,u,v,w),y)),y)**.
% 299.79/300.43 38745[4:SpR:131.0,37987.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),z))*.
% 299.79/300.43 38744[4:SpR:158.0,37987.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),z))*.
% 299.79/300.43 38726[4:SpR:104.0,37987.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),w))*.
% 299.79/300.43 38934[4:SpR:131.0,38042.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),z,t_a)*.
% 299.79/300.43 38933[4:SpR:158.0,38042.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),z,t_a)*.
% 299.79/300.43 38915[4:SpR:104.0,38042.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),w,t_a)*.
% 299.79/300.43 39183[0:SpR:533.0,342.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),tc_fun(u,tc_bool))*.
% 299.79/300.43 39573[0:SpR:532.0,341.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w)),tc_fun(u,tc_bool))*.
% 299.79/300.43 40885[0:Res:8366.1,479.1] || equal(u,v_Procs) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,w,v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),w)))*.
% 299.79/300.43 41166[0:Res:8366.1,478.1] || equal(u,v_Procs) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,u,v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),u)))*.
% 299.79/300.43 41429[0:Res:23961.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),u,tc_fun(w,tc_bool))))*.
% 299.79/300.43 41428[0:Res:19436.1,275.1] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),w))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(x,tc_Com_Opname),v,tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.79/300.43 41427[0:Res:19441.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),w))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(x,tc_Com_Opname),u,tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.79/300.43 41426[0:Res:19452.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v)) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(w,t_a),u,tc_fun(t_a,tc_bool))))*.
% 299.79/300.43 41416[0:Res:9067.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y))* -> hBOOL(hAPP(hAPP(c_in(w),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(z,w),u,tc_fun(w,tc_bool))))*.
% 299.79/300.43 41413[0:Res:3346.1,275.1] || equal(c_Set_Oinsert(u,v),w) hBOOL(hAPP(hAPP(c_in(x),v_x),y)) -> hBOOL(hAPP(hAPP(c_in(v),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,x,tc_fun(v,tc_bool))))*.
% 299.79/300.43 41407[0:Res:1157.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oimage(c_COMBK(x,y,z),tc_Com_Opname,w),u,tc_fun(w,tc_bool))))*.
% 299.79/300.43 41400[0:Res:8366.1,275.1] || equal(hAPP(u,v),v_Procs)** hBOOL(hAPP(hAPP(c_in(w),v),x))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,u,w,tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.79/300.43 41678[0:Res:3346.1,284.0] || equal(c_Set_Oinsert(hAPP(u,v),w),c_Set_Oimage(u,x,w))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w)* -> hBOOL(hAPP(hAPP(c_in(x),v),v_x))*.
% 299.79/300.43 41996[0:Res:82.0,357.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),w) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,w,y),u),hAPP(c_Set_Oimage(x,w,y),v),tc_fun(y,tc_bool)),y)*.
% 299.79/300.43 42004[0:Rew:321.0,41944.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.43 42201[4:SSi:42133.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v_x,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,u,tc_bool,tc_bool),tc_bool) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(w,tc_bool),u),tc_bool,tc_bool))*.
% 299.79/300.43 42202[0:Obv:42054.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u),u)*.
% 299.79/300.43 42752[0:Rew:161.0,42675.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v),x,tc_fun(u,tc_bool)))*.
% 299.79/300.43 43567[0:Rew:507.0,43493.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x)))*.
% 299.79/300.43 43789[0:Rew:162.0,43715.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),x)))*.
% 299.79/300.43 43960[0:Res:13387.1,231.0] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,v) -> c_lessequals(hAPP(c_Set_Ovimage(w,x,v),u),y,tc_fun(x,tc_bool))*.
% 299.79/300.43 44078[0:Res:13387.1,358.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> c_lessequals(x,y,tc_fun(v,tc_bool))*.
% 299.79/300.43 44077[0:Res:13385.1,358.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> c_lessequals(y,x,tc_fun(v,tc_bool))*.
% 299.79/300.43 44717[0:SpR:55.1,36599.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),w),u,tc_fun(t_a,tc_bool))),x),v_x))*.
% 299.79/300.43 45159[0:SpR:55.1,36600.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),x),u,tc_fun(t_a,tc_bool))),v_x))*.
% 299.79/300.43 45220[0:SpR:55.1,36608.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),v),u,tc_fun(t_a,tc_bool)),v_x),w,x),tc_Com_Opname,tc_bool))*.
% 299.79/300.43 45466[0:Res:45357.1,278.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),x,w,u)))*.
% 299.79/300.43 45465[0:Res:45357.1,277.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),w,u)))*.
% 299.79/300.43 45450[0:Res:45357.1,279.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname))**.
% 299.79/300.43 45427[0:SpR:328.1,45357.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname),v,tc_fun(u,tc_bool))* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)) -> hBOOL(v).
% 299.79/300.43 45588[0:SpR:323.0,35656.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),v,w,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.79/300.43 45583[0:SpR:323.0,9568.0] || -> c_lessequals(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),y),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),z),v,w,tc_fun(x,tc_bool)),y),tc_bool)*.
% 299.79/300.43 45580[0:SpR:323.0,9569.0] || -> c_lessequals(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),y),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),u),v,w,tc_fun(x,tc_bool)),y),tc_bool)*.
% 299.79/300.43 45711[0:SpR:323.0,44625.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v,w,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.79/300.43 45942[0:SpL:328.1,45899.0] || c_lessequals(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname),v,tc_fun(u,tc_bool))* hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)).
% 299.79/300.43 46614[4:SpL:130.1,46565.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))* -> .
% 299.79/300.43 46702[0:Res:84.1,44639.0] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(tc_Com_Opname,tc_bool)),w,tc_fun(tc_Com_Opname,tc_bool))* equal(u,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),w),v_x))*.
% 299.79/300.43 46689[0:Res:424.2,44639.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v))* c_lessequals(w,v,tc_fun(tc_Com_Opname,tc_bool))* equal(hAPP(c_Set_Oinsert(u,tc_Com_Opname),w),v_Procs)** -> hBOOL(hAPP(v,v_x)).
% 299.79/300.43 46828[0:Rew:585.0,46703.2] || c_lessequals(u,v,tc_fun(tc_Com_Opname,tc_bool))* equal(hAPP(c_COMBC(c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool),tc_bool),u),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v))*.
% 299.79/300.43 46863[0:Res:84.1,44750.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),v_x)).
% 299.79/300.43 46845[0:SpL:55.1,44750.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(t_a,tc_bool)),w,tc_fun(x,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)) hBOOL(hAPP(w,v_x)).
% 299.79/300.43 46986[0:SpL:55.1,46860.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(t_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)) hBOOL(hAPP(x,v_x))*.
% 299.79/300.43 47004[0:SpL:35.2,38148.0] || c_lessequals(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),tc_fun(w,tc_bool))* c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),x,tc_fun(w,tc_bool))* hBOOL(hAPP(u,v)) -> hBOOL(v).
% 299.79/300.43 47508[4:Res:10697.0,47318.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool)))*.
% 299.79/300.43 48720[4:SpR:55.1,42357.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(y,tc_bool)),v_x))*.
% 299.79/300.43 48881[4:SpR:55.1,42583.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),v)) hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,u),w),v,tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(x,tc_bool)),y))*.
% 299.79/300.43 50057[0:Rew:497.0,50022.0] || -> equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u)))*.
% 299.79/300.43 50110[4:SpR:55.1,43177.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,u),w),v,tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,tc_fun(x,tc_bool)),y,t_a)*.
% 299.79/300.43 50486[0:SpL:223.1,36406.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,t_a),u,t_a),w),v_x),y,tc_bool)* -> hBOOL(y).
% 299.79/300.43 50456[0:SpR:223.1,36264.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,v_x,u,t_a),u,t_a),w),v_x)))*.
% 299.79/300.43 50401[0:SpR:223.1,36471.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,t_a),u,t_a),w),v_x)),y,t_a)*.
% 299.79/300.43 50400[0:SpR:223.1,36407.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,t_a),u,t_a),w),v_x)),y))*.
% 299.79/300.43 50514[0:MRR:50513.0,267.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),hAPP(c_Set_Oinsert(w,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.43 50875[0:MRR:50874.0,394.0] || -> equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_COMBK(v,tc_fun(t_a,tc_bool),u),u,tc_fun(t_a,tc_bool))),hAPP(hAPP(c_in(t_a),v_x),v))**.
% 299.79/300.43 51170[0:SpR:24914.0,26873.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),hAPP(c_Set_Oinsert(u,v),v_x),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.43 51290[0:SpR:24914.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,t_a),tc_Com_Opname,v),hAPP(c_Set_Oinsert(u,t_a),v_x)),v_x),hAPP(hAPP(c_Set_Oinsert(u,t_a),v_x),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.43 51484[0:SpL:24914.0,33513.1] || c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),v)* equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(u,v),v_x),v),c_HOL_Ozero__class_Ozero(tc_nat)) -> .
% 299.79/300.43 51749[0:MRR:51748.0,51748.1,51748.2,51748.4,379.0,59.0,366.0,219.0] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* c_Fun_Oinj__on(u,x,v,w) -> equal(c_Finite__Set_Ocard(x,v),c_HOL_Ozero__class_Ozero(tc_nat)).
% 299.79/300.43 51813[4:SpR:24914.0,40792.1] || c_lessequals(v_x,hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),x),tc_bool)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),x)).
% 299.79/300.43 51984[0:Rew:12944.0,51969.1,12944.0,51969.1] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y,z,x1),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_List_Ofoldl(x2,c_Orderings_Otop__class_Otop(tc_bool),x3,x1,x4),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.43 51985[0:Rew:11473.0,51963.1,11473.0,51963.1] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,x,y),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_List_Ofoldl(z,c_Orderings_Otop__class_Otop(tc_bool),x1,y,x2),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.43 51986[0:Rew:17045.0,51935.1,17045.0,51935.1] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x,y,z),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(c_List_Ofoldl(x1,c_Orderings_Obot__class_Obot(tc_bool),x2,z,x3),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.43 52242[7:SpL:118.0,27265.0] || equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,w,x,y),z,hAPP(u,x1),y,x),v_x)** -> hBOOL(hAPP(u,hAPP(c_Fun_Ofun__upd(v,z,x1,y,w),v_x))).
% 299.79/300.43 52300[0:Res:84.1,35720.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)),y,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y),u)).
% 299.79/300.43 52267[0:SpL:55.1,35720.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)),y,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),u),x)) hBOOL(hAPP(y,u)).
% 299.79/300.43 52494[0:SpL:35.2,38147.0] || c_lessequals(u,c_COMBK(v,w,x),tc_fun(y,tc_bool))* c_lessequals(c_COMBK(v,w,x),z,tc_fun(y,tc_bool))* hBOOL(hAPP(u,x1))* -> hBOOL(v).
% 299.79/300.43 54186[0:SpL:52997.1,215.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__derivs(u,v_x,v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v_Procs,tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.79/300.43 55635[0:Rew:104.0,55528.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_bool)*.
% 299.79/300.43 55821[0:Rew:130.1,55735.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.79/300.43 55965[0:SpL:130.1,55174.1] class_HOL_Ominus(u) || equal(v,c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u))) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u))* -> .
% 299.79/300.43 55882[0:SpL:130.1,55174.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x) equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool),hAPP(x,v_x))* -> .
% 299.79/300.43 57874[0:Obv:57845.0] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* c_lessequals(w,c_Orderings_Obot__class_Obot(u),u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.43 58229[0:SpL:131.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),tc_bool),z,x1),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y))* -> .
% 299.79/300.43 58228[0:SpL:158.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),tc_bool),z,x1),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w))* -> .
% 299.79/300.43 58209[0:SpL:104.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_bool),w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))))** -> .
% 299.79/300.43 58471[0:SpL:181.1,58248.0] || equal(c_COMBK(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w),c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(c_COMBK(x,y,u),u,y),tc_fun(t_a,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(y),x),v_x)).
% 299.79/300.43 58577[0:SpR:21893.0,10771.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(w,u),v_x),c_Set_Oinsert(w,u),tc_Com_Opname,x)))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,u),v_x),v)).
% 299.79/300.43 58576[0:SpR:21267.0,10771.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(w,u),v_x),tc_Com_Opname,x)))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,u),v_x),v)).
% 299.79/300.43 59050[0:Res:46859.0,15629.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,tc_fun(u,tc_bool)),v)))*.
% 299.79/300.43 59047[0:Res:9225.0,15629.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),w)))*.
% 299.79/300.43 59032[0:Res:7309.0,15629.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oimage(u,v,w),u,x,y,z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_COMBS(c_Set_Oimage(u,v,w),u,x,y,z),x1)))*.
% 299.79/300.43 59026[0:Res:21141.0,15629.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Set_Oimage(u,t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)))*.
% 299.79/300.43 59025[0:Res:21130.0,15629.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_in(tc_Com_Opname),v_x)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Set_Oimage(u,v,w),hAPP(c_in(tc_Com_Opname),v_x)),x)))*.
% 299.79/300.43 59023[0:Res:7253.0,15629.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),x)))*.
% 299.79/300.43 58791[0:SpL:336.0,15629.0] || hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))*.
% 299.79/300.43 59125[4:MRR:58703.0,6340.0] || -> hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v)))*.
% 299.79/300.43 59559[0:Res:46859.0,15857.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v_x,t_a),tc_Com_Opname,tc_fun(u,tc_bool)),w)))*.
% 299.79/300.43 59556[0:Res:9225.0,15857.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,tc_fun(v,tc_bool)),x)))*.
% 299.79/300.43 59540[0:Res:7309.0,15857.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oimage(u,v,w),u,x,y,z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_Set_Oimage(u,v,w),u,x,y,z),x2)))*.
% 299.79/300.43 59534[0:Res:21141.0,15857.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(u,t_a,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),y)))*.
% 299.79/300.43 59533[0:Res:21130.0,15857.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_in(tc_Com_Opname),v_x)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(u,v,w),hAPP(c_in(tc_Com_Opname),v_x)),y)))*.
% 299.79/300.43 59531[0:Res:7253.0,15857.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),y)))*.
% 299.79/300.43 59299[0:SpL:336.0,15857.0] || hBOOL(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))*.
% 299.79/300.43 59635[4:MRR:59211.0,6340.0] || -> hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),w)))*.
% 299.79/300.43 59925[0:SSi:59858.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)))** -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)).
% 299.79/300.43 60432[7:Res:58968.1,33.0] || equal(hAPP(c_Set_Ovimage(u,v,w),x),v_x) -> hBOOL(hAPP(x,hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Set_Ovimage(u,v,w),x),y))))*.
% 299.79/300.43 60410[7:SpR:9.0,58968.1] || equal(c_Fun_Ocomp(u,v,w,x,y),v_x) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Fun_Ocomp(u,v,w,x,y),z))))*.
% 299.79/300.43 60381[7:SpR:299.2,58968.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v),x,u)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x) -> hBOOL(x).
% 299.79/300.43 60545[0:Res:58969.1,33.0] || equal(hAPP(c_Set_Ovimage(u,v,w),x),v_Procs) -> hBOOL(hAPP(x,hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Set_Ovimage(u,v,w),x),y))))*.
% 299.79/300.43 60523[0:SpR:9.0,58969.1] || equal(c_Fun_Ocomp(u,v,w,x,y),v_Procs) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Fun_Ocomp(u,v,w,x,y),z))))*.
% 299.79/300.43 60494[0:SpR:299.2,58969.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v),x,u)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_Procs) -> hBOOL(x).
% 299.79/300.43 60618[7:Res:59476.1,33.0] || equal(hAPP(c_Set_Ovimage(u,v,w),x),v_x) -> hBOOL(hAPP(x,hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x),z))))*.
% 299.79/300.43 60596[7:SpR:9.0,59476.1] || equal(c_Fun_Ocomp(u,v,w,x,y),v_x) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Fun_Ocomp(u,v,w,x,y),x1))))*.
% 299.79/300.43 60567[7:SpR:299.2,59476.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w),x,u)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x) -> hBOOL(x).
% 299.79/300.43 60691[0:Res:59477.1,33.0] || equal(hAPP(c_Set_Ovimage(u,v,w),x),v_Procs) -> hBOOL(hAPP(x,hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x),z))))*.
% 299.79/300.43 60669[0:SpR:9.0,59477.1] || equal(c_Fun_Ocomp(u,v,w,x,y),v_Procs) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Fun_Ocomp(u,v,w,x,y),x1))))*.
% 299.79/300.43 60640[0:SpR:299.2,59477.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w),x,u)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_Procs) -> hBOOL(x).
% 299.79/300.43 60876[0:Res:59017.1,33.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Ovimage(v,w,x),y),t_a)* hBOOL(hAPP(y,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_Set_Ovimage(v,w,x),y),z))))*.
% 299.79/300.43 60854[0:SpR:9.0,59017.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Fun_Ocomp(v,w,x,y,z),t_a)* hBOOL(hAPP(v,hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_Fun_Ocomp(v,w,x,y,z),x1))))*.
% 299.79/300.43 60825[0:SpR:299.2,59017.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v),x,u)* -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),t_a)* hBOOL(x).
% 299.79/300.43 60949[0:Res:59525.1,33.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Ovimage(v,w,x),y),t_a)* hBOOL(hAPP(y,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),y),x1))))*.
% 299.79/300.43 60927[0:SpR:9.0,59525.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Fun_Ocomp(v,w,x,y,z),t_a)* hBOOL(hAPP(v,hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Fun_Ocomp(v,w,x,y,z),x2))))*.
% 299.79/300.43 60898[0:SpR:299.2,59525.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w),x,u)* -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),t_a)* hBOOL(x).
% 299.79/300.43 61995[7:MRR:61898.2,27297.0] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.79/300.43 62295[0:Res:111.2,4246.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u),u)*.
% 299.79/300.43 62291[0:Res:52.2,4246.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u)) -> c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ominus__class_Ominus(v,w,u),u)*.
% 299.79/300.43 62414[0:Obv:62278.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),z) -> c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),z,u)*.
% 299.79/300.43 62630[0:Res:111.2,4340.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u),u)* -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ouminus__class_Ouminus(w,u)).
% 299.79/300.43 62626[0:Res:52.2,4340.1] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ominus__class_Ominus(v,w,u),u)* -> equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.43 62749[0:Obv:62613.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),z,u)* -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),z).
% 299.79/300.43 63112[0:Rew:539.1,63022.3] class_OrderedGroup_Opordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ouminus__class_Ouminus(v,u)),c_HOL_Ozero__class_Ozero(u))** -> equal(c_HOL_Ouminus__class_Ouminus(v,u),c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.43 63575[4:Res:62367.1,40105.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),v,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u)) -> hBOOL(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),v,tc_bool))*.
% 299.79/300.43 63574[4:Res:62367.1,40016.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),v,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x)) -> hBOOL(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),v,tc_bool))*.
% 299.79/300.43 63784[0:SSi:63658.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)) -> c_lessequals(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))*.
% 299.79/300.43 64053[0:SpR:56.1,63953.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs)) -> c_lessequals(c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(u,tc_Com_Opname),v)),tc_fun(tc_Com_Opname,tc_bool))*.
% 299.79/300.43 64251[0:SpR:27043.1,646.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),v_x),v_x)**.
% 299.79/300.43 64204[0:SpR:302.1,646.1] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u)),v_x)**.
% 299.79/300.43 64185[0:SpR:15476.0,646.1] || c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),tc_Com_Opname,v),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)),v_x)**.
% 299.79/300.43 64418[0:SpR:27043.1,645.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),v_x),v_x)**.
% 299.79/300.43 64371[0:SpR:302.1,645.1] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u)),v_x)**.
% 299.79/300.43 64352[0:SpR:15476.0,645.1] || c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),tc_Com_Opname,v),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)),v_x)**.
% 299.79/300.43 64486[0:Rew:586.0,64468.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(x,v_x)),y)) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,x,tc_Com_Opname,tc_fun(w,tc_bool))),y))*.
% 299.79/300.43 64487[0:Rew:586.0,64467.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(x,v_x)),y)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,x,tc_Com_Opname,tc_fun(v,tc_bool))),y))*.
% 299.79/300.43 64565[7:MRR:64492.2,27297.0] || equal(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.43 66772[0:SpR:1188.2,584.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,w,x,y),c_HOL_Ozero__class_Ozero(u)),hAPP(c_Orderings_Otop__class_Otop(u),hAPP(v,c_HOL_Ozero__class_Ozero(u))))**.
% 299.79/300.43 66771[0:SpR:1188.2,584.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),w,x,y),c_HOL_Ozero__class_Ozero(u)),hAPP(hAPP(v,c_HOL_Ozero__class_Ozero(u)),c_Orderings_Otop__class_Otop(u)))**.
% 299.79/300.43 66919[0:SpR:66691.3,397.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || -> equal(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.43 67219[0:SpR:66692.3,397.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || -> equal(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.43 67528[0:SpR:1189.2,584.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,w,x,y),c_HOL_Ozero__class_Ozero(u)),hAPP(c_Orderings_Otop__class_Otop(u),hAPP(v,c_HOL_Ozero__class_Ozero(u))))**.
% 299.79/300.43 67527[0:SpR:1189.2,584.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),w,x,y),c_HOL_Ozero__class_Ozero(u)),hAPP(hAPP(v,c_HOL_Ozero__class_Ozero(u)),c_Orderings_Otop__class_Otop(u)))**.
% 299.79/300.43 67653[0:SpR:67115.3,365.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || -> equal(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.43 67940[0:SpR:67416.3,365.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || -> equal(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.43 68547[0:SpR:67446.3,397.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || -> equal(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.43 68849[0:SpR:67447.3,397.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || -> equal(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.43 69127[0:SpR:67573.3,365.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Obot(u) || -> equal(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.43 69419[0:SpR:68745.3,365.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || -> equal(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.43 70091[0:Res:59525.1,11883.0] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(u,tc_bool)),w)),x))* -> c_Hoare__Mirabelle_Ohoare__valids(y,c_HOL_Ouminus__class_Ouminus(x,tc_fun(u,tc_bool)),t_a)*.
% 299.79/300.43 70090[0:Res:59017.1,11883.0] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_HOL_Ouminus__class_Ouminus(x,tc_fun(u,tc_bool)),v)),x))* -> c_Hoare__Mirabelle_Ohoare__valids(y,c_HOL_Ouminus__class_Ouminus(x,tc_fun(u,tc_bool)),t_a)*.
% 299.79/300.43 70087[7:Res:58968.1,11883.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w)),u))* -> .
% 299.79/300.43 70086[0:Res:58969.1,11883.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_Procs) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w)),u))* -> .
% 299.79/300.43 70085[7:Res:59476.1,11883.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),x)),u))* -> .
% 299.79/300.43 70084[0:Res:59477.1,11883.0] || equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_Procs) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),x)),u))* -> .
% 299.79/300.43 70064[0:SpL:128.0,11883.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),y))* hBOOL(hAPP(hAPP(c_in(v),y),hAPP(c_Set_Ovimage(u,v,w),x)))* -> .
% 299.79/300.43 70399[0:Res:151.2,70070.1] || hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)),v_x),tc_bool))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.79/300.43 71064[0:SpR:161.0,7568.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),v,tc_fun(w,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.43 71063[0:SpR:162.0,7568.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(c_Set_Oinsert(y,v),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z))),tc_fun(v,tc_bool))*.
% 299.79/300.43 71062[0:SpR:507.0,7568.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oinsert(y,w),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z))),tc_fun(w,tc_bool))*.
% 299.79/300.43 71246[0:SpR:317.0,7538.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(z,v),x))),tc_fun(w,tc_bool))*.
% 299.79/300.43 71437[7:SpL:131.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),tc_bool))* equal(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_x)** -> .
% 299.79/300.43 71436[7:SpL:158.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),tc_bool))* equal(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x)** -> .
% 299.79/300.43 71417[7:SpL:104.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),v_x) -> .
% 299.79/300.43 72088[0:SpR:161.0,7830.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),u),v,tc_fun(w,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.43 72087[0:SpR:162.0,7830.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(c_Set_Oinsert(y,v),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x))),tc_fun(v,tc_bool))*.
% 299.79/300.43 72086[0:SpR:507.0,7830.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oinsert(y,w),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),x))),tc_fun(w,tc_bool))*.
% 299.79/300.43 72465[0:SpL:113.0,12554.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))),z))* -> hBOOL(hAPP(hAPP(c_in(v),z),hAPP(c_Set_Ovimage(u,v,w),x)))*.
% 299.79/300.43 72832[0:Rew:72818.3,72752.4] class_OrderedGroup_Oab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ominus__class_Ominus(w,v,u),u)* -> equal(c_HOL_Ominus__class_Ominus(w,v,u),c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.43 72833[0:Obv:72789.0] class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),v,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_Orderings_Otop__class_Otop(u)).
% 299.79/300.43 72834[0:Obv:72788.0] class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),w,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_Orderings_Otop__class_Otop(u)).
% 299.79/300.43 73091[7:Res:71608.1,479.1] || equal(u,v_x) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,w,v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w)))*.
% 299.79/300.43 73090[7:Res:71608.1,478.1] || equal(u,v_x) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,u,v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u)))*.
% 299.79/300.43 73056[7:Res:71608.1,275.1] || equal(hAPP(u,v),v_x)** hBOOL(hAPP(hAPP(c_in(w),v),x))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,u,w,tc_fun(t_a,tc_bool))))*.
% 299.79/300.43 74356[7:SpL:71835.1,469.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_x,u,x,v,w)),x)**.
% 299.79/300.43 74355[7:SpL:71835.1,464.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_x,x,u,v,w)),x)**.
% 299.79/300.43 74229[7:SpL:71835.1,215.0] || equal(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(v)),c_Set_Oinsert(v_x,t_a)) c_Hoare__Mirabelle_Ohoare__derivs(w,v_x,v) -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.79/300.43 74141[7:SpL:71835.1,469.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x)))* -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,v_x,w,u)),v_x)**.
% 299.79/300.43 74140[7:SpL:71835.1,464.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x)))* -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(x,v_x,v,w,u)),v_x)**.
% 299.79/300.43 73955[7:SpL:71835.1,496.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u)),u))* c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.79/300.43 73917[7:SpR:71835.1,317.0] || equal(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(u,v)) -> equal(hAPP(c_Set_Oinsert(hAPP(w,u),x),hAPP(c_Set_Oimage(w,v,x),v_x)),hAPP(c_Set_Oimage(w,v,x),v_x))**.
% 299.79/300.43 73910[7:SpR:71835.1,317.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),v_x)),hAPP(c_Set_Oinsert(hAPP(u,x),w),v_x))**.
% 299.79/300.43 73896[7:SpR:71835.1,131.0] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),v_x)**.
% 299.79/300.43 73895[7:SpR:71835.1,131.0] || equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x),hAPP(c_Set_Ovimage(x,y,v),v_x))**.
% 299.79/300.43 73894[7:SpR:71835.1,158.0] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),v_x)**.
% 299.79/300.43 73893[7:SpR:71835.1,158.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_x),hAPP(c_Set_Oimage(x,w,y),v_x))**.
% 299.79/300.43 73769[7:SpR:71835.1,104.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Set_Oinsert(v_x,t_a))** -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),v_x).
% 299.79/300.44 73701[7:SpR:71835.1,317.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(v_x,v),x)),hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(u,v,w),x)))*.
% 299.79/300.44 73700[7:SpR:71835.1,99.1] || equal(c_Set_Oinsert(v_x,t_a),u) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),v_x),v_x)**.
% 299.79/300.44 73699[7:SpR:71835.1,438.1] || equal(c_Set_Oinsert(v_x,t_a),u) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),v_x),v_x)**.
% 299.79/300.44 73650[7:SpR:71835.1,536.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(v_x,w)),hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))**.
% 299.79/300.44 73649[7:SpR:71835.1,535.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(v_x,w)),hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))**.
% 299.79/300.44 73613[7:SpR:71835.1,129.1] || equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_lessequals(x,v_x,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),v_x,tc_fun(v,tc_bool))*.
% 299.79/300.44 73604[7:SpR:71835.1,313.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_lessequals(x,v_x,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),v_x,tc_fun(w,tc_bool))*.
% 299.79/300.44 73603[7:SpR:71835.1,97.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_Fun_Oinj__on(u,v_x,v,w) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v_x,u,v,w),w,v),v_x),v_x)**.
% 299.79/300.44 73551[7:SpR:71835.1,537.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v_x,v)),w),hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))**.
% 299.79/300.44 73550[7:SpR:71835.1,534.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v_x,v)),w),hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))**.
% 299.79/300.44 73282[7:SpR:71835.1,129.1] || equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_lessequals(v_x,x,tc_fun(w,tc_bool)) -> c_lessequals(v_x,hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool))*.
% 299.79/300.44 73232[7:SpR:71835.1,313.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_lessequals(v_x,x,tc_fun(v,tc_bool)) -> c_lessequals(v_x,hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool))*.
% 299.79/300.44 74513[7:Rew:71835.1,74131.3,71835.1,74131.2] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))* -> hBOOL(hAPP(v_x,v)) hBOOL(hAPP(v_x,w)).
% 299.79/300.44 74896[7:SpR:131.0,72297.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),v_x))*.
% 299.79/300.44 74895[7:SpR:158.0,72297.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),v_x))*.
% 299.79/300.44 75606[0:Obv:75359.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w))),u)*.
% 299.79/300.44 75717[7:SpR:71883.1,545.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(v_x,u,w),v)))*.
% 299.79/300.44 75713[7:SpR:71883.1,362.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.44 76074[0:Obv:75816.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y))),u)*.
% 299.79/300.44 76177[0:MRR:76171.0,820.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x3,c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2)))*.
% 299.79/300.44 76178[0:MRR:76170.0,820.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x2,c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool)),c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x3)))*.
% 299.79/300.44 76723[0:Obv:76491.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w))),u)*.
% 299.79/300.44 76726[0:SSi:76601.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),y))),tc_fun(v,tc_bool))*.
% 299.79/300.44 77093[0:Obv:76849.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y))),u)*.
% 299.79/300.44 77171[7:SpL:188.1,74788.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x)** equal(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x)* -> hBOOL(x)*.
% 299.79/300.44 77344[0:SpR:2771.1,2399.2] class_Orderings_Olinorder(tc_bool) class_OrderedGroup_Olordered__ab__group__add(tc_bool) || equal(u,v) -> c_lessequals(hAPP(v,v_x),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),tc_bool)* c_lessequals(c_HOL_Ozero__class_Ozero(tc_bool),hAPP(v,v_x),tc_bool).
% 299.79/300.44 77331[0:SpR:141.1,2399.2] class_OrderedGroup_Oab__group__add(u) class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ominus__class_Ominus(w,v,u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ominus__class_Ominus(v,w,u),u).
% 299.79/300.44 77438[0:MRR:77351.2,12687.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),w))*.
% 299.79/300.44 77458[7:SpR:71894.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_bool)),w))* -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,v_x,v,u),u)*.
% 299.79/300.44 77450[7:SpR:71894.1,176.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Ovimage(v_x,u,v),hAPP(c_Set_Oinsert(v_x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))))*.
% 299.79/300.44 77523[0:SpR:141.1,2429.2] class_OrderedGroup_Oab__group__add(u) class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) || -> c_lessequals(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ominus__class_Ominus(w,v,u),u)* c_lessequals(c_HOL_Ozero__class_Ozero(u),c_HOL_Ominus__class_Ominus(v,w,u),u).
% 299.79/300.44 77897[0:Res:254.1,5892.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,u),w)),w))* -> hBOOL(hAPP(c_COMBS(c_in(x),c_in(u),y,z,x1),hAPP(c_Set_Oinsert(v,u),w)))*.
% 299.79/300.44 77739[0:SpL:538.0,5892.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v))* -> hBOOL(hAPP(c_COMBS(c_in(x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y,z,x1),v))*.
% 299.79/300.44 78355[7:SpR:78167.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_x,u),c_Fun_Ofun__upd(v,w,v_x,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_x,u),v,y,z,x),w,v_x,x,z))*.
% 299.79/300.44 78329[7:SpR:78167.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,w),v,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(v_x,w),u,x),v_x),v_x)**.
% 299.79/300.44 78328[7:SpR:78167.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,w),v,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(v_x,w),u,x),v_x),v_x)**.
% 299.79/300.44 78720[4:Res:78665.1,449.0] || equal(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,u,w,x)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,u,w,x)),v_x)** -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),u),t_a).
% 299.79/300.44 78700[4:Res:78665.1,473.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)),v_x)** -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v)),y))*.
% 299.79/300.44 78686[4:Res:78665.1,356.0] || equal(hAPP(hAPP(c_in(u),v),w),v_x)** -> equal(hAPP(c_Set_Oimage(c_COMBK(x,y,u),u,y),w),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.44 78865[0:SpR:158.0,11064.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Fun_Ocomp(y,u,w,z,v),v,z),x),x1,tc_fun(z,tc_bool)),z)*.
% 299.79/300.44 78862[0:SpR:317.0,11064.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(hAPP(x,u),y),hAPP(c_Set_Oimage(x,v,y),w)),z,tc_fun(y,tc_bool)),y)*.
% 299.79/300.44 79034[0:Res:15630.1,3863.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(x,y),z),x1,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),y)))*.
% 299.79/300.44 79053[0:Rew:586.0,79005.0] || hBOOL(hAPP(u,hAPP(v,w))) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,hAPP(c_COMBB(u,x1,x2,x3),v),x))))*.
% 299.79/300.44 79054[0:Rew:585.0,79004.0] || hBOOL(hAPP(hAPP(u,v),w)) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,x),y),z,hAPP(c_COMBC(u,x1,x2,x3),w),x)),w))*.
% 299.79/300.44 79254[0:Res:15858.1,3863.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(x,z),x1),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),z)))*.
% 299.79/300.44 79273[0:Rew:586.0,79225.0] || hBOOL(hAPP(u,hAPP(v,w))) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(w,y),z),hAPP(c_COMBB(u,x1,x2,x3),v),y))))*.
% 299.79/300.44 79274[0:Rew:585.0,79224.0] || hBOOL(hAPP(hAPP(u,v),w)) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(v,y),z),hAPP(c_COMBC(u,x1,x2,x3),w),y)),w))*.
% 299.79/300.44 80070[0:SpL:21268.0,279.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_in(u),hAPP(c_in(u),v),x,y),u),w),w)**.
% 299.79/300.44 80015[0:SpL:21268.0,18903.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x)* -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,u),y,z))),v,x)*.
% 299.79/300.44 79992[0:SpR:49017.1,21268.0] || -> hBOOL(hAPP(u,v_x)) equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v_Procs,v,w)),v_Procs)**.
% 299.79/300.44 79885[0:SpR:14526.0,21268.0] || -> equal(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),x,y)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.44 79878[0:SpR:297.2,21268.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y)),w)**.
% 299.79/300.44 79875[0:SpR:2098.1,21268.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) equal(hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),v,w,x)),v)**.
% 299.79/300.44 79841[0:SpR:646.1,21268.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),v_x,w,x)),v_x)**.
% 299.79/300.44 79840[0:SpR:645.1,21268.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),v_x,w,x)),v_x)**.
% 299.79/300.44 79740[7:SpR:21268.0,71608.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_in(t_a),v_x),hAPP(hAPP(c_in(t_a),v_x),v),u,w),v_x)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.79/300.44 79666[0:SpR:21268.0,8366.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x),hAPP(hAPP(c_in(tc_Com_Opname),v_x),v),u,w),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v)).
% 299.79/300.44 79460[0:SpR:21268.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_in(u),hAPP(c_in(u),v),x,y),u),z))))*.
% 299.79/300.44 79454[0:SpR:21268.0,9071.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(u),hAPP(c_in(u),v),w,x),u),tc_Com_Opname,tc_fun(u,tc_bool))))*.
% 299.79/300.44 79452[0:SpR:21268.0,9246.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)))) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_in(u),hAPP(c_in(u),v),x,y)))*.
% 299.79/300.44 79449[0:SpR:21268.0,1157.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_COMBK(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(u),hAPP(c_in(u),v),w,x),y,z),tc_Com_Opname,u),v_Procs)))*.
% 299.79/300.44 79369[0:SpR:21268.0,212.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),z))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),x),z)).
% 299.79/300.44 79347[0:SpR:21268.0,3346.1] || equal(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(v),hAPP(c_in(v),w),u,x),v),y)* -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(y,v_x)))*.
% 299.79/300.44 80358[0:Rew:647.0,79372.0] || -> equal(c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),u,w),v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)))**.
% 299.79/300.44 81265[0:SpL:21894.0,279.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),c_in(u),x,y),u),w),w)**.
% 299.79/300.44 81210[0:SpL:21894.0,18903.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x)* -> c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Com_Ocom_OBODY,u),c_Com_Ocom_OBODY,y,z))),v,x)*.
% 299.79/300.44 81186[0:SpR:49017.1,21894.0] || -> hBOOL(hAPP(u,v_x)) equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w)),v_Procs)**.
% 299.79/300.44 81079[0:SpR:14526.0,21894.0] || -> equal(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),x,y)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.44 81072[0:SpR:297.2,21894.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y)),w)**.
% 299.79/300.44 81069[0:SpR:2098.1,21894.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) equal(hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,x)),v)**.
% 299.79/300.44 81035[0:SpR:646.1,21894.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_x,c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,x)),v_x)**.
% 299.79/300.44 81034[0:SpR:645.1,21894.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_x,c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,x)),v_x)**.
% 299.79/300.44 80934[7:SpR:21894.0,71608.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),v),hAPP(c_in(t_a),v_x),u,w),v_x)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.79/300.44 80860[0:SpR:21894.0,8366.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_in(tc_Com_Opname),v_x),v),hAPP(c_in(tc_Com_Opname),v_x),u,w),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v)).
% 299.79/300.44 80653[0:SpR:21894.0,9067.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),c_in(u),x,y),u),z))))*.
% 299.79/300.44 80647[0:SpR:21894.0,9071.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(u),v),c_in(u),w,x),u),tc_Com_Opname,tc_fun(u,tc_bool))))*.
% 299.79/300.44 80645[0:SpR:21894.0,9246.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)))) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),c_in(u),x,y)))*.
% 299.79/300.44 80642[0:SpR:21894.0,1157.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_COMBK(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(u),v),c_in(u),w,x),y,z),tc_Com_Opname,u),v_Procs)))*.
% 299.79/300.44 80562[0:SpR:21894.0,212.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),z))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),x),z)).
% 299.79/300.44 80540[0:SpR:21894.0,3346.1] || equal(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_in(v),w),c_in(v),u,x),v),y)* -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(y,v_x)))*.
% 299.79/300.44 81553[0:Rew:647.0,80565.0] || -> equal(c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),c_Set_Oinsert(v_x,tc_Com_Opname),u,w),v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)))**.
% 299.79/300.44 81756[0:SpR:158.0,5075.1] || c_Finite__Set_Ofinite(u,v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(w,x,v),hAPP(c_Set_Oimage(y,z,x),hAPP(c_Set_Ovimage(c_Fun_Ocomp(w,y,x,v,z),z,v),u))),v)*.
% 299.79/300.44 81749[0:SpR:131.0,5075.1] || c_Finite__Set_Ofinite(u,v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_Fun_Ocomp(w,x,y,v,z),z,v),hAPP(c_Set_Ovimage(x,z,y),hAPP(c_Set_Ovimage(w,y,v),u))),v)*.
% 299.79/300.44 81740[0:SpR:131.0,5075.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),x),v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(y,z,v),hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,y,v,w,z),z,w),x)),v)*.
% 299.79/300.44 81955[0:SpR:21894.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(v,w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(v,w),v,x1,x2)),u)*.
% 299.79/300.44 81951[0:SpR:21268.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(v,w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),v,hAPP(v,w),x1,x2)),u)*.
% 299.79/300.44 81864[0:SpR:538.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y,z,x1),w),u)*.
% 299.79/300.44 82428[0:SpR:21894.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(v,w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(v,w),v,x1,x2)),u)*.
% 299.79/300.44 82424[0:SpR:21268.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(v,w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),v,hAPP(v,w),x1,x2)),u)*.
% 299.79/300.44 82336[0:SpR:538.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y,z,x1),w),u)*.
% 299.79/300.44 82577[7:Res:82148.0,479.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Set_Oinsert(v_x,v),w,u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,v)),w)))*.
% 299.79/300.44 82576[7:Res:82148.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Set_Oinsert(v_x,w),u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),c_Set_Oinsert(v_x,w))))*.
% 299.79/300.44 82815[0:Obv:82732.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* c_lessequals(x,w,u)* c_lessequals(y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),u)* -> c_lessequals(y,w,u)*.
% 299.79/300.44 82918[0:SpR:158.0,22513.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(y,z,x1),hAPP(c_Set_Oimage(c_Fun_Ocomp(x2,u,w,z,v),v,z),x)),x1)*.
% 299.79/300.44 82915[0:SpR:317.0,22513.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x,y,z),hAPP(c_Set_Oinsert(hAPP(x1,u),y),hAPP(c_Set_Oimage(x1,v,y),w))),z)*.
% 299.79/300.44 83119[0:SpL:5924.0,5892.0] || hBOOL(hAPP(hAPP(hAPP(u,v),w),v))* -> hBOOL(hAPP(c_COMBS(c_in(x),c_COMBS(u,c_COMBK(w,y,z),x1,x2,x3),x4,x5,x6),v))*.
% 299.79/300.44 83047[0:SpR:5924.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(v,w),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_COMBS(v,c_COMBK(x,y,z),x1,x2,x3),x4,x5,x6),w),u)*.
% 299.79/300.44 83046[0:SpR:5924.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(v,w),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_COMBS(v,c_COMBK(x,y,z),x1,x2,x3),x4,x5,x6),w),u)*.
% 299.79/300.44 83045[0:SpR:5924.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(v,w),x)),hAPP(c_Set_Oimage(c_COMBS(v,c_COMBK(x,y,z),x1,x2,x3),x4,u),c_Orderings_Otop__class_Otop(tc_fun(x4,tc_bool)))))*.
% 299.79/300.44 83268[7:SpR:131.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),v_x),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))))*.
% 299.79/300.44 83267[7:SpR:158.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),v_x),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))))*.
% 299.79/300.44 83248[7:SpR:104.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w,x),v_x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))*.
% 299.79/300.44 83438[0:SpL:5961.0,5892.0] || hBOOL(hAPP(hAPP(u,hAPP(v,w)),w))* -> hBOOL(hAPP(c_COMBS(c_in(x),c_COMBS(c_COMBK(u,y,z),v,x1,x2,x3),x4,x5,x6),w))*.
% 299.79/300.44 83374[0:SpR:5961.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(v,hAPP(w,x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_COMBS(c_COMBK(v,y,z),w,x1,x2,x3),x4,x5,x6),x),u)*.
% 299.79/300.44 83373[0:SpR:5961.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(v,hAPP(w,x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_COMBS(c_COMBK(v,y,z),w,x1,x2,x3),x4,x5,x6),x),u)*.
% 299.79/300.44 83372[0:SpR:5961.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,x))),hAPP(c_Set_Oimage(c_COMBS(c_COMBK(v,y,z),w,x1,x2,x3),x4,u),c_Orderings_Otop__class_Otop(tc_fun(x4,tc_bool)))))*.
% 299.79/300.44 83880[0:SpL:5899.0,5892.0] || hBOOL(hAPP(hAPP(c_COMBS(u,v,w,x,y),z),z))* -> hBOOL(hAPP(c_COMBS(c_in(x1),c_COMBS(u,v,x2,x3,x4),x5,x6,x7),z))*.
% 299.79/300.44 83756[0:SpR:5899.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_COMBS(v,w,x,y,z),x1),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_COMBS(v,w,x2,x3,x4),x5,x6,x7),x1),u)*.
% 299.79/300.44 83755[0:SpR:5899.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_COMBS(v,w,x,y,z),x1),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_COMBS(v,w,x2,x3,x4),x5,x6,x7),x1),u)*.
% 299.79/300.44 83754[0:SpR:5899.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_COMBS(v,w,x,y,z),x1)),hAPP(c_Set_Oimage(c_COMBS(v,w,x2,x3,x4),x5,u),c_Orderings_Otop__class_Otop(tc_fun(x5,tc_bool)))))*.
% 299.79/300.44 84070[0:Rew:584.0,83774.0] || hBOOL(hAPP(hAPP(u,v_x),hAPP(v,v_x))) -> hBOOL(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,v_Procs,c_COMBS(u,v,x1,x2,x3),tc_Com_Opname)))*.
% 299.79/300.44 84071[0:Rew:584.0,83773.0] || hBOOL(hAPP(hAPP(u,v_x),hAPP(v,v_x))) -> hBOOL(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,z,c_COMBS(u,v,x1,x2,x3),tc_Com_Opname)))*.
% 299.79/300.44 84185[7:SpL:188.1,78767.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool),v_x) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x)** -> .
% 299.79/300.44 84931[4:SpL:5899.0,78744.0] || equal(hAPP(c_COMBS(u,v,w,x,y),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_COMBS(u,v,z,x1,x2),x3)),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBS(u,v,z,x1,x2),x3,t_a).
% 299.79/300.44 84911[4:SpL:328.1,78744.0] || c_lessequals(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v,tc_fun(u,tc_bool))* equal(v,v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,t_a).
% 299.79/300.44 84961[0:Res:77906.0,15629.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oinsert(v,w),x,y,z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_COMBS(c_in(u),c_Set_Oinsert(v,w),x,y,z),x1)))*.
% 299.79/300.44 84960[0:Res:77906.0,15857.0] || -> hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oinsert(v,w),x,y,z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_in(u),c_Set_Oinsert(v,w),x,y,z),x2)))*.
% 299.79/300.44 85034[0:SpR:644.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w,x),c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v))**.
% 299.79/300.44 85215[0:SpR:66691.3,819.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_Orderings_Otop(u) || -> equal(c_Fun_Ofun__upd(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x,c_HOL_Ozero__class_Ozero(u),v,w),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)))**.
% 299.79/300.44 85214[0:SpR:66692.3,819.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) class_Orderings_Otop(u) || -> equal(c_Fun_Ofun__upd(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x,c_HOL_Ozero__class_Ozero(u),v,w),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)))**.
% 299.79/300.44 85213[0:SpR:67446.3,819.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_Orderings_Otop(u) || -> equal(c_Fun_Ofun__upd(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x,c_HOL_Ozero__class_Ozero(u),v,w),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)))**.
% 299.79/300.44 85212[0:SpR:67447.3,819.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) class_Orderings_Otop(u) || -> equal(c_Fun_Ofun__upd(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x,c_HOL_Ozero__class_Ozero(u),v,w),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)))**.
% 299.79/300.44 85265[0:SpR:67115.3,824.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) || -> equal(c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x,c_HOL_Ozero__class_Ozero(u),v,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)))**.
% 299.79/300.44 85264[0:SpR:67416.3,824.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) || -> equal(c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x,c_HOL_Ozero__class_Ozero(u),v,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)))**.
% 299.79/300.44 85262[0:SpR:67573.3,824.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Orderings_Obot(u) || -> equal(c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x,c_HOL_Ozero__class_Ozero(u),v,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)))**.
% 299.79/300.44 85261[0:SpR:68745.3,824.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_Orderings_Obot(u) || -> equal(c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x,c_HOL_Ozero__class_Ozero(u),v,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)))**.
% 299.79/300.44 85318[0:SpL:475.1,26240.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(z,u,x),w)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))** -> .
% 299.79/300.44 85490[4:SpR:78507.0,338.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))**.
% 299.79/300.44 85461[4:SpR:78507.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w)) -> c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,x),v,u),u)*.
% 299.79/300.44 85451[4:SpR:78507.0,339.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v))**.
% 299.79/300.44 85432[4:SpR:78507.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,v),u,w),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 85814[0:SpR:21893.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,w),u),x))))*.
% 299.79/300.44 85812[0:SpR:21267.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,w),u),x))))*.
% 299.79/300.44 85946[0:Res:687.1,13582.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname)),v))* -> .
% 299.79/300.44 85945[0:Res:686.1,13582.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname)),v))* -> .
% 299.79/300.44 86086[0:SpL:131.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),tc_bool))* equal(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_Procs)** -> .
% 299.79/300.44 86085[0:SpL:158.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),tc_bool))* equal(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_Procs)** -> .
% 299.79/300.44 86065[0:SpL:104.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),v_Procs) -> .
% 299.79/300.44 86686[0:Res:86261.1,479.1] || equal(u,v_Procs) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,w,v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w)))*.
% 299.79/300.44 86685[0:Res:86261.1,478.1] || equal(u,v_Procs) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,u,v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u)))*.
% 299.79/300.44 86650[0:Res:86261.1,275.1] || equal(hAPP(u,v),v_Procs)** hBOOL(hAPP(hAPP(c_in(w),v),x))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,u,w,tc_fun(t_a,tc_bool))))*.
% 299.79/300.44 86631[0:SpR:21894.0,86261.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),v),hAPP(c_in(t_a),v_x),u,w),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.79/300.44 86629[0:SpR:21268.0,86261.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_in(t_a),v_x),hAPP(hAPP(c_in(t_a),v_x),v),u,w),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.79/300.44 86730[4:SpL:188.1,86106.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool),v_x) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_Procs)** -> .
% 299.79/300.44 87097[0:Rew:331.0,86971.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(x,v,tc_fun(w,tc_bool)))**.
% 299.79/300.44 87099[0:Rew:330.0,86970.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),v,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(x,v,tc_fun(w,tc_bool)))**.
% 299.79/300.44 87307[7:SpR:181.1,71492.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_x)** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x))*.
% 299.79/300.44 87455[7:SpR:181.1,71493.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_x)** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x,t_a)*.
% 299.79/300.44 87585[7:SpR:181.1,71679.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_x)** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.79/300.44 88298[0:SpR:21893.0,7227.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_COMBK(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,v),w,x),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.79/300.44 88296[0:SpR:21267.0,7227.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_COMBK(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,v),w,x),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.79/300.44 88431[0:Res:8176.1,70.0] || c_lessequals(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.44 88425[0:Res:8176.1,402.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(v,c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),v).
% 299.79/300.44 88420[0:Res:8176.1,6845.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) equal(v,c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool))) -> c_lessequals(v,c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.44 88413[0:SpR:66.0,8176.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(y,w),v),tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))*.
% 299.79/300.44 88545[0:SpL:66.0,8306.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),y),tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* -> c_lessequals(u,c_HOL_Ominus__class_Ominus(v,y,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)).
% 299.79/300.44 88637[7:SpL:188.1,88086.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool))* -> .
% 299.79/300.44 89006[0:SpR:23958.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v),hAPP(c_Set_Oinsert(v_x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w)))*.
% 299.79/300.44 89002[0:SpR:23955.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v),hAPP(c_Set_Oinsert(v_x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w)))*.
% 299.79/300.44 88997[0:SpR:33303.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_Procs))*.
% 299.79/300.44 88993[0:SpR:28903.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_Procs))*.
% 299.79/300.44 88992[0:SpR:28902.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_Procs))*.
% 299.79/300.44 88988[0:SpR:28748.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_Procs))*.
% 299.79/300.44 88987[0:SpR:28747.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_Procs))*.
% 299.79/300.44 88982[0:SpR:52997.1,14196.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v_Procs,u),v,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_x))*.
% 299.79/300.44 88971[0:SpR:584.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_COMBS(u,v,w,x,y),z,x1),hAPP(c_Set_Oinsert(hAPP(hAPP(u,x2),hAPP(v,x2)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),x2))*.
% 299.79/300.44 88961[0:SpR:336.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.79/300.44 88957[0:SpR:5882.1,14196.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),c_Orderings_Otop__class_Otop(u)))*.
% 299.79/300.44 88954[0:SpR:13749.2,14196.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),c_Orderings_Otop__class_Otop(u)))*.
% 299.79/300.44 88953[0:SpR:14043.2,14196.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),c_Orderings_Otop__class_Otop(u)))*.
% 299.79/300.44 88951[0:SpR:26782.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),c_Orderings_Obot__class_Obot(tc_bool)))*.
% 299.79/300.44 88948[0:SpR:3294.1,14196.0] || equal(c_in(t_a),u) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))))*.
% 299.79/300.44 88939[0:SpR:11167.1,14196.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),w,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_Procs))*.
% 299.79/300.44 88934[0:SpR:584.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(u,v),w,x),hAPP(c_Set_Oinsert(hAPP(c_COMBS(u,y,z,x1,x2),v),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),hAPP(y,v)))*.
% 299.79/300.44 88913[0:SpR:337.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),x))*.
% 299.79/300.44 88883[0:SpR:540.1,14196.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),y))*.
% 299.79/300.44 88882[0:SpR:539.1,14196.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),y))*.
% 299.79/300.44 88881[0:SpR:297.2,14196.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),hAPP(c_Set_Oinsert(w,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),w))*.
% 299.79/300.44 88874[0:SpR:30368.2,14196.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),x))*.
% 299.79/300.44 88873[0:SpR:30928.2,14196.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),x))*.
% 299.79/300.44 88870[0:SpR:299.2,14196.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y),hAPP(c_Set_Oinsert(w,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),v))*.
% 299.79/300.44 88857[0:SpR:25.1,14196.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w,x),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_x))*.
% 299.79/300.44 89170[0:SpL:410.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),y),z,x,tc_fun(v,tc_bool))),v)* -> c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,z,x,tc_fun(v,tc_bool)),v).
% 299.79/300.44 89435[7:SpR:78590.1,338.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u))**.
% 299.79/300.44 89355[7:SpR:78590.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Set_Oinsert(v_x,t_a),v) hBOOL(hAPP(hAPP(c_in(w),v),x)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v_x,t_a),w,u),u)*.
% 299.79/300.44 89345[7:SpR:78590.1,339.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))**.
% 299.79/300.44 89327[7:SpR:78590.1,176.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 89692[7:Res:89344.1,516.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.79/300.44 89962[0:Rew:54319.0,89822.0] || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))))**.
% 299.79/300.44 90225[4:SpR:78660.1,338.0] || equal(hAPP(u,v_x),v_x) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u))**.
% 299.79/300.44 90145[4:SpR:78660.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(hAPP(v,v_x),v_x) hBOOL(hAPP(hAPP(c_in(w),v),x)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v_x,t_a),w,u),u)*.
% 299.79/300.44 90135[4:SpR:78660.1,339.0] || equal(hAPP(u,v_x),v_x) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))**.
% 299.79/300.44 90117[4:SpR:78660.1,176.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 90670[0:SpL:486.1,26231.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(x,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,z,u,tc_fun(y,tc_bool))),y)* -> c_Finite__Set_Ofinite(hAPP(z,v),y)*.
% 299.79/300.44 90836[4:Res:90134.1,516.0] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),v_x)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.79/300.44 91038[4:Rew:104.0,90949.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),v_x) hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_bool))* -> .
% 299.79/300.44 91344[0:Rew:91288.1,91078.1] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,x),w)))*.
% 299.79/300.44 91345[0:Rew:91288.1,91074.1] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 91811[4:SpL:8498.1,78747.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname),v_x) -> hBOOL(hAPP(c_Set_Oinsert(u,v),v_x)).
% 299.79/300.44 91880[4:Rew:584.0,91860.1] || equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_COMBS(u,v,z,x1,x2),tc_Com_Opname)),v_x)** -> hBOOL(hAPP(hAPP(u,v_x),hAPP(v,v_x))).
% 299.79/300.44 91965[0:SpR:79073.0,338.0] || -> equal(hAPP(c_Set_Oinsert(v_Procs,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))**.
% 299.79/300.44 91938[0:SpR:79073.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v_Procs,y),v,u),u)*.
% 299.79/300.44 91929[0:SpR:79073.0,339.0] || -> equal(hAPP(c_Set_Oinsert(v_Procs,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w))**.
% 299.79/300.44 91913[0:SpR:79073.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_Procs,w),u,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.44 92121[7:SpR:79101.0,338.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_in(w),v_x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_in(w),v_x)))**.
% 299.79/300.44 92091[7:SpR:79101.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_in(w),v_x)),x)) -> c_lessequals(hAPP(c_in(w),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v_x,y),v,u),u)*.
% 299.79/300.44 92081[7:SpR:79101.0,339.0] || -> equal(hAPP(c_Set_Oinsert(v_x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_in(v),v_x)),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_in(v),v_x)),w))**.
% 299.79/300.44 92062[7:SpR:79101.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(v),v_x)),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,w),u,x),hAPP(c_Set_Oinsert(hAPP(c_in(v),v_x),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.44 92536[7:Res:62367.1,92132.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_in(u),v_x),v_x),v,tc_bool),hAPP(hAPP(c_in(u),v_x),v_x)) -> hBOOL(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_in(u),v_x),v_x),v,tc_bool))*.
% 299.79/300.44 92950[0:SpR:584.0,5876.0] || -> c_lessequals(hAPP(hAPP(u,v),hAPP(w,v)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_COMBS(u,w,y,z,x1),x2,x3,x4),v),tc_fun(x,tc_bool))*.
% 299.79/300.44 92912[0:SpR:584.0,5876.0] || -> c_lessequals(hAPP(c_COMBS(u,v,w,x,y),z),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(u,z),x2,x3,x4),hAPP(v,z)),tc_fun(x1,tc_bool))*.
% 299.79/300.44 92860[0:SpR:540.1,5876.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,z,x1),v),tc_fun(x,tc_bool))*.
% 299.79/300.44 92859[0:SpR:539.1,5876.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,z,x1),v),tc_fun(x,tc_bool))*.
% 299.79/300.44 93207[0:SpR:5878.1,474.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(w,c_Orderings_Obot__class_Obot(u))),hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1,v),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.79/300.44 93191[0:SpR:5878.1,415.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Fun_Ofun__upd(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_Orderings_Obot__class_Obot(u),hAPP(v,c_Orderings_Obot__class_Obot(u)),z,x1),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y))**.
% 299.79/300.44 93353[4:SpR:180.2,85556.1] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> c_lessequals(v_x,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(v_x,u),v),u,u),tc_bool)*.
% 299.79/300.44 93479[0:SpR:181.1,86147.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x))*.
% 299.79/300.44 93630[0:SpR:181.1,86148.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x,t_a)*.
% 299.79/300.44 93774[0:SpR:181.1,86342.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.79/300.44 94190[0:Res:14364.3,12537.0] class_Orderings_Olinorder(tc_bool) || hBOOL(hAPP(u,c_HOL_Ominus__class_Ominus(c_Finite__Set_Olinorder__class_OMin(u,tc_bool),v,tc_bool)))* c_Finite__Set_Ofinite(u,tc_bool) -> equal(c_HOL_Ominus__class_Ominus(c_Finite__Set_Olinorder__class_OMin(u,tc_bool),v,tc_bool),c_Finite__Set_Olinorder__class_OMin(u,tc_bool)).
% 299.79/300.44 94168[0:Res:14364.3,405.1] class_Orderings_Olinorder(u) class_Orderings_Oorder(u) || hBOOL(hAPP(v,w)) c_Finite__Set_Ofinite(v,u) c_lessequals(w,c_Finite__Set_Olinorder__class_OMin(v,u),u)* -> equal(w,c_Finite__Set_Olinorder__class_OMin(v,u)).
% 299.79/300.44 94164[0:Res:14364.3,4340.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(v,w)) c_Finite__Set_Ofinite(v,u) c_lessequals(w,c_Finite__Set_Olinorder__class_OMin(v,u),u)* -> equal(w,c_Finite__Set_Olinorder__class_OMin(v,u)).
% 299.79/300.44 94151[0:Res:14364.3,437.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_Finite__Set_Ofinite(w,u)* -> c_Finite__Set_Ofinite(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),u)*.
% 299.79/300.44 94301[0:Res:14491.3,405.1] class_Orderings_Olinorder(u) class_Orderings_Oorder(u) || hBOOL(hAPP(v,w)) c_Finite__Set_Ofinite(v,u) c_lessequals(c_Finite__Set_Olinorder__class_OMax(v,u),w,u)* -> equal(c_Finite__Set_Olinorder__class_OMax(v,u),w).
% 299.79/300.44 94297[0:Res:14491.3,4340.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(v,w)) c_Finite__Set_Ofinite(v,u) c_lessequals(c_Finite__Set_Olinorder__class_OMax(v,u),w,u)* -> equal(c_Finite__Set_Olinorder__class_OMax(v,u),w).
% 299.79/300.44 94281[0:Res:14491.3,44833.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),v_x))*.
% 299.79/300.44 94279[4:Res:14491.3,42356.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),v_x))*.
% 299.79/300.44 94274[4:Res:14491.3,42582.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))) c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),w))*.
% 299.79/300.44 94273[4:Res:14491.3,43176.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))) c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),w,t_a)*.
% 299.79/300.44 94266[0:Res:14491.3,437.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_Finite__Set_Ofinite(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),u)* -> c_Finite__Set_Ofinite(w,u)*.
% 299.79/300.44 94265[0:Res:14491.3,682.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_in(tc_Com_Opname),v_x))) c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),v_Procs))*.
% 299.79/300.44 94260[0:Res:14491.3,17941.0] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) || hBOOL(hAPP(u,v_Procs)) c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) equal(c_Finite__Set_Olinorder__class_OMax(u,tc_fun(tc_Com_Opname,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))** -> .
% 299.79/300.44 633[0:Res:589.0,481.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)))*.
% 299.79/300.44 634[0:Res:589.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)))*.
% 299.79/300.44 5011[0:Res:989.1,405.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Oorder(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v,w,x),tc_Com_Opname,u),v,u)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v,w,x),tc_Com_Opname,u),v).
% 299.79/300.44 5027[0:SSi:4985.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,tc_fun(x,tc_bool)),u,tc_fun(x,tc_bool))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,tc_fun(x,tc_bool)),u).
% 299.79/300.44 5946[0:SpR:369.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),hAPP(c_Set_Oinsert(u,v),x1)),hAPP(hAPP(c_Set_Oinsert(u,v),x1),hAPP(w,hAPP(c_Set_Oinsert(u,v),x1))))*.
% 299.79/300.44 5945[0:SpR:2089.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oinsert(v_x,tc_Com_Opname),u,v,w,x),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),hAPP(hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs),hAPP(u,hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs))))*.
% 299.79/300.44 5938[0:SpR:336.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y,z),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))**.
% 299.79/300.44 5909[0:SpR:369.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oinsert(v,w),x,y,z),hAPP(c_Set_Oinsert(v,w),x1)),hAPP(hAPP(u,hAPP(c_Set_Oinsert(v,w),x1)),hAPP(c_Set_Oinsert(v,w),x1)))*.
% 299.79/300.44 5908[0:SpR:2089.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oinsert(v_x,tc_Com_Opname),v,w,x),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),hAPP(hAPP(u,hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)))*.
% 299.79/300.44 6822[0:SpR:328.1,687.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname),w,tc_fun(v,tc_bool))* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)) -> hBOOL(w).
% 299.79/300.44 6821[0:SpR:328.1,686.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname),w,tc_fun(v,tc_bool))* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)) -> hBOOL(w).
% 299.79/300.44 7666[0:Res:294.2,48.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),w,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u).
% 299.79/300.44 7665[0:Res:294.2,44.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),w,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u).
% 299.79/300.44 7680[0:SSi:7659.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u))**.
% 299.79/300.44 7730[0:Res:293.2,48.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),v,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u).
% 299.79/300.44 7729[0:Res:293.2,44.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),v,u)* -> c_lessequals(c_HOL_Ozero__class_Ozero(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u).
% 299.79/300.44 7743[0:SSi:7723.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v))**.
% 299.79/300.44 7811[0:Res:49.2,296.1] class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),u)*.
% 299.79/300.44 7810[0:Res:45.2,296.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),u)*.
% 299.79/300.44 8056[0:Res:49.2,295.1] class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),u)*.
% 299.79/300.44 8055[0:Res:45.2,295.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_HOL_Ozero__class_Ozero(u),u) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),u)*.
% 299.79/300.44 8605[0:SpR:8498.1,687.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) hBOOL(hAPP(c_Set_Oinsert(v,w),v_x)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname))*.
% 299.79/300.44 8604[0:SpR:8498.1,686.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,c_Set_Oinsert(v,w),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) hBOOL(hAPP(c_Set_Oinsert(v,w),v_x)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,u,c_Set_Oinsert(v,w),tc_Com_Opname))*.
% 299.79/300.44 9475[0:SpR:328.1,9268.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(u,tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u))**.
% 299.79/300.44 9474[0:SpR:538.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)).
% 299.79/300.44 9544[0:Res:4790.2,251.1] class_Orderings_Obot(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(u,v)),tc_fun(u,v)),x),v)*.
% 299.79/300.44 9521[0:Res:4703.2,251.1] class_Orderings_Otop(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,v)),tc_fun(u,v)),w),hAPP(x,w),v)*.
% 299.79/300.44 10498[0:Res:149.1,454.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) c_Hoare__Mirabelle_Ohoare__valids(c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),u,t_a)*.
% 299.79/300.44 10497[0:Res:1157.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oimage(c_COMBK(u,v,w),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),x,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oimage(c_COMBK(u,v,w),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),x),u,t_a)*.
% 299.79/300.44 11568[0:SpR:8415.2,229.0] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v_x),c_Com_Ocom_OSKIP),c_Set_Oinsert(v_x,tc_Com_Opname)) -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.79/300.44 11565[0:SpR:8415.2,229.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(u)) -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,c_Com_Ocom_OSKIP),v_x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.79/300.44 11756[0:SpL:130.1,3507.1] class_HOL_Ominus(u) || equal(c_Set_Oinsert(v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(t_a,u)))* equal(c_HOL_Ominus__class_Ominus(hAPP(x,v_x),hAPP(y,v_x),u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.79/300.44 11755[0:SpL:130.1,3499.1] class_HOL_Ominus(u) || equal(c_in(v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u))) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.79/300.44 11752[0:SpL:130.1,3484.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Com_Ocom_OBODY) equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),hAPP(c_Com_Ocom_OBODY,x))* -> equal(v_x,x).
% 299.79/300.44 11738[0:SpR:5.2,130.1] class_Int_Onumber__ring(tc_fun(t_a,u)) class_Ring__and__Field_Oidom(tc_fun(t_a,u)) class_HOL_Ominus(u) || -> equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(v,v_x),u),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x))**.
% 299.79/300.44 11730[0:SpR:130.1,415.0] class_HOL_Ominus(u) || -> equal(c_Fun_Ofun__upd(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_x,c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),x,y),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)))**.
% 299.79/300.44 11729[0:SpR:130.1,3346.1] class_HOL_Ominus(u) || equal(c_Set_Oinsert(v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(t_a,u))) -> hBOOL(hAPP(hAPP(c_in(w),v),c_HOL_Ominus__class_Ominus(hAPP(x,v_x),hAPP(y,v_x),u)))*.
% 299.79/300.44 11728[0:SpR:130.1,3317.1] class_HOL_Ominus(u) || equal(c_in(v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u))) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u),hAPP(c_Set_Oinsert(v_x,v),y)))*.
% 299.79/300.44 11727[0:SpR:130.1,3305.1] class_HOL_Ominus(u) || equal(v,c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,y),v_Procs),c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u)))*.
% 299.79/300.44 11723[0:SpR:130.1,2771.1] class_HOL_Ominus(u) || equal(v,c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u))) -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))*.
% 299.79/300.44 11720[0:SpR:130.1,8376.2] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_in(tc_Com_Opname)) equal(x,v_Procs) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),x))*.
% 299.79/300.44 11719[0:SpR:130.1,8415.2] class_HOL_Ominus(u) || equal(v_Procs,v_x) equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),v_x)**.
% 299.79/300.44 11718[0:SpR:130.1,3291.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)),v_Procs))*.
% 299.79/300.44 11717[0:SpR:130.1,3285.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)))*.
% 299.79/300.44 11714[0:SpR:130.1,3279.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),v_Procs),v_x))*.
% 299.79/300.44 12017[0:SpL:8415.2,325.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname))** c_lessequals(v_x,w,tc_fun(u,tc_bool))* -> c_lessequals(v,w,tc_fun(u,tc_bool))*.
% 299.79/300.44 12014[0:SpL:8415.2,325.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(hAPP(v_x,v),w,tc_fun(u,tc_bool))* -> c_lessequals(v_x,w,tc_fun(u,tc_bool)).
% 299.79/300.44 12365[0:SpL:8415.2,324.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(hAPP(v_x,v),w,tc_fun(u,tc_bool))* -> c_lessequals(v,w,tc_fun(u,tc_bool)).
% 299.79/300.44 12630[0:SpL:8415.2,519.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(hAPP(v_x,v),w))* -> hBOOL(hAPP(v_x,w)) hBOOL(hAPP(v,w)).
% 299.79/300.44 12963[0:SpR:8415.2,96.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Fun_Oinj__on(u,v_x,v,w) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(v_x,u,v,w),v_x,w,v)*.
% 299.79/300.44 13163[0:Res:108.1,430.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))*.
% 299.79/300.44 13185[0:SSi:13172.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> c_lessequals(x,c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.44 14185[0:SpR:9.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_Fun_Ocomp(w,x,y,z,x1),u,x2),hAPP(c_Set_Oinsert(hAPP(w,hAPP(x,v)),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))))))*.
% 299.79/300.44 14184[0:SpR:11499.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Ovimage(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),u,y),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.44 14183[0:SpR:10090.1,176.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Ovimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 14178[0:SpR:105.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Ovimage(c_Set_Ovimage(w,x,v),u,y),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.44 14177[0:SpR:1196.1,176.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 14174[0:SpR:38.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Ovimage(c_Set_Ovimage(w,x,v),u,y),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.44 14173[0:SpR:321.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Ovimage(c_Set_Oimage(w,v,x),u,y),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.44 14171[0:SpR:1195.1,176.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 14169[0:SpR:11473.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u,y),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.44 14156[0:SpR:87.1,176.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ouminus__class_Ouminus(w,u)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.44 14155[0:SpR:88.1,176.0] class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),v,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.44 14147[0:SpR:2098.1,176.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,x),hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.44 14137[0:SpR:3586.1,176.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Ovimage(c_Set_Oinsert(v,u),w,x),hAPP(c_Set_Oinsert(v_x,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.44 14124[0:SpR:653.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,v),v,tc_Com_Opname),u,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 14120[0:SpR:9493.1,176.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 14118[0:SpR:8498.1,176.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> hBOOL(hAPP(hAPP(c_in(w),u),hAPP(c_Set_Ovimage(c_Set_Oinsert(x,v),w,y),hAPP(c_Set_Oinsert(u,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.44 14322[0:SpR:11695.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),v)),hAPP(c_Set_Ovimage(hAPP(c_Set_Oinsert(w,x),c_Option_Othe(v)),u,y),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.44 14362[0:Res:149.1,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u) -> hBOOL(hAPP(hAPP(c_in(u),w),v)) c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u),w,u)*.
% 299.79/300.44 14345[0:SpL:584.0,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(c_COMBS(c_in(u),v,w,x,y),z))* c_Finite__Set_Ofinite(hAPP(v,z),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(v,z),u),z,u)*.
% 299.79/300.44 14427[0:SpR:12944.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(hAPP(c_Set_Oinsert(w,x),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),y,z)),u,x1),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.79/300.44 14489[0:Res:149.1,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u) -> hBOOL(hAPP(hAPP(c_in(u),w),v)) c_lessequals(w,c_Finite__Set_Olinorder__class_OMax(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u),u)*.
% 299.79/300.44 14472[0:SpL:584.0,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(c_COMBS(c_in(u),v,w,x,y),z))* c_Finite__Set_Ofinite(hAPP(v,z),u) -> c_lessequals(z,c_Finite__Set_Olinorder__class_OMax(hAPP(v,z),u),u)*.
% 299.79/300.44 14537[0:SSi:14522.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(v),w,tc_fun(x,tc_bool)),c_Option_Ooption_OSome(u,v)),tc_bool)* -> equal(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(v),w,tc_fun(x,tc_bool)),c_Option_Ooption_OSome(u,v)),u).
% 299.79/300.44 14788[0:SpL:128.0,76.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),x),v) c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),v)* -> c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v).
% 299.79/300.44 14728[0:SpR:128.0,149.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y))) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool)))))*.
% 299.79/300.44 15129[0:SpL:181.1,3698.2] || equal(u,c_Set_Ovimage(c_COMBK(v,w,x),x,w))* equal(c_Com_Ocom_OBODY,u) equal(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Com_Ocom_OSKIP) -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)).
% 299.79/300.44 15102[0:SpR:181.1,3339.1] || equal(u,c_Set_Ovimage(c_COMBK(v,w,x),x,w))* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)) equal(c_Fun_Ofun__upd(u,v_x,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y,z),u)**.
% 299.79/300.44 15098[0:SpR:181.1,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,x),x,u),tc_Com_Opname,w),v_Procs)))*.
% 299.79/300.44 15082[0:SpR:181.1,651.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 15184[0:SSi:15168.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),z),tc_bool)* -> equal(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),z),u).
% 299.79/300.44 15229[0:Res:446.1,430.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(hAPP(c_Set_Oinsert(x,w),v),y,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(x,w),u),y,tc_fun(w,tc_bool))*.
% 299.79/300.44 15241[0:SSi:15237.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,hAPP(c_Set_Oinsert(y,w),u),tc_fun(w,tc_bool))* -> c_lessequals(x,hAPP(c_Set_Oinsert(y,w),v),tc_fun(w,tc_bool))*.
% 299.79/300.44 15270[0:SpR:10063.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oinsert(v_x,t_a),v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))**.
% 299.79/300.44 15655[0:Res:687.1,278.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,hAPP(c_in(u),v),tc_Com_Opname),y,w,u)))*.
% 299.79/300.44 15654[0:Res:686.1,278.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,hAPP(c_in(u),v),tc_Com_Opname),y,w,u)))*.
% 299.79/300.44 15797[0:SpR:181.1,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(c_COMBK(u,v,w),w,v),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_bool)).
% 299.79/300.44 15883[0:Res:687.1,277.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,v_Procs,hAPP(c_in(u),v),tc_Com_Opname),w,u)))*.
% 299.79/300.44 15882[0:Res:686.1,277.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,y,hAPP(c_in(u),v),tc_Com_Opname),w,u)))*.
% 299.79/300.44 15937[2:SpR:181.1,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(c_COMBK(u,v,w),w,v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) c_Com_OWT(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_bool)).
% 299.79/300.44 16135[0:SpR:130.1,15262.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_in(t_a)) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.79/300.44 16581[0:SpR:12944.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Set_Oinsert(y,z),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x1,x2)),v,u),u)*.
% 299.79/300.44 16577[0:SpR:9.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(y,hAPP(z,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Fun_Ocomp(y,z,x1,x2,x3),v,u),u)*.
% 299.79/300.44 16575[0:SpR:11499.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z)),v,u),u)*.
% 299.79/300.44 16574[0:SpR:10090.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v) hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Otop__class_Otop(tc_bool)),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(v,v_x),w,u),u)*.
% 299.79/300.44 16569[0:SpR:105.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Ovimage(z,y,w),v,u),u)*.
% 299.79/300.44 16568[0:SpR:1196.1,361.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Otop__class_Otop(u)),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,v),v)*.
% 299.79/300.44 16565[0:SpR:38.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Ovimage(z,y,w),v,u),u)*.
% 299.79/300.44 16564[0:SpR:321.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oimage(z,w,y),v,u),u)*.
% 299.79/300.44 16562[0:SpR:1195.1,361.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Obot__class_Obot(u)),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,v),v)*.
% 299.79/300.44 16560[0:SpR:11695.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),w)),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Set_Oinsert(y,z),c_Option_Othe(w)),v,u),u)*.
% 299.79/300.44 16559[0:SpR:11473.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v,u),u)*.
% 299.79/300.44 16544[0:SpR:87.1,361.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),c_HOL_Ouminus__class_Ouminus(x,u)),y)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,v),v)*.
% 299.79/300.44 16543[0:SpR:88.1,361.2] class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),x),y)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(x,u)),w,v),v)*.
% 299.79/300.44 16534[0:SpR:2098.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_Hoare__Mirabelle_Ohoare__valids(y,w,t_a) c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(y,w),tc_Hoare__Mirabelle_Otriple(t_a)),v,u),u)*.
% 299.79/300.44 16523[0:SpR:3586.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(hAPP(c_in(v),w),v_Procs) hBOOL(hAPP(hAPP(c_in(x),v_x),y)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(w,v),x,u),u)*.
% 299.79/300.44 16509[0:SpR:653.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,x),x,tc_Com_Opname),v,u),u)*.
% 299.79/300.44 16505[0:SpR:9493.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(hAPP(v,v_x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(hAPP(c_in(w),v),x)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v_x,t_a),w,u),u)*.
% 299.79/300.44 16503[0:SpR:8498.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) hBOOL(hAPP(hAPP(c_in(x),v),y)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(z,w),x,u),u)*.
% 299.79/300.44 16937[0:SpR:600.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(y,v,tc_fun(u,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v),tc_bool)*.
% 299.79/300.44 16924[0:SpR:600.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y,z,x1),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))))*.
% 299.79/300.44 17105[0:Res:511.1,278.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w),z,x,u)))*.
% 299.79/300.44 17104[0:Res:511.1,277.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),w),x,u)))*.
% 299.79/300.44 17141[0:SpR:17045.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),z,tc_fun(x1,tc_bool)),v,u),u)*.
% 299.79/300.44 17139[0:SpR:17045.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x,tc_fun(y,tc_bool)),u,z),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.44 17262[0:Res:510.1,278.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y),z,x,u)))*.
% 299.79/300.44 17261[0:Res:510.1,277.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z),x,u)))*.
% 299.79/300.44 17273[0:SpL:130.1,13272.0] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.79/300.44 17368[0:Res:172.2,278.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(w,c_Finite__Set_Olinorder__class_OMax(v,u))) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,x,w,u)))*.
% 299.79/300.44 17367[0:Res:172.2,277.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(w,c_Finite__Set_Olinorder__class_OMax(v,u))) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v,w,u)))*.
% 299.79/300.44 17424[0:SpL:130.1,16327.1] class_HOL_Ominus(u) || equal(v,c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u)))* equal(c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u),c_Orderings_Obot__class_Obot(tc_bool))** equal(v,v_Procs) -> .
% 299.79/300.44 17486[0:Res:171.2,278.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(w,c_Finite__Set_Olinorder__class_OMin(v,u))) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,x,w,u)))*.
% 299.79/300.44 17485[0:Res:171.2,277.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(w,c_Finite__Set_Olinorder__class_OMin(v,u))) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v,w,u)))*.
% 299.79/300.44 17729[0:Res:176.0,255.0] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(u,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),y,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),x),y)).
% 299.79/300.44 17888[0:SpL:188.1,16217.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_Procs)** -> .
% 299.79/300.44 17887[0:SpL:188.1,3929.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.79/300.44 17878[0:SpR:188.1,9567.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,tc_fun(z,tc_bool)),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),tc_bool)*.
% 299.79/300.44 17858[0:SpR:188.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),v_x)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Ovimage(c_COMBK(w,v,x),x,v),tc_Com_Opname,u),u)*.
% 299.79/300.44 18204[0:SpR:9987.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 18202[0:SpR:2095.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(x,v),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 18199[0:SpR:303.1,362.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 18195[0:SpR:330.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 18190[0:SpR:14216.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.44 18188[0:SpR:11176.1,362.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 18186[0:SpR:11177.1,362.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 18159[0:SpR:331.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 18158[0:SpR:302.1,362.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 18145[0:SpR:15476.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,tc_bool)),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 18137[0:SpR:2093.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(tc_Com_Opname),v_x)),v)) -> c_lessequals(hAPP(c_in(tc_Com_Opname),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_Procs,w),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 18135[0:SpR:3744.1,362.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,u),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 18427[0:Res:545.1,278.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,hAPP(y,v)))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(y,u,z),w),x1,x,z)))*.
% 299.79/300.44 18426[0:Res:545.1,277.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,hAPP(y,v)))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,hAPP(c_Set_Oimage(y,u,x1),w),x,x1)))*.
% 299.79/300.44 18424[0:Res:545.1,501.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(x),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(x,hAPP(c_Set_Oimage(y,u,tc_Hoare__Mirabelle_Otriple(t_a)),w)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(y,v),t_a)*.
% 299.79/300.44 18404[0:SpR:9987.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,x),w)))*.
% 299.79/300.44 18402[0:SpR:2095.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(y,v),u,x),w)))*.
% 299.79/300.44 18399[0:SpR:303.1,545.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,x),w)))*.
% 299.79/300.44 18395[0:SpR:330.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),u,x),w)))*.
% 299.79/300.44 18390[0:SpR:14216.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(y,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),u,x),w)))*.
% 299.79/300.44 18388[0:SpR:11176.1,545.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),w),x))* -> hBOOL(hAPP(hAPP(c_in(y),u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,y),x)))*.
% 299.79/300.44 18386[0:SpR:11177.1,545.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> hBOOL(hAPP(hAPP(c_in(x),u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v,x),w)))*.
% 299.79/300.44 18359[0:SpR:331.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),u,x),w)))*.
% 299.79/300.44 18358[0:SpR:302.1,545.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y),x)))*.
% 299.79/300.44 18345[0:SpR:15476.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(hAPP(c_in(w),c_HOL_Ouminus__class_Ouminus(hAPP(x,v_x),tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,tc_bool)),u,w),v)))*.
% 299.79/300.44 18337[0:SpR:2093.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(tc_Com_Opname),v_x)),v)) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,x),u,w),v)))*.
% 299.79/300.44 18335[0:SpR:3744.1,545.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,x),w)))*.
% 299.79/300.44 18595[0:Res:153.1,278.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* hBOOL(hAPP(y,w))* -> hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Ovimage(v,z,u),x),x1,y,z)))*.
% 299.79/300.44 18594[0:Res:153.1,277.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* hBOOL(hAPP(y,w))* -> hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,hAPP(c_Set_Ovimage(v,x1,u),x),y,x1)))*.
% 299.79/300.44 18592[0:Res:153.1,501.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(y),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(y,hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),u),x)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(y,w,t_a)*.
% 299.79/300.44 18656[0:SpR:130.1,9568.0] class_HOL_Ominus(u) || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u))),y),v_x),tc_bool)*.
% 299.79/300.44 18967[0:SpR:130.1,9569.0] class_HOL_Ominus(u) || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u))),v_x),tc_bool)*.
% 299.79/300.44 19112[0:SpR:196.1,9567.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Ovimage(u,v,w),x,tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(u,v,w),z)),z,tc_bool)*.
% 299.79/300.44 19097[0:SpR:196.1,5875.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(x,y),c_Set_Ovimage(u,v,w),z,x1,x2),hAPP(c_Set_Oimage(u,v,w),x)))*.
% 299.79/300.44 19096[0:SpR:196.1,415.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Fun_Ofun__upd(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),x),x,y,z),c_Set_Ovimage(u,v,w))**.
% 299.79/300.44 19345[0:SSi:19330.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_bool)* c_lessequals(w,v,tc_bool)* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),v)*.
% 299.79/300.44 19347[0:SSi:19313.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,v,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(v,w) -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),w)*.
% 299.79/300.44 19421[0:SSi:19395.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_bool),tc_bool)* c_lessequals(x,c_HOL_Ominus__class_Ominus(v,w,tc_bool),tc_bool)* -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x),y,tc_bool),v,tc_bool)*.
% 299.79/300.44 19660[0:Res:9246.0,496.0] || -> hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)))),c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))))* c_Hoare__Mirabelle_Otriple__valid(w,v,t_a)*.
% 299.79/300.44 19651[0:Res:648.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oimage(v,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))),hAPP(c_Set_Oimage(v,tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs)))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(v,v_x),t_a).
% 299.79/300.44 19687[4:MRR:19645.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,v_x)),v_x))* c_Hoare__Mirabelle_Otriple__valid(v,u,t_a)*.
% 299.79/300.44 19699[0:SpL:297.2,19641.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u)* hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,t_a).
% 299.79/300.44 19867[0:SpL:104.0,3506.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(w,x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))* -> .
% 299.79/300.44 19822[0:SpR:104.0,510.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))*.
% 299.79/300.44 19789[0:SpR:104.0,9566.0] || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)))),v),tc_bool)*.
% 299.79/300.44 20015[0:SpL:64.0,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),x)) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),x))* equal(u,x).
% 299.79/300.44 19969[0:SpR:64.0,9566.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(c_Set_Oinsert(x,y),c_Set_Oinsert(u,v)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),tc_bool)*.
% 299.79/300.44 19967[0:SpR:64.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(u,v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),x,y),c_Set_Oinsert(u,v))**.
% 299.79/300.44 20074[0:SpL:353.0,215.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(w)),y)),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w).
% 299.79/300.44 20138[0:Res:19747.0,402.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool))* -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v).
% 299.79/300.44 20204[0:Res:20152.0,402.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(v,c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),u).
% 299.79/300.44 20258[0:Res:20186.0,402.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(w,u,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(w,u,tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))).
% 299.79/300.44 20284[0:SpR:438.1,7253.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),z))*.
% 299.79/300.44 20276[0:SpR:438.1,9566.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(hAPP(c_Set_Oinsert(y,z),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w)),hAPP(u,x)),tc_bool)*.
% 299.79/300.44 20409[0:Rew:20358.1,20329.2] || c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y)* -> hBOOL(hAPP(hAPP(c_in(v),u),z))* equal(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),z).
% 299.79/300.44 20426[0:SpR:99.1,7253.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),z))*.
% 299.79/300.44 20418[0:SpR:99.1,9566.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(hAPP(c_Set_Oinsert(y,z),c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w)),hAPP(u,x)),tc_bool)*.
% 299.79/300.44 20731[0:Res:313.1,431.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,hAPP(c_Set_Oimage(y,w,z),v),z,x1)* -> c_Fun_Oinj__on(x,hAPP(c_Set_Oimage(y,w,z),u),z,x1)*.
% 299.79/300.44 20777[0:Res:129.1,431.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,hAPP(c_Set_Ovimage(y,z,w),v),z,x1)* -> c_Fun_Oinj__on(x,hAPP(c_Set_Ovimage(y,z,w),u),z,x1)*.
% 299.79/300.44 21020[0:SpL:317.0,371.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),z))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),y),z)) equal(hAPP(u,x),z).
% 299.79/300.44 20958[0:SpR:10463.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w),y)))*.
% 299.79/300.44 20957[0:SpR:9911.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w),y)))*.
% 299.79/300.44 20886[0:SpR:317.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(y,w),z))),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(v,y),x),x1,u),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.79/300.44 20872[0:SpR:317.0,9566.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(hAPP(c_Set_Oinsert(z,x1),c_Set_Oinsert(hAPP(u,x),w)),hAPP(c_Set_Oimage(u,v,w),y)),tc_bool)*.
% 299.79/300.44 20835[0:SpR:317.0,9566.0] || -> c_lessequals(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),y)),hAPP(hAPP(c_Set_Oinsert(z,x1),c_Set_Oimage(u,x,w)),hAPP(c_Set_Oinsert(v,x),y)),tc_bool)*.
% 299.79/300.44 21051[0:SpR:130.1,20881.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x,y),hAPP(c_Set_Oinsert(v_x,x),z)),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)))*.
% 299.79/300.44 21172[0:SpR:181.1,21130.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_Procs)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,w),w,u),x,y),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.79/300.44 21233[0:SpR:181.1,21141.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,w),w,u),t_a,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.79/300.44 21654[0:SpL:21267.0,11894.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> .
% 299.79/300.44 21639[0:SpL:21267.0,4439.0] || equal(hAPP(c_Set_Ovimage(u,v,w),v_x),v_Procs) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x),tc_Com_Opname,x),hAPP(u,v_x)))*.
% 299.79/300.44 21624[0:SpL:21267.0,363.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),v_x),w,tc_fun(v,tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,x),w,tc_fun(v,tc_bool))*.
% 299.79/300.44 21471[0:SpR:21267.0,9935.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),tc_Com_Opname,v),tc_bool)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.79/300.44 21422[0:SpR:21267.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,hAPP(w,v_x),tc_Com_Opname,x)),y))* -> c_lessequals(hAPP(w,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,v,u),u)*.
% 299.79/300.44 21377[0:SpR:21267.0,364.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),v_x),tc_Com_Opname,x),tc_fun(w,tc_bool))* -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),v_x),tc_fun(w,tc_bool)).
% 299.79/300.44 21375[0:SpR:21267.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)),hAPP(c_Set_Ovimage(v,u,x),hAPP(c_Set_Oinsert(hAPP(v,v_x),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.44 21368[0:SpR:21267.0,212.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),u),hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x),tc_Com_Opname,x)))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x)).
% 299.79/300.44 21759[0:SpR:130.1,21143.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),t_a,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)))*.
% 299.79/300.44 21828[0:SpR:130.1,21131.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_Com_Opname,x),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)))*.
% 299.79/300.44 22282[0:SpL:21893.0,11894.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> .
% 299.79/300.44 22267[0:SpL:21893.0,4439.0] || equal(hAPP(c_Set_Ovimage(u,v,w),v_x),v_Procs) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),v_x),c_Set_Ovimage(u,v,w),tc_Com_Opname,x),hAPP(u,v_x)))*.
% 299.79/300.44 22252[0:SpL:21893.0,363.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),v_x),w,tc_fun(v,tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,x),w,tc_fun(v,tc_bool))*.
% 299.79/300.44 22097[0:SpR:21893.0,9935.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),tc_bool)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.79/300.44 22048[0:SpR:21893.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(w,v_x),w,tc_Com_Opname,x)),y))* -> c_lessequals(hAPP(w,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,v,u),u)*.
% 299.79/300.44 22003[0:SpR:21893.0,364.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),v_x),c_Set_Oinsert(v,w),tc_Com_Opname,x),tc_fun(w,tc_bool))* -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),v_x),tc_fun(w,tc_bool)).
% 299.79/300.44 22001[0:SpR:21893.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)),hAPP(c_Set_Ovimage(v,u,x),hAPP(c_Set_Oinsert(hAPP(v,v_x),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.44 21994[0:SpR:21893.0,212.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x),hAPP(c_Set_Oinsert(v,w),u),tc_Com_Opname,x)))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x)).
% 299.79/300.44 22407[0:SpR:97.1,474.0] || c_Fun_Oinj__on(u,v,w,x) -> hBOOL(hAPP(hAPP(c_in(y),v),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),z,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.44 22397[0:SpR:97.1,9566.0] || c_Fun_Oinj__on(u,v,w,x) -> c_lessequals(v,hAPP(hAPP(c_Set_Oinsert(y,z),c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w)),hAPP(c_Set_Oimage(u,w,x),v)),tc_bool)*.
% 299.79/300.44 22460[0:SpR:130.1,21126.1] class_HOL_Ominus(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u)),tc_Com_Opname,y),v),c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u)))*.
% 299.79/300.44 22665[0:SpL:158.0,319.0] || equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))** -> equal(hAPP(c_Set_Oimage(v,y,w),z),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.44 22657[0:SpL:158.0,447.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),w)* c_Fun_Oinj__on(c_Fun_Ocomp(u,x,v,w,y),z,y,w)* -> c_Finite__Set_Ofinite(z,y).
% 299.79/300.44 22646[0:SpL:158.0,3506.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(z,x1),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))* -> .
% 299.79/300.44 22615[0:SpR:158.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1)),hAPP(c_Set_Oimage(c_Set_Oimage(v,x,y),x2,u),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)))))*.
% 299.79/300.44 22605[0:SpR:158.0,9566.0] || -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(hAPP(c_Set_Oinsert(x1,x2),c_Set_Oimage(u,w,x)),hAPP(c_Set_Oimage(v,y,w),z)),tc_bool)*.
% 299.79/300.44 22567[0:SpR:158.0,98.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),z,y,x)* -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),z)),x),c_Finite__Set_Ocard(z,y))**.
% 299.79/300.44 22563[0:SpR:158.0,9566.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(hAPP(c_Set_Oinsert(x1,x2),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w)),z),tc_bool)*.
% 299.79/300.44 22784[0:SpR:3294.1,584.0] || equal(c_in(t_a),u) -> equal(hAPP(c_COMBS(hAPP(u,v_x),v,w,x,y),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))))**.
% 299.79/300.44 22783[0:SpR:3294.1,584.0] || equal(c_in(t_a),u) -> equal(hAPP(c_COMBS(v,hAPP(u,v_x),w,x,y),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),hAPP(hAPP(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))**.
% 299.79/300.44 23024[0:SpL:131.0,3506.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(z,x1),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)))* -> .
% 299.79/300.44 22992[0:SpR:131.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1)),hAPP(c_Set_Oimage(c_Set_Ovimage(w,z,x),x2,u),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)))))*.
% 299.79/300.44 22985[0:SpR:131.0,9566.0] || -> c_lessequals(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(hAPP(c_Set_Oinsert(x1,x2),c_Set_Ovimage(v,y,w)),hAPP(c_Set_Ovimage(u,w,x),z)),tc_bool)*.
% 299.79/300.44 22950[0:SpR:131.0,9566.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),z)),hAPP(hAPP(c_Set_Oinsert(x1,x2),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y)),z),tc_bool)*.
% 299.79/300.44 23050[0:Rew:9.0,22910.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),hAPP(c_Set_Ovimage(y,x,z),hAPP(c_Set_Oinsert(hAPP(y,hAPP(w,v)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))))))*.
% 299.79/300.44 23400[0:SpL:460.1,16286.0] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_Procs) -> .
% 299.79/300.44 23367[0:SpR:460.1,3229.1] || class_Lattices_Olattice(t_b) equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)) -> equal(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))*.
% 299.79/300.44 23347[0:SpR:460.1,3283.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),v_Procs))*.
% 299.79/300.44 23341[0:SpR:460.1,1158.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,u),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))))*.
% 299.79/300.44 23578[0:SpL:523.1,16286.0] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_Procs) -> .
% 299.79/300.44 23565[0:SpR:303.1,523.1] class_Lattices_Obounded__lattice(tc_fun(t_a,u)) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x))**.
% 299.79/300.44 23544[0:SpR:302.1,523.1] class_Lattices_Obounded__lattice(tc_fun(t_a,u)) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x)),hAPP(v,v_x)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x))**.
% 299.79/300.44 23536[0:SpR:3229.1,523.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w)) -> equal(hAPP(hAPP(v,v_x),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(v_x,v_x)))*.
% 299.79/300.44 23531[0:SpR:3229.1,523.1] class_Lattices_Olattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u))) -> equal(hAPP(hAPP(hAPP(v,v_x),w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v_x,v_x)),hAPP(w,v_x)))*.
% 299.79/300.44 23528[0:SpR:523.1,8376.2] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),c_in(tc_Com_Opname)) equal(v_Procs,v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(v_x,v_x)))*.
% 299.79/300.44 23498[0:SpR:523.1,3229.1] class_Lattices_Olattice(u) || equal(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x)) -> equal(hAPP(v,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)))*.
% 299.79/300.44 23478[0:SpR:523.1,3283.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),v_Procs))*.
% 299.79/300.44 23472[0:SpR:523.1,1158.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_Com_Opname,x),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))))*.
% 299.79/300.44 23885[0:SpR:23840.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),v),x)),hAPP(c_Set_Oinsert(u,w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),x)))*.
% 299.79/300.44 23884[0:SpR:23840.0,99.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),u),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.44 23883[0:SpR:23840.0,438.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),u),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.44 24177[0:SpR:542.0,8376.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(tc_Com_Opname)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))*.
% 299.79/300.44 24403[0:AED:24.0,24328.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(v,w,x),x,w),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.79/300.44 24438[0:SpL:3229.1,208.0] || equal(u,c_Set_Oinsert(v,w))* c_lessequals(x,hAPP(u,v_x),tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),v),x))* c_lessequals(x,v_x,tc_fun(w,tc_bool)).
% 299.79/300.44 24670[0:SpR:131.0,24020.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),v_x),v_x)**.
% 299.79/300.44 24669[0:SpR:158.0,24020.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),v_x),v_x)**.
% 299.79/300.44 24653[0:SpR:104.0,24020.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),v_x),v_x)**.
% 299.79/300.44 24908[0:SpL:3229.1,467.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(w,x,v),y)))* -> equal(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,v),v_x)),v_x)**.
% 299.79/300.44 24901[0:SpL:3229.1,467.0] || equal(u,c_Set_Oimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(u,v_x)))* -> equal(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_x,v,w,x),y)),y)**.
% 299.79/300.44 24952[0:SpR:23902.1,545.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_bool)),w)) -> hBOOL(hAPP(hAPP(c_in(x),v_x),hAPP(c_Set_Oimage(hAPP(u,v_x),v,x),w)))*.
% 299.79/300.44 24951[0:SpR:23902.1,362.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_bool)),w)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 25430[0:SpL:512.0,16286.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,y),x),y,w),v_Procs)** -> .
% 299.79/300.44 25408[0:SpR:3229.1,512.0] || equal(u,c_COMBB(v,w,x,y)) -> equal(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v_x,y,w),z)),hAPP(c_Set_Oimage(hAPP(u,v_x),y,x),z))*.
% 299.79/300.44 25350[0:SpR:512.0,3229.1] || equal(u,c_Set_Oimage(hAPP(c_COMBB(v,w,x,y),z),y,x))* -> equal(hAPP(u,v_x),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(z,y,w),v_x)))*.
% 299.79/300.44 25328[0:SpR:512.0,3283.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),v_Procs))*.
% 299.79/300.44 25322[0:SpR:512.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),tc_Com_Opname,z),v_Procs),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x))))*.
% 299.79/300.44 25636[0:Res:9569.0,24120.1] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(w,x)).
% 299.79/300.44 25991[0:SpL:339.0,519.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),y)) hBOOL(hAPP(x,y)).
% 299.79/300.44 25990[0:SpL:339.0,325.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),y,tc_fun(v,tc_bool)).
% 299.79/300.44 25965[0:SpL:339.0,3483.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Com_Ocom_OBODY) equal(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.44 25949[0:SpR:3586.1,339.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),w))**.
% 299.79/300.44 25938[0:SpR:9493.1,339.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))**.
% 299.79/300.44 25936[0:SpR:8498.1,339.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),x))**.
% 299.79/300.44 26008[0:SSi:25906.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),tc_fun(w,tc_bool))*.
% 299.79/300.44 26237[0:SpL:338.0,519.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y))* -> hBOOL(hAPP(w,y)) hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),x),y)).
% 299.79/300.44 26235[0:SpL:338.0,324.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(u,v),x),y,tc_fun(v,tc_bool)).
% 299.79/300.44 26219[0:SpR:10090.1,338.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(c_Set_Oinsert(v,u),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Oinsert(v,u),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.79/300.44 26175[0:SpR:8415.2,338.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(v_x,w)),hAPP(v_x,hAPP(c_Set_Oinsert(v,u),w)))**.
% 299.79/300.44 26159[0:SpR:3586.1,338.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))**.
% 299.79/300.44 26148[0:SpR:9493.1,338.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u))**.
% 299.79/300.44 26146[0:SpR:8498.1,338.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),u))**.
% 299.79/300.44 26125[0:SpR:338.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),y))),hAPP(c_Set_Oimage(c_Set_Oinsert(x,v),z,u),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.44 26096[0:SpR:338.0,7539.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(y,u),w))),tc_fun(u,tc_bool))*.
% 299.79/300.44 26060[0:SpR:338.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(c_Set_Oinsert(y,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z))))*.
% 299.79/300.44 26291[0:SSi:26068.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),x)),tc_fun(w,tc_bool))*.
% 299.79/300.44 26313[0:Res:23960.1,405.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Oorder(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x,u)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x).
% 299.79/300.44 26325[0:SSi:26307.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(u,tc_bool)),v_x,tc_fun(u,tc_bool))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(u,tc_bool)),v_x).
% 299.79/300.44 26382[0:Res:83.0,85.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y))),x,tc_fun(w,tc_bool)),y,tc_fun(w,tc_bool))*.
% 299.79/300.44 26524[0:Res:84.1,436.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* hBOOL(hAPP(u,y))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),y))*.
% 299.79/300.44 26517[0:SpR:10090.1,84.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_fun(u,tc_bool))* -> c_lessequals(v,c_Orderings_Otop__class_Otop(tc_bool),tc_fun(u,tc_bool)).
% 299.79/300.44 26784[0:Res:23997.0,10214.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),u),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),u),u).
% 299.79/300.44 26798[0:SSi:26778.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),u),tc_bool)* -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),u),u).
% 299.79/300.44 26870[0:SpL:56.1,103.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Finite__Set_Ofinite(w,u) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),u)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),x),u)*.
% 299.79/300.44 26821[0:SpR:56.1,114.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(x,hAPP(c_Set_Oinsert(v,u),y),u,z)* -> c_Fun_Oinj__on(x,c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool)),u,z)*.
% 299.79/300.44 26953[0:Res:424.2,436.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(x,w,tc_fun(u,tc_bool))* hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),x),y))* -> hBOOL(hAPP(w,y))*.
% 299.79/300.44 27086[0:Res:149.1,280.1] || hBOOL(hAPP(hAPP(u,v),w))* -> hBOOL(hAPP(hAPP(c_in(x),v),y))* hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool)),u,x,tc_fun(z,tc_bool)),w))*.
% 299.79/300.44 27154[0:SpR:9924.0,450.0] || -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,v,w))) c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v),u),t_a)*.
% 299.79/300.44 27845[7:SpR:181.1,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(c_COMBK(u,v,w),w,v),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_bool)).
% 299.79/300.44 27992[0:SpR:181.1,27381.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.44 28077[0:SpR:523.1,28032.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_Com_Opname,x)))*.
% 299.79/300.44 28076[0:SpR:460.1,28032.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,u)))*.
% 299.79/300.44 28227[0:SpL:465.1,3483.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Com_Ocom_OBODY)** equal(hAPP(c_Set_Oimage(u,x,y),v_x),c_Com_Ocom_OSKIP) -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)).
% 299.79/300.44 28294[0:SpR:181.1,27441.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.44 28381[0:SpR:523.1,28335.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_Com_Opname,x)))*.
% 299.79/300.44 28380[0:SpR:460.1,28335.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_Com_Opname,u)))*.
% 299.79/300.44 28428[0:SpR:118.0,395.0] || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,w,x,y,z),z,x1,y),w,x2,y,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,z,x1,y),w,x2,y,x1))**.
% 299.79/300.44 28583[0:Rew:9.0,28571.1] || equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,w,x,y,z),z,x1,y),c_Fun_Ocomp(u,v,z,x1,y))** -> equal(hAPP(u,hAPP(v,w)),hAPP(u,x)).
% 299.79/300.44 28753[0:SpR:181.1,28031.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.44 28812[0:Rew:25912.0,28718.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs))**.
% 299.79/300.44 28702[0:SpR:28031.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(x,v_x),x,tc_Com_Opname,y),tc_Com_Opname),v,u),u)*.
% 299.79/300.44 28685[0:SpR:28031.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w),tc_Com_Opname),u,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.44 28908[0:SpR:181.1,28334.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.44 28967[0:Rew:25912.0,28873.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs))**.
% 299.79/300.44 28857[0:SpR:28334.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,x,hAPP(x,v_x),tc_Com_Opname,y),tc_Com_Opname),v,u),u)*.
% 299.79/300.44 28840[0:SpR:28334.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w),tc_Com_Opname),u,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.44 29152[0:SpR:23902.1,537.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(tc_bool)),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))**.
% 299.79/300.44 29245[0:SSi:29086.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v))**.
% 299.79/300.44 29252[0:SSi:29184.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),u)* -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u).
% 299.79/300.44 29413[7:SpR:27278.1,338.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))**.
% 299.79/300.44 29395[7:SpR:27278.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(hAPP(c_in(v),w),v_x) hBOOL(hAPP(hAPP(c_in(x),v_x),y)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(w,v),x,u),u)*.
% 299.79/300.44 29389[7:SpR:27278.1,339.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),w))**.
% 299.79/300.44 29376[7:SpR:27278.1,176.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Ovimage(c_Set_Oinsert(v,u),w,x),hAPP(c_Set_Oinsert(v_x,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.44 29677[0:SpR:23902.1,534.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(tc_bool)),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))**.
% 299.79/300.44 30262[0:SpR:23902.1,536.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x))**.
% 299.79/300.44 30098[0:SpR:536.1,7253.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z))))*.
% 299.79/300.44 30408[0:SSi:30137.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v))**.
% 299.79/300.44 30419[0:SSi:30305.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),u)* -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),u).
% 299.79/300.44 30826[0:SpR:23902.1,535.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x))**.
% 299.79/300.44 30654[0:SpR:535.1,7253.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z))))*.
% 299.79/300.44 31067[0:SpR:28771.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v_Procs,v_Procs,v,w),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname))**.
% 299.79/300.44 31153[0:SpR:28926.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v_Procs,v_Procs,v,w),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname))**.
% 299.79/300.44 31306[0:Res:8376.2,356.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(v,v_Procs) -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,u),u,x),v),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.79/300.44 31284[0:Res:15262.1,356.0] || equal(c_in(t_a),c_in(u)) -> equal(hAPP(c_Set_Oimage(c_COMBK(v,w,u),u,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.79/300.44 31283[0:Res:3285.1,356.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(hAPP(c_Set_Oimage(c_COMBK(v,w,u),u,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.79/300.44 31282[0:Res:3317.1,356.0] || equal(c_in(u),c_in(v)) -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,v),v,x),hAPP(c_Set_Oinsert(v_x,u),y)),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.79/300.44 31366[0:Res:23961.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),u,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),u),v_x,t_a)*.
% 299.79/300.44 31452[0:SpL:130.1,24254.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.79/300.44 31548[0:Res:8376.2,473.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Oimage(v,w,u),x),v_Procs) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),v_x)),x))*.
% 299.79/300.44 31816[7:SpL:188.1,31778.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x)** -> .
% 299.79/300.44 31912[7:SpL:523.1,31868.0] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_x) -> .
% 299.79/300.44 31911[7:SpL:460.1,31868.0] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_x) -> .
% 299.79/300.44 31997[0:SpR:10540.0,383.1] || -> equal(u,v) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),u,x,y,z),v,c_Orderings_Obot__class_Obot(tc_bool),y,z),c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),u,x,y,z))**.
% 299.79/300.44 31996[0:SpR:9961.0,383.1] || -> equal(u,v) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,x,y,z),v,c_Orderings_Otop__class_Otop(tc_bool),y,z),c_Fun_Ofun__upd(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,x,y,z))**.
% 299.79/300.44 31974[0:SpR:383.1,445.1] || -> equal(u,v) equal(w,u) equal(hAPP(c_Fun_Ofun__upd(c_Fun_Ofun__upd(x,u,y,z,x1),v,x2,z,x1),w),hAPP(c_Fun_Ofun__upd(x,v,x2,z,x1),w))**.
% 299.79/300.44 32052[0:Res:151.2,2629.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),u)) equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v)).
% 299.79/300.44 32604[0:SpR:130.1,31533.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_Com_Opname,x),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))),v_Procs))*.
% 299.79/300.44 32739[0:SpR:131.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)))))*.
% 299.79/300.44 32738[0:SpR:158.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))))*.
% 299.79/300.44 32720[0:SpR:104.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),tc_Com_Opname,w),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))))*.
% 299.79/300.44 32783[0:SpR:35.2,15172.0] || c_lessequals(u,c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),tc_fun(x,tc_bool))* c_lessequals(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),y,tc_fun(x,tc_bool))* -> equal(hAPP(u,z),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.44 32898[0:SpR:3229.1,475.1] || equal(u,c_Set_Oimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(w),y),v_x))* -> equal(hAPP(c_Set_Oinsert(hAPP(v,y),x),hAPP(u,v_x)),hAPP(u,v_x))**.
% 299.79/300.44 33086[0:Res:16753.1,94.1] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) c_Fun_Oinj__on(u,x,v,w) -> c_Fun_Oinj__on(c_Fun_Ocomp(y,u,w,w,v),x,v,w)*.
% 299.79/300.44 33260[0:SpR:130.1,32668.0] class_HOL_Ominus(u) || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_Com_Opname,x),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.44 33208[0:SpR:32668.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),v_Procs,v_Procs,w,x),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname))**.
% 299.79/300.44 33352[0:SpR:35.2,23789.0] || c_lessequals(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_fun(v,tc_bool))* c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(u,x),x,tc_bool)*.
% 299.79/300.44 33425[0:Res:23961.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v)),u))* c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.79/300.44 33413[0:Res:3346.1,453.0] || equal(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),v)* c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(v,v_x),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x)),w))* c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.79/300.44 33407[0:Res:9246.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)* -> hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,x)),u))* c_Hoare__Mirabelle_Otriple__valid(x,w,t_a)*.
% 299.79/300.44 33403[0:Res:1157.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(c_COMBK(v,w,x),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,y)),u))* c_Hoare__Mirabelle_Otriple__valid(y,v,t_a)*.
% 299.79/300.44 33512[0:SpL:61.1,509.0] || c_Finite__Set_Ofinite(u,v) equal(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,v),u),v))** -> .
% 299.79/300.44 33546[0:SpR:130.1,28704.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u),c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u)),tc_Com_Opname,y)))*.
% 299.79/300.44 33637[0:SpR:130.1,28859.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u)),c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u),tc_Com_Opname,y)))*.
% 299.79/300.44 33728[7:SpL:130.1,31886.1] class_HOL_Ominus(u) || equal(v,c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u)))* equal(c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u),c_Orderings_Obot__class_Obot(tc_bool))** equal(v,v_x) -> .
% 299.79/300.44 33855[0:SpR:23965.1,383.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> equal(v,v_x) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v,w,x,y),v_x,v_x,x,y),c_Fun_Ofun__upd(u,v,w,x,y))**.
% 299.79/300.44 34354[0:SpL:24914.0,442.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),v_x),w) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,x),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),v_x)),w)*.
% 299.79/300.44 34337[0:SpL:24914.0,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),v_x),w)) -> hBOOL(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,x),hAPP(c_Set_Oinsert(u,v),v_x)),w))* equal(u,w).
% 299.79/300.44 34296[0:SpL:24914.0,355.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,w),hAPP(c_in(u),v_x)),v)*.
% 299.79/300.44 34238[0:SpR:329.1,24914.0] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),v_x)),v_x)**.
% 299.79/300.44 34237[0:SpR:328.1,24914.0] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),u)),u)**.
% 299.79/300.44 34195[0:SpR:445.1,24914.0] || -> equal(v_x,u) equal(hAPP(c_Fun_Ofun__upd(v,u,w,x,y),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ofun__upd(v,u,w,x,y),tc_Com_Opname,z),hAPP(v,v_x))),hAPP(v,v_x))**.
% 299.79/300.44 34109[0:SpR:24914.0,8375.1] || equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,w),hAPP(hAPP(c_in(u),v),v_x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)).
% 299.79/300.44 34028[0:SpR:24914.0,12687.1] || -> hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_Com_Opname,w),hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x))))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x)).
% 299.79/300.44 34014[0:SpR:24914.0,9566.0] || -> c_lessequals(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(v,w),u),tc_Com_Opname,x),hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x))),hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x),tc_bool)*.
% 299.79/300.44 33959[0:SpR:24914.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(v),v_x)),w)) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(v),tc_Com_Opname,x),u,v),w)))*.
% 299.79/300.44 33928[0:SpR:24914.0,16776.0] || -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),w,v)*.
% 299.79/300.44 34557[0:SpR:34427.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,x),u,w),v)))*.
% 299.79/300.44 34553[0:SpR:34427.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,w),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 34654[0:SpL:55.1,377.0] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)),v)* -> hBOOL(hAPP(hAPP(c_in(v),u),x)) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),v).
% 299.79/300.44 34651[0:SpL:55.1,2693.0] || equal(u,c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),w,tc_fun(tc_Com_Opname,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),w)).
% 299.79/300.44 34577[0:SpR:55.1,378.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),w) -> hBOOL(hAPP(hAPP(c_in(w),x),v)) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,w),u),v,tc_fun(w,tc_bool)),w)*.
% 299.79/300.44 34740[0:SpR:34428.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,x),u,w),v)))*.
% 299.79/300.44 34736[0:SpR:34428.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,w),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 34854[0:SpR:130.1,28053.1] class_HOL_Ominus(u) || equal(v,c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u),v,tc_Com_Opname,y)))*.
% 299.79/300.44 34933[0:SpR:130.1,28356.1] class_HOL_Ominus(u) || equal(v,c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u),tc_Com_Opname,y)))*.
% 299.79/300.44 35024[0:SpR:28755.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),v_Procs,v_Procs,y,z),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname))**.
% 299.79/300.44 35113[0:SpR:28910.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),v_Procs,v_Procs,y,z),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname))**.
% 299.79/300.44 35235[0:SpR:410.0,538.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),hAPP(w,y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(y,x),v),w,x,tc_fun(u,tc_bool)))*.
% 299.79/300.44 35540[0:Rew:10.0,35508.0] || -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),v),tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),c_HOL_Ominus__class_Ominus(v_Procs,v,tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.79/300.44 35651[0:Rew:35438.0,35630.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,hAPP(c_COMBB(w,x,tc_fun(y,tc_bool),v),c_COMBK(z,x,v)),v,tc_fun(y,tc_bool)),hAPP(w,z))**.
% 299.79/300.44 36190[0:Res:13238.1,516.0] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.79/300.44 36189[0:Res:8375.1,516.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(u),x),v))* hBOOL(hAPP(hAPP(c_in(u),x),w))*.
% 299.79/300.44 36183[0:Res:652.1,516.0] || c_lessequals(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),u)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v)).
% 299.79/300.44 36754[0:SpR:177.1,67.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),w),hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)))**.
% 299.79/300.44 36716[0:SpR:67.0,115.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),w)*.
% 299.79/300.44 37494[0:SpL:205.1,357.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w)* c_lessequals(y,x,tc_fun(v,tc_bool))* -> c_Finite__Set_Ofinite(y,v).
% 299.79/300.44 38213[0:SpR:6.0,13.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_fun(w,tc_bool)) -> c_lessequals(u,c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.44 38199[0:SpR:7.0,13.2] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(v,x,tc_fun(w,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.44 38332[0:SSi:38320.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),u),v))* c_Finite__Set_Ofinite(v,tc_bool) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w))* -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,v,tc_bool,tc_bool))*.
% 299.79/300.44 38665[0:Res:9258.0,184.0] || c_Fun_Oinj__on(u,v,w,t_a) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(u,w,t_a),v),v_x),tc_bool))* equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(v,u,w,t_a),v_x)),v_x)**.
% 299.79/300.44 38719[4:SpR:523.1,37987.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),x))*.
% 299.79/300.44 38718[4:SpR:460.1,37987.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),u))*.
% 299.79/300.44 38908[4:SpR:523.1,38042.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),x,t_a)*.
% 299.79/300.44 38907[4:SpR:460.1,38042.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),u,t_a)*.
% 299.79/300.44 40901[0:Res:526.1,479.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(w,v))* -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,y,w,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),y)))*.
% 299.79/300.44 41182[0:Res:526.1,478.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(w,v))* -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,u,w,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u)))*.
% 299.79/300.44 41411[0:Res:526.1,275.1] || hBOOL(hAPP(hAPP(u,v),w))* hBOOL(hAPP(hAPP(c_in(x),v),y))* -> hBOOL(hAPP(hAPP(c_in(z),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,u,x,tc_fun(z,tc_bool))))*.
% 299.79/300.44 41680[0:Res:8375.1,284.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> hBOOL(hAPP(hAPP(c_in(v),y),x))*.
% 299.79/300.44 41677[0:Res:526.1,284.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),hAPP(u,y)))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> hBOOL(hAPP(hAPP(c_in(v),y),x)).
% 299.79/300.44 42203[0:SSi:42181.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(w,tc_bool),u),tc_bool,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,u,tc_bool,tc_bool),w).
% 299.79/300.44 42208[0:SSi:42048.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v,hAPP(c_Set_Oinsert(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),u),tc_fun(tc_Com_Opname,tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.79/300.44 42740[0:SpL:161.0,347.0] || c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,tc_fun(v,tc_bool)),v,z)* -> c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(w,y,tc_fun(v,tc_bool)),v,z).
% 299.79/300.44 42739[0:SpL:161.0,346.0] || c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,tc_fun(v,tc_bool)),v,z)* -> c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)),v,z).
% 299.79/300.44 43559[0:SpL:507.0,347.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)),x,x1)* -> c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(v,w,x),y),x,x1).
% 299.79/300.44 43558[0:SpL:507.0,346.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)),x,x1)* -> c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(v,w,x),z),x,x1).
% 299.79/300.44 43781[0:SpL:162.0,347.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),w,x1)* -> c_Fun_Oinj__on(u,hAPP(c_Set_Ovimage(v,w,x),y),w,x1).
% 299.79/300.44 43780[0:SpL:162.0,346.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),w,x1)* -> c_Fun_Oinj__on(u,hAPP(c_Set_Ovimage(v,w,x),z),w,x1).
% 299.79/300.44 44642[0:SpR:486.1,35656.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.79/300.44 45460[0:Res:45357.1,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.44 45447[0:Res:45357.1,255.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),w,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),w)).
% 299.79/300.44 45582[0:SpR:323.0,517.1] || hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),y)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),z),v,w,tc_fun(x,tc_bool)),y))*.
% 299.79/300.44 45579[0:SpR:323.0,518.1] || hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),y)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),u),v,w,tc_fun(x,tc_bool)),y))*.
% 299.79/300.44 46596[0:Rew:35438.0,46595.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(c_Set_Oinsert(w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_COMBK(y,tc_fun(x,tc_bool),v),v,tc_fun(x,tc_bool))),hAPP(c_Set_Oinsert(w,x),y))**.
% 299.79/300.44 48108[4:SpR:130.1,39023.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)),z))*.
% 299.79/300.44 48223[4:SpR:130.1,39064.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(x,y),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)),z,t_a)*.
% 299.79/300.44 49093[0:SpR:49017.1,338.0] || -> hBOOL(hAPP(u,v_x)) equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs))**.
% 299.79/300.44 49077[0:SpR:49017.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> hBOOL(hAPP(x,v_x)) c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,x,tc_Com_Opname),tc_Com_Opname),v,u),u)*.
% 299.79/300.44 49073[0:SpR:49017.1,339.0] || -> hBOOL(hAPP(u,v_x)) equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v))**.
% 299.79/300.44 49058[0:SpR:49017.1,176.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 49658[0:MRR:33072.1,49657.0] || c_Fun_Oinj__on(c_COMBK(u,v,w),x,w,v) -> equal(x,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) c_Fun_Oinj__on(c_Fun_Ocomp(y,c_COMBK(u,v,w),v,z,w),x,w,z)*.
% 299.79/300.44 50457[0:SpR:223.1,36687.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(x,t_a),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,v_x,u,t_a),u,t_a),w)),tc_Com_Opname,tc_bool))*.
% 299.79/300.44 51239[0:Rew:331.0,51130.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Set_Oinsert(x,u),v),tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,u),v),tc_fun(u,tc_bool)))**.
% 299.79/300.44 51240[0:Rew:330.0,51129.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Set_Oinsert(x,u),w),tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(x,u),w),tc_fun(u,tc_bool)))**.
% 299.79/300.44 51319[0:SpR:130.1,51231.0] class_HOL_Ominus(u) || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),hAPP(hAPP(c_Set_Oinsert(x,t_a),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.44 51447[7:SpL:21893.0,27284.0] || equal(hAPP(c_Set_Ovimage(u,v,w),v_x),v_x) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),v_x),c_Set_Ovimage(u,v,w),tc_Com_Opname,x),hAPP(u,v_x)))*.
% 299.79/300.44 51446[7:SpL:21267.0,27284.0] || equal(hAPP(c_Set_Ovimage(u,v,w),v_x),v_x) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x),tc_Com_Opname,x),hAPP(u,v_x)))*.
% 299.79/300.44 51979[0:Rew:9936.1,51960.2,9936.1,51960.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_List_Ofoldl(y,c_Orderings_Otop__class_Otop(tc_bool),z,x,x1),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.44 51989[0:Rew:15172.0,51970.1,15172.0,51970.1] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y,z,x1),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(c_List_Ofoldl(x2,c_Orderings_Obot__class_Obot(tc_bool),x3,x1,x4),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.44 53002[0:Res:23739.1,453.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v)),u))* c_Hoare__Mirabelle_Otriple__valid(v,v_Procs,t_a).
% 299.79/300.44 53764[0:Res:7226.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_Option_Othe(z),v,x),u,tc_fun(x,tc_bool))))*.
% 299.79/300.44 54137[0:SpR:52997.1,317.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(hAPP(u,v_Procs),v),hAPP(c_Set_Oimage(u,w,v),v_x)),hAPP(c_Set_Oimage(u,w,v),v_x))**.
% 299.79/300.44 54230[0:SpR:8667.0,63.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),w),tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool)),v)* -> c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),w),tc_fun(v,tc_bool)),v).
% 299.79/300.44 54306[0:MRR:54228.0,19747.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),u,tc_fun(w,tc_bool))* -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v).
% 299.79/300.44 54319[0:SpR:54251.0,66.0] || -> equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))**.
% 299.79/300.44 54409[0:Rew:32817.1,54342.2] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* c_lessequals(w,u,tc_fun(v,tc_bool)) -> equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.79/300.44 54924[0:SSi:54791.1,555.1,550.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x))**.
% 299.79/300.44 55824[0:Rew:104.0,55774.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.79/300.44 55990[0:SpL:181.1,55174.1] || equal(u,c_Set_Ovimage(c_COMBK(v,w,x),x,w))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)).
% 299.79/300.44 55908[0:SpL:181.1,55174.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),x)* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_bool),hAPP(x,v_x))* -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)).
% 299.79/300.44 56463[0:SSi:56279.1,555.1,550.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x)),hAPP(v,v_x)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x))**.
% 299.79/300.44 57909[0:SpL:130.1,55910.1] class_HOL_Ominus(u) || equal(c_COMBK(v,w,x),c_HOL_Ominus__class_Ominus(y,z,tc_fun(t_a,u)))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),c_HOL_Ominus__class_Ominus(hAPP(y,v_x),hAPP(z,v_x),u))* -> .
% 299.79/300.44 58066[0:SpL:130.1,55992.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_COMBK(x,y,z))* equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool),x)* -> .
% 299.79/300.44 58201[0:SpL:523.1,58055.0] class_Lattices_Olattice(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool),x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w))** -> .
% 299.79/300.44 58200[0:SpL:460.1,58055.0] || class_Lattices_Olattice(t_b) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool),u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g))** -> .
% 299.79/300.44 58470[0:SpL:188.1,58248.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_COMBK(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,y),c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_fun(t_a,tc_bool)))* -> .
% 299.79/300.44 58555[0:SpR:24914.0,10771.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(w,u),tc_Com_Opname,x),hAPP(c_Set_Oinsert(w,u),v_x))))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,u),v_x),v)).
% 299.79/300.44 58887[0:Res:34.1,15629.0] || hBOOL(hAPP(u,hAPP(v,w)))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,x,y),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_Set_Ovimage(v,x,y),u),z)))*.
% 299.79/300.44 58820[0:SpL:49017.1,15629.0] || hBOOL(v_Procs) -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v)))*.
% 299.79/300.44 58721[0:SpL:540.1,15629.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))*.
% 299.79/300.44 58720[0:SpL:539.1,15629.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))*.
% 299.79/300.44 58719[0:SpL:297.2,15629.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* hBOOL(w) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))*.
% 299.79/300.44 58716[0:SpL:2098.1,15629.0] || hBOOL(u) -> c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a) hBOOL(hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,u),tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,u),tc_Hoare__Mirabelle_Otriple(t_a)),w)))*.
% 299.79/300.44 59395[0:Res:34.1,15857.0] || hBOOL(hAPP(u,hAPP(v,w)))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,x,y),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_Set_Ovimage(v,x,y),u),x1)))*.
% 299.79/300.44 59328[0:SpL:49017.1,15857.0] || hBOOL(v_Procs) -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),w)))*.
% 299.79/300.44 59229[0:SpL:540.1,15857.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)))*.
% 299.79/300.44 59228[0:SpL:539.1,15857.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)))*.
% 299.79/300.44 59227[0:SpL:297.2,15857.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* hBOOL(w) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)))*.
% 299.79/300.44 59224[0:SpL:2098.1,15857.0] || hBOOL(u) -> c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a) hBOOL(hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,u),tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,u),tc_Hoare__Mirabelle_Otriple(t_a)),x)))*.
% 299.79/300.44 59751[0:SpL:55.1,21018.0] || equal(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,v),y),z,tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(v),x),z)).
% 299.79/300.44 60178[0:SpL:130.1,58170.1] class_HOL_Ominus(u) || equal(v,c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u))) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u),tc_bool),y,z),v)* -> .
% 299.79/300.44 60431[7:Res:58968.1,8513.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w),u)**.
% 299.79/300.44 60544[0:Res:58969.1,8513.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_Procs) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w),u)**.
% 299.79/300.44 60617[7:Res:59476.1,8513.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),x),u)**.
% 299.79/300.44 60690[0:Res:59477.1,8513.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_Procs) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),x),u)**.
% 299.79/300.44 60875[0:Res:59017.1,8513.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),t_a)* equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x),v)**.
% 299.79/300.44 60948[0:Res:59525.1,8513.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),t_a)* equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),y),v)**.
% 299.79/300.44 61122[0:Res:61046.3,251.1] class_Lattices_Obounded__lattice(tc_fun(u,v)) class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,v)))* -> c_lessequals(hAPP(w,x),hAPP(y,x),v)*.
% 299.79/300.44 61415[0:Res:61338.3,251.1] class_Lattices_Obounded__lattice(tc_fun(u,v)) class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || equal(c_Orderings_Otop__class_Otop(tc_fun(u,v)),w)* -> c_lessequals(hAPP(x,y),hAPP(w,y),v)*.
% 299.79/300.44 61723[0:SpL:55.1,10885.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,tc_Com_Opname),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),w,tc_fun(tc_Com_Opname,tc_bool))),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),w)).
% 299.79/300.44 62168[0:Res:23754.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,w),u,tc_fun(w,tc_bool))))*.
% 299.79/300.44 62316[0:Res:23960.1,4246.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x,u)*.
% 299.79/300.44 62279[0:Res:989.1,4246.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v,w,x),tc_Com_Opname,u),v) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v,w,x),tc_Com_Opname,u),v,u)*.
% 299.79/300.44 62416[0:SSi:62347.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),u),u) -> c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),u),tc_bool)*.
% 299.79/300.44 62417[0:SSi:62346.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),z),u) -> c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(c_COMBK(u,v,w),x,tc_fun(y,tc_bool)),z),tc_bool)*.
% 299.79/300.44 62418[0:SSi:62345.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Option_Ooption_OSome(x,u)),x) -> c_lessequals(x,hAPP(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Option_Ooption_OSome(x,u)),tc_bool)*.
% 299.79/300.44 62431[0:SSi:62233.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v) -> c_lessequals(v,c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.44 62432[0:SSi:62226.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.44 62433[0:SSi:62225.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool))*.
% 299.79/300.44 62434[0:SSi:62213.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(u,tc_bool)),v_x) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(u,tc_bool)),v_x,tc_fun(u,tc_bool))*.
% 299.79/300.44 62435[0:SSi:62207.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,tc_fun(x,tc_bool)),u) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(u,v,w),tc_Com_Opname,tc_fun(x,tc_bool)),u,tc_fun(x,tc_bool))*.
% 299.79/300.44 62651[0:Res:23960.1,4340.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x,u)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x).
% 299.79/300.44 62614[0:Res:989.1,4340.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v,w,x),tc_Com_Opname,u),v,u)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v,w,x),tc_Com_Opname,u),v).
% 299.79/300.44 62808[0:SpR:62726.2,25.1] class_OrderedGroup_Opordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_HOL_Ouminus(u) || -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),u),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x))**.
% 299.79/300.44 64061[0:Res:63953.0,402.0] || c_lessequals(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u)).
% 299.79/300.44 64081[0:SSi:64069.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u)) -> c_lessequals(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))*.
% 299.79/300.44 64250[0:SpR:52997.1,646.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),v_x),v_x)**.
% 299.79/300.44 64237[0:SpR:9936.1,646.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool)),v_x)**.
% 299.79/300.44 64233[0:SpR:9935.1,646.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool)),v_x)**.
% 299.79/300.44 64175[0:SpR:646.1,584.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_COMBS(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,x,y,z),hAPP(u,v_x)),hAPP(v_x,hAPP(w,hAPP(u,v_x))))**.
% 299.79/300.44 64174[0:SpR:646.1,584.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_COMBS(w,c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),x,y,z),hAPP(u,v_x)),hAPP(hAPP(w,hAPP(u,v_x)),v_x))**.
% 299.79/300.44 64417[0:SpR:52997.1,645.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_Procs,u),tc_Com_Opname,v),v_x),v_x)**.
% 299.79/300.44 64404[0:SpR:9936.1,645.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool)),v_x)**.
% 299.79/300.44 64400[0:SpR:9935.1,645.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_x,tc_bool) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool)),v_x)**.
% 299.79/300.44 64342[0:SpR:645.1,584.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_COMBS(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,x,y,z),hAPP(u,v_x)),hAPP(v_x,hAPP(w,hAPP(u,v_x))))**.
% 299.79/300.44 64341[0:SpR:645.1,584.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_COMBS(w,c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),x,y,z),hAPP(u,v_x)),hAPP(hAPP(w,hAPP(u,v_x)),v_x))**.
% 299.79/300.44 64580[0:SpR:26782.0,415.0] || -> equal(c_Fun_Ofun__upd(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_bool),w,x),c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)))**.
% 299.79/300.44 66389[0:SpR:131.0,65575.1] || equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),v_x))*.
% 299.79/300.44 66388[0:SpR:158.0,65575.1] || equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),v_x))*.
% 299.79/300.44 67062[7:SpL:66691.3,27216.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.79/300.44 67061[2:SpL:66691.3,4253.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(u)).
% 299.79/300.44 67059[0:SpL:66691.3,3565.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_Procs)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.79/300.44 67363[7:SpL:66692.3,27216.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.79/300.44 67362[2:SpL:66692.3,4253.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(u)).
% 299.79/300.44 67360[0:SpL:66692.3,3565.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_Procs)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.79/300.44 67806[7:SpL:67115.3,27217.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x)** -> hBOOL(c_Orderings_Obot__class_Obot(u)).
% 299.79/300.44 67805[2:SpL:67115.3,4255.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(u)).
% 299.79/300.44 67803[0:SpL:67115.3,3567.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_Procs)** -> hBOOL(c_Orderings_Obot__class_Obot(u)).
% 299.79/300.44 68094[7:SpL:67416.3,27217.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x)** -> hBOOL(c_Orderings_Obot__class_Obot(u)).
% 299.79/300.44 68093[2:SpL:67416.3,4255.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(u)).
% 299.79/300.44 68091[0:SpL:67416.3,3567.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_Procs)** -> hBOOL(c_Orderings_Obot__class_Obot(u)).
% 299.79/300.44 68462[0:Rew:1250.3,68391.6] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Ogroup__add(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)* -> equal(v,c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.44 68389[0:SpL:1250.3,8252.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Ogroup__add(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) c_lessequals(v,c_HOL_Ozero__class_Ozero(u),u)* -> c_lessequals(v,w,u)*.
% 299.79/300.44 68692[7:SpL:67446.3,27216.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.79/300.44 68691[2:SpL:67446.3,4253.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(u)).
% 299.79/300.44 68689[0:SpL:67446.3,3565.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_Procs)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.79/300.44 68995[7:SpL:67447.3,27216.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.79/300.44 68994[2:SpL:67447.3,4253.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Otop__class_Otop(u)).
% 299.79/300.44 68992[0:SpL:67447.3,3565.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_Procs)** -> hBOOL(c_Orderings_Otop__class_Otop(u)).
% 299.79/300.44 69283[7:SpL:67573.3,27217.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x)** -> hBOOL(c_Orderings_Obot__class_Obot(u)).
% 299.79/300.44 69282[2:SpL:67573.3,4255.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(u)).
% 299.79/300.44 69280[0:SpL:67573.3,3567.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_Procs)** -> hBOOL(c_Orderings_Obot__class_Obot(u)).
% 299.79/300.44 69576[7:SpL:68745.3,27217.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x)** -> hBOOL(c_Orderings_Obot__class_Obot(u)).
% 299.79/300.44 69575[2:SpL:68745.3,4255.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_Orderings_Obot__class_Obot(u)).
% 299.79/300.44 69573[0:SpL:68745.3,3567.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_Procs)** -> hBOOL(c_Orderings_Obot__class_Obot(u)).
% 299.79/300.44 70718[0:SpL:131.0,70400.1] || hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x))* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_bool))* -> .
% 299.79/300.44 70717[0:SpL:158.0,70400.1] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x))* hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_bool))* -> .
% 299.79/300.44 71268[0:SpR:21893.0,7538.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(u,v),v_x)),tc_fun(v,tc_bool))*.
% 299.79/300.44 71267[0:SpR:21267.0,7538.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(u,v),v_x)),tc_fun(v,tc_bool))*.
% 299.79/300.44 71409[7:SpL:523.1,71221.0] class_Lattices_Olattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_x) -> .
% 299.79/300.44 71408[7:SpL:460.1,71221.0] || class_Lattices_Olattice(t_b) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_x) -> .
% 299.79/300.44 72495[0:Res:59525.1,12554.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),t_a)* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),z)),v))*.
% 299.79/300.44 72494[0:Res:59017.1,12554.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),t_a)* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),y)),v))*.
% 299.79/300.44 72491[7:Res:58968.1,12554.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)),u))*.
% 299.79/300.44 72490[0:Res:58969.1,12554.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_Procs) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)),u))*.
% 299.79/300.44 72489[7:Res:59476.1,12554.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),y)),u))*.
% 299.79/300.44 72488[0:Res:59477.1,12554.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_Procs) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),y)),u))*.
% 299.79/300.44 74354[7:SpL:71835.1,467.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_x,u,v,w),x)),x)**.
% 299.79/300.44 74139[7:SpL:71835.1,467.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x))) -> equal(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),v_x)),v_x)**.
% 299.79/300.44 73948[7:SpR:71835.1,523.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v_x,v_x)),hAPP(v,v_x)),hAPP(hAPP(v_x,v),v_x))**.
% 299.79/300.44 73793[7:SpR:71835.1,523.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(v_x,v_x)),hAPP(v_x,v_x))**.
% 299.79/300.44 73738[7:SpR:71835.1,523.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),v_x)**.
% 299.79/300.44 73737[7:SpR:71835.1,460.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Set_Oinsert(v_x,t_a)) class_Lattices_Olattice(t_b) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),v_x)**.
% 299.79/300.44 74669[7:SSi:74628.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(v_x,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v_x))*.
% 299.79/300.44 74868[7:SpR:523.1,72297.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),v_x))*.
% 299.79/300.44 74867[7:SpR:460.1,72297.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),v_x))*.
% 299.79/300.44 75610[0:SSi:75370.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),w))),tc_fun(v,tc_bool))*.
% 299.79/300.44 75725[7:SpR:71883.1,317.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Set_Oimage(v_x,u,v),hAPP(c_Set_Oinsert(v_x,u),w)),hAPP(c_Set_Oinsert(v_x,v),hAPP(c_Set_Oimage(v_x,u,v),w)))*.
% 299.79/300.44 76081[0:SSi:75829.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y))),tc_fun(v,tc_bool))*.
% 299.79/300.44 76141[0:SpR:9915.0,415.0] || -> equal(c_Fun_Ofun__upd(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),x2,x3),c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1))**.
% 299.79/300.44 76261[0:SpR:10469.0,415.0] || -> equal(c_Fun_Ofun__upd(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),x2,x3),c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1))**.
% 299.79/300.44 76391[0:SpR:10470.0,415.0] || -> equal(c_Fun_Ofun__upd(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),x2,x3),c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1))**.
% 299.79/300.44 77205[7:SpL:131.0,74788.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)** equal(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),z)* -> hBOOL(z)*.
% 299.79/300.44 77204[7:SpL:158.0,74788.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)** equal(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),z)* -> hBOOL(z)*.
% 299.79/300.44 77185[7:SpL:104.0,74788.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_x)** equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),w)* -> hBOOL(w)*.
% 299.79/300.44 77455[7:SpR:71894.1,545.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(v_x,u,w),v)))*.
% 299.79/300.44 77451[7:SpR:71894.1,362.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.44 77759[0:SpL:584.0,5892.0] || hBOOL(hAPP(hAPP(c_COMBS(u,v,w,x,y),z),hAPP(v,z)))* -> hBOOL(hAPP(c_COMBS(c_in(x1),hAPP(u,z),x2,x3,x4),hAPP(v,z)))*.
% 299.79/300.44 78161[7:Res:77996.0,481.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w)))*.
% 299.79/300.44 78160[7:Res:77996.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)))*.
% 299.79/300.44 78746[4:Res:78665.1,477.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,v)),v_x)** hBOOL(hAPP(hAPP(c_in(v),y),w))* -> hBOOL(hAPP(u,y))*.
% 299.79/300.44 78745[4:Res:78665.1,476.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,v)),v_x)** hBOOL(hAPP(hAPP(c_in(v),y),x))* -> hBOOL(hAPP(u,y))*.
% 299.79/300.44 80209[0:SpL:21268.0,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),x,y),v))*.
% 299.79/300.44 80007[0:SpL:21268.0,591.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_G)) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v,w),t_a)*.
% 299.79/300.44 79993[0:SpR:49342.1,21268.0] || hBOOL(hAPP(u,v_x)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v_Procs,v,w)),v_Procs)**.
% 299.79/300.44 79842[0:SpR:196.1,21268.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Ovimage(u,v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),y,x,z)),y)**.
% 299.79/300.44 79725[4:SpR:21268.0,38631.1] || c_lessequals(v_x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),u,x),tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)).
% 299.79/300.44 79665[0:SpR:21268.0,526.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_in(v),w),hAPP(hAPP(c_in(v),w),x),u,y),w))* -> hBOOL(hAPP(hAPP(c_in(v),w),x)).
% 299.79/300.44 79517[0:SpR:21268.0,309.1] class_Lattices_Olattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),v,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),u)*.
% 299.79/300.44 79516[0:SpR:21268.0,306.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),v,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),u)*.
% 299.79/300.44 79383[0:SpR:21268.0,318.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),u,z),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,x),y),x).
% 299.79/300.44 79363[0:SpR:21268.0,7539.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),hAPP(c_Set_Oinsert(z,w),hAPP(c_Set_Oinsert(v,w),x)),tc_fun(w,tc_bool))*.
% 299.79/300.44 80354[0:Rew:9.0,79964.0] || -> equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Fun_Ocomp(u,v,x,y,z),hAPP(u,hAPP(v,x1)),w,x2))),hAPP(u,hAPP(v,x1)))**.
% 299.79/300.44 80403[0:Rew:196.1,79654.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),y),x,z),y)**.
% 299.79/300.44 81404[0:SpL:21894.0,527.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),x,y),v))*.
% 299.79/300.44 81202[0:SpL:21894.0,591.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_G)) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v,w),t_a)*.
% 299.79/300.44 81187[0:SpR:49342.1,21894.0] || hBOOL(hAPP(u,v_x)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w)),v_Procs)**.
% 299.79/300.44 81036[0:SpR:196.1,21894.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Ovimage(u,v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Set_Ovimage(u,v,w),x,z)),y)**.
% 299.79/300.44 80919[4:SpR:21894.0,38631.1] || c_lessequals(v_x,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,x),tc_bool)* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)).
% 299.79/300.44 80859[0:SpR:21894.0,526.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_in(v),w),x),hAPP(c_in(v),w),u,y),w))* -> hBOOL(hAPP(hAPP(c_in(v),w),x)).
% 299.79/300.44 80710[0:SpR:21894.0,309.1] class_Lattices_Olattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),u)*.
% 299.79/300.44 80709[0:SpR:21894.0,306.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),u)*.
% 299.79/300.44 80576[0:SpR:21894.0,318.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),u,z),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,x),y),x).
% 299.79/300.44 80556[0:SpR:21894.0,7539.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),hAPP(c_Set_Oinsert(z,w),hAPP(c_Set_Oinsert(v,w),x)),tc_fun(w,tc_bool))*.
% 299.79/300.44 81549[0:Rew:9.0,81158.0] || -> equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(u,hAPP(v,x)),c_Fun_Ocomp(u,v,y,z,x1),w,x2))),hAPP(u,hAPP(v,x)))**.
% 299.79/300.44 81598[0:Rew:196.1,80848.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(u,v,w),y),c_Set_Oimage(u,v,w),x,z),y)**.
% 299.79/300.44 81978[0:Res:5879.1,251.1] class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(hAPP(w,x),y),hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),w,z,x1,x2),x),y),v)*.
% 299.79/300.44 82451[0:Res:5880.1,251.1] class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(hAPP(w,x),y),hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),w,z,x1,x2),x),y),v)*.
% 299.79/300.44 83074[0:SpR:5924.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2),t_a) hBOOL(hAPP(hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2))),w))*.
% 299.79/300.44 83029[0:SpR:5924.0,415.0] || -> equal(c_Fun_Ofun__upd(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,hAPP(hAPP(u,x2),v),x3,x4),c_COMBS(u,c_COMBK(v,w,x),y,z,x1))**.
% 299.79/300.44 83151[0:Rew:5924.0,83118.1] || hBOOL(hAPP(hAPP(u,v),w))* -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_COMBS(u,c_COMBK(w,z,x1),x2,x3,x4),x)),w))*.
% 299.79/300.44 83152[0:Rew:5924.0,83117.1] || hBOOL(hAPP(hAPP(u,v),w))* -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_COMBS(u,c_COMBK(w,z,x1),x2,x3,x4),y)),w))*.
% 299.79/300.44 83153[0:Rew:5924.0,83002.0] || -> equal(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(u,v_x),v),c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname,x2)),v),hAPP(hAPP(u,v_x),v))**.
% 299.79/300.44 83154[0:Rew:5924.0,82996.0] || -> equal(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),hAPP(hAPP(u,v_x),v),tc_Com_Opname,x2)),v),hAPP(hAPP(u,v_x),v))**.
% 299.79/300.44 83240[7:SpR:523.1,78357.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x,y),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))))*.
% 299.79/300.44 83239[7:SpR:460.1,78357.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,v),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))))*.
% 299.79/300.44 83394[0:SpR:5961.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2),t_a) hBOOL(hAPP(v,hAPP(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2)))))*.
% 299.79/300.44 83360[0:SpR:5961.0,415.0] || -> equal(c_Fun_Ofun__upd(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2,hAPP(u,hAPP(x,x2)),x3,x4),c_COMBS(c_COMBK(u,v,w),x,y,z,x1))**.
% 299.79/300.44 83461[0:Rew:5961.0,83437.1] || hBOOL(hAPP(u,hAPP(v,w)))* -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_COMBS(c_COMBK(u,z,x1),v,x2,x3,x4),x))))*.
% 299.79/300.44 83462[0:Rew:5961.0,83436.1] || hBOOL(hAPP(u,hAPP(v,w)))* -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_COMBS(c_COMBK(u,z,x1),v,x2,x3,x4),y))))*.
% 299.79/300.44 83463[0:Rew:5961.0,83332.0] || -> equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,hAPP(v,v_x)),c_COMBS(c_COMBK(u,w,x),v,y,z,x1),tc_Com_Opname,x2))),hAPP(u,hAPP(v,v_x)))**.
% 299.79/300.44 83464[0:Rew:5961.0,83326.0] || -> equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(c_COMBK(u,w,x),v,y,z,x1),hAPP(u,hAPP(v,v_x)),tc_Com_Opname,x2))),hAPP(u,hAPP(v,v_x)))**.
% 299.79/300.44 84220[7:SpL:131.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),tc_bool),v_x)** equal(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_x)** -> .
% 299.79/300.44 84219[7:SpL:158.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),tc_bool),v_x)** equal(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x)** -> .
% 299.79/300.44 84199[7:SpL:104.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),v_x) -> .
% 299.79/300.44 85072[0:SpR:644.0,158.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,c_COMBK(v,w,tc_Com_Opname),w,x,tc_Com_Opname),tc_Com_Opname,x),v_Procs),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))))*.
% 299.79/300.44 85043[0:SpR:644.0,313.1] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(c_COMBK(v,w,tc_Com_Opname),tc_Com_Opname,w),u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.44 85443[4:SpR:78507.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,x),u,w),v)))*.
% 299.79/300.44 85439[4:SpR:78507.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)) -> c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,w),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 85832[0:Res:9066.0,280.1] || hBOOL(hAPP(hAPP(u,v),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oinsert(v,x),z)),u,x,tc_fun(x1,tc_bool)),w))*.
% 299.79/300.44 85811[0:SpR:24914.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,w),hAPP(c_in(u),v_x)),u),x))))*.
% 299.79/300.44 85923[0:SpL:113.0,13582.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))),z))* hBOOL(hAPP(hAPP(c_in(v),z),hAPP(c_Set_Ovimage(u,v,w),y)))* -> .
% 299.79/300.44 86057[0:SpL:523.1,86011.0] class_Lattices_Olattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_Procs) -> .
% 299.79/300.44 86056[0:SpL:460.1,86011.0] || class_Lattices_Olattice(t_b) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_Procs) -> .
% 299.79/300.44 86564[0:SpR:113.0,19823.1] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(z,x,tc_fun(w,tc_bool))),tc_fun(v,tc_bool)),y))*.
% 299.79/300.44 86765[4:SpL:131.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),tc_bool),v_x)** equal(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_Procs)** -> .
% 299.79/300.44 86764[4:SpL:158.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),tc_bool),v_x)** equal(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_Procs)** -> .
% 299.79/300.44 86744[4:SpL:104.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),v_Procs) -> .
% 299.79/300.44 87306[7:SpR:188.1,71492.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x))*.
% 299.79/300.44 87454[7:SpR:188.1,71493.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,t_a)*.
% 299.79/300.44 87584[7:SpR:188.1,71679.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.79/300.44 88327[0:Res:7227.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(c_COMBK(v,w,x),y,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),t_a)* c_Hoare__Mirabelle_Otriple__valid(z,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,z),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(z,v,t_a)*.
% 299.79/300.44 88320[0:Res:7227.0,280.1] || hBOOL(hAPP(hAPP(u,v),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(c_COMBK(v,x,y),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),u,x1,tc_fun(x2,tc_bool)),w))*.
% 299.79/300.44 88295[0:SpR:24914.0,7227.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_COMBK(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),hAPP(c_in(u),v_x)),w,x),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.79/300.44 88436[0:Res:8176.1,32820.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,c_HOL_Ominus__class_Ominus(u,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(u,w,tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))).
% 299.79/300.44 88409[0:SpR:113.0,8176.1] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),y,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,z,tc_fun(w,tc_bool))),y,tc_fun(v,tc_bool))*.
% 299.79/300.44 88541[0:SpL:113.0,8306.0] || c_lessequals(u,hAPP(c_Set_Ovimage(v,w,x),c_HOL_Ominus__class_Ominus(y,z,tc_fun(x,tc_bool))),tc_fun(w,tc_bool))* -> c_lessequals(u,hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool)).
% 299.79/300.44 88672[7:SpL:131.0,88086.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_bool))* -> .
% 299.79/300.44 88671[7:SpL:158.0,88086.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_bool))* -> .
% 299.79/300.44 88651[7:SpL:104.0,88086.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_x) hBOOL(c_HOL_Ominus__class_Ominus(w,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),tc_bool))* -> .
% 299.79/300.44 89011[0:SpR:5899.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_COMBS(u,v,w,x,y),z,x1),hAPP(c_Set_Oinsert(hAPP(c_COMBS(u,v,x2,x3,x4),x5),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),x5))*.
% 299.79/300.44 89010[0:SpR:5961.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2,x3),hAPP(c_Set_Oinsert(hAPP(u,hAPP(x,x4)),x3),c_Orderings_Obot__class_Obot(tc_fun(x3,tc_bool)))),x4))*.
% 299.79/300.44 89009[0:SpR:5924.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,x3),hAPP(c_Set_Oinsert(hAPP(hAPP(u,x4),v),x3),c_Orderings_Obot__class_Obot(tc_fun(x3,tc_bool)))),x4))*.
% 299.79/300.44 89008[0:SpR:21894.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(u,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(u,x),u,y,z)))*.
% 299.79/300.44 89004[0:SpR:21268.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(u,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),u,hAPP(u,x),y,z)))*.
% 299.79/300.44 88959[0:SpR:9915.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x3),c_Orderings_Obot__class_Obot(tc_fun(x3,tc_bool)))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.79/300.44 88946[0:SpR:10470.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x3),c_Orderings_Obot__class_Obot(tc_fun(x3,tc_bool)))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.79/300.44 88944[0:SpR:10469.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),x2,x3),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x3),c_Orderings_Obot__class_Obot(tc_fun(x3,tc_bool)))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))*.
% 299.79/300.44 88924[0:SpR:329.1,14196.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y),hAPP(c_Set_Oinsert(v,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),v))*.
% 299.79/300.44 88923[0:SpR:328.1,14196.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,y),hAPP(c_Set_Oinsert(v,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),u))*.
% 299.79/300.44 88914[0:SpR:538.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),y))*.
% 299.79/300.44 88907[0:SpR:1188.2,14196.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_HOL_Ozero__class_Ozero(u)))*.
% 299.79/300.44 88906[0:SpR:1189.2,14196.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_HOL_Ozero__class_Ozero(u)))*.
% 299.79/300.44 88844[0:SpR:646.1,14196.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,x),hAPP(c_Set_Oinsert(v_x,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),hAPP(u,v_x)))*.
% 299.79/300.44 88843[0:SpR:645.1,14196.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,x),hAPP(c_Set_Oinsert(v_x,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),hAPP(u,v_x)))*.
% 299.79/300.44 89166[0:SpL:161.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,tc_fun(v,tc_bool))),v)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)),v).
% 299.79/300.44 89165[0:SpL:162.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Ovimage(w,v,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(w,v,x),z),v).
% 299.79/300.44 89164[0:SpL:507.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oimage(w,x,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(w,x,v),z),v).
% 299.79/300.44 89338[7:SpR:78590.1,545.1] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> hBOOL(hAPP(hAPP(c_in(x),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,x),w)))*.
% 299.79/300.44 89334[7:SpR:78590.1,362.1] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 89664[7:MRR:89422.1,56.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(t_a,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)))**.
% 299.79/300.44 89709[7:Res:89344.1,184.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),c_Set_Oinsert(v_x,t_a)) c_Fun_Oinj__on(u,w,v,t_a) -> equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(w,u,v,t_a),v_x)),v_x)**.
% 299.79/300.44 89920[0:SpL:26183.0,15629.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))*.
% 299.79/300.44 89919[0:SpL:26183.0,15857.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)))*.
% 299.79/300.44 90128[4:SpR:78660.1,545.1] || equal(hAPP(u,v_x),v_x) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> hBOOL(hAPP(hAPP(c_in(x),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,x),w)))*.
% 299.79/300.44 90124[4:SpR:78660.1,362.1] || equal(hAPP(u,v_x),v_x) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 90441[4:MRR:90212.1,56.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)),v_x),v_x) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(t_a,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)))**.
% 299.79/300.44 90665[0:SpL:161.0,26231.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,tc_fun(v,tc_bool))),v)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,y,tc_fun(v,tc_bool)),v).
% 299.79/300.44 90664[0:SpL:162.0,26231.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Ovimage(w,v,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(w,v,x),y),v).
% 299.79/300.44 90663[0:SpL:507.0,26231.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oimage(w,x,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(w,x,v),y),v).
% 299.79/300.44 90853[4:Res:90134.1,184.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),v_x) c_Fun_Oinj__on(u,w,v,t_a) -> equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(w,u,v,t_a),v_x)),v_x)**.
% 299.79/300.44 91840[4:SpL:328.1,78747.0] || c_lessequals(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname),v,tc_fun(u,tc_bool))* equal(v,v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)).
% 299.79/300.44 91921[0:SpR:79073.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,y),u,x),w)))*.
% 299.79/300.44 91917[0:SpR:79073.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_Procs,x),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 92073[7:SpR:79101.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(v),v_x)),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_in(v),v_x)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,y),u,x),w)))*.
% 299.79/300.44 92069[7:SpR:79101.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(v),v_x)),w)) -> c_lessequals(hAPP(c_in(v),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,x),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 92419[0:SSi:92418.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),w,tc_fun(v,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),w).
% 299.79/300.44 92422[0:SSi:92421.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),x,tc_fun(v,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),x).
% 299.79/300.44 92701[7:Res:82151.1,453.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a)) c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Oinsert(v_x,v),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w)),u))* c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.79/300.44 92992[0:SpR:5899.0,5876.0] || -> c_lessequals(hAPP(c_COMBS(u,v,w,x,y),z),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_COMBS(u,v,x2,x3,x4),x5,x6,x7),z),tc_fun(x1,tc_bool))*.
% 299.79/300.44 92991[0:SpR:5961.0,5876.0] || -> c_lessequals(hAPP(u,hAPP(v,w)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_COMBS(c_COMBK(u,y,z),v,x1,x2,x3),x4,x5,x6),w),tc_fun(x,tc_bool))*.
% 299.79/300.44 92990[0:SpR:5924.0,5876.0] || -> c_lessequals(hAPP(hAPP(u,v),w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_COMBS(u,c_COMBK(w,y,z),x1,x2,x3),x4,x5,x6),v),tc_fun(x,tc_bool))*.
% 299.79/300.44 92989[0:SpR:21894.0,5876.0] || -> c_lessequals(hAPP(u,v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u,x,y,z),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(u,v),u,x1,x2)),tc_fun(w,tc_bool))*.
% 299.79/300.44 92985[0:SpR:21268.0,5876.0] || -> c_lessequals(hAPP(u,v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u,x,y,z),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),u,hAPP(u,v),x1,x2)),tc_fun(w,tc_bool))*.
% 299.79/300.44 92891[0:SpR:538.0,5876.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y,z,x1),v),tc_fun(x,tc_bool))*.
% 299.79/300.44 93225[0:SpR:5878.1,584.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1,x2,x3),c_Orderings_Obot__class_Obot(u)),hAPP(hAPP(v,c_Orderings_Obot__class_Obot(u)),hAPP(z,c_Orderings_Obot__class_Obot(u))))**.
% 299.79/300.44 93224[0:SpR:5878.1,584.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(v,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1,x2,x3),c_Orderings_Obot__class_Obot(u)),hAPP(hAPP(v,c_Orderings_Obot__class_Obot(u)),hAPP(w,c_Orderings_Obot__class_Obot(u))))**.
% 299.79/300.44 93478[0:SpR:188.1,86147.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x))*.
% 299.79/300.44 93629[0:SpR:188.1,86148.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,t_a)*.
% 299.79/300.44 93701[0:SpL:317.0,7462.1] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(z,w),y)),x)* -> c_Finite__Set_Ofinite(u,x).
% 299.79/300.44 93773[0:SpR:188.1,86342.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.79/300.44 93962[0:SpR:317.0,10791.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oimage(w,x,v),y)),hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oimage(w,x,v),hAPP(c_Set_Oinsert(z,x),y))),tc_fun(v,tc_bool))*.
% 299.79/300.44 94144[0:Res:14364.3,18625.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,w)) c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),x),hAPP(w,x),tc_bool)*.
% 299.79/300.44 94288[0:Res:14491.3,4219.2] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(v,c_HOL_Ouminus__class_Ouminus(c_Finite__Set_Olinorder__class_OMax(v,u),u)))* c_Finite__Set_Ofinite(v,u) -> equal(c_Finite__Set_Olinorder__class_OMax(v,u),c_Orderings_Otop__class_Otop(u)).
% 299.79/300.44 94280[0:Res:14491.3,44750.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Set_Oinsert(v_x,t_a),w)))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),v_x))*.
% 299.79/300.44 94275[0:Res:14491.3,18768.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,c_Set_Oinsert(v_x,tc_Com_Opname))) c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> c_lessequals(v_Procs,hAPP(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),v_Procs),tc_bool)*.
% 299.79/300.44 94268[0:Res:14491.3,35720.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Set_Oinsert(w,u),x)))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),w))*.
% 299.79/300.44 94267[0:Res:14491.3,32232.0] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) || hBOOL(hAPP(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))* c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMax(u,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.79/300.44 94263[0:Res:14491.3,1937.1] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) || hBOOL(hAPP(u,v_Procs)) c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(c_Finite__Set_Olinorder__class_OMax(u,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.44 94261[0:Res:14491.3,6546.0] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) || hBOOL(hAPP(u,v_Procs)) c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) equal(c_Finite__Set_Olinorder__class_OMax(u,tc_fun(tc_Com_Opname,tc_bool)),v)* -> hBOOL(hAPP(v,v_x))*.
% 299.79/300.44 94249[0:Res:14491.3,18625.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,w)) c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(w,x),hAPP(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),x),tc_bool)*.
% 299.79/300.44 632[0:Res:589.0,241.0] || c_lessequals(v_Procs,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(v_Procs,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),tc_fun(tc_Com_Opname,tc_bool)),u,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.79/300.44 631[0:Res:589.0,242.0] || c_lessequals(c_HOL_Ominus__class_Ominus(v_Procs,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),tc_fun(tc_Com_Opname,tc_bool)),u,tc_fun(tc_Com_Opname,tc_bool))* -> c_lessequals(v_Procs,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),tc_fun(tc_Com_Opname,tc_bool)).
% 299.79/300.44 671[0:Res:589.0,479.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,w,hAPP(c_in(tc_Com_Opname),v_x),u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))*.
% 299.79/300.44 672[0:Res:589.0,478.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v,hAPP(c_in(tc_Com_Opname),v_x),u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v)))*.
% 299.79/300.44 2100[0:Res:687.1,279.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_in(u),v),tc_Com_Opname)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_in(u),v),tc_Com_Opname))**.
% 299.79/300.44 2099[0:Res:686.1,279.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_in(u),v),tc_Com_Opname)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_in(u),v),tc_Com_Opname))**.
% 299.79/300.44 2158[0:SpR:135.0,47.2] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.44 2314[0:SpR:2267.1,47.2] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || equal(v,w) c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))*.
% 299.79/300.44 2397[0:SpL:2267.1,48.1] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || equal(v,w) c_lessequals(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)).
% 299.79/300.44 2457[0:SpR:2267.1,49.2] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || equal(v,w) c_lessequals(v,c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.44 2453[0:SpR:135.0,49.2] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))*.
% 299.79/300.44 2513[0:SpL:2267.1,50.1] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || equal(v,w) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> c_lessequals(v,c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)).
% 299.79/300.44 9560[0:Res:4785.2,251.1] class_Orderings_Olinorder(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),tc_fun(u,v)),x),v)*.
% 299.79/300.44 9559[0:Res:4787.2,251.1] class_Orderings_Opreorder(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),tc_fun(u,v)),x),v)*.
% 299.79/300.44 9526[0:Res:4805.3,251.1] class_Lattices_Oboolean__algebra(tc_fun(u,v)) class_Orderings_Obot(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_Orderings_Otop__class_Otop(tc_fun(u,v)),x),v)*.
% 299.79/300.44 9523[0:Res:4693.2,251.1] class_Orderings_Olinorder(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),tc_fun(u,v)),x),hAPP(w,x),v)*.
% 299.79/300.44 9522[0:Res:4695.2,251.1] class_Orderings_Opreorder(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),tc_fun(u,v)),x),hAPP(w,x),v)*.
% 299.79/300.44 9514[0:Res:4714.3,251.1] class_Lattices_Oboolean__algebra(tc_fun(u,v)) class_Lattices_Olattice(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,v)),w),hAPP(x,w),v)*.
% 299.79/300.44 9512[0:Res:4722.3,251.1] class_Lattices_Oboolean__algebra(tc_fun(u,v)) class_Orderings_Otop(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,v)),w),hAPP(x,w),v)*.
% 299.79/300.44 10584[0:SpL:141.1,57.1] class_OrderedGroup_Oab__group__add(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ominus__class_Ominus(v,w,u)),c_HOL_Ominus__class_Ominus(w,v,u)),c_HOL_Ozero__class_Ozero(u))** -> equal(c_HOL_Ominus__class_Ominus(v,w,u),c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.44 10772[0:Res:254.1,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),v),x,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),v),x),u,t_a)*.
% 299.79/300.44 13001[0:Res:687.1,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.44 13000[0:Res:686.1,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.44 12972[0:SpL:8415.2,501.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(v_x,u)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.79/300.44 14191[0:SpR:8415.2,176.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(v_x,hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(hAPP(v,v_x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 14187[0:SpR:586.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(hAPP(c_COMBB(w,x,y,z),x1),u,x2),hAPP(c_Set_Oinsert(hAPP(w,hAPP(x1,v)),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))))))*.
% 299.79/300.44 14186[0:SpR:585.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(hAPP(c_COMBC(w,x,y,z),x1),u,x2),hAPP(c_Set_Oinsert(hAPP(hAPP(w,v),x1),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))))))*.
% 299.79/300.44 14134[0:SpR:8415.2,176.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 14127[0:SpR:369.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Ovimage(c_Set_Oinsert(v,w),u,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),x),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.44 14126[0:SpR:2089.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,w),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 14121[0:SpR:445.1,176.0] || -> equal(u,v) hBOOL(hAPP(hAPP(c_in(w),u),hAPP(c_Set_Ovimage(c_Fun_Ofun__upd(x,v,y,z,x1),w,x2),hAPP(c_Set_Oinsert(hAPP(x,u),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))))))*.
% 299.79/300.44 14363[0:Res:9071.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,tc_fun(u,tc_bool)),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,tc_fun(u,tc_bool)),u),v,u)*.
% 299.79/300.44 14360[0:Res:1157.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_COMBK(v,w,x),tc_Com_Opname,u),v_Procs),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(c_COMBK(v,w,x),tc_Com_Opname,u),v_Procs),u),v,u)*.
% 299.79/300.44 14359[0:Res:254.1,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(x,u),w),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(x,u),w),u),v,u)*.
% 299.79/300.44 14339[0:SpL:8415.2,170.1] class_Orderings_Olinorder(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,v)) c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),v_x,u)*.
% 299.79/300.44 14490[0:Res:9071.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,tc_fun(u,tc_bool)),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,tc_fun(u,tc_bool)),u),u)*.
% 299.79/300.44 14487[0:Res:1157.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_COMBK(v,w,x),tc_Com_Opname,u),v_Procs),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(c_COMBK(v,w,x),tc_Com_Opname,u),v_Procs),u),u)*.
% 299.79/300.44 14486[0:Res:254.1,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(x,u),w),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(x,u),w),u),u)*.
% 299.79/300.44 14466[0:SpL:8415.2,169.1] class_Orderings_Olinorder(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,v)) c_Finite__Set_Ofinite(v,u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.79/300.44 14758[0:SpR:8415.2,128.0] || equal(v_Procs,v_x) equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(v,tc_bool)))**.
% 299.79/300.44 14877[0:Res:11007.2,251.1] class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),tc_fun(u,v)),x),v)*.
% 299.79/300.44 15005[0:Res:11008.2,251.1] class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),tc_fun(u,v)),x),hAPP(w,x),v)*.
% 299.79/300.44 15132[0:SpL:181.1,3507.1] || equal(c_Set_Oinsert(u,v),c_Set_Ovimage(c_COMBK(w,x,y),y,x))* equal(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(x),w),v_x)).
% 299.79/300.44 15128[0:SpL:181.1,3484.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),hAPP(c_Com_Ocom_OBODY,x))* -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) equal(v_x,x).
% 299.79/300.44 15121[0:SpR:181.1,128.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)))) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),w),tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))**.
% 299.79/300.44 15105[0:SpR:181.1,3346.1] || equal(c_Set_Oinsert(u,v),c_Set_Ovimage(c_COMBK(w,x,y),y,x))* -> hBOOL(hAPP(hAPP(c_in(x),w),v_x)) hBOOL(hAPP(hAPP(c_in(v),u),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))*.
% 299.79/300.44 15103[0:SpR:181.1,3305.1] || equal(u,c_Set_Ovimage(c_COMBK(v,w,x),x,w))* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,y),v_Procs),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))*.
% 299.79/300.44 15099[0:SpR:181.1,2771.1] || equal(u,c_Set_Ovimage(c_COMBK(v,w,x),x,w))* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)) equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.79/300.44 15221[0:SpR:353.0,446.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(y,v),w)),hAPP(c_Set_Oinsert(y,v),x),tc_fun(v,tc_bool))*.
% 299.79/300.44 15204[0:SpR:8415.2,446.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Set_Oinsert(u,v)) c_lessequals(w,v_x,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),v_x,tc_fun(v,tc_bool))*.
% 299.79/300.44 15203[0:SpR:353.0,446.1] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(y,w),u),hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(y,w),x)),tc_fun(w,tc_bool))*.
% 299.79/300.44 15256[0:SpR:10063.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_x,t_a),u,v),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))))*.
% 299.79/300.44 15309[0:SpR:353.0,63.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),w) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(y,w),x)),tc_fun(w,tc_bool)),w)*.
% 299.79/300.44 15347[0:SpL:353.0,62.0] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),y)),tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),y),tc_fun(w,tc_bool)),w).
% 299.79/300.44 15611[0:SpL:8415.2,278.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,w)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,x,v,u)))*.
% 299.79/300.44 15839[0:SpL:8415.2,277.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,w)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,w,v,u)))*.
% 299.79/300.44 16007[0:SpL:8415.2,515.0] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),x),y),z),v_x)** -> equal(x,v)*.
% 299.79/300.44 16002[0:SpL:8415.2,515.0] || equal(v_Procs,v_x) equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),hAPP(v_x,z))* -> equal(w,v)*.
% 299.79/300.44 15999[0:SpL:8415.2,515.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(u)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(v_x,y),z))* -> equal(v,v_x).
% 299.79/300.44 16115[0:SpL:8415.2,514.0] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),x),y),z),v_x)** -> equal(y,w)*.
% 299.79/300.44 16110[0:SpL:8415.2,514.0] || equal(v_Procs,v_x) equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),hAPP(v_x,z))* -> equal(x,v_x).
% 299.79/300.44 16107[0:SpL:8415.2,514.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(u)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(v_x,y),z))* -> equal(w,y).
% 299.79/300.44 16311[0:SpL:8415.2,513.0] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),x),y),z),v_x)** -> equal(z,v_x).
% 299.79/300.44 16306[0:SpL:8415.2,513.0] || equal(v_Procs,v_x) equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),hAPP(v_x,z))* -> equal(y,z).
% 299.79/300.44 16303[0:SpL:8415.2,513.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(u)) equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(v_x,y),z))* -> equal(x,z).
% 299.79/300.44 16417[0:SpR:9935.1,176.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.44 16596[0:Res:361.2,427.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Opreorder(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,u),z,u)* -> c_lessequals(hAPP(y,w),z,u)*.
% 299.79/300.44 16595[0:Res:361.2,426.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Oorder(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* c_lessequals(y,hAPP(z,w),u)* -> c_lessequals(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,z,v,u),u)*.
% 299.79/300.44 16582[0:SpR:10063.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w)) -> c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,u),u)*.
% 299.79/300.44 16579[0:SpR:586.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(y,hAPP(z,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_COMBB(y,x1,x2,x3),z),v,u),u)*.
% 299.79/300.44 16578[0:SpR:585.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(hAPP(y,w),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_COMBC(y,x1,x2,x3),z),v,u),u)*.
% 299.79/300.44 16554[0:SpR:9935.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v,tc_bool) hBOOL(hAPP(hAPP(c_in(w),v),x))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),w,u),u)*.
% 299.79/300.44 16520[0:SpR:8415.2,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),v) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,w,u),u)*.
% 299.79/300.44 16512[0:SpR:369.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Set_Oinsert(w,x),y)),z)) -> c_lessequals(hAPP(c_Set_Oinsert(w,x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oinsert(w,x),v,u),u)*.
% 299.79/300.44 16511[0:SpR:2089.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),x)) -> c_lessequals(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v_x,tc_Com_Opname),v,u),u)*.
% 299.79/300.44 16506[0:SpR:445.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(w,y) c_lessequals(hAPP(z,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Fun_Ofun__upd(z,y,x1,x2,x3),v,u),u)*.
% 299.79/300.44 16662[0:SpR:9936.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v,tc_bool) hBOOL(hAPP(hAPP(c_in(w),x),y))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,u),u)*.
% 299.79/300.44 16653[0:SpR:9936.1,176.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.44 16772[0:SpL:8415.2,390.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(x,v_x,tc_fun(w,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_x,u,v,w),x,w,v)*.
% 299.79/300.44 17102[0:Res:511.1,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),x),v)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.44 17100[0:Res:511.1,279.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w))**.
% 299.79/300.44 17259[0:Res:510.1,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),x)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.44 17257[0:Res:510.1,279.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x))**.
% 299.79/300.44 17294[0:SpL:181.1,13272.0] || equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Ovimage(c_COMBK(v,w,u),u,w),x)* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)) hBOOL(hAPP(x,v_x))*.
% 299.79/300.44 17366[0:Res:172.2,454.0] class_Orderings_Olinorder(tc_Hoare__Mirabelle_Otriple(t_a)) || c_Finite__Set_Ofinite(u,tc_Hoare__Mirabelle_Otriple(t_a)) -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))) c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(u,v),c_Finite__Set_Olinorder__class_OMax(u,tc_Hoare__Mirabelle_Otriple(t_a)),t_a)*.
% 299.79/300.44 17377[0:SpR:14526.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),w)),x)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_HOL_Ominus__class_Ominus(c_Option_Othe(w),y,tc_fun(z,tc_bool)),v,u),u)*.
% 299.79/300.44 17375[0:SpR:14526.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v)),hAPP(c_Set_Ovimage(c_HOL_Ominus__class_Ominus(c_Option_Othe(v),w,tc_fun(x,tc_bool)),u,y),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.44 17445[0:SpL:181.1,16327.1] || equal(u,c_Set_Ovimage(c_COMBK(v,w,x),x,w))* equal(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)).
% 299.79/300.44 17484[0:Res:171.2,454.0] class_Orderings_Olinorder(tc_Hoare__Mirabelle_Otriple(t_a)) || c_Finite__Set_Ofinite(u,tc_Hoare__Mirabelle_Otriple(t_a)) -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))) c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(u,v),c_Finite__Set_Olinorder__class_OMin(u,tc_Hoare__Mirabelle_Otriple(t_a)),t_a)*.
% 299.79/300.44 17756[0:Res:687.1,255.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_in(u),v),tc_Com_Opname),x,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),x)).
% 299.79/300.44 17755[0:Res:686.1,255.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_in(u),v),tc_Com_Opname),x,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),x)).
% 299.79/300.44 17753[0:Res:171.2,255.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(v,w,tc_fun(u,tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMin(v,u)),w))*.
% 299.79/300.44 17752[0:Res:172.2,255.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(v,w,tc_fun(u,tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMax(v,u)),w))*.
% 299.79/300.44 17731[0:Res:510.1,255.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),y,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),y))*.
% 299.79/300.44 17730[0:Res:511.1,255.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w),y,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),y))*.
% 299.79/300.44 17895[0:SpL:188.1,3698.2] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u))* equal(c_Com_Ocom_OBODY,w) equal(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Com_Ocom_OSKIP) -> .
% 299.79/300.44 17863[0:SpR:188.1,3339.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u))* -> equal(c_Fun_Ofun__upd(w,v_x,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,z),w)**.
% 299.79/300.44 17859[0:SpR:188.1,648.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,x),x,u),tc_Com_Opname,w),v_Procs)))*.
% 299.79/300.44 17845[2:SpR:188.1,15483.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool)).
% 299.79/300.44 17843[0:SpR:188.1,15482.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool)).
% 299.79/300.44 17840[0:SpR:188.1,651.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 18213[0:SpR:12944.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(x,y),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),z,x1)),u,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.79/300.44 18209[0:SpR:9.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,hAPP(y,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ocomp(x,y,z,x1,x2),u,tc_fun(x3,tc_bool)),tc_fun(x3,tc_bool))*.
% 299.79/300.44 18207[0:SpR:11499.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),v)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y)),u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.44 18206[0:SpR:10090.1,362.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 18201[0:SpR:105.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(y,x,v),u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.44 18200[0:SpR:1196.1,362.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 18197[0:SpR:38.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(y,x,v),u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.44 18196[0:SpR:321.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(y,v,x),u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.44 18194[0:SpR:1195.1,362.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 18192[0:SpR:11695.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),v)),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(x,y),c_Option_Othe(v)),u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.44 18191[0:SpR:11473.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.44 18174[0:SpR:87.1,362.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ouminus__class_Ouminus(w,u)),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 18173[0:SpR:88.1,362.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 18172[0:SpR:17045.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y,tc_fun(z,tc_bool)),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.44 18161[0:SpR:2098.1,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(x,v,t_a) c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,v),tc_Hoare__Mirabelle_Otriple(t_a)),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 18150[0:SpR:3586.1,362.1] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v,u),w,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 18136[0:SpR:653.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,w),w,tc_Com_Opname),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 18132[0:SpR:9493.1,362.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 18130[0:SpR:8498.1,362.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),u),x)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(y,v),w,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.44 18234[0:SSi:18227.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(x,hAPP(y,v),tc_fun(z,tc_bool))* -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.44 18270[0:SpR:15172.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),y,z),x1,tc_fun(x2,tc_bool)),v,u),u)*.
% 299.79/300.44 18267[0:SpR:15172.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),y,tc_fun(z,tc_bool)),u,x1),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.79/300.44 18413[0:SpR:12944.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(y,z),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x1,x2)),u,x),w)))*.
% 299.79/300.44 18409[0:SpR:9.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,hAPP(z,v))),hAPP(c_Set_Oimage(c_Fun_Ocomp(y,z,x1,x2,x3),u,x),w)))*.
% 299.79/300.44 18407[0:SpR:11499.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),v)) -> hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z)),u,w),v)))*.
% 299.79/300.44 18406[0:SpR:10090.1,545.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(u,v_x),v,x),w)))*.
% 299.79/300.44 18401[0:SpR:105.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(z,y,v),u,x),w)))*.
% 299.79/300.44 18400[0:SpR:1196.1,545.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,x),w)))*.
% 299.79/300.44 18397[0:SpR:38.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(z,y,v),u,x),w)))*.
% 299.79/300.44 18396[0:SpR:321.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oimage(z,v,y),u,x),w)))*.
% 299.79/300.44 18394[0:SpR:1195.1,545.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,x),w)))*.
% 299.79/300.44 18392[0:SpR:11695.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),v)),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(y,z),c_Option_Othe(v)),u,x),w)))*.
% 299.79/300.44 18391[0:SpR:11473.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u,x),w)))*.
% 299.79/300.44 18374[0:SpR:87.1,545.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ouminus__class_Ouminus(w,u)),x)) -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),x)))*.
% 299.79/300.44 18373[0:SpR:88.1,545.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),v,y),x)))*.
% 299.79/300.44 18372[0:SpR:17045.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),z,tc_fun(x1,tc_bool)),u,x),w)))*.
% 299.79/300.44 18361[0:SpR:2098.1,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(x,v,t_a) hBOOL(hAPP(hAPP(c_in(y),v),hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,v),tc_Hoare__Mirabelle_Otriple(t_a)),u,y),w)))*.
% 299.79/300.44 18350[0:SpR:3586.1,545.1] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> hBOOL(hAPP(hAPP(c_in(y),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,y),x)))*.
% 299.79/300.44 18336[0:SpR:653.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,x),x,tc_Com_Opname),u,w),v)))*.
% 299.79/300.44 18332[0:SpR:9493.1,545.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> hBOOL(hAPP(hAPP(c_in(x),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,x),w)))*.
% 299.79/300.44 18330[0:SpR:8498.1,545.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),u),x)) -> hBOOL(hAPP(hAPP(c_in(y),u),hAPP(c_Set_Oimage(c_Set_Oinsert(z,v),w,y),x)))*.
% 299.79/300.44 18585[0:Res:153.1,255.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* c_lessequals(hAPP(c_Set_Ovimage(v,y,u),x),z,tc_fun(y,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(y),w),z))*.
% 299.79/300.44 18718[0:SpR:128.0,9568.0] || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Ovimage(u,v,w)),z),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),tc_bool)*.
% 299.79/300.44 18686[0:SpR:544.1,9568.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_bool)*.
% 299.79/300.44 18685[0:SpR:543.1,9568.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_bool)*.
% 299.79/300.44 18678[0:SpR:181.1,9568.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,x),x,u)),z),w),tc_bool)*.
% 299.79/300.44 18868[0:Res:49.2,18768.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_Set_Oinsert(v_x,tc_Com_Opname),c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> c_lessequals(v_Procs,hAPP(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_x,tc_Com_Opname),tc_fun(u,tc_bool)),v_Procs),tc_bool)*.
% 299.79/300.44 19029[0:SpR:128.0,9569.0] || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),c_Set_Ovimage(u,v,w)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),tc_bool)*.
% 299.79/300.44 18997[0:SpR:544.1,9569.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_bool)*.
% 299.79/300.44 18996[0:SpR:543.1,9569.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_bool)*.
% 299.79/300.44 18989[0:SpR:181.1,9569.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),c_Set_Ovimage(c_COMBK(v,u,x),x,u)),w),tc_bool)*.
% 299.79/300.44 19470[0:Res:9067.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(w,u),x)),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(w,u),x)),u),w,u)*.
% 299.79/300.44 19469[0:Res:9067.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(w,u),x)),u) -> c_lessequals(w,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(w,u),x)),u),u)*.
% 299.79/300.44 19531[0:Res:19452.0,170.1] class_Orderings_Olinorder(t_a) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),t_a) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),t_a),v_x,t_a)*.
% 299.79/300.44 19530[0:Res:19452.0,169.1] class_Orderings_Olinorder(t_a) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),t_a) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(u,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),t_a),t_a)*.
% 299.79/300.44 19595[0:Res:19441.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),tc_Com_Opname),v_x,tc_Com_Opname)*.
% 299.79/300.44 19594[0:Res:19441.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),tc_Com_Opname) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),tc_Com_Opname),tc_Com_Opname)*.
% 299.79/300.44 19675[0:Res:15262.1,496.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.79/300.44 19674[0:Res:3285.1,496.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))* c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.79/300.44 19673[0:Res:3317.1,496.0] || equal(c_in(u),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,hAPP(c_Set_Oinsert(v_x,u),w))),hAPP(c_Set_Oinsert(v_x,u),w)))* c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.79/300.44 19865[0:SpL:104.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),v_Procs) -> .
% 299.79/300.44 19864[0:SpL:104.0,3929.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.79/300.44 19807[0:SpR:104.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w,tc_fun(x,tc_bool)),y),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,y,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),tc_bool)*.
% 299.79/300.44 19788[0:SpR:104.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),y,z,x1),v))*.
% 299.79/300.44 19770[0:SpR:104.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),tc_Com_Opname,u),u)*.
% 299.79/300.44 20019[0:SpL:64.0,442.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),x),w) -> c_Hoare__Mirabelle_Ohoare__derivs(u,c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),w)*.
% 299.79/300.44 20018[0:SpL:64.0,363.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),x,tc_fun(v,tc_bool))*.
% 299.79/300.44 19990[0:SpR:64.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(u,v),w,tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),hAPP(c_Set_Oinsert(u,v),y),tc_bool)*.
% 299.79/300.44 19973[0:SpR:64.0,364.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* -> c_lessequals(u,hAPP(c_Set_Oinsert(w,x),v),tc_fun(x,tc_bool)).
% 299.79/300.44 19968[0:SpR:64.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),w),x),c_Set_Oinsert(u,v),y,z,x1),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))))*.
% 299.79/300.44 20366[0:SpR:9925.0,438.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.44 20291[0:SpR:8385.1,438.1] || equal(u,v_Procs) c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),v,w),u),u)**.
% 299.79/300.44 20285[0:SpR:438.1,9567.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,tc_fun(y,tc_bool)),hAPP(u,z)),z,tc_bool)*.
% 299.79/300.44 20275[0:SpR:438.1,5875.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(x,y),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x1,x2),hAPP(u,x)))*.
% 299.79/300.44 20410[0:Rew:20362.1,20328.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v,u,x),x,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,z)* -> equal(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w).
% 299.79/300.44 20510[0:SpR:9925.0,99.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.44 20434[0:SpR:8385.1,99.1] || equal(u,v_Procs) c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),v,w),u),u)**.
% 299.79/300.44 20427[0:SpR:99.1,9567.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,tc_fun(y,tc_bool)),hAPP(u,z)),z,tc_bool)*.
% 299.79/300.44 20417[0:SpR:99.1,5875.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(x,y),c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x1,x2),hAPP(u,x)))*.
% 299.79/300.44 20678[0:SSi:20639.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),y),hAPP(v,y),tc_bool)*.
% 299.79/300.44 21014[0:SpL:317.0,357.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v)* c_lessequals(x,hAPP(c_Set_Oinsert(hAPP(y,u),z),hAPP(c_Set_Oimage(y,v,z),w)),tc_fun(z,tc_bool))* -> c_Finite__Set_Ofinite(x,z).
% 299.79/300.44 21000[0:SpR:9925.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),v),x)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),x)))*.
% 299.79/300.44 20923[0:SpR:8385.1,317.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(u,v),x)),hAPP(c_Set_Oinsert(u,w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,w),x)))*.
% 299.79/300.44 20892[0:SpR:317.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(u,v),w),x,tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(u,z,w),x1)),hAPP(c_Set_Oimage(u,z,w),hAPP(c_Set_Oinsert(v,z),x1)),tc_bool)*.
% 299.79/300.44 20885[0:SpR:317.0,254.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oinsert(z,x),y))))*.
% 299.79/300.44 20871[0:SpR:317.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),z),c_Set_Oinsert(hAPP(u,x),w),x1,x2,x3),hAPP(c_Set_Oimage(u,v,w),y)))*.
% 299.79/300.44 20862[0:SpR:317.0,8498.1] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(y,v),x)),hAPP(c_Set_Oimage(u,v,w),x))**.
% 299.79/300.44 20858[0:SpR:317.0,2097.1] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),hAPP(u,y)))* -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(y,v),x)),hAPP(c_Set_Oimage(u,v,w),x))**.
% 299.79/300.44 20848[0:SpR:317.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oimage(u,v,w),x,tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(z,v),x1)),hAPP(c_Set_Oinsert(hAPP(u,z),w),hAPP(c_Set_Oimage(u,v,w),x1)),tc_bool)*.
% 299.79/300.44 20844[0:SpR:317.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(hAPP(v,w),x),hAPP(c_Set_Oimage(v,y,x),z))),hAPP(c_Set_Oimage(c_Set_Oimage(v,y,x),x1,u),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.79/300.44 20834[0:SpR:317.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),y)),z),c_Set_Oimage(u,x,w),x1,x2,x3),hAPP(c_Set_Oinsert(v,x),y)))*.
% 299.79/300.44 20833[0:SpR:317.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y),hAPP(c_Set_Oinsert(hAPP(u,x),w),hAPP(c_Set_Oimage(u,v,w),y)),z,x1),c_Set_Oimage(u,v,w))**.
% 299.79/300.44 21113[0:SpR:128.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(z,tc_fun(w,tc_bool)),x),x1)),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),z),tc_fun(v,tc_bool))))*.
% 299.79/300.44 21081[0:SpR:544.1,20881.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),w),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)))*.
% 299.79/300.44 21080[0:SpR:543.1,20881.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),w),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)))*.
% 299.79/300.44 21073[0:SpR:181.1,20881.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z),hAPP(c_Set_Oinsert(w,y),x1)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))*.
% 299.79/300.44 21171[0:SpR:188.1,21130.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_Procs)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,w),w,u),x,y),hAPP(c_in(tc_Com_Opname),v_x)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.79/300.44 21232[0:SpR:188.1,21141.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,w),w,u),t_a,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.79/300.44 21638[0:SpL:21267.0,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),v_x),x)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x),tc_Com_Opname,y),hAPP(u,x)))*.
% 299.79/300.44 21533[0:SpR:540.1,21267.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_Com_Opname,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))**.
% 299.79/300.44 21532[0:SpR:539.1,21267.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),tc_Com_Opname,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))**.
% 299.79/300.44 21511[0:SpR:25.1,21267.0] class_HOL_Ouminus(u) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),tc_Com_Opname,w)),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))**.
% 299.79/300.44 21433[0:SpR:21267.0,83.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x),tc_Com_Opname,x),tc_fun(w,tc_bool))*.
% 299.79/300.44 21419[0:SpR:21267.0,229.0] || -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),v_x),c_Com_Ocom_OSKIP),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),v_x),tc_Com_Opname,w)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.79/300.44 21390[0:SpR:21267.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)),x))* -> hBOOL(hAPP(hAPP(c_in(y),hAPP(v,v_x)),hAPP(c_Set_Oimage(v,u,y),x)))*.
% 299.79/300.44 21389[0:SpR:21267.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)),x))* -> c_lessequals(hAPP(v,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 21364[0:SpR:21267.0,299.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,w),v,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),v).
% 299.79/300.44 21323[0:SpR:21267.0,34.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x),tc_Com_Opname,x),hAPP(u,y)))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),v_x),y)).
% 299.79/300.44 21781[0:SpR:181.1,21143.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,w),w,u),t_a,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.79/300.44 21850[0:SpR:181.1,21131.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.79/300.44 22266[0:SpL:21893.0,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),v_x),x)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),v_x),c_Set_Ovimage(u,v,w),tc_Com_Opname,y),hAPP(u,x)))*.
% 299.79/300.44 22160[0:SpR:540.1,21893.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))**.
% 299.79/300.44 22159[0:SpR:539.1,21893.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))**.
% 299.79/300.44 22138[0:SpR:25.1,21893.0] class_HOL_Ouminus(u) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_Com_Opname,w)),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))**.
% 299.79/300.44 22059[0:SpR:21893.0,83.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),v_x),c_Set_Ovimage(u,v,w),tc_Com_Opname,x),tc_fun(w,tc_bool))*.
% 299.79/300.44 22045[0:SpR:21893.0,229.0] || -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),v_x),c_Com_Ocom_OSKIP),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),v_x),c_Hoare__Mirabelle_Otriple_Otriple(v),tc_Com_Opname,w)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.79/300.44 22016[0:SpR:21893.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)),x))* -> hBOOL(hAPP(hAPP(c_in(y),hAPP(v,v_x)),hAPP(c_Set_Oimage(v,u,y),x)))*.
% 299.79/300.44 22015[0:SpR:21893.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)),x))* -> c_lessequals(hAPP(v,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 21990[0:SpR:21893.0,299.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),v).
% 299.79/300.44 21949[0:SpR:21893.0,34.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),v_x),c_Set_Ovimage(u,v,w),tc_Com_Opname,x),hAPP(u,y)))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),v_x),y)).
% 299.79/300.44 22411[0:SpR:97.1,9567.0] || c_Fun_Oinj__on(u,v,w,x) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(u,w,x),v)),v,tc_bool)*.
% 299.79/300.44 22482[0:SpR:181.1,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),w),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(w,v,x),x,v),tc_Com_Opname,y),u),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))*.
% 299.79/300.44 22664[0:SpL:158.0,357.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w)* c_lessequals(y,hAPP(c_Set_Oimage(c_Fun_Ocomp(z,u,w,x1,v),v,x1),x),tc_fun(x1,tc_bool))* -> c_Finite__Set_Ofinite(y,x1).
% 299.79/300.44 22644[0:SpL:158.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_Procs)** -> .
% 299.79/300.44 22643[0:SpL:158.0,3929.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)))* equal(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.79/300.44 22619[0:SpR:158.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oimage(u,v,w),x,tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(z,x1,v),x2)),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,z,v,w,x1),x1,w),x2),tc_bool)*.
% 299.79/300.44 22604[0:SpR:158.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),x1),c_Set_Oimage(u,w,x),x2,x3,x4),hAPP(c_Set_Oimage(v,y,w),z)))*.
% 299.79/300.44 22603[0:SpR:158.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z),x1,x2),c_Set_Oimage(u,v,w))**.
% 299.79/300.44 22577[0:SpR:158.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,tc_fun(x1,tc_bool)),x2),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x2)),tc_bool)*.
% 299.79/300.44 22562[0:SpR:158.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),x1),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x2,x3,x4),z))*.
% 299.79/300.44 22551[0:SpR:158.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,z,w),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oimage(c_Fun_Ocomp(v,y,w,x,z),z,x),tc_Com_Opname,u),u)*.
% 299.79/300.44 22682[0:Rew:9.0,22575.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,hAPP(z,v))),hAPP(c_Set_Oimage(y,x1,x),hAPP(c_Set_Oimage(z,u,x1),w))))*.
% 299.79/300.44 22797[0:SpR:130.1,3294.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_in(t_a)) -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.44 23022[0:SpL:131.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_Procs)** -> .
% 299.79/300.44 23021[0:SpL:131.0,3929.0] || hBOOL(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)))* equal(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.79/300.44 23000[0:SpR:131.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Ovimage(u,v,w),x,tc_fun(y,tc_bool)),hAPP(c_Set_Ovimage(z,w,x1),x2)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(z,u,w,x1,v),v,x1),x2),tc_bool)*.
% 299.79/300.44 22984[0:SpR:131.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),x1),c_Set_Ovimage(v,y,w),x2,x3,x4),hAPP(c_Set_Ovimage(u,w,x),z)))*.
% 299.79/300.44 22983[0:SpR:131.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),z),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z),x1,x2),c_Set_Ovimage(u,v,w))**.
% 299.79/300.44 22963[0:SpR:131.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,tc_fun(x1,tc_bool)),x2),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x2)),tc_bool)*.
% 299.79/300.44 22949[0:SpR:131.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),z)),x1),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x2,x3,x4),z))*.
% 299.79/300.44 22938[0:SpR:131.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),hAPP(c_Set_Ovimage(y,x,z),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(y,v,x,z,w),w,z),tc_Com_Opname,u),u)*.
% 299.79/300.44 23051[0:Rew:9.0,23037.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),hAPP(c_Set_Ovimage(y,x,z),x1))))* -> hBOOL(hAPP(hAPP(c_in(z),hAPP(y,hAPP(w,v))),x1)).
% 299.79/300.44 23053[0:Rew:9.0,22961.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,x))),y)) -> hBOOL(hAPP(hAPP(c_in(z),x),hAPP(c_Set_Ovimage(w,z,x1),hAPP(c_Set_Ovimage(v,x1,u),y))))*.
% 299.79/300.44 23177[0:SpL:130.1,3487.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.44 23254[0:SpL:130.1,3489.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_in(tc_Com_Opname)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.79/300.44 23396[0:SpL:460.1,3506.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))* -> .
% 299.79/300.44 23392[0:SpR:297.2,460.1] class_Lattices_Oupper__semilattice(tc_fun(t_a,t_b)) || c_lessequals(v_f,v_g,tc_fun(t_a,t_b)) class_Lattices_Olattice(t_b) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(v_g,v_x))**.
% 299.79/300.44 23391[0:SpR:299.2,460.1] class_Lattices_Oupper__semilattice(tc_fun(t_a,t_b)) || c_lessequals(v_g,v_f,tc_fun(t_a,t_b)) class_Lattices_Olattice(t_b) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(v_f,v_x))**.
% 299.79/300.44 23376[0:SpR:460.1,9566.0] || class_Lattices_Olattice(t_b) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)),v_x),tc_bool)*.
% 299.79/300.44 23574[0:SpL:523.1,3506.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)))* -> .
% 299.79/300.44 23560[0:SpR:584.0,523.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v,w,x,y),z),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(z,v_x)),hAPP(hAPP(v,z),v_x)))*.
% 299.79/300.44 23550[0:SpR:87.1,523.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_x)),hAPP(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v_x))**.
% 299.79/300.44 23507[0:SpR:523.1,9566.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w)),v_x),tc_bool)*.
% 299.79/300.44 23792[0:SpR:23682.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v),hAPP(c_Set_Oinsert(w,u),x)),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v),x)))*.
% 299.79/300.44 23791[0:SpR:23682.0,99.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v),w),w)**.
% 299.79/300.44 23790[0:SpR:23682.0,438.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v),w),w)**.
% 299.79/300.44 24136[0:SpR:542.0,9566.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_bool)*.
% 299.79/300.44 24318[0:SpR:393.1,9566.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) c_lessequals(hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),hAPP(hAPP(c_Set_Oinsert(y,z),c_Set_Oimage(c_COMBK(w,x,v),v,x)),u),tc_bool)*.
% 299.79/300.44 24648[0:SpR:523.1,24020.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),v_x),v_x)**.
% 299.79/300.44 24647[0:SpR:460.1,24020.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),v_x),v_x)**.
% 299.79/300.44 24768[0:SpR:614.2,9566.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u),hAPP(hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u)),tc_bool)*.
% 299.79/300.44 25063[0:SpR:131.0,23902.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.44 25062[0:SpR:158.0,23902.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.44 25045[0:SpR:104.0,23902.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.44 25439[0:SpL:512.0,447.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),w)* c_Fun_Oinj__on(hAPP(c_COMBB(u,v,w,y),x),z,y,w)* -> c_Finite__Set_Ofinite(z,y).
% 299.79/300.44 25426[0:SpL:512.0,3506.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(z,x1),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)))* -> .
% 299.79/300.44 25363[0:SpR:512.0,98.1] || c_Fun_Oinj__on(hAPP(c_COMBB(u,v,w,x),y),z,x,w)* -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),z)),w),c_Finite__Set_Ocard(z,x))**.
% 299.79/300.44 25359[0:SpR:512.0,9566.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(hAPP(c_Set_Oinsert(x1,x2),c_Set_Oimage(hAPP(c_COMBB(u,v,w,y),x),y,w)),z),tc_bool)*.
% 299.79/300.44 25332[0:SpR:512.0,24020.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),v_x),v_x)**.
% 299.79/300.44 25710[0:Res:149.1,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x),v))* c_Hoare__Mirabelle_Otriple__valid(w,x,t_a)*.
% 299.79/300.44 25691[0:SpL:3229.1,455.0] || equal(u,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v))* hBOOL(hAPP(u,v_x))* c_Hoare__Mirabelle_Ohoare__valids(w,v_x,t_a) c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,v,t_a)*.
% 299.79/300.44 25686[0:SpL:3229.1,455.0] || equal(u,c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(hAPP(u,v_x),v))* c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,v_x,t_a).
% 299.79/300.44 25811[0:SpL:3229.1,273.0] || equal(u,c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool)) equal(hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),w),hAPP(u,v_x))* -> equal(w,v_x).
% 299.79/300.44 25970[0:SpL:339.0,16286.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),v_Procs) -> .
% 299.79/300.44 25954[0:SpR:10063.0,339.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u))**.
% 299.79/300.44 25948[0:SpR:3229.1,339.0] || equal(u,c_Set_Oinsert(v,w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(u,v_x)),x),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),x)))*.
% 299.79/300.44 26001[0:Rew:339.0,25942.0] || -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v))),hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)))**.
% 299.79/300.44 25918[0:SpR:339.0,328.1] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)) -> equal(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u)),hAPP(c_Set_Oinsert(v,w),x))**.
% 299.79/300.44 25861[0:SpR:339.0,3229.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x))) -> equal(hAPP(u,v_x),hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)))*.
% 299.79/300.44 25839[0:SpR:339.0,3283.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),v_Procs))*.
% 299.79/300.44 25833[0:SpR:339.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),tc_Com_Opname,x),v_Procs),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.44 26251[0:SpL:338.0,7600.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),y))),v)* -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y),v).
% 299.79/300.44 26248[0:SpL:338.0,360.0] || c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),y)),v,z)* -> c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y),v,z).
% 299.79/300.44 26243[0:SpL:338.0,4382.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),v_Procs)** -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),v_x)) equal(w,v_x).
% 299.79/300.44 26232[0:SpL:338.0,327.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Oinsert(u,v),x))** -> c_lessequals(w,hAPP(c_Set_Oinsert(u,v),x),tc_fun(v,tc_bool)).
% 299.79/300.44 26182[0:SpR:3229.1,338.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),v_x)),hAPP(c_Set_Oinsert(x,v),hAPP(u,v_x)))*.
% 299.79/300.44 26164[0:SpR:10063.0,338.0] || -> equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))**.
% 299.79/300.44 26158[0:SpR:3229.1,338.0] || equal(u,c_Set_Oinsert(v,w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(u,v_x)),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))*.
% 299.79/300.44 26153[0:SpR:369.0,338.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(u,v),x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(u,v),x)))**.
% 299.79/300.44 26152[0:SpR:2089.0,338.0] || -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))**.
% 299.79/300.44 26105[0:SpR:338.0,19436.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_Procs) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v))))*.
% 299.79/300.44 26104[0:SpR:338.0,7460.1] || c_lessequals(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v)),v_x))*.
% 299.79/300.44 26090[0:SpR:338.0,8376.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(tc_Com_Opname)) equal(hAPP(c_Set_Oinsert(v,u),w),v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),w)))*.
% 299.79/300.44 26086[0:SpR:338.0,329.1] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)) -> equal(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x)),hAPP(c_Set_Oinsert(v,w),x))**.
% 299.79/300.44 26279[0:Rew:104.0,26205.0] || -> equal(hAPP(c_Set_Oinsert(u,v),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),x),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))**.
% 299.79/300.44 26286[0:SSi:26285.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oinsert(u,t_a),v),v_x)),hAPP(w,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v,v_x)),hAPP(hAPP(c_Set_Oinsert(u,t_a),w),v_x)))**.
% 299.79/300.44 26287[0:Rew:26286.0,26005.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(v,v_x)),hAPP(hAPP(c_Set_Oinsert(u,t_a),w),v_x)))**.
% 299.79/300.44 26405[0:Res:448.1,85.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool))* c_lessequals(c_HOL_Ominus__class_Ominus(x,v,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool)).
% 299.79/300.44 26334[0:SpL:3229.1,85.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* c_lessequals(x,hAPP(u,v_x),tc_fun(v,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(x,w,tc_fun(v,tc_bool)),v_x,tc_fun(v,tc_bool))*.
% 299.79/300.44 26329[0:SpL:3229.1,85.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) c_lessequals(w,hAPP(hAPP(u,v_x),x),tc_fun(v,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),x,tc_fun(v,tc_bool))*.
% 299.79/300.44 26535[0:Res:84.1,363.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)),y,tc_fun(v,tc_bool))* -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y),tc_fun(v,tc_bool)).
% 299.79/300.44 26479[0:SpR:3229.1,84.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* c_lessequals(c_HOL_Ominus__class_Ominus(x,w,tc_fun(v,tc_bool)),v_x,tc_fun(v,tc_bool))* -> c_lessequals(x,hAPP(u,v_x),tc_fun(v,tc_bool))*.
% 299.79/300.44 26474[0:SpR:3229.1,84.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) c_lessequals(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),x,tc_fun(v,tc_bool))* -> c_lessequals(w,hAPP(hAPP(u,v_x),x),tc_fun(v,tc_bool))*.
% 299.79/300.44 26690[0:SpR:3229.1,244.2] || equal(u,c_Set_Oinsert(v,w))* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x))* equal(c_Finite__Set_Ocard(v_x,w),c_HOL_Ozero__class_Ozero(tc_nat)) equal(c_Finite__Set_Ocard(hAPP(u,v_x),w),c_Suc(c_Finite__Set_Ocard(v_x,w)))**.
% 299.79/300.44 26839[0:SpR:3229.1,56.1] || equal(u,c_Set_Oinsert(v,w))* hBOOL(hAPP(hAPP(c_in(w),v),x))* -> equal(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),x,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(v_x,x,tc_fun(w,tc_bool)))**.
% 299.79/300.44 26877[0:SSi:26876.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(t_a),u),v)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(u,t_a),w),v_x),hAPP(v,v_x),tc_bool),c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(v,v_x),tc_bool))**.
% 299.79/300.44 26934[0:SpR:3229.1,424.2] || equal(u,c_Set_Oinsert(v,w))* hBOOL(hAPP(hAPP(c_in(w),v),x))* c_lessequals(v_x,x,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(u,v_x),x,tc_fun(w,tc_bool))*.
% 299.79/300.44 26999[0:SpL:3229.1,175.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Ovimage(w,v,x),hAPP(c_Set_Oinsert(y,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))* -> equal(hAPP(w,v_x),y).
% 299.79/300.44 27121[0:Res:1103.1,280.1] || hBOOL(hAPP(hAPP(u,v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(x,hAPP(c_in(y),v),t_a) hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,hAPP(c_in(y),v)),u,y,tc_fun(z,tc_bool)),w))*.
% 299.79/300.44 27080[0:Res:254.1,280.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(x,v),y))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(z,u),w),x,u,tc_fun(x1,tc_bool)),y))*.
% 299.79/300.44 27060[0:SpL:3229.1,280.1] || equal(u,hAPP(c_in(v),w))* hBOOL(hAPP(hAPP(x,w),y))* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,x,v,tc_fun(z,tc_bool)),y))*.
% 299.79/300.44 27055[0:SpL:3229.1,280.1] || equal(u,c_in(v))* hBOOL(hAPP(hAPP(w,v_x),x)) hBOOL(hAPP(hAPP(u,v_x),y))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,v,tc_fun(z,tc_bool)),x))*.
% 299.79/300.44 27375[0:SpL:3229.1,470.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(w,x,v),y)))* -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__XimageE__1__1(y,v_x,w,x,v)),y))*.
% 299.79/300.44 27368[0:SpL:3229.1,470.0] || equal(u,c_Set_Oimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(u,v_x)))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_x,y,v,w,x)),v_x))*.
% 299.79/300.44 27435[0:SpL:3229.1,466.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(w,x,v),y)))* -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(y,w,v_x,x,v)),y))*.
% 299.79/300.44 27428[0:SpL:3229.1,466.0] || equal(u,c_Set_Oimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(u,v_x)))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_x,v,y,w,x)),v_x))*.
% 299.79/300.44 27610[0:SpR:23912.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,x),v),v)**.
% 299.79/300.44 27587[0:SpR:351.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(c_COMBK(x,y,z),w,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_COMBK(x,y,z),u,x1),x),v)*.
% 299.79/300.44 27585[0:SpR:456.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(v,w)),x))* c_Fun_Oinj__on(c_Option_Othe(w),x,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,c_Option_Othe(w),u,y),v),c_Option_Ooption_OSome(v,w))**.
% 299.79/300.44 27565[0:SpR:3229.1,373.2] || equal(u,v) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) c_Fun_Oinj__on(v,x,w,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,y),hAPP(u,v_x)),v_x)**.
% 299.79/300.44 27763[0:SpR:23912.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,x),v),v)**.
% 299.79/300.44 27740[0:SpR:351.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(c_COMBK(x,y,z),w,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_COMBK(x,y,z),u,x1),x),v)*.
% 299.79/300.44 27738[0:SpR:456.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(v,w)),x))* c_Fun_Oinj__on(c_Option_Othe(w),x,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,c_Option_Othe(w),u,y),v),c_Option_Ooption_OSome(v,w))**.
% 299.79/300.44 27718[0:SpR:3229.1,71.2] || equal(u,v) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) c_Fun_Oinj__on(v,x,w,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,v,w,y),hAPP(u,v_x)),v_x)**.
% 299.79/300.44 27844[7:SpR:188.1,27219.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool)).
% 299.79/300.44 27943[0:Res:468.0,3929.0] || equal(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v_x,v,w,u,x)),y)* -> equal(hAPP(c_Set_Oimage(v,u,x),v_x),hAPP(c_Set_Oimage(w,u,x),v_x)) hBOOL(hAPP(y,v_x))*.
% 299.79/300.44 27991[0:SpR:188.1,27381.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.44 28083[0:SpR:339.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),tc_Com_Opname,x)))*.
% 299.79/300.44 28232[0:SpL:465.1,16286.0] || equal(hAPP(c_Set_Oimage(u,v,w),v_x),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(v),x),v_x)).
% 299.79/300.44 28204[0:SpR:465.1,21141.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))) hBOOL(hAPP(hAPP(c_Set_Oimage(w,t_a,x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Fun_Ofun__upd(w,u,y,t_a,x),v_x)))*.
% 299.79/300.44 28165[0:SpR:465.1,3229.1] || equal(u,c_Set_Oimage(c_Fun_Ofun__upd(v,w,x,y,z),y,z))* -> hBOOL(hAPP(hAPP(c_in(y),w),v_x)) equal(hAPP(u,v_x),hAPP(c_Set_Oimage(v,y,z),v_x))*.
% 299.79/300.44 28158[0:SpR:465.1,28032.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,u,x),v_x),c_Set_Oimage(c_Fun_Ofun__upd(w,v,y,u,x),u,x),tc_Com_Opname,z)))*.
% 299.79/300.44 28141[0:SpR:465.1,3283.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(u,x,y),v_x),v_Procs)).
% 299.79/300.44 28134[0:SpR:465.1,1158.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),tc_Com_Opname,z),v_Procs),hAPP(c_Set_Oimage(w,u,y),v_x)))*.
% 299.79/300.44 28125[0:SpR:465.1,21130.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_in(tc_Com_Opname),v_x))) hBOOL(hAPP(hAPP(c_Set_Oimage(w,u,x),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_Fun_Ofun__upd(w,v,y,u,x),v_Procs)))*.
% 299.79/300.44 28293[0:SpR:188.1,27441.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.44 28387[0:SpR:339.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_Com_Opname,x)))*.
% 299.79/300.44 28377[0:SpR:465.1,28335.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),hAPP(c_Set_Oimage(w,u,y),v_x),tc_Com_Opname,z)))*.
% 299.79/300.44 28521[0:SpR:23912.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Fun_Ofun__upd(v,w,u,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,y,z,x),w,u,x,z))*.
% 299.79/300.44 28498[0:SpR:351.0,118.0] || -> equal(c_Fun_Ocomp(c_COMBK(u,v,w),c_Fun_Ofun__upd(x,y,z,x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_COMBK(u,v,w),x,x2,x3,x1),y,u,x1,x3))*.
% 299.79/300.44 28475[0:SpR:3229.1,118.0] || equal(u,v) -> equal(c_Fun_Ocomp(v,c_Fun_Ofun__upd(w,x,v_x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(v,w,z,x1,y),x,hAPP(u,v_x),y,x1))*.
% 299.79/300.44 28752[0:SpR:188.1,28031.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.44 28692[0:SpR:28031.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(x,v_x),x,tc_Com_Opname,y),tc_Com_Opname),u,w),v)))*.
% 299.79/300.44 28689[0:SpR:28031.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(w,v_x),w,tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 28907[0:SpR:188.1,28334.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.44 28847[0:SpR:28334.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,x,hAPP(x,v_x),tc_Com_Opname,y),tc_Com_Opname),u,w),v)))*.
% 299.79/300.44 28844[0:SpR:28334.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,hAPP(w,v_x),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 29165[0:SpL:537.1,3483.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.44 29157[0:SpR:10090.1,537.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(tc_bool)),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(tc_bool)),v))**.
% 299.79/300.44 29105[0:SpR:3229.1,537.1] class_Lattices_Olattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(v,v_x),w)),x),hAPP(hAPP(v,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))**.
% 299.79/300.44 29256[0:SSi:29079.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)),x),tc_bool)*.
% 299.79/300.44 29257[0:SSi:29072.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w))))*.
% 299.79/300.44 29384[7:SpR:27278.1,545.1] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> hBOOL(hAPP(hAPP(c_in(y),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,y),x)))*.
% 299.79/300.44 29381[7:SpR:27278.1,362.1] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v,u),w,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 29690[0:SpL:534.1,3483.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.44 29682[0:SpR:10090.1,534.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(tc_bool)),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(tc_bool)),v))**.
% 299.79/300.44 29629[0:SpR:3229.1,534.1] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(v,v_x),w)),x),hAPP(hAPP(v,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))**.
% 299.79/300.44 29935[0:SpR:27043.1,338.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x))**.
% 299.79/300.44 29918[0:SpR:27043.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_Procs,x),v,u),u)*.
% 299.79/300.44 29913[0:SpR:27043.1,339.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))**.
% 299.79/300.44 29901[0:SpR:27043.1,176.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_Procs,v),u,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 30272[0:SpR:3229.1,536.1] class_Lattices_Olattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(v,v_x),x)),hAPP(hAPP(v,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))*.
% 299.79/300.44 30267[0:SpR:10090.1,536.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.79/300.44 30423[0:SSi:30129.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w)),x),tc_bool)*.
% 299.79/300.44 30424[0:SSi:30125.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y))))*.
% 299.79/300.44 30836[0:SpR:3229.1,535.1] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(v,v_x),x)),hAPP(hAPP(v,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))*.
% 299.79/300.44 30831[0:SpR:10090.1,535.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.79/300.44 31131[0:Rew:25912.0,31105.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs))**.
% 299.79/300.44 31089[0:SpR:28771.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,x),tc_Com_Opname),v,u),u)*.
% 299.79/300.44 31072[0:SpR:28771.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),tc_Com_Opname),u,w),hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 31217[0:Rew:25912.0,31191.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs))**.
% 299.79/300.44 31175[0:SpR:28926.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,x),tc_Com_Opname),v,u),u)*.
% 299.79/300.44 31158[0:SpR:28926.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v),tc_Com_Opname),u,w),hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 31270[0:Res:149.1,356.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(hAPP(c_Set_Oimage(c_COMBK(x,y,u),u,y),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.44 31353[0:Res:23961.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_Procs),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_Procs),u),v_x,u)*.
% 299.79/300.44 31352[0:Res:23961.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_Procs),u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_Procs),u),u)*.
% 299.79/300.44 31394[0:SpL:9924.0,449.0] || hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v,w))) -> c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),t_a)*.
% 299.79/300.44 31848[7:SpL:131.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_x)** -> .
% 299.79/300.44 31847[7:SpL:158.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x)** -> .
% 299.79/300.44 31829[7:SpL:104.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),v_x) -> .
% 299.79/300.44 31920[7:SpL:339.0,31868.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),v_x) -> .
% 299.79/300.44 31908[7:SpL:465.1,31868.0] || equal(hAPP(c_Set_Oimage(u,v,w),v_x),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),v_x)** -> hBOOL(hAPP(hAPP(c_in(v),x),v_x)).
% 299.79/300.44 32071[0:Rew:8415.2,32046.3,8415.2,32046.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(v_x,w)) hBOOL(hAPP(v_x,c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))))*.
% 299.79/300.44 32329[0:SpL:10090.1,477.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Orderings_Otop__class_Otop(tc_bool),v,u)))* hBOOL(hAPP(hAPP(c_in(u),w),v_x))* -> hBOOL(hAPP(v,w))*.
% 299.79/300.44 32324[0:SpL:3294.1,477.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Orderings_Obot__class_Obot(tc_bool),v,u)))* hBOOL(hAPP(hAPP(c_in(u),w),v_x))* -> hBOOL(hAPP(v,w))*.
% 299.79/300.44 32505[0:SpL:23902.1,476.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,v,u)))* hBOOL(hAPP(hAPP(c_in(u),w),c_Orderings_Obot__class_Obot(tc_bool)))* -> hBOOL(hAPP(v,w))*.
% 299.79/300.44 32495[0:SpL:104.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),u,x)))* hBOOL(hAPP(hAPP(c_in(x),y),w))* -> hBOOL(hAPP(u,y))*.
% 299.79/300.44 32627[0:SpR:181.1,31533.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),v_Procs))*.
% 299.79/300.44 32713[0:SpR:523.1,32669.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)))))*.
% 299.79/300.44 32712[0:SpR:460.1,32669.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))))*.
% 299.79/300.44 32956[0:SpR:456.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(v,w)),x)) -> equal(hAPP(c_Set_Oinsert(v,y),hAPP(c_Set_Oimage(c_Option_Othe(w),u,y),x)),hAPP(c_Set_Oimage(c_Option_Othe(w),u,y),x))**.
% 299.79/300.44 32910[0:SpR:659.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,w),v))**.
% 299.79/300.44 32873[0:SpR:475.1,7253.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(x,v),y),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),hAPP(c_Set_Oimage(x,u,y),w)))*.
% 299.79/300.44 33283[0:SpR:181.1,32668.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.44 33341[0:Rew:25912.0,33247.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs))**.
% 299.79/300.44 33231[0:SpR:32668.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,x,tc_Com_Opname,y),hAPP(x,v_x)),tc_Com_Opname),v,u),u)*.
% 299.79/300.44 33213[0:SpR:32668.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x)),tc_Com_Opname),u,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.44 33424[0:Res:11030.1,453.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a)) c_Hoare__Mirabelle_Ohoare__valids(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w)),u))* c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.79/300.44 33420[0:Res:3316.1,453.0] || equal(c_in(u),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) c_Hoare__Mirabelle_Ohoare__valids(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.79/300.44 33416[0:Res:9067.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x)),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,y)),u))* c_Hoare__Mirabelle_Otriple__valid(y,w,t_a)*.
% 299.79/300.44 33409[0:Res:9071.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w)),u))* c_Hoare__Mirabelle_Otriple__valid(w,v,t_a)*.
% 299.79/300.44 33521[0:Rew:2095.0,33507.1] || c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u) -> equal(c_Suc(c_Finite__Set_Ocard(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),u)),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u))**.
% 299.79/300.44 33569[0:SpR:181.1,28704.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,x),x,u),tc_Com_Opname,y)))*.
% 299.79/300.44 33660[0:SpR:181.1,28859.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_COMBK(v,u,x),x,u),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),tc_Com_Opname,y)))*.
% 299.79/300.44 33751[7:SpL:181.1,31886.1] || equal(u,c_Set_Ovimage(c_COMBK(v,w,x),x,w))* equal(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_x) -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)).
% 299.79/300.44 33808[0:MRR:33807.1,1088.0] class_Orderings_Olinorder(u) || c_lessequals(v,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))* -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) c_lessequals(w,c_Finite__Set_Olinorder__class_OMin(v,u),u).
% 299.79/300.44 33818[0:SpR:23864.0,383.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,w,x,y),c_Orderings_Obot__class_Obot(tc_bool),v,x,y),c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,w,x,y))**.
% 299.79/300.44 33890[0:MRR:33889.1,1088.0] class_Orderings_Olinorder(u) || c_lessequals(v,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))* -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) c_lessequals(c_Finite__Set_Olinorder__class_OMax(v,u),w,u).
% 299.79/300.44 34379[0:SpL:24914.0,11894.1] || equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,w),hAPP(hAPP(c_in(u),v),v_x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> .
% 299.79/300.44 34360[0:SpL:24914.0,4439.0] || equal(hAPP(c_Set_Ovimage(u,v,w),v_x),v_Procs) -> hBOOL(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Ovimage(u,v,w),v_x)),hAPP(u,v_x)))*.
% 299.79/300.44 34340[0:SpL:24914.0,363.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),v_x),w,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,x),hAPP(c_Set_Oinsert(u,v),v_x)),w,tc_fun(v,tc_bool))*.
% 299.79/300.44 34144[0:SpR:24914.0,9935.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x)),tc_bool)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.79/300.44 34078[0:SpR:24914.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,w,tc_Com_Opname,x),hAPP(w,v_x))),y))* -> c_lessequals(hAPP(w,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,v,u),u)*.
% 299.79/300.44 34022[0:SpR:24914.0,364.1] || c_lessequals(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,x),hAPP(c_Set_Oinsert(v,w),v_x)),tc_fun(w,tc_bool))* -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),v_x),tc_fun(w,tc_bool)).
% 299.79/300.44 34020[0:SpR:24914.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))),hAPP(c_Set_Ovimage(v,u,x),hAPP(c_Set_Oinsert(hAPP(v,v_x),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.44 34013[0:SpR:24914.0,212.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(v,w),u),tc_Com_Opname,x),hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x))))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x)).
% 299.79/300.44 34644[0:SpR:11.0,55.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),w,tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))**.
% 299.79/300.44 34633[0:SpR:55.1,19744.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) c_Hoare__Mirabelle_Ohoare__valids(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),w),v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),c_HOL_Ominus__class_Ominus(w,v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)*.
% 299.79/300.44 34604[0:SpR:55.1,15367.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),u)*.
% 299.79/300.44 34581[0:SpR:55.1,9566.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),y),hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),y),tc_bool)*.
% 299.79/300.44 34671[0:MRR:34586.1,56.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,t_a),u),v,tc_fun(t_a,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)))**.
% 299.79/300.44 34672[0:MRR:34578.1,56.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,w),u),v,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)))**.
% 299.79/300.44 34802[7:SpL:338.0,27282.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),v_x)** -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),v_x)) equal(w,v_x).
% 299.79/300.44 34878[0:SpR:181.1,28053.1] || equal(u,c_Set_Ovimage(c_COMBK(v,w,x),x,w))* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),u,tc_Com_Opname,y)))*.
% 299.79/300.44 34957[0:SpR:181.1,28356.1] || equal(u,c_Set_Ovimage(c_COMBK(v,w,x),x,w))* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),tc_Com_Opname,y)))*.
% 299.79/300.44 35088[0:Rew:25912.0,35063.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),y),v_Procs))**.
% 299.79/300.44 35047[0:SpR:28755.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,x,c_COMBK(x,y,z),tc_Com_Opname,x1),tc_Com_Opname),v,u),u)*.
% 299.79/300.44 35029[0:SpR:28755.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y),tc_Com_Opname),u,z),hAPP(c_Set_Oinsert(v_Procs,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.44 35177[0:Rew:25912.0,35152.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),y),v_Procs))**.
% 299.79/300.44 35136[0:SpR:28910.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(x,y,z),x,tc_Com_Opname,x1),tc_Com_Opname),v,u),u)*.
% 299.79/300.44 35118[0:SpR:28910.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y),tc_Com_Opname),u,z),hAPP(c_Set_Oinsert(v_Procs,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.44 35430[0:SpL:410.0,324.0] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),z,tc_fun(y,tc_bool))* -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool)),z,tc_fun(y,tc_bool)).
% 299.79/300.44 35428[0:SpL:410.0,344.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))** -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))).
% 299.79/300.44 35252[0:SpR:2097.1,410.0] || hBOOL(hAPP(u,v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(x,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,x,y,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,x,y,tc_fun(w,tc_bool)))**.
% 299.79/300.44 35217[0:SpR:410.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,z),x1),v,z,tc_fun(u,tc_bool))))*.
% 299.79/300.44 35214[0:SpR:410.0,335.2] || c_Finite__Set_Ofinite(hAPP(u,v),w) c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,u,y,tc_fun(w,tc_bool)),w) -> c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,y),x),u,y,tc_fun(w,tc_bool)),w)*.
% 299.79/300.44 35440[0:SSi:35227.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool)),tc_fun(y,tc_bool)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(z,x),v),w,x,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.44 35649[0:Rew:586.0,35611.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,hAPP(y,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(y,u,z),w),x,z,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.44 36764[7:SpL:67.0,27293.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),v_x)** -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),v_x))*.
% 299.79/300.44 36763[0:SpL:67.0,4964.0] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),v_Procs)** -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),v_x))*.
% 299.79/300.44 36719[0:SpR:67.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),y),hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),y),tc_bool)*.
% 299.79/300.44 36893[0:SpL:66.0,148.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,u),y),tc_fun(u,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool)))).
% 299.79/300.44 36917[0:Rew:6.0,36916.0] || -> equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),y)),tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oinsert(v,w),y)),tc_fun(w,tc_bool)))*.
% 299.79/300.44 36980[0:Res:13387.1,375.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))** hBOOL(hAPP(hAPP(c_in(w),y),u))* -> c_lessequals(hAPP(v,y),z,tc_fun(x,tc_bool))*.
% 299.79/300.44 36974[0:Res:341.0,375.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))),tc_fun(y,tc_bool))*.
% 299.79/300.44 36973[0:Res:342.0,375.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))),z),tc_fun(y,tc_bool))*.
% 299.79/300.44 37152[0:Res:313.1,471.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(w),x),u))* -> hBOOL(hAPP(hAPP(c_in(y),hAPP(z,x)),hAPP(c_Set_Oimage(z,w,y),v)))*.
% 299.79/300.44 37140[0:Res:341.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),hAPP(c_Set_Oimage(y,u,x),w))))*.
% 299.79/300.44 37139[0:Res:342.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(y,u,x),w)),z)))*.
% 299.79/300.44 37444[0:SpR:205.1,158.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),u,w,v,v),v,v),x),x)**.
% 299.79/300.44 37680[0:SpR:198.1,23.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Fun_Ocomp(x,c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),u,w,v,v),v,y,v),x)**.
% 299.79/300.44 38121[0:Res:247.4,37920.0] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* hBOOL(c_Finite__Set_Olinorder__class_OMax(v,tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) hBOOL(c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.79/300.44 38120[0:Res:248.4,37920.0] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* hBOOL(c_Finite__Set_Olinorder__class_OMin(u,tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) hBOOL(c_Finite__Set_Olinorder__class_OMin(v,tc_bool)).
% 299.79/300.44 38333[0:SSi:38288.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(tc_bool),u),v))* c_Finite__Set_Ofinite(v,tc_bool) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,v,tc_bool,tc_bool),tc_bool)*.
% 299.79/300.44 38334[0:SSi:38284.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(tc_bool),v),w))* c_Finite__Set_Ofinite(w,tc_bool) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,w,tc_bool,tc_bool),tc_bool)*.
% 299.79/300.44 38664[0:Res:13238.1,184.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),c_Orderings_Otop__class_Otop(tc_bool)) c_Fun_Oinj__on(u,w,v,t_a) -> equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(w,u,v,t_a),v_x)),v_x)**.
% 299.79/300.44 38663[0:Res:8375.1,184.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) c_Fun_Oinj__on(u,x,v,w) -> equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(x,u,v,w),y)),y)**.
% 299.79/300.44 38655[0:Res:652.1,184.0] || c_lessequals(v_Procs,hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),tc_fun(tc_Com_Opname,tc_bool))* c_Fun_Oinj__on(u,w,v,tc_Com_Opname) -> equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(w,u,v,tc_Com_Opname),v_x)),v_x)**.
% 299.79/300.44 38727[4:SpR:339.0,37987.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),x))*.
% 299.79/300.44 38715[4:SpR:465.1,37987.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(u,x,y),v_x),z))*.
% 299.79/300.44 38916[4:SpR:339.0,38042.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),x,t_a)*.
% 299.79/300.44 38904[4:SpR:465.1,38042.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oimage(u,x,y),v_x),z,t_a)*.
% 299.79/300.44 40917[0:Res:11029.0,479.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)))*.
% 299.79/300.44 40916[0:Res:9258.0,479.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,w,u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)))*.
% 299.79/300.44 40909[0:Res:3283.1,479.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_Procs),w)))*.
% 299.79/300.44 40887[0:Res:678.0,479.1] || hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_in(tc_Com_Opname),v_x),w,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),w)))*.
% 299.79/300.44 41198[0:Res:11029.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.79/300.44 41197[0:Res:9258.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v,u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),v)))*.
% 299.79/300.44 41190[0:Res:3283.1,478.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_Procs)))*.
% 299.79/300.44 41168[0:Res:678.0,478.1] || hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_in(tc_Com_Opname),v_x),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_in(tc_Com_Opname),v_x))))*.
% 299.79/300.44 41423[0:Res:9258.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(x,v),v_x),tc_bool))* hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(t_a,tc_bool))))*.
% 299.79/300.44 41421[0:Res:15262.1,275.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),w)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(u,tc_bool))))*.
% 299.79/300.44 41420[0:Res:3285.1,275.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(x,tc_Com_Opname),v,tc_fun(u,tc_bool))))*.
% 299.79/300.44 41419[0:Res:3317.1,275.1] || equal(c_in(u),c_in(v)) hBOOL(hAPP(hAPP(c_in(w),x),y))* -> hBOOL(hAPP(hAPP(c_in(v),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(v_x,u),w,tc_fun(v,tc_bool))))*.
% 299.79/300.44 41404[0:Res:474.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,z)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(y,v,x),u,tc_fun(x,tc_bool))))*.
% 299.79/300.44 41506[4:SpR:131.0,38236.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_Com_Opname,tc_bool))*.
% 299.79/300.44 41505[4:SpR:158.0,38236.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_Com_Opname,tc_bool))*.
% 299.79/300.44 41486[4:SpR:104.0,38236.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),tc_Com_Opname,tc_bool))*.
% 299.79/300.44 41994[0:Res:82.0,390.0] || -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,w,y),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,w,y),u),hAPP(c_Set_Oimage(x,w,y),v),tc_fun(y,tc_bool)),y,w)*.
% 299.79/300.44 42160[0:SpL:180.2,311.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_Finite__Set_Ofinite(v,u) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u),c_Orderings_Obot__class_Obot(u))** -> equal(x,c_Orderings_Obot__class_Obot(u)).
% 299.79/300.44 42205[0:SSi:42179.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(w,tc_bool),u),tc_bool,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,u,tc_bool,tc_bool),x,tc_bool)*.
% 299.79/300.44 42206[0:SSi:42136.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,u,tc_bool,tc_bool),tc_bool),u),tc_bool,tc_bool),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,u,tc_bool,tc_bool))**.
% 299.79/300.44 43641[4:Res:49.2,43176.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(u,tc_bool)),v,t_a)*.
% 299.79/300.44 43811[0:Rew:337.0,43755.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))**.
% 299.79/300.44 43812[0:Rew:336.0,43740.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))**.
% 299.79/300.44 44297[0:Res:8366.1,268.0] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v),u))* equal(hAPP(w,v_x),hAPP(w,v))* c_Fun_Oinj__on(w,u,tc_Com_Opname,x)* -> equal(v_x,v).
% 299.79/300.44 44635[0:SpR:532.0,35656.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v)),v_x))*.
% 299.79/300.44 45260[0:SpR:338.0,37394.1] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),hAPP(c_Set_Oinsert(w,t_a),v)),tc_Com_Opname,tc_bool))*.
% 299.79/300.44 45346[0:Res:3284.1,487.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) hBOOL(hAPP(w,v_Procs)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,u)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,w,u)))*.
% 299.79/300.44 45635[0:Rew:323.0,45572.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v),x,u,tc_fun(y,tc_bool)))*.
% 299.79/300.44 45706[0:SpR:533.0,44625.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),w)),v_x))*.
% 299.79/300.44 46080[0:SpR:338.0,36802.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(x,u),w)),v_x))*.
% 299.79/300.44 46539[4:SpR:338.0,42029.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(x,u),w)),v_x))*.
% 299.79/300.44 46707[0:Res:340.2,44639.0] || c_lessequals(u,v,tc_fun(tc_Com_Opname,tc_bool))* c_lessequals(w,v,tc_fun(tc_Com_Opname,tc_bool))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),w),v_Procs)** -> hBOOL(hAPP(v,v_x)).
% 299.79/300.44 47723[4:Res:10697.0,47549.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool)))*.
% 299.79/300.44 49066[0:SpR:49017.1,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(x),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,w,tc_Com_Opname),tc_Com_Opname),u,x),v)))*.
% 299.79/300.44 49062[0:SpR:49017.1,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(w,v_x)) c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,w,tc_Com_Opname),tc_Com_Opname),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.44 49416[0:SpR:49342.1,338.0] || hBOOL(hAPP(u,v_x)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs))**.
% 299.79/300.44 49400[0:SpR:49342.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(w),v_Procs),x)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,v,tc_Com_Opname),tc_Com_Opname),w,u),u)*.
% 299.79/300.44 49396[0:SpR:49342.1,339.0] || hBOOL(hAPP(u,v_x)) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v))**.
% 299.79/300.44 49381[0:SpR:49342.1,176.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.44 50489[0:SpL:223.1,46860.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,t_a),u,t_a),w),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))* -> hBOOL(hAPP(z,v_x))*.
% 299.79/300.44 50488[0:SpL:223.1,44750.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,t_a),u,t_a),w),y,tc_fun(z,tc_bool))* -> hBOOL(hAPP(y,v_x)).
% 299.79/300.44 50465[0:SpR:223.1,21035.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),x,y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,v_Procs,u,x),u,x),w)),v_Procs))*.
% 299.79/300.44 50462[0:SpR:223.1,26119.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,x1,u,x),u,x),w)),x1))*.
% 299.79/300.44 50460[0:SpR:223.1,36600.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,v_x,u,t_a),u,t_a),w)),v_x))*.
% 299.79/300.44 50458[0:SpR:223.1,36599.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,v_x,u,t_a),u,t_a),w)),z),v_x))*.
% 299.79/300.44 50450[0:SpR:223.1,9067.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oinsert(z,x),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x1,v,y,u,x),u,x),w))))*.
% 299.79/300.44 50449[0:SpR:223.1,20881.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(x,y,z),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x1,v,x2,u,y),u,y),w)),hAPP(x,x2)))*.
% 299.79/300.44 50432[0:SpR:223.1,3317.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_in(x),y) -> hBOOL(hAPP(hAPP(y,v_x),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,v_x,u,x),u,x),w)))*.
% 299.79/300.44 50414[4:SpR:223.1,43177.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,y),u,y),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y,tc_fun(z,tc_bool)),x1,t_a)*.
% 299.79/300.44 50413[4:SpR:223.1,42583.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,y),u,y),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y,tc_fun(z,tc_bool)),x1))*.
% 299.79/300.44 50412[0:SpR:223.1,35192.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,y),u,y),w),c_in(tc_Com_Opname),y,tc_fun(z,tc_bool)),v_Procs))*.
% 299.79/300.44 50402[0:SpR:223.1,36608.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,t_a),u,t_a),w),v_x),y,z),tc_Com_Opname,tc_bool))*.
% 299.79/300.44 51177[0:SpR:338.0,26873.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(x,u),w)),tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))**.
% 299.79/300.44 51344[0:SpR:181.1,51231.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),hAPP(hAPP(c_Set_Oinsert(x,t_a),c_Set_Ovimage(c_COMBK(v,u,w),w,u)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.44 51297[0:SpR:338.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),hAPP(c_Set_Oinsert(w,t_a),v)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.44 51442[7:SpL:24914.0,27284.0] || equal(hAPP(c_Set_Ovimage(u,v,w),v_x),v_x) -> hBOOL(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Ovimage(u,v,w),v_x)),hAPP(u,v_x)))*.
% 299.79/300.44 51491[0:SpL:338.0,33513.1] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) equal(c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(x,u),w)),u),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.79/300.44 51489[0:SpL:475.1,33513.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x,u,y),w),y) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(x,u,y),w),y),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.79/300.44 51820[4:SpR:338.0,40792.1] || c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),tc_bool) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(y,u),w)),x))*.
% 299.79/300.44 52019[4:MRR:38410.3,52007.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(c_Set_Oimage(v,u,w),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(v,u,w),v_x))** c_Fun_Oinj__on(v,v_x,u,w) -> .
% 299.79/300.44 52282[0:SpL:223.1,35720.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),x1,tc_fun(z,tc_bool))* -> hBOOL(hAPP(x1,y)).
% 299.79/300.44 53777[0:Res:7226.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(c_Option_Othe(v),w,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,x)),u))* c_Hoare__Mirabelle_Otriple__valid(x,y,t_a)*.
% 299.79/300.44 53802[0:SpR:53771.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Option_Othe(y),w,z)),x1))* -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Option_Othe(y),v,u),u)*.
% 299.79/300.44 53794[0:SpR:53771.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Option_Othe(x),v,y)),hAPP(c_Set_Ovimage(c_Option_Othe(x),u,z),hAPP(c_Set_Oinsert(w,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.44 53833[0:SpR:53772.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Option_Othe(x),y,w,z)),x1))* -> c_lessequals(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Option_Othe(x),v,u),u)*.
% 299.79/300.44 53825[0:SpR:53772.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(w),x,v,y)),hAPP(c_Set_Ovimage(c_Option_Othe(w),u,z),hAPP(c_Set_Oinsert(x,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.44 54341[0:SpR:54251.0,13.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)) -> c_lessequals(u,c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.44 55548[0:SpR:131.0,54593.1] || equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> c_lessequals(z,hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_bool)*.
% 299.79/300.44 55547[0:SpR:158.0,54593.1] || equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> c_lessequals(z,hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_bool)*.
% 299.79/300.44 55989[0:SpL:188.1,55174.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))* -> .
% 299.79/300.44 55907[0:SpL:188.1,55174.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),x)* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool),hAPP(x,v_x))* -> .
% 299.79/300.44 56477[0:Rew:30368.2,56391.3,30368.2,56391.3] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w,x),c_Orderings_Otop__class_Otop(u))** -> equal(c_List_Ofoldl(y,c_Orderings_Otop__class_Otop(u),z,x,x1),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.44 56924[0:Rew:30928.2,56833.3,30928.2,56833.3] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w,x),c_Orderings_Otop__class_Otop(u))** -> equal(c_List_Ofoldl(y,c_Orderings_Otop__class_Otop(u),z,x,x1),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.44 57937[0:SpL:181.1,55910.1] || equal(c_COMBK(u,v,w),c_Set_Ovimage(c_COMBK(x,y,z),z,y))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))) -> hBOOL(hAPP(hAPP(c_in(y),x),v_x)).
% 299.79/300.44 58094[0:SpL:181.1,55992.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_COMBK(x,y,z))* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_bool),x) -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)).
% 299.79/300.44 58210[0:SpL:339.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),tc_bool),x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)))** -> .
% 299.79/300.44 58197[0:SpL:465.1,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),v_x),tc_bool),x,y),c_Set_Oimage(c_Fun_Ofun__upd(u,z,x1,v,w),v,w))* -> hBOOL(hAPP(hAPP(c_in(v),z),v_x)).
% 299.79/300.44 58504[0:SpL:131.0,58248.0] || equal(c_COMBK(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),z,x1),c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),tc_fun(t_a,tc_bool)))* -> .
% 299.79/300.44 58503[0:SpL:158.0,58248.0] || equal(c_COMBK(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),z,x1),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),tc_fun(t_a,tc_bool)))* -> .
% 299.79/300.44 58484[0:SpL:104.0,58248.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),w,x),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),tc_fun(t_a,tc_bool)))* -> .
% 299.79/300.44 59056[0:Res:35449.1,15629.0] || equal(u,v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(v,tc_bool)),w)))*.
% 299.79/300.44 59027[0:Res:21143.0,15629.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Set_Oimage(u,t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w)))*.
% 299.79/300.44 59024[0:Res:20881.0,15629.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),z)))*.
% 299.79/300.44 58970[0:Res:1586.0,15629.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_Procs,u,v),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_Procs,u,v),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)),w)))*.
% 299.79/300.44 58937[0:Res:44625.1,15629.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),w)))*.
% 299.79/300.44 58933[0:Res:35656.1,15629.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u),w)))*.
% 299.79/300.44 58921[0:Res:19749.0,15629.0] || -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v)))*.
% 299.79/300.44 58821[0:SpL:49342.1,15629.0] || hBOOL(hAPP(u,v_x)) hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v)))*.
% 299.79/300.44 58809[0:SpL:338.0,15629.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)))* -> hBOOL(hAPP(c_Set_Oinsert(w,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_Set_Oinsert(w,u),y)))*.
% 299.79/300.44 58796[0:SpL:128.0,15629.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)))* -> hBOOL(hAPP(c_Set_Ovimage(u,v,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_Set_Ovimage(u,v,w),y)))*.
% 299.79/300.44 58693[0:SpL:25.1,15629.0] class_HOL_Ouminus(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w)))*.
% 299.79/300.44 58681[0:SpL:196.1,15629.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(x)* -> hBOOL(hAPP(c_Set_Ovimage(u,v,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_Set_Ovimage(u,v,w),y)))*.
% 299.79/300.44 58670[0:SpL:445.1,15629.0] || hBOOL(hAPP(u,v))* -> equal(v,w)* hBOOL(hAPP(c_Fun_Ofun__upd(u,w,x,y,z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_Fun_Ofun__upd(u,w,x,y,z),x1)))*.
% 299.79/300.44 59565[0:Res:35449.1,15857.0] || equal(u,v_Procs) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(v,tc_bool)),x)))*.
% 299.79/300.44 59535[0:Res:21143.0,15857.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(u,t_a,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),x)))*.
% 299.79/300.44 59532[0:Res:20881.0,15857.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),x1)))*.
% 299.79/300.44 59478[0:Res:1586.0,15857.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_Procs,u,v),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_Procs,u,v),tc_Com_Opname,tc_fun(tc_Com_Opname,tc_bool)),x)))*.
% 299.79/300.44 59445[0:Res:44625.1,15857.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),x)))*.
% 299.79/300.44 59441[0:Res:35656.1,15857.0] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u),x)))*.
% 299.79/300.44 59429[0:Res:19749.0,15857.0] || -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),w)))*.
% 299.79/300.44 59329[0:SpL:49342.1,15857.0] || hBOOL(hAPP(u,v_x)) hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),w)))*.
% 299.79/300.44 59317[0:SpL:338.0,15857.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)))* -> hBOOL(hAPP(c_Set_Oinsert(w,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oinsert(w,u),z)))*.
% 299.79/300.44 59304[0:SpL:128.0,15857.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)))* -> hBOOL(hAPP(c_Set_Ovimage(u,v,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Ovimage(u,v,w),z)))*.
% 299.79/300.44 59201[0:SpL:25.1,15857.0] class_HOL_Ouminus(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),x)))*.
% 299.79/300.44 59189[0:SpL:196.1,15857.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(x)* -> hBOOL(hAPP(c_Set_Ovimage(u,v,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Ovimage(u,v,w),z)))*.
% 299.79/300.44 59178[0:SpL:445.1,15857.0] || hBOOL(hAPP(u,v))* -> equal(v,w)* hBOOL(hAPP(c_Fun_Ofun__upd(u,w,x,y,z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Fun_Ofun__upd(u,w,x,y,z),x2)))*.
% 299.79/300.44 59895[0:SpL:21893.0,4126.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),v) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v,u)*.
% 299.79/300.44 59893[0:SpL:21267.0,4126.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),v) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,w),v,u)*.
% 299.79/300.44 59926[0:SSi:59859.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Oinsert(u,v),w))** -> c_lessequals(x,hAPP(c_Set_Oinsert(u,v),w),tc_fun(v,tc_bool)).
% 299.79/300.44 60206[0:SpL:181.1,58170.1] || equal(u,c_Set_Ovimage(c_COMBK(v,w,x),x,w))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),tc_bool),y,z),u)* -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)).
% 299.79/300.44 60412[7:SpR:586.0,58968.1] || equal(hAPP(c_COMBB(u,v,w,x),y),v_x) -> hBOOL(hAPP(u,hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_COMBB(u,v,w,x),y),z))))*.
% 299.79/300.44 60411[7:SpR:585.0,58968.1] || equal(hAPP(c_COMBC(u,v,w,x),y),v_x) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_COMBC(u,v,w,x),y),z)),y))*.
% 299.79/300.44 60385[7:SpR:331.0,58968.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v))*.
% 299.79/300.44 60525[0:SpR:586.0,58969.1] || equal(hAPP(c_COMBB(u,v,w,x),y),v_Procs) -> hBOOL(hAPP(u,hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_COMBB(u,v,w,x),y),z))))*.
% 299.79/300.44 60524[0:SpR:585.0,58969.1] || equal(hAPP(c_COMBC(u,v,w,x),y),v_Procs) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_COMBC(u,v,w,x),y),z)),y))*.
% 299.79/300.44 60498[0:SpR:331.0,58969.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v))*.
% 299.79/300.44 60598[7:SpR:586.0,59476.1] || equal(hAPP(c_COMBB(u,v,w,x),y),v_x) -> hBOOL(hAPP(u,hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_COMBB(u,v,w,x),y),x1))))*.
% 299.79/300.44 60597[7:SpR:585.0,59476.1] || equal(hAPP(c_COMBC(u,v,w,x),y),v_x) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_COMBC(u,v,w,x),y),x1)),y))*.
% 299.79/300.44 60571[7:SpR:331.0,59476.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),w))*.
% 299.79/300.44 60671[0:SpR:586.0,59477.1] || equal(hAPP(c_COMBB(u,v,w,x),y),v_Procs) -> hBOOL(hAPP(u,hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_COMBB(u,v,w,x),y),x1))))*.
% 299.79/300.44 60670[0:SpR:585.0,59477.1] || equal(hAPP(c_COMBC(u,v,w,x),y),v_Procs) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_COMBC(u,v,w,x),y),x1)),y))*.
% 299.79/300.44 60644[0:SpR:331.0,59477.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),w))*.
% 299.79/300.44 60720[0:SpL:35.2,59706.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(v,x,tc_fun(w,tc_bool))* equal(u,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),w)*.
% 299.79/300.44 60856[0:SpR:586.0,59017.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_COMBB(v,w,x,y),z),t_a)* hBOOL(hAPP(v,hAPP(z,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,hAPP(c_COMBB(v,w,x,y),z),x1))))*.
% 299.79/300.44 60855[0:SpR:585.0,59017.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_COMBC(v,w,x,y),z),t_a)* hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,hAPP(c_COMBC(v,w,x,y),z),x1)),z))*.
% 299.79/300.44 60829[0:SpR:331.0,59017.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w))*.
% 299.79/300.44 60929[0:SpR:586.0,59525.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_COMBB(v,w,x,y),z),t_a)* hBOOL(hAPP(v,hAPP(z,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(c_COMBB(v,w,x,y),z),x2))))*.
% 299.79/300.44 60928[0:SpR:585.0,59525.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_COMBC(v,w,x,y),z),t_a)* hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(c_COMBC(v,w,x,y),z),x2)),z))*.
% 299.79/300.44 60902[0:SpR:331.0,59525.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),x))*.
% 299.79/300.44 61904[0:SpL:130.1,15487.1] class_HOL_Ominus(u) || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.44 62181[0:Res:23754.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v)),u))* c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.79/300.44 63595[0:SSi:63549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)) -> c_lessequals(v,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool),tc_bool)*.
% 299.79/300.44 63596[0:SSi:63548.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)) -> c_lessequals(u,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool),tc_bool)*.
% 299.79/300.44 64242[0:SpR:9.0,646.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),v_Procs,tc_Com_Opname,z) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname,z),hAPP(u,hAPP(v,v_x))),v_x)**.
% 299.79/300.44 64221[0:SpR:88.1,646.1] class_Lattices_Oboolean__algebra(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u)),v_x)**.
% 299.79/300.44 64212[0:SpR:540.1,646.1] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),v_x)**.
% 299.79/300.44 64211[0:SpR:539.1,646.1] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),v_x)**.
% 299.79/300.44 64210[0:SpR:297.2,646.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v_x),v_x)**.
% 299.79/300.44 64207[0:SpR:2098.1,646.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,v) -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,v),v_x),v_x)**.
% 299.79/300.44 64199[0:SpR:299.2,646.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v),v_x)**.
% 299.79/300.44 64409[0:SpR:9.0,645.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),v_Procs,tc_Com_Opname,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ocomp(u,v,w,x,y),tc_Com_Opname,z),hAPP(u,hAPP(v,v_x))),v_x)**.
% 299.79/300.44 64388[0:SpR:88.1,645.1] class_Lattices_Oboolean__algebra(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v_x,u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u)),v_x)**.
% 299.79/300.44 64379[0:SpR:540.1,645.1] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),v_x)**.
% 299.79/300.44 64378[0:SpR:539.1,645.1] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v)),v_x)**.
% 299.79/300.44 64377[0:SpR:297.2,645.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_x,u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v_x),v_x)**.
% 299.79/300.44 64374[0:SpR:2098.1,645.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs,tc_Com_Opname,v) -> c_Hoare__Mirabelle_Ohoare__valids(u,v_x,t_a) equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v_x),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,v),v_x),v_x)**.
% 299.79/300.44 64366[0:SpR:299.2,645.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_x,v,u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),v),v_x)**.
% 299.79/300.44 64498[0:SpL:130.1,24257.1] class_HOL_Ominus(u) || equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.44 64613[0:SpR:35.2,26782.0] || c_lessequals(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_fun(v,tc_bool))* c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,tc_fun(v,tc_bool))* -> equal(hAPP(u,c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.79/300.44 66621[0:Res:65888.2,251.1] class_Lattices_Olattice(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),tc_fun(u,v)),x),v)*.
% 299.79/300.44 69818[0:Res:67118.3,251.1] class_OrderedGroup_Ogroup__add(tc_fun(u,v)) class_Lattices_Oboolean__algebra(tc_fun(u,v)) class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),x),v)*.
% 299.79/300.44 69901[0:Res:67418.3,251.1] class_OrderedGroup_Ogroup__add(tc_fun(u,v)) class_Lattices_Oboolean__algebra(tc_fun(u,v)) class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),x),v)*.
% 299.79/300.44 69990[0:Res:67577.3,251.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(u,v)) class_Lattices_Oboolean__algebra(tc_fun(u,v)) class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),x),v)*.
% 299.79/300.44 70131[0:Res:68748.3,251.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(u,v)) class_Lattices_Oboolean__algebra(tc_fun(u,v)) class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),x),v)*.
% 299.79/300.44 70246[0:Res:65893.2,251.1] class_Lattices_Olattice(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),tc_fun(u,v)),x),hAPP(w,x),v)*.
% 299.79/300.44 71065[0:SpR:323.0,7568.0] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),z),v,w,tc_fun(x,tc_bool))),tc_fun(x,tc_bool))*.
% 299.79/300.44 71242[0:SpR:24914.0,7538.0] || -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(u,v),v_x)),tc_fun(v,tc_bool))*.
% 299.79/300.44 71418[7:SpL:339.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),v_x) -> .
% 299.79/300.44 71405[7:SpL:465.1,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),v_x),tc_bool)) equal(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),v_x)** -> hBOOL(hAPP(hAPP(c_in(v),x),v_x)).
% 299.79/300.44 71623[7:SpR:71455.1,317.0] || equal(u,v_x) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,v),x)),hAPP(c_Set_Oinsert(u,w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),x)))*.
% 299.79/300.44 71622[7:SpR:71455.1,99.1] || equal(u,v_x) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v,w),u),u)**.
% 299.79/300.44 71621[7:SpR:71455.1,438.1] || equal(u,v_x) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v,w),u),u)**.
% 299.79/300.44 72131[0:Res:7830.0,2092.0] || -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs))),hAPP(c_Set_Oinsert(u,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)))**.
% 299.79/300.44 72089[0:SpR:323.0,7830.0] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),u),v,w,tc_fun(x,tc_bool))),tc_fun(x,tc_bool))*.
% 299.79/300.44 72463[0:SpL:56.1,12554.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),y))* -> hBOOL(hAPP(hAPP(c_in(u),y),hAPP(c_Set_Oinsert(v,u),x)))*.
% 299.79/300.44 73046[7:Res:71608.1,268.0] || equal(u,v_x) hBOOL(hAPP(hAPP(c_in(t_a),v),u))* equal(hAPP(w,v_x),hAPP(w,v))* c_Fun_Oinj__on(w,u,t_a,x)* -> equal(v_x,v).
% 299.79/300.44 74368[7:SpL:71835.1,280.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(hAPP(v,v_x),w)) hBOOL(hAPP(v_x,x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,u,tc_fun(y,tc_bool)),w))*.
% 299.79/300.44 74353[7:SpL:71835.1,470.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_x,x,u,v,w)),v_x))*.
% 299.79/300.44 74352[7:SpL:71835.1,466.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_x,u,x,v,w)),v_x))*.
% 299.79/300.44 74224[7:SpL:71835.1,273.0] || equal(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),c_Set_Oinsert(v_x,t_a)) equal(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),v_x)** -> equal(v,v_x).
% 299.79/300.44 74211[7:SpL:71835.1,85.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) c_lessequals(v,hAPP(v_x,w),tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))*.
% 299.79/300.44 74142[7:SpL:71835.1,175.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))* -> equal(hAPP(v,v_x),x).
% 299.79/300.44 74138[7:SpL:71835.1,470.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x))) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(x,v_x,v,w,u)),x))*.
% 299.79/300.44 74137[7:SpL:71835.1,466.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x))) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,v_x,w,u)),x))*.
% 299.79/300.44 73954[7:SpL:71835.1,455.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(v_x,u)) c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.79/300.44 73932[7:SpR:71835.1,338.0] || equal(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(u,v)) -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x))**.
% 299.79/300.44 73789[7:SpR:71835.1,84.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a)) c_lessequals(c_HOL_Ominus__class_Ominus(w,v,tc_fun(u,tc_bool)),v_x,tc_fun(u,tc_bool))* -> c_lessequals(w,v_x,tc_fun(u,tc_bool)).
% 299.79/300.44 73777[7:SpR:71835.1,338.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),v_x)),hAPP(c_Set_Oinsert(w,u),v_x))**.
% 299.79/300.44 73775[7:SpR:71835.1,339.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),v_x)**.
% 299.79/300.44 73703[7:SpR:71835.1,118.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,w,v_x,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,y,z,x),w,v_x,x,z))*.
% 299.79/300.44 73670[7:SpR:71835.1,465.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) equal(hAPP(c_Set_Oimage(u,x,y),v_x),v_x).
% 299.79/300.44 73627[7:SpR:71835.1,339.0] || equal(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(u,v)) -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w))**.
% 299.79/300.44 73609[7:SpR:71835.1,71.2] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(u,w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,u,v,x),v_x),v_x)**.
% 299.79/300.44 73608[7:SpR:71835.1,373.2] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(u,w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,x),v_x),v_x)**.
% 299.79/300.44 73532[7:SpR:71835.1,84.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) c_lessequals(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))* -> c_lessequals(v,hAPP(v_x,w),tc_fun(u,tc_bool)).
% 299.79/300.44 74512[7:MRR:74266.1,6340.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_Set_Oinsert(v_x,t_a))** c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.44 74864[7:SpR:465.1,72297.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(u,x,y),v_x),v_x)).
% 299.79/300.44 75613[0:SSi:75384.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(z,w),u),v,w,tc_fun(x,tc_bool))),tc_fun(x,tc_bool))*.
% 299.79/300.44 76164[0:SpR:9915.0,584.0] || -> equal(hAPP(c_COMBS(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3,x4,x5),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(c_Orderings_Otop__class_Otop(tc_bool),hAPP(x2,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))**.
% 299.79/300.44 76163[0:SpR:9915.0,584.0] || -> equal(hAPP(c_COMBS(u,c_COMBS(c_Set_Ovimage(v,w,x),y,z,x1,x2),x3,x4,x5),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.79/300.44 76284[0:SpR:10469.0,584.0] || -> equal(hAPP(c_COMBS(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),x2,x3,x4,x5),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(x2,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))**.
% 299.79/300.44 76283[0:SpR:10469.0,584.0] || -> equal(hAPP(c_COMBS(u,c_COMBS(c_Set_Oimage(v,w,x),y,z,x1,x2),x3,x4,x5),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),hAPP(hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))**.
% 299.79/300.44 76414[0:SpR:10470.0,584.0] || -> equal(hAPP(c_COMBS(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3,x4,x5),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),hAPP(c_Orderings_Obot__class_Obot(tc_bool),hAPP(x2,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))))**.
% 299.79/300.44 76413[0:SpR:10470.0,584.0] || -> equal(hAPP(c_COMBS(u,c_COMBS(c_Set_Ovimage(v,w,x),y,z,x1,x2),x3,x4,x5),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),hAPP(hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)))**.
% 299.79/300.44 76759[7:SpR:55.1,71682.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x) -> hBOOL(hAPP(hAPP(c_in(w),x),v)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,w),u),v,tc_fun(w,tc_bool)),v_x))*.
% 299.79/300.44 77177[7:SpL:523.1,74788.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),x)* -> hBOOL(x)*.
% 299.79/300.44 77176[7:SpL:460.1,74788.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),u)* -> hBOOL(u)*.
% 299.79/300.44 77225[0:SpR:801.1,118.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),w,hAPP(v,w),z,y),c_Fun_Ocomp(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z))**.
% 299.79/300.44 77463[7:SpR:71894.1,317.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Set_Oimage(v_x,u,v),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),u),w)),hAPP(c_Set_Oinsert(v_x,v),hAPP(c_Set_Oimage(v_x,u,v),w)))*.
% 299.79/300.44 78113[0:Rew:584.0,77848.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(v_x,v_x))) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),v_x)))*.
% 299.79/300.44 78330[7:SpR:78167.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,x),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,x),u,w),v))**.
% 299.79/300.44 78521[4:Res:77988.0,479.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w)))*.
% 299.79/300.44 78520[4:Res:77988.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))))*.
% 299.79/300.44 78736[4:Res:78665.1,453.0] || equal(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),v_x)** c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x)),w))* c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.79/300.44 79042[0:Res:15630.1,11883.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),x)),u))* -> .
% 299.79/300.44 79024[0:Res:15630.1,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y)) -> hBOOL(hAPP(x,hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(y,z),x1),x2,hAPP(c_Set_Ovimage(u,v,w),x),z))))*.
% 299.79/300.44 78974[0:SpR:299.2,15630.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,w),x),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w),z,u)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v)) -> hBOOL(z).
% 299.79/300.44 78941[0:SpR:55.1,15630.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),v),x)) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,w),y),x,tc_fun(w,tc_bool)),z,u,w)))*.
% 299.79/300.44 79085[0:Res:78077.0,479.1] || hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)))*.
% 299.79/300.44 79084[0:Res:78077.0,478.1] || hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.79/300.44 79115[7:Res:78199.0,479.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_in(w),v_x),x,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_in(w),v_x)),x)))*.
% 299.79/300.44 79114[7:Res:78199.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_in(x),v_x),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_in(x),v_x))))*.
% 299.79/300.44 79262[0:Res:15858.1,11883.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(w,y),z),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),y)),u))* -> .
% 299.79/300.44 79244[0:Res:15858.1,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y)) -> hBOOL(hAPP(x,hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,hAPP(c_Set_Oinsert(y,x1),x2),hAPP(c_Set_Ovimage(u,v,w),x),x1))))*.
% 299.79/300.44 79194[0:SpR:299.2,15858.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(w,x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x),z,u)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w)) -> hBOOL(z).
% 299.79/300.44 79161[0:SpR:55.1,15858.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),v),x)) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,w),z),x,tc_fun(w,tc_bool)),u,w)))*.
% 299.79/300.44 80182[0:SpL:21268.0,7600.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),v)* -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(w,v),x),y,z),v)*.
% 299.79/300.44 80179[0:SpL:21268.0,360.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),x),w,y) -> c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),z,x1),w,y)*.
% 299.79/300.44 80149[7:SpL:21268.0,27282.0] || equal(hAPP(c_Set_Oinsert(u,v),w),v_x) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),w),x,y),v_x))* equal(u,v_x).
% 299.79/300.44 80145[0:SpL:21268.0,4382.0] || equal(hAPP(c_Set_Oinsert(u,v),w),v_Procs) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),w),x,y),v_x))* equal(u,v_x).
% 299.79/300.44 80022[0:SpL:21268.0,33513.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),w)* equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(v,w),x),w),c_HOL_Ozero__class_Ozero(tc_nat)) -> .
% 299.79/300.44 80021[0:SpL:21268.0,505.0] || c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u)),v,w,x) -> c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Com_Obody,hAPP(c_Com_Obody,u),y,z)),v,c_Suc(w),x)*.
% 299.79/300.44 79962[0:SpR:11499.0,21268.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),c_Orderings_Otop__class_Otop(tc_bool),x,y)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.44 79958[0:SpR:336.0,21268.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w,x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.79/300.44 79862[0:SpR:34428.0,21268.0] || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x,v,w)),v_x)**.
% 299.79/300.44 79855[0:SpR:15476.0,21268.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),v,w)),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))**.
% 299.79/300.44 79802[0:SpR:21268.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,t_a),hAPP(c_Set_Oinsert(v,t_a),w),u,x),v_x),hAPP(hAPP(c_Set_Oinsert(v,t_a),w),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.44 79801[0:SpR:21268.0,37394.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,t_a),hAPP(c_Set_Oinsert(v,t_a),w),u,x),v_x))* -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(v,t_a),w),tc_Com_Opname,tc_bool)).
% 299.79/300.44 79746[0:SpR:21268.0,8376.2] || equal(c_in(tc_Com_Opname),u) equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(u,v_x),hAPP(hAPP(u,v_x),w),v,x),v_Procs)** -> hBOOL(hAPP(hAPP(u,v_x),w)).
% 299.79/300.44 79742[0:SpR:21268.0,9258.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(t_a),v_x),hAPP(hAPP(c_in(t_a),v_x),u),v,w),v_x),tc_bool))*.
% 299.79/300.44 79376[0:SpR:21268.0,19436.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),w),u,x),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(c_Set_Oinsert(v,tc_Com_Opname),w))).
% 299.79/300.44 79375[0:SpR:21268.0,7460.1] || c_lessequals(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(v,tc_Com_Opname),w),u,x),tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),w),v_x)).
% 299.79/300.44 79368[4:SpR:21268.0,40792.1] || c_lessequals(v_x,hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),z),tc_bool)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),x),z)).
% 299.79/300.44 79362[0:SpR:21268.0,26873.0] || -> equal(c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.79/300.44 79361[0:SpR:21268.0,36802.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),x),v_x)).
% 299.79/300.44 79360[4:SpR:21268.0,42029.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),x),v_x)).
% 299.79/300.44 80365[0:Rew:586.0,79966.0] || -> equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_COMBB(u,x,y,z),v),hAPP(u,hAPP(v,x1)),w,x2))),hAPP(u,hAPP(v,x1)))**.
% 299.79/300.44 80366[0:Rew:585.0,79965.0] || -> equal(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_COMBC(u,w,x,y),z),hAPP(hAPP(u,x1),z),v,x2)),z),hAPP(hAPP(u,x1),z))**.
% 299.79/300.44 80367[0:Rew:586.0,79781.0] || -> equal(hAPP(u,hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_COMBB(u,w,x,y),hAPP(c_COMBB(u,w,x,y),z),v,x1),x2)),hAPP(u,hAPP(z,x2)))**.
% 299.79/300.44 80368[0:Rew:585.0,79780.0] || -> equal(hAPP(hAPP(u,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_COMBC(u,x,y,z),hAPP(c_COMBC(u,x,y,z),x1),w,x2)),hAPP(hAPP(u,v),x1))**.
% 299.79/300.44 81377[0:SpL:21894.0,7600.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),v)* -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(w,v),x),c_Set_Oinsert(w,v),y,z),v)*.
% 299.79/300.44 81374[0:SpL:21894.0,360.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),x),w,y) -> c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),z,x1),w,y)*.
% 299.79/300.44 81344[7:SpL:21894.0,27282.0] || equal(hAPP(c_Set_Oinsert(u,v),w),v_x) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(u,v),x,y),v_x))* equal(u,v_x).
% 299.79/300.44 81340[0:SpL:21894.0,4382.0] || equal(hAPP(c_Set_Oinsert(u,v),w),v_Procs) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(u,v),x,y),v_x))* equal(u,v_x).
% 299.79/300.44 81217[0:SpL:21894.0,33513.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),w)* equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(v,w),x),w),c_HOL_Ozero__class_Ozero(tc_nat)) -> .
% 299.79/300.44 81216[0:SpL:21894.0,505.0] || c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u)),v,w,x) -> c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Com_Obody,u),c_Com_Obody,y,z)),v,c_Suc(w),x)*.
% 299.79/300.44 81156[0:SpR:11499.0,21894.0] || -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x,y)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.44 81152[0:SpR:336.0,21894.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.79/300.44 81056[0:SpR:34428.0,21894.0] || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v_x,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v,w)),v_x)**.
% 299.79/300.44 81049[0:SpR:15476.0,21894.0] || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v,w)),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))**.
% 299.79/300.44 80996[0:SpR:21894.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,t_a),w),c_Set_Oinsert(v,t_a),u,x),v_x),hAPP(hAPP(c_Set_Oinsert(v,t_a),w),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.44 80995[0:SpR:21894.0,37394.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,t_a),w),c_Set_Oinsert(v,t_a),u,x),v_x))* -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(v,t_a),w),tc_Com_Opname,tc_bool)).
% 299.79/300.44 80940[0:SpR:21894.0,8376.2] || equal(c_in(tc_Com_Opname),u) equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(u,v_x),w),hAPP(u,v_x),v,x),v_Procs)** -> hBOOL(hAPP(hAPP(u,v_x),w)).
% 299.79/300.44 80936[0:SpR:21894.0,9258.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),u)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),u),hAPP(c_in(t_a),v_x),v,w),v_x),tc_bool))*.
% 299.79/300.44 80569[0:SpR:21894.0,19436.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),w),c_Set_Oinsert(v,tc_Com_Opname),u,x),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(c_Set_Oinsert(v,tc_Com_Opname),w))).
% 299.79/300.44 80568[0:SpR:21894.0,7460.1] || c_lessequals(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),w),c_Set_Oinsert(v,tc_Com_Opname),u,x),tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),w),v_x)).
% 299.79/300.44 80561[4:SpR:21894.0,40792.1] || c_lessequals(v_x,hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),z),tc_bool)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),x),z)).
% 299.79/300.44 80555[0:SpR:21894.0,26873.0] || -> equal(c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.79/300.44 80554[0:SpR:21894.0,36802.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),x),v_x)).
% 299.79/300.44 80553[4:SpR:21894.0,42029.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),x),v_x)).
% 299.79/300.44 81560[0:Rew:586.0,81160.0] || -> equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(u,hAPP(v,x)),hAPP(c_COMBB(u,y,z,x1),v),w,x2))),hAPP(u,hAPP(v,x)))**.
% 299.79/300.44 81561[0:Rew:585.0,81159.0] || -> equal(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(u,w),x),hAPP(c_COMBC(u,y,z,x1),x),v,x2)),x),hAPP(hAPP(u,w),x))**.
% 299.79/300.44 81562[0:Rew:586.0,80975.0] || -> equal(hAPP(u,hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_COMBB(u,w,x,y),z),c_COMBB(u,w,x,y),v,x1),x2)),hAPP(u,hAPP(z,x2)))**.
% 299.79/300.44 81563[0:Rew:585.0,80974.0] || -> equal(hAPP(hAPP(u,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_COMBC(u,x,y,z),x1),c_COMBC(u,x,y,z),w,x2)),hAPP(hAPP(u,v),x1))**.
% 299.79/300.44 81791[0:SpR:353.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oinsert(x,w),z,x1,x2),hAPP(c_Set_Oinsert(v,w),y)),u)*.
% 299.79/300.44 82167[7:SpR:78597.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,v),hAPP(c_Set_Oinsert(c_Set_Oinsert(v_x,w),u),x)),hAPP(c_Set_Oinsert(c_Set_Oinsert(v_x,w),v),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,v),x)))*.
% 299.79/300.44 82166[7:SpR:78597.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),u,v),c_Set_Oinsert(v_x,w)),c_Set_Oinsert(v_x,w))**.
% 299.79/300.44 82165[7:SpR:78597.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),u,v),c_Set_Oinsert(v_x,w)),c_Set_Oinsert(v_x,w))**.
% 299.79/300.44 82263[0:SpR:353.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oinsert(x,w),z,x1,x2),hAPP(c_Set_Oinsert(v,w),y)),u)*.
% 299.79/300.44 82564[7:Res:82148.0,268.0] || hBOOL(hAPP(hAPP(c_in(t_a),u),c_Set_Oinsert(v_x,v)))* equal(hAPP(w,v_x),hAPP(w,u))* c_Fun_Oinj__on(w,c_Set_Oinsert(v_x,v),t_a,x)* -> equal(v_x,u).
% 299.79/300.44 82729[0:Res:361.2,7671.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* c_lessequals(y,hAPP(z,w),u)* -> c_lessequals(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,z,v,u),u)*.
% 299.79/300.44 83130[0:SpL:5924.0,19641.0] || hBOOL(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2)),v))* -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,t_a).
% 299.79/300.44 83155[0:Rew:5924.0,83087.0] || hBOOL(hAPP(hAPP(u,v),w)) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(v,y),z),c_COMBS(u,c_COMBK(w,x1,x2),x3,x4,x5),y)),w))*.
% 299.79/300.44 83156[0:Rew:5924.0,83086.0] || hBOOL(hAPP(hAPP(u,v),w)) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,x),y),z,c_COMBS(u,c_COMBK(w,x1,x2),x3,x4,x5),x)),w))*.
% 299.79/300.44 83157[0:Rew:5924.0,83009.0] || -> equal(hAPP(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname,x2),hAPP(hAPP(u,v_x),v))),v),hAPP(hAPP(u,v_x),v))**.
% 299.79/300.44 83249[7:SpR:339.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x,y),v_x),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.44 83236[7:SpR:465.1,78357.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),z,x1),v_x),hAPP(c_Set_Oimage(w,u,y),v_x)))*.
% 299.79/300.44 83449[0:SpL:5961.0,19641.0] || hBOOL(hAPP(u,hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),x2))))* -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),x2,t_a).
% 299.79/300.44 83465[0:Rew:5961.0,83407.0] || hBOOL(hAPP(u,hAPP(v,w))) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(w,y),z),c_COMBS(c_COMBK(u,x1,x2),v,x3,x4,x5),y))))*.
% 299.79/300.44 83466[0:Rew:5961.0,83406.0] || hBOOL(hAPP(u,hAPP(v,w))) -> hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,c_COMBS(c_COMBK(u,x1,x2),v,x3,x4,x5),x))))*.
% 299.79/300.44 83467[0:Rew:5961.0,83339.0] || -> equal(hAPP(u,hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(c_COMBK(u,w,x),v,y,z,x1),tc_Com_Opname,x2),hAPP(u,hAPP(v,v_x))))),hAPP(u,hAPP(v,v_x)))**.
% 299.79/300.44 84191[7:SpL:523.1,78767.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool),v_x)** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_x) -> .
% 299.79/300.44 84190[7:SpL:460.1,78767.0] || class_Lattices_Olattice(t_b) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool),v_x)** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_x) -> .
% 299.79/300.44 84307[0:SpL:118.0,10287.0] || equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,w,x,y),z,x1,y,x),c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,z,x2,y,w),w,x,y))* -> equal(hAPP(u,x2),x1).
% 299.79/300.44 84899[4:SpL:297.2,78744.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u)* equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,t_a).
% 299.79/300.44 84984[0:SpR:21893.0,84957.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,v),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,v))))*.
% 299.79/300.44 84982[0:SpR:21267.0,84957.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,v),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,v))))*.
% 299.79/300.44 85295[7:Res:75156.0,15629.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(u,tc_bool)),v)))*.
% 299.79/300.44 85294[7:Res:75156.0,15857.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(u,tc_bool)),w)))*.
% 299.79/300.44 85842[0:Res:9066.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x)),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,y),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(y,w,t_a)*.
% 299.79/300.44 85822[0:Res:9066.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(y,w),z))),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.79/300.44 85956[0:Res:59525.1,13582.0] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(x,y,tc_fun(u,tc_bool)),w)),y))* -> c_Hoare__Mirabelle_Ohoare__valids(z,c_HOL_Ominus__class_Ominus(x,y,tc_fun(u,tc_bool)),t_a)*.
% 299.79/300.44 85955[0:Res:59017.1,13582.0] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_HOL_Ominus__class_Ominus(x,y,tc_fun(u,tc_bool)),v)),y))* -> c_Hoare__Mirabelle_Ohoare__valids(z,c_HOL_Ominus__class_Ominus(x,y,tc_fun(u,tc_bool)),t_a)*.
% 299.79/300.44 85952[7:Res:58968.1,13582.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)),v))* -> .
% 299.79/300.44 85951[0:Res:58969.1,13582.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_Procs) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)),v))* -> .
% 299.79/300.44 85949[7:Res:59476.1,13582.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),y)),v))* -> .
% 299.79/300.44 85948[0:Res:59477.1,13582.0] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_Procs) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),y)),v))* -> .
% 299.79/300.44 85927[0:SpL:66.0,13582.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),y))* hBOOL(hAPP(hAPP(c_in(w),y),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))))* -> .
% 299.79/300.44 86066[0:SpL:339.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),v_Procs) -> .
% 299.79/300.44 86053[0:SpL:465.1,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),v_x),tc_bool)) equal(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(v),x),v_x)).
% 299.79/300.44 86281[0:SpR:86109.1,317.0] || equal(u,v_Procs) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,v),x)),hAPP(c_Set_Oinsert(u,w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),x)))*.
% 299.79/300.44 86280[0:SpR:86109.1,99.1] || equal(u,v_Procs) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v,w),u),u)**.
% 299.79/300.44 86279[0:SpR:86109.1,438.1] || equal(u,v_Procs) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v,w),u),u)**.
% 299.79/300.44 86596[0:Res:19823.1,19641.0] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),x)))* -> c_Hoare__Mirabelle_Ohoare__valids(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),x,t_a).
% 299.79/300.44 86568[0:SpR:66.0,19823.1] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(u,v),y),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),w))*.
% 299.79/300.44 86640[0:Res:86261.1,268.0] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(t_a),v),u))* equal(hAPP(w,v_x),hAPP(w,v))* c_Fun_Oinj__on(w,u,t_a,x)* -> equal(v_x,v).
% 299.79/300.44 86736[4:SpL:523.1,86106.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool),v_x)** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_Procs) -> .
% 299.79/300.44 86735[4:SpL:460.1,86106.0] || class_Lattices_Olattice(t_b) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool),v_x)** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_Procs) -> .
% 299.79/300.44 86862[0:SpR:55.1,86345.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_Procs) -> hBOOL(hAPP(hAPP(c_in(w),x),v)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,w),u),v,tc_fun(w,tc_bool)),v_x))*.
% 299.79/300.44 87094[0:Rew:60.0,86978.2] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(u,w) -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(v,w),u),w),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 299.79/300.44 87134[7:Res:82132.0,15629.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(v_x,u),c_in(tc_Com_Opname),t_a,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(v_x,u),c_in(tc_Com_Opname),t_a,tc_fun(v,tc_bool)),w)))*.
% 299.79/300.44 87133[7:Res:82132.0,15857.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(v_x,u),c_in(tc_Com_Opname),t_a,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(v_x,u),c_in(tc_Com_Opname),t_a,tc_fun(v,tc_bool)),x)))*.
% 299.79/300.44 87341[7:SpR:131.0,71492.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))),z))*.
% 299.79/300.44 87340[7:SpR:158.0,71492.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))),z))*.
% 299.79/300.44 87320[7:SpR:104.0,71492.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))),w))*.
% 299.79/300.44 87489[7:SpR:131.0,71493.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))),z,t_a)*.
% 299.79/300.44 87488[7:SpR:158.0,71493.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))),z,t_a)*.
% 299.79/300.44 87468[7:SpR:104.0,71493.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))),w,t_a)*.
% 299.79/300.44 87619[7:SpR:131.0,71679.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))))*.
% 299.79/300.44 87618[7:SpR:158.0,71679.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))))*.
% 299.79/300.44 87598[7:SpR:104.0,71679.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))*.
% 299.79/300.44 87828[7:Res:74701.0,15629.0] || -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),w)))*.
% 299.79/300.44 87827[7:Res:74701.0,15857.0] || -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),x)))*.
% 299.79/300.44 88309[0:Res:7227.0,279.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oimage(c_COMBK(u,w,x),y,v),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),hAPP(c_Set_Oimage(c_COMBK(u,w,x),y,v),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))))**.
% 299.79/300.44 88643[7:SpL:523.1,88086.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_x) hBOOL(c_HOL_Ominus__class_Ominus(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool))* -> .
% 299.79/300.44 88642[7:SpL:460.1,88086.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_x) hBOOL(c_HOL_Ominus__class_Ominus(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool))* -> .
% 299.79/300.44 88835[0:SpR:644.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),w,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_Procs))*.
% 299.79/300.44 89031[7:Res:75153.0,15629.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_x,u,v),tc_Com_Opname,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_x,u,v),tc_Com_Opname,tc_fun(w,tc_bool)),x)))*.
% 299.79/300.44 89030[7:Res:75153.0,15857.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_x,u,v),tc_Com_Opname,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v_x,u,v),tc_Com_Opname,tc_fun(w,tc_bool)),y)))*.
% 299.79/300.44 89742[7:Res:89344.1,479.1] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,w,v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w)))*.
% 299.79/300.44 89741[7:Res:89344.1,478.1] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,u,v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u)))*.
% 299.79/300.44 89706[7:Res:89344.1,275.1] || equal(hAPP(u,v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(hAPP(c_in(w),v),x))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,u,w,tc_fun(t_a,tc_bool))))*.
% 299.79/300.44 89687[7:SpR:21894.0,89344.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),v),hAPP(c_in(t_a),v_x),u,w),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.79/300.44 89685[7:SpR:21268.0,89344.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_in(t_a),v_x),hAPP(hAPP(c_in(t_a),v_x),v),u,w),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.79/300.44 89796[0:SpR:26183.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(y,u),v),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),hAPP(c_Set_Oinsert(y,u),v)))*.
% 299.79/300.44 90886[4:Res:90134.1,479.1] || equal(hAPP(u,v_x),v_x) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,w,v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w)))*.
% 299.79/300.44 90885[4:Res:90134.1,478.1] || equal(hAPP(u,v_x),v_x) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,u,v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u)))*.
% 299.79/300.44 90850[4:Res:90134.1,275.1] || equal(hAPP(hAPP(u,v),v_x),v_x)** hBOOL(hAPP(hAPP(c_in(w),v),x))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,u,w,tc_fun(t_a,tc_bool))))*.
% 299.79/300.44 90831[4:SpR:21894.0,90134.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),v),hAPP(c_in(t_a),v_x),u,w),v_x),v_x)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.79/300.44 90829[4:SpR:21268.0,90134.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_in(t_a),v_x),hAPP(hAPP(c_in(t_a),v_x),v),u,w),v_x),v_x)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.79/300.44 90970[4:SpL:131.0,90278.1] || equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x),v_x)** hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_bool))* -> .
% 299.79/300.44 90969[4:SpL:158.0,90278.1] || equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x),v_x)** hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_bool))* -> .
% 299.79/300.44 92665[7:SpR:131.0,82151.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),c_Set_Oinsert(v_x,z)))*.
% 299.79/300.44 92664[7:SpR:158.0,82151.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),c_Set_Oinsert(v_x,z)))*.
% 299.79/300.44 92644[7:SpR:104.0,82151.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_in(t_a)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,w)))*.
% 299.79/300.44 92766[7:Res:82185.0,15629.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,v)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,v)),w),x)))*.
% 299.79/300.44 92765[7:Res:82185.0,15857.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,v)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,v)),w),y)))*.
% 299.79/300.44 93137[7:Res:82187.0,15629.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,w)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,w)),x)))*.
% 299.79/300.44 93136[7:Res:82187.0,15857.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,w)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,w)),y)))*.
% 299.79/300.44 93220[0:SpR:5878.1,14196.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1),hAPP(c_Set_Oinsert(hAPP(v,c_Orderings_Obot__class_Obot(u)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),c_Orderings_Obot__class_Obot(u)))*.
% 299.79/300.44 93325[4:SpR:131.0,85556.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),z),tc_bool)*.
% 299.79/300.44 93324[4:SpR:158.0,85556.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),z),tc_bool)*.
% 299.79/300.44 93304[4:SpR:104.0,85556.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),w),tc_bool)*.
% 299.79/300.44 93513[0:SpR:131.0,86147.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))),z))*.
% 299.79/300.44 93512[0:SpR:158.0,86147.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))),z))*.
% 299.79/300.44 93492[0:SpR:104.0,86147.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))),w))*.
% 299.79/300.44 93664[0:SpR:131.0,86148.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))),z,t_a)*.
% 299.79/300.44 93663[0:SpR:158.0,86148.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))),z,t_a)*.
% 299.79/300.45 93643[0:SpR:104.0,86148.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))),w,t_a)*.
% 299.79/300.45 93729[0:SpL:21893.0,7462.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),v_x),c_Set_Oinsert(v,w),tc_Com_Opname,x),tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,w),v_x),w) -> c_Finite__Set_Ofinite(u,w).
% 299.79/300.45 93727[0:SpL:21267.0,7462.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),v_x),tc_Com_Opname,x),tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,w),v_x),w) -> c_Finite__Set_Ofinite(u,w).
% 299.79/300.45 93808[0:SpR:131.0,86342.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))))*.
% 299.79/300.45 93807[0:SpR:158.0,86342.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))))*.
% 299.79/300.45 93787[0:SpR:104.0,86342.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))*.
% 299.79/300.45 93990[0:SpR:21893.0,10791.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(w,v),v_x),c_Set_Oinsert(w,v),tc_Com_Opname,x)),hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),tc_fun(v,tc_bool))*.
% 299.79/300.45 93988[0:SpR:21267.0,10791.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(w,v),v_x),tc_Com_Opname,x)),hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),tc_fun(v,tc_bool))*.
% 299.79/300.45 94148[0:Res:14364.3,436.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),x))* -> hBOOL(hAPP(w,x))*.
% 299.79/300.45 94141[0:Res:14364.3,416.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> equal(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.79/300.45 94258[0:Res:14491.3,4247.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> equal(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))).
% 299.79/300.45 94253[0:Res:14491.3,436.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) hBOOL(hAPP(w,x))* -> hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),x))*.
% 299.79/300.45 695[0:Res:252.0,590.0] || -> c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(v_P,v_x),hAPP(v_Q,v_x),hAPP(c_Com_Ocom_OBODY,v_x),c_Suc(v_na)),c_Suc(v_na),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(hAPP(v_P,v_x),hAPP(v_Q,v_x),hAPP(c_Com_Ocom_OBODY,v_x),c_Suc(v_na)))*.
% 299.79/300.45 694[0:Res:450.0,590.0] || -> hBOOL(hAPP(hAPP(hAPP(v_P,v_x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(v_P,v_x),hAPP(v_Q,v_x),hAPP(c_Com_Ocom_OBODY,v_x),c_Suc(v_na))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(v_P,v_x),hAPP(v_Q,v_x),hAPP(c_Com_Ocom_OBODY,v_x),c_Suc(v_na))))*.
% 299.79/300.45 630[0:Res:589.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,tc_Com_Opname,tc_fun(v,tc_bool)),v_Procs),c_Set_Oinsert(w,v),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool))))**.
% 299.79/300.45 2603[0:SpR:445.1,1103.1] || -> equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Fun_Ofun__upd(v,w,x,y,z)),w) c_Hoare__Mirabelle_Ohoare__valids(u,c_Fun_Ofun__upd(v,w,x,y,z),t_a) hBOOL(hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Fun_Ofun__upd(v,w,x,y,z))))*.
% 299.79/300.45 5080[0:SSi:5076.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Ovimage(v,w,x),u)),tc_fun(x,tc_bool))* -> equal(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Ovimage(v,w,x),u)),u).
% 299.79/300.45 6207[0:SpR:599.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y,z),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))),hAPP(hAPP(u,c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))**.
% 299.79/300.45 8207[0:SSi:8186.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),z,tc_fun(u,tc_bool))* -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),z).
% 299.79/300.45 8221[0:Res:5888.1,405.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),z,u)* -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),z).
% 299.79/300.45 9473[0:SpR:337.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))**.
% 299.79/300.45 9543[0:Res:49.2,251.1] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || c_lessequals(w,c_HOL_Ozero__class_Ozero(tc_fun(u,v)),tc_fun(u,v))* -> c_lessequals(hAPP(w,x),hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),x),v)*.
% 299.79/300.45 9542[0:Res:45.2,251.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || c_lessequals(w,c_HOL_Ozero__class_Ozero(tc_fun(u,v)),tc_fun(u,v))* -> c_lessequals(hAPP(w,x),hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),x),v)*.
% 299.79/300.45 9538[0:Res:293.2,251.1] class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || c_lessequals(w,x,tc_fun(u,v)) -> c_lessequals(hAPP(w,y),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),x),z),y),v)*.
% 299.79/300.45 9535[0:Res:294.2,251.1] class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || c_lessequals(w,x,tc_fun(u,v)) -> c_lessequals(hAPP(w,y),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),z),x),y),v)*.
% 299.79/300.45 9520[0:Res:47.2,251.1] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w,tc_fun(u,v))* -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),x),hAPP(w,x),v)*.
% 299.79/300.45 9519[0:Res:43.2,251.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w,tc_fun(u,v))* -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),x),hAPP(w,x),v)*.
% 299.79/300.45 10149[0:Res:49.2,431.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(v,c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) c_Fun_Oinj__on(w,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u,x)* -> c_Fun_Oinj__on(w,v,u,x).
% 299.79/300.45 10126[0:Res:47.2,431.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)) c_Fun_Oinj__on(w,v,u,x) -> c_Fun_Oinj__on(w,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u,x)*.
% 299.79/300.45 10514[0:Res:1103.1,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v),t_a) c_Hoare__Mirabelle_Ohoare__valids(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v)),w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v)),w),v,t_a)*.
% 299.79/300.45 10499[0:Res:9071.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),u,t_a)*.
% 299.79/300.45 10494[0:Res:474.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oimage(u,v,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oimage(u,v,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w),hAPP(u,x),t_a)*.
% 299.79/300.45 11733[0:SpR:130.1,474.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u)),y,v),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.79/300.45 14188[0:SpR:584.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_COMBS(w,x,y,z,x1),u,x2),hAPP(c_Set_Oinsert(hAPP(hAPP(w,v),hAPP(x,v)),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))))))*.
% 299.79/300.45 14180[0:SpR:336.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 14168[0:SpR:584.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Ovimage(hAPP(x,w),u,y),hAPP(c_Set_Oinsert(hAPP(c_COMBS(x,v,z,x1,x2),w),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.45 14161[0:SpR:337.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 14152[0:SpR:540.1,176.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.45 14151[0:SpR:539.1,176.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.45 14150[0:SpR:297.2,176.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> hBOOL(hAPP(hAPP(c_in(x),w),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),hAPP(c_Set_Oinsert(w,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.45 14141[0:SpR:299.2,176.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> hBOOL(hAPP(hAPP(c_in(x),v),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y),hAPP(c_Set_Oinsert(w,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.45 14132[0:SpR:25.1,176.0] class_HOL_Ouminus(u) || -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Ovimage(c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u)),v,x),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 14383[0:Res:1103.1,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(c_in(u),w)),u) -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_in(u),w),t_a) c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(c_in(u),w)),u),w,u)*.
% 299.79/300.45 14510[0:Res:1103.1,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(c_in(u),w)),u) -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_in(u),w),t_a) c_lessequals(w,c_Finite__Set_Olinorder__class_OMax(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(c_in(u),w)),u),u)*.
% 299.79/300.45 14792[0:SpL:128.0,150.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y))) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool)))))* -> .
% 299.79/300.45 15122[0:SpR:181.1,584.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_COMBS(x,c_Set_Ovimage(c_COMBK(v,u,y),y,u),z,x1,x2),w),hAPP(hAPP(x,w),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.45 15120[0:SpR:181.1,1103.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u))))* c_Hoare__Mirabelle_Ohoare__valids(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u),t_a) hBOOL(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))).
% 299.79/300.45 15106[0:SpR:181.1,415.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_Fun_Ofun__upd(c_Set_Ovimage(c_COMBK(v,u,x),x,u),w,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y,z),c_Set_Ovimage(c_COMBK(v,u,x),x,u))**.
% 299.79/300.45 16580[0:SpR:584.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(hAPP(y,w),hAPP(z,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_COMBS(y,z,x1,x2,x3),v,u),u)*.
% 299.79/300.45 16571[0:SpR:336.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v,u),u)*.
% 299.79/300.45 16557[0:SpR:584.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(w,x)),y)) -> c_lessequals(hAPP(c_COMBS(z,w,x1,x2,x3),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(z,x),v,u),u)*.
% 299.79/300.45 16549[0:SpR:337.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),v,u),u)*.
% 299.79/300.45 16539[0:SpR:540.1,361.2] class_Lattices_Olattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),x),y)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w,v),v)*.
% 299.79/300.45 16538[0:SpR:539.1,361.2] class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),x),y)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w,v),v)*.
% 299.79/300.45 16537[0:SpR:297.2,361.2] class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || c_lessequals(w,x,u) hBOOL(hAPP(hAPP(c_in(y),x),z)) -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,v),v)*.
% 299.79/300.45 16528[0:SpR:299.2,361.2] class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || c_lessequals(w,x,u)* hBOOL(hAPP(hAPP(c_in(y),w),z))* -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y,v),v)*.
% 299.79/300.45 16517[0:SpR:25.1,361.2] class_HOL_Ouminus(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(y,v_x),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_HOL_Ouminus__class_Ouminus(y,tc_fun(t_a,u)),w,v),v)*.
% 299.79/300.45 16923[0:SpR:600.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_HOL_Ominus__class_Ominus(w,v,tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v),x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v))**.
% 299.79/300.45 16996[0:Res:9952.1,405.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Oorder(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_bool),u)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.79/300.45 17008[0:SSi:16990.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_fun(v,tc_bool))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.79/300.45 17021[0:Res:10531.1,405.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Oorder(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,u),c_Orderings_Obot__class_Obot(tc_bool),u)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,u),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.79/300.45 17027[0:SSi:17015.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_fun(v,tc_bool))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.79/300.45 17056[0:SpR:8415.2,511.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(v_x,w)))*.
% 299.79/300.45 17216[0:SpR:8415.2,510.1] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),w),v))* -> hBOOL(hAPP(hAPP(c_in(u),w),v_x))*.
% 299.79/300.45 17213[0:SpR:8415.2,510.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(v_x,w)))*.
% 299.79/300.45 17898[0:SpL:188.1,16327.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u))* equal(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(w,v_Procs) -> .
% 299.79/300.45 17893[0:SpL:188.1,13272.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.79/300.45 17892[0:SpL:188.1,3484.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Com_Ocom_OBODY,x))* -> equal(v_x,x).
% 299.79/300.45 17884[0:SpR:188.1,128.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)))) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),w),tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))**.
% 299.79/300.45 17866[0:SpR:188.1,3346.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Oinsert(w,x),c_Set_Ovimage(c_COMBK(v,u,y),y,u))* -> hBOOL(hAPP(hAPP(c_in(x),w),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))))*.
% 299.79/300.45 17864[0:SpR:188.1,3305.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(w,tc_Com_Opname,y),v_Procs),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.79/300.45 17860[0:SpR:188.1,2771.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u))* -> equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool))*.
% 299.79/300.45 17992[0:SpL:353.0,263.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(x,u),y))))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),y))) equal(v,x).
% 299.79/300.45 18214[0:SpR:10063.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v)) -> c_lessequals(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,t_a),u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.45 18211[0:SpR:586.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,hAPP(y,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_COMBB(x,z,x1,x2),y),u,tc_fun(x3,tc_bool)),tc_fun(x3,tc_bool))*.
% 299.79/300.45 18210[0:SpR:585.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(hAPP(x,v),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_COMBC(x,z,x1,x2),y),u,tc_fun(x3,tc_bool)),tc_fun(x3,tc_bool))*.
% 299.79/300.45 18187[0:SpR:9936.1,362.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 18185[0:SpR:9935.1,362.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),u),w))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 18170[0:SpR:14526.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v)),w)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(c_Option_Othe(v),x,tc_fun(y,tc_bool)),u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.45 18147[0:SpR:8415.2,362.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,u,v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.45 18139[0:SpR:369.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> c_lessequals(hAPP(c_Set_Oinsert(v,w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(v,w),u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.45 18138[0:SpR:2089.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),w)) -> c_lessequals(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.45 18133[0:SpR:445.1,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(v,x) c_lessequals(hAPP(y,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ofun__upd(y,x,z,x1,x2),u,tc_fun(x3,tc_bool)),tc_fun(x3,tc_bool))*.
% 299.79/300.45 18268[0:SpR:15172.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),x,y),z,tc_fun(x1,tc_bool)),u,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.79/300.45 18415[0:SpR:10063.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v)) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,w),v)))*.
% 299.79/300.45 18414[0:SpR:15172.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),y,z),x1,tc_fun(x2,tc_bool)),u,x),w)))*.
% 299.79/300.45 18411[0:SpR:586.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,hAPP(z,v))),hAPP(c_Set_Oimage(hAPP(c_COMBB(y,x1,x2,x3),z),u,x),w)))*.
% 299.79/300.45 18410[0:SpR:585.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(hAPP(y,v),z)),hAPP(c_Set_Oimage(hAPP(c_COMBC(y,x1,x2,x3),z),u,x),w)))*.
% 299.79/300.45 18387[0:SpR:9936.1,545.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),w),x))* -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,y),x)))*.
% 299.79/300.45 18385[0:SpR:9935.1,545.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),u),w))* -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v,x),w)))*.
% 299.79/300.45 18370[0:SpR:14526.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v)),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Option_Othe(v),y,tc_fun(z,tc_bool)),u,x),w)))*.
% 299.79/300.45 18347[0:SpR:8415.2,545.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> hBOOL(hAPP(hAPP(c_in(x),v_x),hAPP(c_Set_Oimage(u,v,x),w)))*.
% 299.79/300.45 18339[0:SpR:369.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Oimage(c_Set_Oinsert(v,w),u,z),y)))*.
% 299.79/300.45 18338[0:SpR:2089.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,x),w)))*.
% 299.79/300.45 18333[0:SpR:445.1,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(v,x) hBOOL(hAPP(hAPP(c_in(y),hAPP(z,v)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,x,x1,x2,x3),u,y),w)))*.
% 299.79/300.45 18325[0:SpR:8415.2,545.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(hAPP(c_in(v),x),v_x))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,x)),v_x))*.
% 299.79/300.45 18444[0:SpL:8415.2,156.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Ovimage(v,u,w),x)))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(v,v_x)),x))*.
% 299.79/300.45 18443[0:SpL:128.0,156.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(w,u,x),y),tc_fun(u,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,v)),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))))*.
% 299.79/300.45 18436[0:SpL:8415.2,156.0] || equal(v_Procs,v_x) equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(hAPP(c_in(v),x),v_x))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,x)),v_x))*.
% 299.79/300.45 18580[0:SpR:8415.2,153.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(c_in(v),hAPP(w,v_x)),x))* -> hBOOL(hAPP(v_x,hAPP(c_Set_Ovimage(w,u,v),x)))*.
% 299.79/300.45 18579[0:SpR:128.0,153.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(u,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(y),w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,y,u),x),tc_fun(y,tc_bool))))*.
% 299.79/300.45 18572[0:SpR:8415.2,153.1] || equal(v_Procs,v_x) equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(hAPP(c_in(w),hAPP(u,x)),v_x))* -> hBOOL(hAPP(hAPP(c_in(v),x),v_x))*.
% 299.79/300.45 18689[0:SpR:600.0,9568.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w)),y),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),tc_bool)*.
% 299.79/300.45 18677[0:SpR:188.1,9568.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,x),x,u)),z),w),tc_bool)*.
% 299.79/300.45 18747[0:SSi:18729.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(v,x),tc_bool)* -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(v,x)).
% 299.79/300.45 18793[0:SSi:18776.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),v),v_Procs),v_Procs,tc_bool)* -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),v),v_Procs),v_Procs).
% 299.79/300.45 18833[0:SSi:18817.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),v_Procs,tc_bool)* -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),v_Procs).
% 299.79/300.45 18897[0:SpR:8415.2,463.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Com_Obody) c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,v_x),u,v,w) -> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),v_x),u,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(v_x,v,u,w),w)*.
% 299.79/300.45 19000[0:SpR:600.0,9569.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),tc_bool)*.
% 299.79/300.45 18988[0:SpR:188.1,9569.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),c_Set_Ovimage(c_COMBK(v,u,x),x,u)),w),tc_bool)*.
% 299.79/300.45 19058[0:SSi:19040.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(w,x),tc_bool)* -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(w,x)).
% 299.79/300.45 19093[0:SSi:19072.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x)),x),x,tc_bool)* -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x)),x),x).
% 299.79/300.45 19115[0:SpR:8415.2,196.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(hAPP(c_Set_Ovimage(u,v,w),v_x),v_x).
% 299.79/300.45 19109[0:SpR:196.1,128.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool)))**.
% 299.79/300.45 19100[0:SpR:196.1,9569.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),c_Set_Ovimage(u,v,w)),hAPP(c_Set_Oimage(u,v,w),x)),tc_bool)*.
% 299.79/300.45 19099[0:SpR:196.1,9568.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Ovimage(u,v,w)),z),hAPP(c_Set_Oimage(u,v,w),x)),tc_bool)*.
% 299.79/300.45 19129[0:SpR:353.0,10931.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w),t_a) hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(t_a)),w)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w))))*.
% 299.79/300.45 19319[0:Res:304.3,427.1] class_Lattices_Oupper__semilattice(u) class_Orderings_Opreorder(u) || c_lessequals(v,w,u)* c_lessequals(x,w,u)* c_lessequals(w,y,u)* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),y,u)*.
% 299.79/300.45 19261[0:SpR:8415.2,304.3] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) c_lessequals(v_x,v,u) c_lessequals(w,v,u) -> c_lessequals(hAPP(v_x,w),v,u)*.
% 299.79/300.45 19349[0:SSi:19309.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,v,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),y))* -> hBOOL(hAPP(v,y))*.
% 299.79/300.45 19428[0:SpL:8415.2,193.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Finite__Set_Ofinite(v_x,v) equal(c_Finite__Set_Ocard(v_x,w),c_Finite__Set_Ocard(v_x,v)) -> c_Fun_Oinj__on(u,v_x,v,w)*.
% 299.79/300.45 19475[0:Res:9067.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w)),x,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w)),x),v,t_a)*.
% 299.79/300.45 19669[0:Res:19440.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Com_Opname),v_x)))),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Com_Opname),v_x))))* c_Hoare__Mirabelle_Otriple__valid(u,v_Procs,t_a).
% 299.79/300.45 19648[0:SpL:584.0,496.0] || hBOOL(hAPP(c_COMBS(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u,v,w,x),y))* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(z,hAPP(u,y))),hAPP(u,y)))* c_Hoare__Mirabelle_Otriple__valid(z,y,t_a).
% 299.79/300.45 19872[0:SpL:104.0,3698.2] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))))* equal(c_Com_Ocom_OBODY,u) equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Com_Ocom_OSKIP) -> .
% 299.79/300.45 19868[0:SpL:104.0,3493.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_in(tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.79/300.45 19806[0:SpR:104.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,y,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))*.
% 299.79/300.45 19775[0:SpR:104.0,3339.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)))) -> equal(c_Fun_Ofun__upd(u,v_x,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),x,y),u)**.
% 299.79/300.45 19774[0:SpR:104.0,3316.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)))) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.79/300.45 19771[0:SpR:104.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),tc_Com_Opname,u),v_Procs)))*.
% 299.79/300.45 19768[0:SpR:104.0,11030.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_in(t_a)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.79/300.45 19767[0:SpR:104.0,10090.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.45 19762[0:SpR:104.0,3284.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))*.
% 299.79/300.45 19757[2:SpR:104.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),tc_bool)).
% 299.79/300.45 19755[0:SpR:104.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),tc_bool)).
% 299.79/300.45 19752[0:SpR:104.0,651.0] || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.45 19915[0:Rew:19819.0,19817.0] || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(v,c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)))**.
% 299.79/300.45 19921[0:SSi:19920.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)))**.
% 299.79/300.45 20289[0:SpR:2097.1,438.1] || hBOOL(hAPP(u,v)) c_Fun_Oinj__on(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(v,w),x,y),u),u)**.
% 299.79/300.45 20458[0:SpR:525.1,99.1] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),v),v)**.
% 299.79/300.45 20432[0:SpR:2097.1,99.1] || hBOOL(hAPP(u,v)) c_Fun_Oinj__on(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(v,w),x,y),u),u)**.
% 299.79/300.45 20719[0:SSi:20697.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,y,z,x1)),x),y,tc_bool)* -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,y,z,x1)),x),y).
% 299.79/300.45 20730[0:Res:313.1,430.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(hAPP(c_Set_Oimage(x,w,y),v),z,tc_fun(y,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(x,w,y),u),z,tc_fun(y,tc_bool))*.
% 299.79/300.45 20742[0:SSi:20739.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,hAPP(c_Set_Oimage(y,w,z),u),tc_fun(z,tc_bool))* -> c_lessequals(x,hAPP(c_Set_Oimage(y,w,z),v),tc_fun(z,tc_bool))*.
% 299.79/300.45 20776[0:Res:129.1,430.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(hAPP(c_Set_Ovimage(x,y,w),v),z,tc_fun(y,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(x,y,w),u),z,tc_fun(y,tc_bool))*.
% 299.79/300.45 20785[0:SSi:20782.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,hAPP(c_Set_Ovimage(y,z,w),u),tc_fun(z,tc_bool))* -> c_lessequals(x,hAPP(c_Set_Ovimage(y,z,w),v),tc_fun(z,tc_bool))*.
% 299.79/300.45 21024[0:SpL:317.0,215.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(x)),hAPP(c_Set_Oinsert(y,w),z)),x)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(v,y),tc_Hoare__Mirabelle_Otriple(x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(x),tc_bool))),x)*.
% 299.79/300.45 20979[0:SpR:9924.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,v),hAPP(c_Set_Oinsert(w,u),x)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,v),x)))*.
% 299.79/300.45 20948[0:SpR:525.1,317.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(v,w),y)),hAPP(c_Set_Oinsert(v,x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),y)))*.
% 299.79/300.45 20921[0:SpR:2097.1,317.0] || hBOOL(hAPP(u,v)) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v,w),x,y),hAPP(c_Set_Oinsert(u,x),z)),hAPP(c_Set_Oinsert(u,y),hAPP(c_Set_Oimage(c_Set_Oinsert(v,w),x,y),z)))*.
% 299.79/300.45 20870[0:SpR:317.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),y),hAPP(c_Set_Oimage(u,x,w),hAPP(c_Set_Oinsert(v,x),y)),z,x1),c_Set_Oinsert(hAPP(u,v),w))**.
% 299.79/300.45 21083[0:SpR:600.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(y,v,tc_fun(u,tc_bool)),w),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v)))*.
% 299.79/300.45 21072[0:SpR:188.1,20881.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z),hAPP(c_Set_Oinsert(w,y),x1)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.79/300.45 21044[0:SpR:196.1,20881.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),z),x),x1)),z))*.
% 299.79/300.45 21179[0:SpR:104.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w,x),hAPP(c_in(tc_Com_Opname),v_x)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))*.
% 299.79/300.45 21240[0:SpR:104.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))*.
% 299.79/300.45 21683[0:SpL:21267.0,515.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v_x),y),z))* -> equal(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Hoare__Mirabelle_Otriple_Otriple(u),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v_x),tc_Com_Opname,x1))*.
% 299.79/300.45 21629[0:SpL:21267.0,296.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),w,u) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,x),w,u)*.
% 299.79/300.45 21627[0:SpL:21267.0,312.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),c_Orderings_Obot__class_Obot(u)) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,w),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.45 21596[0:SpL:21267.0,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(v),hAPP(c_in(v),v_x),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,y,u,v)))*.
% 299.79/300.45 21595[0:SpL:21267.0,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(v),hAPP(c_in(v),v_x),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,x,u,v)))*.
% 299.79/300.45 21583[0:SpL:21267.0,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,w),u)*.
% 299.79/300.45 21582[0:SpL:21267.0,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,w),c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.79/300.45 21561[0:SpL:21267.0,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),u)) -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(u,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),tc_Com_Opname,w),t_a)*.
% 299.79/300.45 21486[0:SpR:21267.0,584.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,z)),hAPP(hAPP(u,v_x),hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,z))))**.
% 299.79/300.45 21484[0:SpR:21267.0,584.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,z)),hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,z)),hAPP(v,v_x)))**.
% 299.79/300.45 21456[0:SpR:21267.0,294.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x),tc_Com_Opname,x),u)* -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x),u).
% 299.79/300.45 21442[0:SpR:21267.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,x),v),y)),hAPP(c_Set_Oinsert(hAPP(u,v_x),w),hAPP(c_Set_Oimage(u,v,w),y)))*.
% 299.79/300.45 21436[0:SpR:21267.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x),hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x),tc_Com_Opname,x)),tc_bool)*.
% 299.79/300.45 21427[0:SpR:21267.0,353.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,x))),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(u,v),v_x)))**.
% 299.79/300.45 21398[0:SpR:21267.0,254.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(w,u),v_x),tc_Com_Opname,x)))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),v_x))).
% 299.79/300.45 21382[0:SpR:21267.0,8369.1] || -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),v_x),tc_Com_Opname,w)),v))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),v_x)).
% 299.79/300.45 21333[0:SpR:21267.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,x)),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.45 21286[0:SpR:21267.0,341.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_fun(u,tc_bool))*.
% 299.79/300.45 21780[0:SpR:188.1,21143.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,w),w,u),t_a,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.79/300.45 21849[0:SpR:188.1,21131.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.79/300.45 22311[0:SpL:21893.0,515.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v_x),y),z))* -> equal(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v_x),c_Hoare__Mirabelle_Otriple_Otriple(u),tc_Com_Opname,x1))*.
% 299.79/300.45 22257[0:SpL:21893.0,296.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),w,u) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,x),w,u)*.
% 299.79/300.45 22255[0:SpL:21893.0,312.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),c_Orderings_Obot__class_Obot(u)) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.45 22224[0:SpL:21893.0,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(v),v_x),c_in(v),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,y,u,v)))*.
% 299.79/300.45 22223[0:SpL:21893.0,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(v),v_x),c_in(v),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,x,u,v)))*.
% 299.79/300.45 22210[0:SpL:21893.0,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,w),u)*.
% 299.79/300.45 22209[0:SpL:21893.0,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,w),c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.79/300.45 22188[0:SpL:21893.0,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),u)) -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(u,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,w),t_a)*.
% 299.79/300.45 22112[0:SpR:21893.0,584.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,z)),hAPP(hAPP(u,v_x),hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,z))))**.
% 299.79/300.45 22110[0:SpR:21893.0,584.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,z)),hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,z)),hAPP(v,v_x)))**.
% 299.79/300.45 22082[0:SpR:21893.0,294.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),tc_Com_Opname,x),u)* -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x),u).
% 299.79/300.45 22068[0:SpR:21893.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,x),v),y)),hAPP(c_Set_Oinsert(hAPP(u,v_x),w),hAPP(c_Set_Oimage(u,v,w),y)))*.
% 299.79/300.45 22062[0:SpR:21893.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x),hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x)),tc_bool)*.
% 299.79/300.45 22053[0:SpR:21893.0,353.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,x))),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(u,v),v_x)))**.
% 299.79/300.45 22024[0:SpR:21893.0,254.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(w,u),v_x),c_Set_Oinsert(w,u),tc_Com_Opname,x)))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),v_x))).
% 299.79/300.45 22008[0:SpR:21893.0,8369.1] || -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),v_x),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),tc_Com_Opname,w)),v))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),v_x)).
% 299.79/300.45 21959[0:SpR:21893.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,x)),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.45 21912[0:SpR:21893.0,341.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_fun(u,tc_bool))*.
% 299.79/300.45 22481[0:SpR:188.1,21126.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(w,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,x),x,u),tc_Com_Opname,y),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.79/300.45 22651[0:SpL:158.0,3698.2] || equal(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.45 22647[0:SpL:158.0,3493.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(tc_Com_Opname))** equal(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))* -> .
% 299.79/300.45 22576[0:SpR:158.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x2))))*.
% 299.79/300.45 22556[0:SpR:158.0,3339.1] || equal(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x)),x1,x2),u)**.
% 299.79/300.45 22555[0:SpR:158.0,3316.1] || equal(c_in(u),c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.79/300.45 22552[0:SpR:158.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,z,w),v_x))),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(v,y,w,x,z),z,x),tc_Com_Opname,u),v_Procs)))*.
% 299.79/300.45 22546[0:SpR:158.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),t_a,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))))*.
% 299.79/300.45 22544[0:SpR:158.0,11030.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))*.
% 299.79/300.45 22543[0:SpR:158.0,10090.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.45 22538[0:SpR:158.0,3284.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(z),v_Procs),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))))*.
% 299.79/300.45 22533[2:SpR:158.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_bool))*.
% 299.79/300.45 22531[0:SpR:158.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_bool))*.
% 299.79/300.45 22528[0:SpR:158.0,651.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),tc_Com_Opname,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.45 22517[0:SpR:158.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_Procs))))*.
% 299.79/300.45 22744[0:SpR:3294.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_in(t_a),v) hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),x)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(v,v_x),w,u),u)*.
% 299.79/300.45 22733[0:SpR:3294.1,176.0] || equal(c_in(t_a),u) -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),hAPP(c_Set_Ovimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.45 23029[0:SpL:131.0,3698.2] || equal(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.45 23025[0:SpL:131.0,3493.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(tc_Com_Opname))** equal(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))* -> .
% 299.79/300.45 22962[0:SpR:131.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x2))))*.
% 299.79/300.45 22943[0:SpR:131.0,3339.1] || equal(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x)),x1,x2),u)**.
% 299.79/300.45 22942[0:SpR:131.0,3316.1] || equal(c_in(u),c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.79/300.45 22939[0:SpR:131.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),hAPP(c_Set_Ovimage(y,x,z),v_x))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(y,v,x,z,w),w,z),tc_Com_Opname,u),v_Procs)))*.
% 299.79/300.45 22932[0:SpR:131.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),t_a,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))))*.
% 299.79/300.45 22930[0:SpR:131.0,11030.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))*.
% 299.79/300.45 22929[0:SpR:131.0,10090.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.45 22924[0:SpR:131.0,3284.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(z),v_Procs),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))))*.
% 299.79/300.45 22919[2:SpR:131.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_bool))*.
% 299.79/300.45 22917[0:SpR:131.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_bool))*.
% 299.79/300.45 22914[0:SpR:131.0,651.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),tc_Com_Opname,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.45 22909[0:SpR:131.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_Procs))))*.
% 299.79/300.45 23199[0:SpL:181.1,3487.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)).
% 299.79/300.45 23394[0:SpL:460.1,16217.0] || class_Lattices_Olattice(t_b) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_Procs) -> .
% 299.79/300.45 23393[0:SpL:460.1,3929.0] || class_Lattices_Olattice(t_b) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u)* -> hBOOL(hAPP(u,v_x))*.
% 299.79/300.45 23385[0:SpR:460.1,9567.0] || class_Lattices_Olattice(t_b) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,tc_fun(v,tc_bool)),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool)*.
% 299.79/300.45 23364[0:SpR:460.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || class_Lattices_Olattice(t_b) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,u),u)*.
% 299.79/300.45 23572[0:SpL:523.1,16217.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_Procs) -> .
% 299.79/300.45 23571[0:SpL:523.1,3929.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.79/300.45 23516[0:SpR:523.1,9567.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x,tc_fun(y,tc_bool)),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool)*.
% 299.79/300.45 23495[0:SpR:523.1,683.1] class_Lattices_Olattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x),tc_Com_Opname,v),v)*.
% 299.79/300.45 24211[0:SpR:584.0,542.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w,x,y,z),v)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w,x,y,z),v))**.
% 299.79/300.45 24152[0:SpR:542.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),tc_bool)*.
% 299.79/300.45 24135[0:SpR:542.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y,z,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))*.
% 299.79/300.45 24332[0:SpR:393.1,9567.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oimage(c_COMBK(w,x,v),v,x),y,tc_fun(z,tc_bool)),u),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_bool)*.
% 299.79/300.45 24568[0:SpR:24020.1,317.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),x)))*.
% 299.79/300.45 24784[0:SpR:614.2,9567.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u),tc_bool)*.
% 299.79/300.45 24781[0:SpR:614.2,474.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),z,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.45 24767[0:SpR:614.2,5875.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),z,x1,x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u)))*.
% 299.79/300.45 25040[0:SpR:523.1,23902.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.45 25039[0:SpR:460.1,23902.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.45 25424[0:SpL:512.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,y),x),y,w),v_Procs)** -> .
% 299.79/300.45 25423[0:SpL:512.0,3929.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)))* equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,y),x),y,w),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.79/300.45 25373[0:SpR:512.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),z,tc_fun(x1,tc_bool)),x2),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),x2)),tc_bool)*.
% 299.79/300.45 25358[0:SpR:512.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),x1),c_Set_Oimage(hAPP(c_COMBB(u,v,w,y),x),y,w),x2,x3,x4),z))*.
% 299.79/300.45 25347[0:SpR:512.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,z,w),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oimage(hAPP(c_COMBB(v,w,x,z),y),z,x),tc_Com_Opname,u),u)*.
% 299.79/300.45 25346[0:SpR:512.0,23902.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.45 25734[0:Res:1103.1,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),w)),t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,x),t_a)* -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),w),t_a) c_Hoare__Mirabelle_Otriple__valid(x,w,t_a)*.
% 299.79/300.45 25704[0:Res:254.1,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(t_a)),v),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,y),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.45 25692[0:SpL:584.0,455.0] || hBOOL(hAPP(c_COMBS(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u,v,w,x),y))* c_Hoare__Mirabelle_Ohoare__valids(z,hAPP(u,y),t_a)* c_Hoare__Mirabelle_Otriple__valid(x1,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(z,x1),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x1,y,t_a)*.
% 299.79/300.45 25738[4:MRR:25689.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_Set_Oinsert(v_x,tc_Com_Opname))** c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.45 25966[0:SpL:339.0,3506.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(x,y),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))* -> .
% 299.79/300.45 25950[0:SpR:2098.1,339.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) equal(hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w))**.
% 299.79/300.45 25914[0:SpR:339.0,510.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y))))*.
% 299.79/300.45 25878[0:SpR:339.0,9566.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w))),x),tc_bool)*.
% 299.79/300.45 25843[0:SpR:339.0,24020.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),v_x),v_x)**.
% 299.79/300.45 26247[0:SpL:338.0,442.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),w),hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(v)),y)),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),w),y),v).
% 299.79/300.45 26242[0:SpL:338.0,371.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),y))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),y)) equal(w,y).
% 299.79/300.45 26214[0:SpR:3294.1,338.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_bool)))**.
% 299.79/300.45 26209[0:SpR:584.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),hAPP(x,v))),hAPP(c_Set_Oinsert(w,u),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x,y,z,x1),v)))*.
% 299.79/300.45 26201[0:SpR:600.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),c_HOL_Ominus__class_Ominus(x,v,tc_fun(u,tc_bool)))),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v)))**.
% 299.79/300.45 26160[0:SpR:2098.1,338.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) equal(hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),v))**.
% 299.79/300.45 26109[0:SpR:338.0,9566.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),hAPP(hAPP(c_Set_Oinsert(y,z),c_Set_Oinsert(w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)),tc_bool)*.
% 299.79/300.45 26107[0:SpR:338.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(u,v),x)),y,z),c_Set_Oinsert(u,v))**.
% 299.79/300.45 26076[0:SpR:338.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),x))))*.
% 299.79/300.45 26043[0:SpR:338.0,9566.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)),hAPP(c_Set_Oinsert(u,v),x)),tc_bool)*.
% 299.79/300.45 26367[0:SpL:3294.1,85.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_lessequals(v,c_Orderings_Obot__class_Obot(tc_bool),tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.45 26362[0:SpL:584.0,85.0] || c_lessequals(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),x1),tc_fun(v,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,x1,tc_fun(v,tc_bool)),hAPP(w,x1),tc_fun(v,tc_bool))*.
% 299.79/300.45 26353[0:SpL:600.0,85.0] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,x,tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.79/300.45 26534[0:Res:84.1,214.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)),y,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))).
% 299.79/300.45 26522[0:Res:84.1,431.0] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* c_Fun_Oinj__on(y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),w,z)* -> c_Fun_Oinj__on(y,u,w,z)*.
% 299.79/300.45 26512[0:SpR:3294.1,84.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_lessequals(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),tc_fun(u,tc_bool))* -> c_lessequals(v,c_Orderings_Obot__class_Obot(tc_bool),tc_fun(u,tc_bool)).
% 299.79/300.45 26507[0:SpR:584.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(x,v),tc_fun(w,tc_bool))* -> c_lessequals(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,y,z,x1),v),tc_fun(w,tc_bool))*.
% 299.79/300.45 26498[0:SpR:600.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(x,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v),tc_fun(w,tc_bool)).
% 299.79/300.45 26884[0:Rew:64.0,26820.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> equal(hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(v,u),x)),hAPP(c_Set_Oinsert(w,u),x))**.
% 299.79/300.45 26951[0:Res:424.2,431.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(x,w,tc_fun(u,tc_bool))* c_Fun_Oinj__on(y,w,u,z)* -> c_Fun_Oinj__on(y,hAPP(c_Set_Oinsert(v,u),x),u,z)*.
% 299.79/300.45 27061[0:SpL:584.0,280.1] || hBOOL(hAPP(hAPP(u,v),w)) hBOOL(hAPP(c_COMBS(c_in(x),y,z,x1,x2),v))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(y,v),u,x,tc_fun(x3,tc_bool)),w))*.
% 299.79/300.45 27125[4:MRR:27058.3,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(hAPP(w,v),x))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,w,u,tc_fun(y,tc_bool)),x))*.
% 299.79/300.45 27159[0:SpR:11176.1,450.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x)))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),w),v),t_a)*.
% 299.79/300.45 27342[7:MRR:24286.0,27297.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Set_Oimage(c_COMBK(u,v,w),w,v)),c_Set_Oimage(c_COMBK(u,v,w),w,v))**.
% 299.79/300.45 27579[0:SpR:10463.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),w,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),u,y),c_Orderings_Obot__class_Obot(tc_bool)),v)*.
% 299.79/300.45 27578[0:SpR:9911.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),w,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,y),c_Orderings_Otop__class_Otop(tc_bool)),v)*.
% 299.79/300.45 27529[0:SpR:373.2,7253.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),v))*.
% 299.79/300.45 27520[0:SpR:373.2,9566.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> c_lessequals(v,hAPP(hAPP(c_Set_Oinsert(z,x1),c_Hilbert__Choice_Oinv__into(w,x,u,y)),hAPP(x,v)),tc_bool)*.
% 299.79/300.45 27732[0:SpR:10463.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),w,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),u,y),c_Orderings_Obot__class_Obot(tc_bool)),v)*.
% 299.79/300.45 27731[0:SpR:9911.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),w,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,y),c_Orderings_Otop__class_Otop(tc_bool)),v)*.
% 299.79/300.45 27681[0:SpR:71.2,7253.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(w,x,u,y),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),v))*.
% 299.79/300.45 27671[0:SpR:71.2,9566.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> c_lessequals(v,hAPP(hAPP(c_Set_Oinsert(z,x1),c_Fun_Othe__inv__into(w,x,u,y)),hAPP(x,v)),tc_bool)*.
% 299.79/300.45 27873[7:SpR:131.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_bool))*.
% 299.79/300.45 27872[7:SpR:158.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_bool))*.
% 299.79/300.45 27854[7:SpR:104.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),tc_bool)).
% 299.79/300.45 28020[0:SpR:131.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),tc_Com_Opname,z)),v_Procs))*.
% 299.79/300.45 28019[0:SpR:158.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),tc_Com_Opname,z)),v_Procs))*.
% 299.79/300.45 28001[0:SpR:104.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),tc_Com_Opname,w)),v_Procs))*.
% 299.79/300.45 28240[0:SpL:465.1,447.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w) c_Fun_Oinj__on(c_Fun_Ofun__upd(u,y,z,v,w),x,v,w)* -> hBOOL(hAPP(hAPP(c_in(v),y),x)) c_Finite__Set_Ofinite(x,v).
% 299.79/300.45 28228[0:SpL:465.1,3506.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(z,x1),hAPP(c_Set_Oimage(u,x,y),v_x))* -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)).
% 299.79/300.45 28178[0:SpR:465.1,98.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),z,x,y)* -> hBOOL(hAPP(hAPP(c_in(x),v),z)) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,x,y),z),y),c_Finite__Set_Ocard(z,x)).
% 299.79/300.45 28174[0:SpR:465.1,9566.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_Set_Oimage(x,u,y),w),hAPP(hAPP(c_Set_Oinsert(z,x1),c_Set_Oimage(c_Fun_Ofun__upd(x,v,x2,u,y),u,y)),w),tc_bool)*.
% 299.79/300.45 28145[0:SpR:465.1,24020.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) equal(hAPP(hAPP(c_Set_Oimage(u,x,y),v_x),v_x),v_x).
% 299.79/300.45 28323[0:SpR:131.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_Com_Opname,z)),v_Procs))*.
% 299.79/300.45 28322[0:SpR:158.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_Com_Opname,z)),v_Procs))*.
% 299.79/300.45 28304[0:SpR:104.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),tc_Com_Opname,w)),v_Procs))*.
% 299.79/300.45 28536[0:SpR:23840.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Fun_Ofun__upd(v,w,c_Orderings_Obot__class_Obot(tc_bool),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,y,z,x),w,u,x,z))*.
% 299.79/300.45 28489[0:SpR:10463.0,118.0] || -> equal(c_Fun_Ocomp(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Fun_Ofun__upd(v,w,x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,z,x1,y),w,c_Orderings_Obot__class_Obot(tc_bool),y,x1))*.
% 299.79/300.45 28488[0:SpR:9911.0,118.0] || -> equal(c_Fun_Ocomp(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Fun_Ofun__upd(v,w,x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,z,x1,y),w,c_Orderings_Otop__class_Otop(tc_bool),y,x1))*.
% 299.79/300.45 28647[0:SpL:177.1,147.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* hBOOL(hAPP(hAPP(c_in(u),v),x))* -> hBOOL(hAPP(hAPP(c_in(u),w),x))*.
% 299.79/300.45 28624[0:SpR:3229.1,177.1] || equal(u,c_Set_Oinsert(v,w)) -> hBOOL(hAPP(hAPP(c_in(w),v),v_x)) equal(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),v_x)**.
% 299.79/300.45 28655[0:SSi:28605.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),u),v)) equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(u,t_a),v),v_x),hAPP(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x),tc_bool),hAPP(v,v_x))**.
% 299.79/300.45 28782[0:SpR:131.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.45 28781[0:SpR:158.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.45 28763[0:SpR:104.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.45 28937[0:SpR:131.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.45 28936[0:SpR:158.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.45 28918[0:SpR:104.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.45 29178[0:SpL:537.1,311.1] class_Lattices_Olattice(u) class_Lattices_Obounded__lattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),c_Orderings_Obot__class_Obot(u))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_Orderings_Obot__class_Obot(u)).
% 299.79/300.45 29170[0:SpL:537.1,16286.0] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> .
% 299.79/300.45 29110[0:SpR:3229.1,537.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),x)))*.
% 299.79/300.45 29014[0:SpR:537.1,3229.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> equal(hAPP(v,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)))*.
% 299.79/300.45 29006[0:SpR:537.1,28032.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x)))*.
% 299.79/300.45 29000[0:SpR:537.1,28335.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_Com_Opname,x)))*.
% 299.79/300.45 28986[0:SpR:537.1,3283.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),v_Procs))*.
% 299.79/300.45 28979[0:SpR:537.1,1158.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.45 29260[0:SSi:29078.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)),x))*.
% 299.79/300.45 29703[0:SpL:534.1,311.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),c_Orderings_Obot__class_Obot(u))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_Orderings_Obot__class_Obot(u)).
% 299.79/300.45 29695[0:SpL:534.1,16286.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> .
% 299.79/300.45 29634[0:SpR:3229.1,534.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),x)))*.
% 299.79/300.45 29536[0:SpR:534.1,3229.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> equal(hAPP(v,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)))*.
% 299.79/300.45 29528[0:SpR:534.1,28032.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x)))*.
% 299.79/300.45 29522[0:SpR:534.1,28335.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_Com_Opname,x)))*.
% 299.79/300.45 29508[0:SpR:534.1,3283.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),v_Procs))*.
% 299.79/300.45 29501[0:SpR:534.1,1158.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.45 29908[0:SpR:27043.1,545.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,x),u,w),v)))*.
% 299.79/300.45 29905[0:SpR:27043.1,362.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_Procs,w),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.45 30302[0:SpL:536.1,312.1] class_Lattices_Olattice(u) class_Lattices_Obounded__lattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),c_Orderings_Obot__class_Obot(u))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),c_Orderings_Obot__class_Obot(u)).
% 299.79/300.45 30218[0:SpR:3229.1,536.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(v,v_x)))*.
% 299.79/300.45 30144[0:SpR:536.1,8376.2] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)))*.
% 299.79/300.45 30431[0:SSi:30128.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w)),x))*.
% 299.79/300.45 30496[0:Rew:30495.2,20327.2] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),y),y)**.
% 299.79/300.45 30866[0:SpL:535.1,312.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),c_Orderings_Obot__class_Obot(u))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),c_Orderings_Obot__class_Obot(u)).
% 299.79/300.45 30780[0:SpR:3229.1,535.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(v,v_x)))*.
% 299.79/300.45 30704[0:SpR:535.1,8376.2] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)))*.
% 299.79/300.45 31043[0:Rew:31042.2,20326.2] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),y),y)**.
% 299.79/300.45 31079[0:SpR:28771.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,x),tc_Com_Opname),u,w),v)))*.
% 299.79/300.45 31076[0:SpR:28771.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),tc_Com_Opname),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.45 31165[0:SpR:28926.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,x),tc_Com_Opname),u,w),v)))*.
% 299.79/300.45 31162[0:SpR:28926.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w),tc_Com_Opname),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.45 31313[0:Res:1103.1,356.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a) equal(hAPP(c_Set_Oimage(c_COMBK(x,y,v),v,y),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(v),w))),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.45 31239[0:SpL:3229.1,356.0] || equal(u,c_in(v))* hBOOL(hAPP(hAPP(u,v_x),w))* -> equal(hAPP(c_Set_Oimage(c_COMBK(x,y,v),v,y),w),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.45 31430[0:Res:517.1,449.0] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y)))* -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u)),t_a)*.
% 299.79/300.45 31428[0:Res:212.1,449.0] || hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,c_Set_Oinsert(v,w),x,y),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_Set_Oinsert(v,w),x,y)))* -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),x),c_Set_Oinsert(v,w)),t_a).
% 299.79/300.45 31527[0:SpL:3229.1,473.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(w,x,v),y)))* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,v),v_x)),y))*.
% 299.79/300.45 31519[0:SpL:3229.1,473.0] || equal(u,c_Set_Oimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(u,v_x)))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(v_x,v,w,x),y)),v_x))*.
% 299.79/300.45 31747[0:SpL:3229.1,389.0] || equal(u,c_Set_Oimage(v,w,x)) equal(hAPP(c_Set_Oimage(v,w,x),y),hAPP(u,v_x))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> equal(y,v_x).
% 299.79/300.45 31822[7:SpL:523.1,31778.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_x) -> .
% 299.79/300.45 31821[7:SpL:460.1,31778.0] || class_Lattices_Olattice(t_b) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_x) -> .
% 299.79/300.45 31915[7:SpL:537.1,31868.0] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> .
% 299.79/300.45 31914[7:SpL:534.1,31868.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> .
% 299.79/300.45 32196[0:SSi:32188.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(hAPP(v_Procs,u),hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u),tc_bool)* -> equal(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u),hAPP(v_Procs,u)).
% 299.79/300.45 32265[0:Res:23753.1,405.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Oorder(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x,u)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x).
% 299.79/300.45 32277[0:SSi:32259.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_fun(u,tc_bool)),v_x,tc_fun(u,tc_bool))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_fun(u,tc_bool)),v_x).
% 299.79/300.45 32319[0:SpL:584.0,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),x1),u,v)))* hBOOL(hAPP(hAPP(c_in(v),x2),x1))* -> hBOOL(hAPP(u,x2))*.
% 299.79/300.45 32398[0:Rew:300.1,32338.3] class_Lattices_Obounded__lattice(u) || hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v))* hBOOL(hAPP(hAPP(c_in(v),y),w))* -> hBOOL(y).
% 299.79/300.45 32578[0:Rew:300.1,32518.3] class_Lattices_Obounded__lattice(u) || hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v))* hBOOL(hAPP(hAPP(c_in(v),y),x))* -> hBOOL(y).
% 299.79/300.45 32626[0:SpR:188.1,31533.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))),v_Procs))*.
% 299.79/300.45 32721[0:SpR:339.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),tc_Com_Opname,x),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))))*.
% 299.79/300.45 32709[0:SpR:465.1,32669.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),tc_Com_Opname,z),hAPP(c_Set_Oimage(w,u,y),v_x))))*.
% 299.79/300.45 32809[0:SpL:35.2,103.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(v,x,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),w)* c_Finite__Set_Ofinite(u,w) -> c_Finite__Set_Ofinite(v,w).
% 299.79/300.45 32896[0:SpR:8415.2,475.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(hAPP(c_in(v),x),v_x))* -> equal(hAPP(c_Set_Oinsert(hAPP(u,x),w),v_x),v_x)**.
% 299.79/300.45 33282[0:SpR:188.1,32668.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.45 33221[0:SpR:32668.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,x,tc_Com_Opname,y),hAPP(x,v_x)),tc_Com_Opname),u,w),v)))*.
% 299.79/300.45 33217[0:SpR:32668.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,w,tc_Com_Opname,x),hAPP(w,v_x)),tc_Com_Opname),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 33367[0:Res:23789.0,10214.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w),w).
% 299.79/300.45 33381[0:SSi:33361.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,tc_fun(w,tc_bool)),u),tc_bool)* -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,tc_fun(w,tc_bool)),u),u).
% 299.79/300.45 33436[0:Res:8376.2,453.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) equal(u,v_Procs) c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.79/300.45 33423[0:Res:15262.1,453.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(t_a)) c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),t_a) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,v)),u))* c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.79/300.45 33422[0:Res:3285.1,453.0] || equal(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_in(tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w)),u))* c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.79/300.45 33421[0:Res:3317.1,453.0] || equal(c_in(u),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Set_Oinsert(v_x,u),w),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,x)),v))* c_Hoare__Mirabelle_Otriple__valid(x,v_x,t_a).
% 299.79/300.45 33399[0:Res:474.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,x)),u))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(v,y),t_a)*.
% 299.79/300.45 33465[0:Res:23882.0,10214.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),u).
% 299.79/300.45 33480[0:SSi:33459.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool)* -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),u).
% 299.79/300.45 33568[0:SpR:188.1,28704.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,x),x,u),tc_Com_Opname,y)))*.
% 299.79/300.45 33659[0:SpR:188.1,28859.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_COMBK(v,u,x),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),tc_Com_Opname,y)))*.
% 299.79/300.45 33750[7:SpL:188.1,31886.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u))* equal(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(w,v_x) -> .
% 299.79/300.45 34359[0:SpL:24914.0,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),v_x),x)) -> hBOOL(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(u,v,w),tc_Com_Opname,y),hAPP(c_Set_Ovimage(u,v,w),v_x)),hAPP(u,x)))*.
% 299.79/300.45 34221[0:SpR:540.1,24914.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))**.
% 299.79/300.45 34220[0:SpR:539.1,24914.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),v))**.
% 299.79/300.45 34198[0:SpR:25.1,24914.0] class_HOL_Ouminus(u) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_Com_Opname,w),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))**.
% 299.79/300.45 34092[0:SpR:24914.0,83.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Ovimage(u,v,w),v_x)),tc_fun(w,tc_bool))*.
% 299.79/300.45 34075[0:SpR:24914.0,229.0] || -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),v_x),c_Com_Ocom_OSKIP),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Hoare__Mirabelle_Otriple_Otriple(v),tc_Com_Opname,w),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),v_x))),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.79/300.45 34039[0:SpR:24914.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))),x))* -> hBOOL(hAPP(hAPP(c_in(y),hAPP(v,v_x)),hAPP(c_Set_Oimage(v,u,y),x)))*.
% 299.79/300.45 34035[0:SpR:24914.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))),x))* -> c_lessequals(hAPP(v,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 34009[0:SpR:24914.0,299.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),v,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),v).
% 299.79/300.45 33955[0:SpR:24914.0,34.1] || hBOOL(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Ovimage(u,v,w),v_x)),hAPP(u,y)))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),v_x),y)).
% 299.79/300.45 34657[0:SpL:55.1,214.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)),y,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),u),x)) hBOOL(hAPP(hAPP(c_in(v),u),y)).
% 299.79/300.45 34616[0:SpR:55.1,7253.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),z),w,tc_fun(u,tc_bool))))*.
% 299.79/300.45 34580[0:SpR:55.1,212.1] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) -> hBOOL(hAPP(hAPP(c_in(w),y),v)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(y,w),u),v,tc_fun(w,tc_bool)),x))*.
% 299.79/300.45 34877[0:SpR:188.1,28053.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),w,tc_Com_Opname,y)))*.
% 299.79/300.45 34956[0:SpR:188.1,28356.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),tc_Com_Opname,y)))*.
% 299.79/300.45 35037[0:SpR:28755.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,x,c_COMBK(x,y,z),tc_Com_Opname,x1),tc_Com_Opname),u,w),v)))*.
% 299.79/300.45 35033[0:SpR:28755.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,w,c_COMBK(w,x,y),tc_Com_Opname,z),tc_Com_Opname),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.45 35126[0:SpR:28910.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(x,y,z),x,tc_Com_Opname,x1),tc_Com_Opname),u,w),v)))*.
% 299.79/300.45 35122[0:SpR:28910.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(w,x,y),w,tc_Com_Opname,z),tc_Com_Opname),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.45 35333[0:SpR:456.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(u,v),w),x),c_Option_Othe(v),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Option_Othe(v),w,tc_fun(y,tc_bool))))*.
% 299.79/300.45 35285[0:SpR:659.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.45 35265[0:SpR:2095.0,410.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),v,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),v,x,tc_fun(u,tc_bool)))**.
% 299.79/300.45 35255[0:SpR:2093.0,410.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,v_Procs)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_in(tc_Com_Opname),v_x),v,w,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_in(tc_Com_Opname),v_x),v,w,tc_fun(u,tc_bool)))**.
% 299.79/300.45 35254[0:SpR:3744.1,410.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(w,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,w,u,tc_fun(v,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,w,u,tc_fun(v,tc_bool)))**.
% 299.79/300.45 35242[0:SpR:410.0,328.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),hAPP(v,y),tc_fun(x,tc_bool))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(y,w),u),v,w,tc_fun(x,tc_bool)),hAPP(v,y))**.
% 299.79/300.45 35532[0:SpL:113.0,148.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),c_HOL_Ominus__class_Ominus(y,z,tc_fun(x,tc_bool)))))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y))).
% 299.79/300.45 36179[0:SpL:584.0,516.0] || hBOOL(hAPP(c_COMBS(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y),z))* -> hBOOL(hAPP(hAPP(c_in(u),z),v)) hBOOL(hAPP(hAPP(c_in(u),z),z))*.
% 299.79/300.45 36762[0:SpL:67.0,3863.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),y))* -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),y))*.
% 299.79/300.45 36976[0:Res:7539.0,375.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,v),hAPP(c_Set_Oinsert(y,z),hAPP(c_Set_Oinsert(x1,z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(z,tc_bool)))),tc_fun(z,tc_bool))*.
% 299.79/300.45 37142[0:Res:7539.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,v)),hAPP(c_Set_Oinsert(z,x),hAPP(c_Set_Oinsert(x1,x),hAPP(c_Set_Oimage(y,u,x),w)))))*.
% 299.79/300.45 37439[0:SpR:205.1,16776.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,v,w),x),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,v,w)*.
% 299.79/300.45 37762[0:SpR:131.0,36342.1] || hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))))*.
% 299.79/300.45 37761[0:SpR:158.0,36342.1] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))))*.
% 299.79/300.45 38335[0:Obv:38259.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,w,u,u),u)*.
% 299.79/300.45 38402[0:SpL:329.1,493.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* equal(hAPP(c_Set_Oimage(x,w,y),u),hAPP(c_Set_Oimage(x,w,y),v))* c_Fun_Oinj__on(x,v,w,y) -> equal(u,v).
% 299.79/300.45 38489[0:Res:13387.1,385.1] || equal(hAPP(c_Set_Oimage(u,v,v),w),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** c_Finite__Set_Ofinite(w,v) c_Fun_Oinj__on(u,w,v,v) -> equal(hAPP(c_Set_Oimage(u,v,v),w),w).
% 299.79/300.45 38486[0:Res:420.0,385.1] || c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,u) -> equal(hAPP(c_Set_Oimage(v,u,u),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.79/300.45 38722[4:SpR:537.1,37987.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),x))*.
% 299.79/300.45 38721[4:SpR:534.1,37987.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),x))*.
% 299.79/300.45 38911[4:SpR:537.1,38042.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),x,t_a)*.
% 299.79/300.45 38910[4:SpR:534.1,38042.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),x,t_a)*.
% 299.79/300.45 38947[0:SpR:354.2,158.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(v,x,w,y),x,y,w,w),w,w),u),u)**.
% 299.79/300.45 39938[0:Rew:39935.1,20342.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,y,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),y)**.
% 299.79/300.45 40848[4:SSi:40779.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),u),v))* c_Finite__Set_Ofinite(v,tc_bool) c_lessequals(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),tc_bool)* -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,v,tc_bool,tc_bool))*.
% 299.79/300.45 40941[0:Res:27441.0,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))*.
% 299.79/300.45 40938[0:Res:27381.0,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))*.
% 299.79/300.45 40931[0:Res:3282.1,479.1] || equal(hAPP(c_in(u),v),v_Procs)** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,x,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),x)))*.
% 299.79/300.45 40930[7:Res:27207.1,479.1] || equal(hAPP(c_in(u),v),v_x)** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,x,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),x)))*.
% 299.79/300.45 40915[0:Res:13238.1,479.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,w,v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w)))*.
% 299.79/300.45 40908[0:Res:8375.1,479.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) hBOOL(hAPP(w,x))* -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,y,w,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),y)))*.
% 299.79/300.45 40886[0:Res:652.1,479.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,w,v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),w)))*.
% 299.79/300.45 41222[0:Res:27441.0,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs)))*.
% 299.79/300.45 41219[0:Res:27381.0,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs)))*.
% 299.79/300.45 41212[0:Res:3282.1,478.1] || equal(hAPP(c_in(u),v),v_Procs)** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_x,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v_x)))*.
% 299.79/300.45 41211[7:Res:27207.1,478.1] || equal(hAPP(c_in(u),v),v_x)** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_x,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v_x)))*.
% 299.79/300.45 41196[0:Res:13238.1,478.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,u,v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u)))*.
% 299.79/300.45 41167[0:Res:652.1,478.1] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,u,v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),u)))*.
% 299.79/300.45 41422[0:Res:13238.1,275.1] || equal(hAPP(hAPP(u,v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(hAPP(c_in(w),v),x))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,u,w,tc_fun(t_a,tc_bool))))*.
% 299.79/300.45 41418[0:Res:8375.1,275.1] || equal(hAPP(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))* hBOOL(hAPP(hAPP(c_in(x),v),y))* -> hBOOL(hAPP(hAPP(c_in(w),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,u,x,tc_fun(w,tc_bool))))*.
% 299.79/300.45 41401[0:Res:652.1,275.1] || c_lessequals(v_Procs,hAPP(u,v),tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(hAPP(c_in(w),v),x))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,u,w,tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.79/300.45 41479[4:SpR:523.1,38236.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_Com_Opname,tc_bool))*.
% 299.79/300.45 41478[4:SpR:460.1,38236.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_Com_Opname,tc_bool))*.
% 299.79/300.45 42053[0:SpR:180.2,300.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),u),v),u,u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u))**.
% 299.79/300.45 42207[0:SSi:42132.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,u,tc_bool,tc_bool),tc_bool) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(w,tc_bool),u),tc_bool,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.45 42483[0:SpL:351.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_COMBK(w,x,y),z,x1)),w)** -> equal(hAPP(c_Set_Oimage(u,z,x1),v),hAPP(c_Set_Oimage(c_COMBK(w,x,y),z,x1),v)).
% 299.79/300.45 42442[0:SpL:351.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,c_COMBK(w,x,y),u,z,x1)),w)** -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,y),z,x1),v),hAPP(c_Set_Oimage(u,z,x1),v)).
% 299.79/300.45 42736[0:SpL:161.0,325.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool)).
% 299.79/300.45 42735[0:SpL:161.0,324.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool)).
% 299.79/300.45 42734[0:SpL:161.0,345.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> equal(c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.79/300.45 42733[0:SpL:161.0,344.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> equal(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.79/300.45 42760[0:SSi:42669.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)) -> c_lessequals(u,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),y),w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.45 42761[0:SSi:42668.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)) -> c_lessequals(u,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),v),w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.45 43555[0:SpL:507.0,325.0] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),z,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),z,tc_fun(w,tc_bool)).
% 299.79/300.45 43554[0:SpL:507.0,324.0] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),z,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),y),z,tc_fun(w,tc_bool)).
% 299.79/300.45 43553[0:SpL:507.0,345.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.45 43552[0:SpL:507.0,344.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** -> equal(hAPP(c_Set_Oimage(u,v,w),y),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.45 43571[0:SSi:43487.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) -> c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)),tc_fun(x,tc_bool))*.
% 299.79/300.45 43572[0:SSi:43486.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) -> c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),y)),tc_fun(x,tc_bool))*.
% 299.79/300.45 43777[0:SpL:162.0,325.0] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),z,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),z,tc_fun(v,tc_bool)).
% 299.79/300.45 43776[0:SpL:162.0,324.0] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),z,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),y),z,tc_fun(v,tc_bool)).
% 299.79/300.45 43775[0:SpL:162.0,345.0] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> equal(hAPP(c_Set_Ovimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.79/300.45 43774[0:SpL:162.0,344.0] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> equal(hAPP(c_Set_Ovimage(u,v,w),y),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.79/300.45 43795[0:SSi:43709.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),tc_fun(w,tc_bool))*.
% 299.79/300.45 43796[0:SSi:43708.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),y)),tc_fun(w,tc_bool))*.
% 299.79/300.45 44313[0:Res:526.1,268.0] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),x),u))* equal(hAPP(y,v),hAPP(y,x))* c_Fun_Oinj__on(y,u,w,z)* -> equal(v,x).
% 299.79/300.45 45043[0:SpR:330.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v,tc_fun(w,tc_bool))*.
% 299.79/300.45 45005[0:SpR:331.0,326.2] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool)) c_lessequals(w,x,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),x,tc_fun(v,tc_bool))*.
% 299.79/300.45 45347[0:Res:3346.1,487.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,u))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,v)))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,x,v)))*.
% 299.79/300.45 45341[0:Res:8366.1,487.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_Procs)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,tc_Com_Opname)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,tc_Com_Opname)))*.
% 299.79/300.45 45454[0:Res:45357.1,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Set_Oinsert(u,v),w),tc_Com_Opname)))* equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Set_Oinsert(u,v),w),tc_Com_Opname),u).
% 299.79/300.45 45415[0:SpR:297.2,45357.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname),u)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname)).
% 299.79/300.45 45497[0:Res:8366.1,237.0] || equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_Procs)** c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,tc_Com_Opname) -> equal(hAPP(u,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v_x,u,tc_Com_Opname,v)),v_x)**.
% 299.79/300.45 45624[0:SpL:323.0,347.0] || c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,v,tc_fun(z,tc_bool)),z,x1)* -> c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,v,tc_fun(z,tc_bool)),z,x1).
% 299.79/300.45 45623[0:SpL:323.0,346.0] || c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,v,tc_fun(z,tc_bool)),z,x1)* -> c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,tc_fun(z,tc_bool)),z,x1).
% 299.79/300.45 45888[0:Res:3284.1,482.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,u)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,w,u)))* -> hBOOL(hAPP(w,v_Procs)).
% 299.79/300.45 45930[0:SpL:297.2,45899.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname),u)* hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)).
% 299.79/300.45 46670[4:SpL:131.0,46565.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)))* -> .
% 299.79/300.45 46669[4:SpL:158.0,46565.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))* -> .
% 299.79/300.45 46650[4:SpL:104.0,46565.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))* -> .
% 299.79/300.45 47415[0:MRR:47414.1,264.0] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,u,x)))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool)),u,x)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool))))*.
% 299.79/300.45 47984[0:MRR:47983.1,264.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),u,w)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))))*.
% 299.79/300.45 48464[0:Res:545.1,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))* c_Fun_Oinj__on(x,hAPP(c_Set_Oinsert(v,u),w),u,y)* -> .
% 299.79/300.45 48621[0:SpR:197.1,124.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool))*.
% 299.79/300.45 49022[0:Res:48989.1,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,v,tc_Com_Opname)))* -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w)))*.
% 299.79/300.45 49021[0:Res:48989.1,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,v,tc_Com_Opname)))* -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.79/300.45 49389[0:SpR:49342.1,545.1] || hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,x),w)))*.
% 299.79/300.45 49385[0:SpR:49342.1,362.1] || hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.45 50060[0:SSi:50059.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_in(t_a),v_x),u)),hAPP(hAPP(c_in(t_a),v_x),v)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)))**.
% 299.79/300.45 50383[0:SSi:50288.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(w,tc_bool),u),tc_bool,tc_bool),x,tc_bool)* hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,u,tc_bool,tc_bool)) -> hBOOL(x).
% 299.79/300.45 50490[0:SpL:223.1,2693.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(x,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,v_x,u,tc_Com_Opname),u,tc_Com_Opname),w))* equal(c_HOL_Ouminus__class_Ouminus(x,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.45 50582[0:SSi:50546.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(w,tc_bool),u),tc_bool,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,u,tc_bool,tc_bool)) -> hBOOL(x)*.
% 299.79/300.45 51343[0:SpR:188.1,51231.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Set_Oinsert(x,t_a),c_Set_Ovimage(c_COMBK(v,u,w),w,u)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.45 51849[4:SpR:21893.0,40792.1] || c_lessequals(v_x,hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x),hAPP(c_Set_Oinsert(v,w),u),tc_Com_Opname,x)),tc_bool)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x)).
% 299.79/300.45 51848[4:SpR:21267.0,40792.1] || c_lessequals(v_x,hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),u),hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x),tc_Com_Opname,x)),tc_bool)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x)).
% 299.79/300.45 52821[0:SpR:24019.2,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,v_x,v,u),u)*.
% 299.79/300.45 52813[0:SpR:24019.2,176.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(v_x,u,v),hAPP(c_Set_Oinsert(v_x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))))*.
% 299.79/300.45 53051[0:SpR:23955.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w)),x))* -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,u),u)*.
% 299.79/300.45 53036[0:SpR:23955.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.45 53183[0:SpR:23958.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w)),x))* -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,u),u)*.
% 299.79/300.45 53168[0:SpR:23958.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.45 53499[0:Rew:25912.0,53454.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs))**.
% 299.79/300.45 53438[0:SpR:33303.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,x),v_x),tc_Com_Opname),v,u),u)*.
% 299.79/300.45 53419[0:SpR:33303.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x),tc_Com_Opname),u,w),hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.45 53414[0:SpR:33303.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v_Procs,v_Procs,v,w),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname))**.
% 299.79/300.45 53799[0:SpR:53771.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Option_Othe(x),v,y)),z))* -> hBOOL(hAPP(hAPP(c_in(x1),w),hAPP(c_Set_Oimage(c_Option_Othe(x),u,x1),z)))*.
% 299.79/300.45 53795[0:SpR:53771.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Option_Othe(x),v,y)),z))* -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Option_Othe(x),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.45 53830[0:SpR:53772.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(w),x,v,y)),z))* -> hBOOL(hAPP(hAPP(c_in(x1),x),hAPP(c_Set_Oimage(c_Option_Othe(w),u,x1),z)))*.
% 299.79/300.45 53826[0:SpR:53772.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(w),x,v,y)),z))* -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Option_Othe(w),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.45 54146[0:SpR:52997.1,338.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x))**.
% 299.79/300.45 54126[0:SpR:52997.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_Procs,x),v,u),u)*.
% 299.79/300.45 54122[0:SpR:52997.1,339.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v_Procs,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))**.
% 299.79/300.45 54106[0:SpR:52997.1,176.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(c_Set_Oinsert(v_Procs,v),u,w),hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.45 54741[0:SpR:13749.2,361.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Otop__class_Otop(u)),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w,v),v)*.
% 299.79/300.45 54722[0:SpR:13749.2,176.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 55215[0:SpR:14043.2,361.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Otop__class_Otop(u)),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w,v),v)*.
% 299.79/300.45 55196[0:SpR:14043.2,176.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 55794[0:SpL:131.0,55605.1] || equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.79/300.45 55793[0:SpL:158.0,55605.1] || equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** -> .
% 299.79/300.45 56023[0:SpL:131.0,55174.1] || equal(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x)))* -> .
% 299.79/300.45 56022[0:SpL:158.0,55174.1] || equal(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x)))* -> .
% 299.79/300.45 56003[0:SpL:104.0,55174.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))* -> .
% 299.79/300.45 55941[0:SpL:131.0,55174.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_bool),hAPP(z,v_x))* -> .
% 299.79/300.45 55940[0:SpL:158.0,55174.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_bool),hAPP(z,v_x))* -> .
% 299.79/300.45 55921[0:SpL:104.0,55174.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w) equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),tc_bool),hAPP(w,v_x))* -> .
% 299.79/300.45 56219[0:SpR:30368.2,361.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),x),y))* -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,v),v)*.
% 299.79/300.45 56200[0:SpR:30368.2,176.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 56661[0:SpR:30928.2,361.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),x),y))* -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,v),v)*.
% 299.79/300.45 56642[0:SpR:30928.2,176.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 57936[0:SpL:188.1,55910.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_COMBK(w,x,y),c_Set_Ovimage(c_COMBK(v,u,z),z,u))* equal(c_HOL_Ouminus__class_Ouminus(w,tc_bool),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))) -> .
% 299.79/300.45 58093[0:SpL:188.1,55992.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_COMBK(x,y,z))* equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool),x) -> .
% 299.79/300.45 58205[0:SpL:537.1,58055.0] class_Lattices_Olattice(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))** -> .
% 299.79/300.45 58204[0:SpL:534.1,58055.0] class_Lattices_Oupper__semilattice(u) || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))** -> .
% 299.79/300.45 58294[0:Res:304.3,4996.2] class_Lattices_Oupper__semilattice(u) class_Orderings_Obot(u) class_Orderings_Oorder(u) || c_lessequals(v,c_Orderings_Obot__class_Obot(u),u)* c_lessequals(w,c_Orderings_Obot__class_Obot(u),u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.45 58476[0:SpL:523.1,58248.0] class_Lattices_Olattice(u) || equal(c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),x,y),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_fun(t_a,tc_bool)))** -> .
% 299.79/300.45 58475[0:SpL:460.1,58248.0] || class_Lattices_Olattice(t_b) equal(c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),u,v),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_fun(t_a,tc_bool)))** -> .
% 299.79/300.45 58562[0:SpR:338.0,10771.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(y,u),x)),v))*.
% 299.79/300.45 58981[0:Res:517.1,15629.0] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),y)))*.
% 299.79/300.45 58973[0:Res:518.1,15629.0] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),y)))*.
% 299.79/300.45 58800[0:SpL:584.0,15629.0] || hBOOL(hAPP(hAPP(u,v),hAPP(w,v)))* -> hBOOL(hAPP(c_COMBS(u,w,x,y,z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_COMBS(u,w,x,y,z),x1)))*.
% 299.79/300.45 58688[0:SpL:131.0,15629.0] || hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z))* -> hBOOL(hAPP(c_Set_Ovimage(v,y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_Set_Ovimage(v,y,w),x1)))*.
% 299.79/300.45 58686[0:SpL:158.0,15629.0] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z))* -> hBOOL(hAPP(c_Set_Oimage(u,w,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_Set_Oimage(u,w,x),x1)))*.
% 299.79/300.45 59489[0:Res:517.1,15857.0] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),z)))*.
% 299.79/300.45 59481[0:Res:518.1,15857.0] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),z)))*.
% 299.79/300.45 59308[0:SpL:584.0,15857.0] || hBOOL(hAPP(hAPP(u,v),hAPP(w,v)))* -> hBOOL(hAPP(c_COMBS(u,w,x,y,z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(u,w,x,y,z),x2)))*.
% 299.79/300.45 59196[0:SpL:131.0,15857.0] || hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z))* -> hBOOL(hAPP(c_Set_Ovimage(v,y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Set_Ovimage(v,y,w),x2)))*.
% 299.79/300.45 59194[0:SpL:158.0,15857.0] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z))* -> hBOOL(hAPP(c_Set_Oimage(u,w,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Set_Oimage(u,w,x),x2)))*.
% 299.79/300.45 59885[0:SpL:24914.0,4126.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),v) -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),v,u)*.
% 299.79/300.45 59931[0:SSi:59868.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),hAPP(x,u))** -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool)),hAPP(x,u),tc_fun(y,tc_bool))*.
% 299.79/300.45 60205[0:SpL:188.1,58170.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),tc_bool),y,z),w)* -> .
% 299.79/300.45 60444[7:Res:58968.1,278.1] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(u),v),x),z,w,u)))*.
% 299.79/300.45 60443[7:Res:58968.1,277.1] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y),w,u)))*.
% 299.79/300.45 60400[7:SpR:328.1,58968.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),x,tc_fun(w,tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x) -> hBOOL(x).
% 299.79/300.45 60376[7:SpR:8385.1,58968.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,tc_Com_Opname),u),v_Procs) equal(c_Set_Oinsert(v_x,tc_Com_Opname),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,tc_Com_Opname),u))*.
% 299.79/300.45 60481[0:SpL:5882.1,15629.0] class_Lattices_Obounded__lattice(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z)))*.
% 299.79/300.45 60480[0:SpL:5882.1,15857.0] class_Lattices_Obounded__lattice(u) || hBOOL(c_Orderings_Otop__class_Otop(u)) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),x1)))*.
% 299.79/300.45 60466[0:SpR:5882.1,361.2] class_Lattices_Obounded__lattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Otop__class_Otop(u)),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),y,z,x1,x2),w,v),v)*.
% 299.79/300.45 60455[0:SpR:5882.1,176.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Ovimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),v,x1),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.79/300.45 60557[0:Res:58969.1,278.1] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(u),v),x),z,w,u)))*.
% 299.79/300.45 60556[0:Res:58969.1,277.1] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y),w,u)))*.
% 299.79/300.45 60513[0:SpR:328.1,58969.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),x,tc_fun(w,tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_Procs) -> hBOOL(x).
% 299.79/300.45 60489[0:SpR:8385.1,58969.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,tc_Com_Opname),u),v_Procs) equal(c_Set_Oinsert(v_x,tc_Com_Opname),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,tc_Com_Opname),u))*.
% 299.79/300.45 60630[7:Res:59476.1,278.1] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),y),z,w,u)))*.
% 299.79/300.45 60629[7:Res:59476.1,277.1] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z),w,u)))*.
% 299.79/300.45 60586[7:SpR:328.1,59476.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v),x,tc_fun(w,tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x) -> hBOOL(x).
% 299.79/300.45 60562[7:SpR:8385.1,59476.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),v),v_Procs) equal(c_Set_Oinsert(v_x,tc_Com_Opname),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),v))*.
% 299.79/300.45 60703[0:Res:59477.1,278.1] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),y),z,w,u)))*.
% 299.79/300.45 60702[0:Res:59477.1,277.1] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z),w,u)))*.
% 299.79/300.45 60659[0:SpR:328.1,59477.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v),x,tc_fun(w,tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_Procs) -> hBOOL(x).
% 299.79/300.45 60635[0:SpR:8385.1,59477.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),v),v_Procs) equal(c_Set_Oinsert(v_x,tc_Com_Opname),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),v))*.
% 299.79/300.45 60888[0:Res:59017.1,278.1] || hBOOL(hAPP(u,v)) -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(x),v),t_a)* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(x),v),y),x1,u,x)))*.
% 299.79/300.45 60887[0:Res:59017.1,277.1] || hBOOL(hAPP(u,v)) -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(x),v),t_a)* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_in(x),v),z),u,x)))*.
% 299.79/300.45 60844[0:SpR:328.1,59017.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),x,tc_fun(w,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),t_a)* hBOOL(x).
% 299.79/300.45 60820[0:SpR:8385.1,59017.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,tc_Com_Opname),u),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(w,c_Set_Oinsert(v_x,tc_Com_Opname),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,tc_Com_Opname),u))*.
% 299.79/300.45 60961[0:Res:59525.1,278.1] || hBOOL(hAPP(u,v)) -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(x),v),t_a)* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(x),v),z),x1,u,x)))*.
% 299.79/300.45 60960[0:Res:59525.1,277.1] || hBOOL(hAPP(u,v)) -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(x),v),t_a)* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_in(x),v),x1),u,x)))*.
% 299.79/300.45 60917[0:SpR:328.1,59525.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v),x,tc_fun(w,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),t_a)* hBOOL(x).
% 299.79/300.45 60893[0:SpR:8385.1,59525.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),v),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(w,c_Set_Oinsert(v_x,tc_Com_Opname),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),v))*.
% 299.79/300.45 61724[0:SpL:223.1,10885.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(x,tc_Com_Opname),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,v_x,u,tc_Com_Opname),u,tc_Com_Opname),w)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.45 61788[0:SpR:11167.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(x,y),c_Set_Oinsert(v_x,tc_Com_Opname)),v,u),u)*.
% 299.79/300.45 61780[0:SpR:11167.1,176.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,tc_Com_Opname)),u,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 61932[0:SpL:181.1,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(c_COMBK(u,v,w),w,v),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_bool),c_Com_Ocom_OSKIP) -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)).
% 299.79/300.45 62185[0:Res:23754.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),u,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs),u),v_x,t_a)*.
% 299.79/300.45 62317[0:Res:23753.1,4246.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x,u)*.
% 299.79/300.45 62285[0:Res:10531.1,4246.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,u),c_Orderings_Obot__class_Obot(tc_bool)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,u),c_Orderings_Obot__class_Obot(tc_bool),u)*.
% 299.79/300.45 62284[0:Res:9952.1,4246.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_bool),u)*.
% 299.79/300.45 62422[0:SSi:62351.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u),hAPP(v_Procs,u)) -> c_lessequals(hAPP(v_Procs,u),hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u),tc_bool)*.
% 299.79/300.45 62423[0:SSi:62350.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(w,x)) -> c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(w,x),tc_bool)*.
% 299.79/300.45 62424[0:SSi:62349.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(v,x)) -> c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(v,x),tc_bool)*.
% 299.79/300.45 62425[0:SSi:62348.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),u) -> c_lessequals(u,hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),tc_bool)*.
% 299.79/300.45 62426[0:SSi:62344.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w),w) -> c_lessequals(w,hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w),tc_bool)*.
% 299.79/300.45 62427[0:SSi:62335.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,y,z,x1)),x),y) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,y,z,x1)),x),y,tc_bool)*.
% 299.79/300.45 62428[0:SSi:62332.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x)),x),x) -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x)),x),x,tc_bool)*.
% 299.79/300.45 62429[0:SSi:62326.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),v_Procs) -> c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs),v_Procs,tc_bool)*.
% 299.79/300.45 62430[0:SSi:62325.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),v),v_Procs),v_Procs) -> c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)),v),v_Procs),v_Procs,tc_bool)*.
% 299.79/300.45 62437[0:SSi:62223.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),x)),x) -> c_lessequals(x,hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),x)),tc_fun(w,tc_bool))*.
% 299.79/300.45 62438[0:SSi:62214.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_fun(u,tc_bool)),v_x) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_fun(u,tc_bool)),v_x,tc_fun(u,tc_bool))*.
% 299.79/300.45 62652[0:Res:23753.1,4340.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x,u)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_x).
% 299.79/300.45 62620[0:Res:10531.1,4340.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,u),c_Orderings_Obot__class_Obot(tc_bool),u)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,u),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.79/300.45 62619[0:Res:9952.1,4340.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_bool),u)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.79/300.45 63577[0:Res:62367.1,46309.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)) hBOOL(v) -> hBOOL(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool))*.
% 299.79/300.45 63576[0:Res:62367.1,46413.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)) hBOOL(u) -> hBOOL(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool))*.
% 299.79/300.45 63573[0:Res:62367.1,36406.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),u),v_x),v,tc_bool),hAPP(hAPP(c_Set_Oinsert(v_x,t_a),u),v_x)) -> hBOOL(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oinsert(v_x,t_a),u),v_x),v,tc_bool))*.
% 299.79/300.45 64240[0:SpR:14216.0,646.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_Com_Opname,x),c_Orderings_Otop__class_Otop(tc_bool)),v_x)**.
% 299.79/300.45 64203[0:SpR:30368.2,646.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u)),v_x)**.
% 299.79/300.45 64202[0:SpR:30928.2,646.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u)),v_x)**.
% 299.79/300.45 64184[0:SpR:25.1,646.1] class_HOL_Ouminus(u) || c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_Com_Opname,w),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)),v_x)**.
% 299.79/300.45 64181[0:SpR:445.1,646.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),v_Procs,tc_Com_Opname,z) -> equal(v_x,v) equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname,z),hAPP(u,v_x)),v_x)**.
% 299.79/300.45 64407[0:SpR:14216.0,645.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),tc_Com_Opname,x),c_Orderings_Otop__class_Otop(tc_bool)),v_x)**.
% 299.79/300.45 64370[0:SpR:30368.2,645.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u)),v_x)**.
% 299.79/300.45 64369[0:SpR:30928.2,645.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(u)),v_x)**.
% 299.79/300.45 64351[0:SpR:25.1,645.1] class_HOL_Ouminus(u) || c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),tc_Com_Opname,w),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)),v_x)**.
% 299.79/300.45 64348[0:SpR:445.1,645.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),v_Procs,tc_Com_Opname,z) -> equal(v_x,v) equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname,z),hAPP(u,v_x)),v_x)**.
% 299.79/300.45 64478[0:Res:662.1,15629.0] || hBOOL(hAPP(hAPP(u,v_x),v))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(w,tc_bool)),x)))*.
% 299.79/300.45 64477[0:Res:662.1,15857.0] || hBOOL(hAPP(hAPP(u,v_x),v))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(w,tc_bool)),y)))*.
% 299.79/300.45 64593[0:SpR:26782.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_bool)),w)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),x,tc_fun(y,tc_bool)),v,u),u)*.
% 299.79/300.45 64585[0:SpR:26782.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Ovimage(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,tc_fun(w,tc_bool)),u,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 64888[0:Rew:25912.0,64845.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs))**.
% 299.79/300.45 64829[0:SpR:28747.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),tc_Com_Opname,y),tc_Com_Opname),v,u),u)*.
% 299.79/300.45 64809[0:SpR:28747.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w),tc_Com_Opname),u,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 64804[0:SpR:28747.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),v_Procs,v_Procs,w,x),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname))**.
% 299.79/300.45 65008[0:Rew:25912.0,64965.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs))**.
% 299.79/300.45 64949[0:SpR:28748.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),tc_Com_Opname,y),tc_Com_Opname),v,u),u)*.
% 299.79/300.45 64929[0:SpR:28748.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w),tc_Com_Opname),u,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 64924[0:SpR:28748.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),v_Procs,v_Procs,w,x),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname))**.
% 299.79/300.45 65128[0:Rew:25912.0,65085.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs))**.
% 299.79/300.45 65069[0:SpR:28902.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,y),tc_Com_Opname),v,u),u)*.
% 299.79/300.45 65049[0:SpR:28902.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w),tc_Com_Opname),u,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 65044[0:SpR:28902.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),v_Procs,v_Procs,w,x),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname))**.
% 299.79/300.45 65248[0:Rew:25912.0,65205.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs))**.
% 299.79/300.45 65189[0:SpR:28903.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,y),tc_Com_Opname),v,u),u)*.
% 299.79/300.45 65169[0:SpR:28903.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w),tc_Com_Opname),u,x),hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 65164[0:SpR:28903.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),v_Procs,v_Procs,w,x),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname))**.
% 299.79/300.45 66049[0:SpR:65404.1,317.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(v,w),y)),hAPP(c_Set_Oinsert(v,x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),y)))*.
% 299.79/300.45 66048[0:SpR:65404.1,99.1] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),v),v)**.
% 299.79/300.45 67060[0:SpL:66691.3,3693.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OSKIP) -> .
% 299.79/300.45 67361[0:SpL:66692.3,3693.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OSKIP) -> .
% 299.79/300.45 67804[0:SpL:67115.3,3695.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(u),c_Com_Ocom_OSKIP) -> .
% 299.79/300.45 68092[0:SpL:67416.3,3695.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(u),c_Com_Ocom_OSKIP) -> .
% 299.79/300.45 68690[0:SpL:67446.3,3693.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OSKIP) -> .
% 299.79/300.45 68993[0:SpL:67447.3,3693.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Otop__class_Otop(u),c_Com_Ocom_OSKIP) -> .
% 299.79/300.45 69281[0:SpL:67573.3,3695.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(u),c_Com_Ocom_OSKIP) -> .
% 299.79/300.45 69574[0:SpL:68745.3,3695.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY)** equal(c_Orderings_Obot__class_Obot(u),c_Com_Ocom_OSKIP) -> .
% 299.79/300.45 71413[7:SpL:537.1,71221.0] class_Lattices_Olattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> .
% 299.79/300.45 71412[7:SpL:534.1,71221.0] class_Lattices_Oupper__semilattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> .
% 299.79/300.45 73079[7:Res:71608.1,237.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x)** c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,t_a) -> equal(hAPP(u,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v_x,u,t_a,v)),v_x)**.
% 299.79/300.45 73078[7:Res:71608.1,487.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)))*.
% 299.79/300.45 74351[7:SpL:71835.1,473.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(v_x,u,v,w),x)),v_x))*.
% 299.79/300.45 74347[7:SpL:71835.1,389.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) equal(hAPP(c_Set_Oimage(u,v,w),x),v_x)** c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(x,v_x).
% 299.79/300.45 74136[7:SpL:71835.1,473.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x))) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),v_x)),x))*.
% 299.79/300.45 74119[7:SpL:71835.1,356.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,v)) -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,u),u,x),v),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.79/300.45 73759[7:SpR:71835.1,537.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),v_x)**.
% 299.79/300.45 73758[7:SpR:71835.1,534.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),v_x)**.
% 299.79/300.45 73757[7:SpR:71835.1,536.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))**.
% 299.79/300.45 73756[7:SpR:71835.1,535.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))**.
% 299.79/300.45 73656[7:SpR:71835.1,532.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(v_x,w)),hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))**.
% 299.79/300.45 73640[7:SpR:71835.1,537.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w))**.
% 299.79/300.45 73639[7:SpR:71835.1,534.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w))**.
% 299.79/300.45 73524[7:SpR:71835.1,533.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v_x,v)),w),hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))**.
% 299.79/300.45 74872[7:SpR:537.1,72297.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),v_x))*.
% 299.79/300.45 74871[7:SpR:534.1,72297.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),v_x))*.
% 299.79/300.45 75022[0:Res:5890.0,6845.0] || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),z) -> c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),z,tc_fun(u,tc_bool))*.
% 299.79/300.45 75138[0:SSi:75092.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_fun(v,tc_bool))*.
% 299.79/300.45 75139[0:SSi:75091.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_fun(v,tc_bool))*.
% 299.79/300.45 75498[0:Res:7820.1,251.1] class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),z),w)),x),v)*.
% 299.79/300.45 75411[0:SpR:21893.0,7820.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),u)*.
% 299.79/300.45 75409[0:SpR:21267.0,7820.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),u)*.
% 299.79/300.45 75614[0:SSi:75380.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),u),v,tc_fun(w,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.45 75615[0:SSi:75379.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x))),tc_fun(v,tc_bool))*.
% 299.79/300.45 75616[0:SSi:75378.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),x))),tc_fun(w,tc_bool))*.
% 299.79/300.45 75727[7:SpR:71883.1,118.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_Fun_Ocomp(v_x,c_Fun_Ofun__upd(u,v,v_x,w,x),x,y,w),c_Fun_Ofun__upd(c_Fun_Ocomp(v_x,u,x,y,w),v,v_x,w,y))*.
% 299.79/300.45 75715[7:SpR:71883.1,71.2] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(v_x,v,u,w) -> equal(hAPP(c_Fun_Othe__inv__into(v,v_x,u,w),v_x),v_x)**.
% 299.79/300.45 75714[7:SpR:71883.1,373.2] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(v_x,v,u,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,v_x,u,w),v_x),v_x)**.
% 299.79/300.45 75952[0:Res:7823.1,251.1] class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),w),z)),x),v)*.
% 299.79/300.45 76084[0:SSi:75834.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),v,tc_fun(w,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.45 76085[0:SSi:75833.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z))),tc_fun(v,tc_bool))*.
% 299.79/300.45 76086[0:SSi:75832.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z))),tc_fun(w,tc_bool))*.
% 299.79/300.45 76629[0:Res:29199.1,251.1] class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),z),w)),x),v)*.
% 299.79/300.45 76542[0:SpR:21893.0,29199.1] class_Lattices_Olattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),u)*.
% 299.79/300.45 76540[0:SpR:21267.0,29199.1] class_Lattices_Olattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),u)*.
% 299.79/300.45 76984[0:Res:30321.1,251.1] class_Lattices_Olattice(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),w),z)),x),v)*.
% 299.79/300.45 77186[7:SpL:339.0,74788.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_x) equal(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),x)* -> hBOOL(x)*.
% 299.79/300.45 77173[7:SpL:465.1,74788.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_x)** equal(hAPP(c_Set_Oimage(u,x,y),v_x),z)* -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(z)*.
% 299.79/300.45 77227[0:SpR:801.1,383.1] class_Lattices_Oupper__semilattice(u) || -> equal(v,w) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x,y,z),w,w,y,z),c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x,y,z))**.
% 299.79/300.45 77402[0:Res:2399.2,296.1] class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),u)*.
% 299.79/300.45 77401[0:Res:2399.2,295.1] class_Orderings_Olinorder(u) class_OrderedGroup_Olordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),u)*.
% 299.79/300.45 77364[0:Res:2399.2,437.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u) -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* c_Finite__Set_Ofinite(v,u).
% 299.79/300.45 77594[0:Res:2429.2,296.1] class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),u)*.
% 299.79/300.45 77593[0:Res:2429.2,295.1] class_Orderings_Olinorder(u) class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_HOL_Ozero__class_Ozero(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),u)*.
% 299.79/300.45 78159[7:Res:77996.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x),c_Set_Oinsert(x,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,u,v,tc_fun(w,tc_bool))))**.
% 299.79/300.45 78243[7:SpR:78167.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),c_Set_Oinsert(v_x,w),u,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,w),u,tc_fun(x,tc_bool))))*.
% 299.79/300.45 78668[7:MRR:71792.1,78665.1] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u),v_x)** hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),x)).
% 299.79/300.45 78669[7:MRR:71791.1,78665.1] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u),v_x)** hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),x)).
% 299.79/300.45 78681[4:Res:78665.1,516.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),v_x)** -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),x)).
% 299.79/300.45 78874[0:SpR:21893.0,11064.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),v_x),y,tc_fun(w,tc_bool)),w)*.
% 299.79/300.45 78873[0:SpR:21267.0,11064.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),v_x),y,tc_fun(w,tc_bool)),w)*.
% 299.79/300.45 78864[0:SpR:354.2,11064.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,v,w,y)* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x,w,y),u),y)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,z,tc_fun(w,tc_bool)),w)*.
% 299.79/300.45 79033[0:Res:15630.1,12554.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(x,y),z),x1,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),y)),u))*.
% 299.79/300.45 79023[0:Res:15630.1,8513.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),x),u)**.
% 299.79/300.45 79253[0:Res:15858.1,12554.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(x,z),x1),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),z)),u))*.
% 299.79/300.45 79243[0:Res:15858.1,8513.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(w,y),z),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),y),u)**.
% 299.79/300.45 80178[0:SpL:21268.0,442.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),x),w) -> c_Hoare__Mirabelle_Ohoare__derivs(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),x),y,z),w)*.
% 299.79/300.45 80144[0:SpL:21268.0,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),x)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),w),y,z),x))* equal(u,x).
% 299.79/300.45 80074[0:SpL:21268.0,355.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_in(u),hAPP(c_in(u),v),x,y),w)*.
% 299.79/300.45 79954[0:SpR:5882.1,21268.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_Orderings_Otop__class_Otop(u),z,x1)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.45 79936[0:SpR:11167.1,21268.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),v_Procs,w,x)),v_Procs)**.
% 299.79/300.45 79921[0:SpR:329.1,21268.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v,x,y)),v)**.
% 299.79/300.45 79829[0:SpR:445.1,21268.0] || -> equal(u,v) equal(hAPP(c_Fun_Ofun__upd(w,v,x,y,z),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Fun_Ofun__upd(w,v,x,y,z),hAPP(w,u),x1,x2)),hAPP(w,u))**.
% 299.79/300.45 79741[0:SpR:21268.0,13238.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_in(t_a),v_x),hAPP(hAPP(c_in(t_a),v_x),v),u,w),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.79/300.45 79668[0:SpR:21268.0,8375.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_in(v),w),hAPP(hAPP(c_in(v),w),x),u,y),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(v),w),x)).
% 299.79/300.45 79667[0:SpR:21268.0,652.1] || c_lessequals(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x),hAPP(hAPP(c_in(tc_Com_Opname),v_x),v),u,w),tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v)).
% 299.79/300.45 79575[0:SpR:21268.0,10771.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(x,u),hAPP(c_Set_Oinsert(x,u),y),w,z)))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,u),y),v)).
% 299.79/300.45 79545[0:SpR:21268.0,12687.1] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),x),v,y)))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),x)).
% 299.79/300.45 79526[0:SpR:21268.0,9566.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,x),u),hAPP(hAPP(c_Set_Oinsert(w,x),u),y),v,z)),hAPP(hAPP(c_Set_Oinsert(w,x),u),y),tc_bool)*.
% 299.79/300.45 79388[0:SpR:21268.0,16776.0] || -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),u,z),v,w,x),hAPP(c_Set_Oimage(v,w,x),y),x,w)*.
% 299.79/300.45 81373[0:SpL:21894.0,442.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),x),w) -> c_Hoare__Mirabelle_Ohoare__derivs(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),x),c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),y,z),w)*.
% 299.79/300.45 81339[0:SpL:21894.0,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),x)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(u,v),y,z),x))* equal(u,x).
% 299.79/300.45 81269[0:SpL:21894.0,355.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),c_in(u),x,y),w)*.
% 299.79/300.45 81148[0:SpR:5882.1,21894.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Orderings_Otop__class_Otop(u),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.45 81130[0:SpR:11167.1,21894.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> equal(hAPP(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_Procs,hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),w,x)),v_Procs)**.
% 299.79/300.45 81115[0:SpR:329.1,21894.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y)),v)**.
% 299.79/300.45 81023[0:SpR:445.1,21894.0] || -> equal(u,v) equal(hAPP(c_Fun_Ofun__upd(w,v,x,y,z),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(w,u),c_Fun_Ofun__upd(w,v,x,y,z),x1,x2)),hAPP(w,u))**.
% 299.79/300.45 80935[0:SpR:21894.0,13238.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),v),hAPP(c_in(t_a),v_x),u,w),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.79/300.45 80862[0:SpR:21894.0,8375.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_in(v),w),x),hAPP(c_in(v),w),u,y),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(v),w),x)).
% 299.79/300.45 80861[0:SpR:21894.0,652.1] || c_lessequals(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_in(tc_Com_Opname),v_x),v),hAPP(c_in(tc_Com_Opname),v_x),u,w),tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v)).
% 299.79/300.45 80768[0:SpR:21894.0,10771.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,u),y),c_Set_Oinsert(x,u),w,z)))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,u),y),v)).
% 299.79/300.45 80738[0:SpR:21894.0,12687.1] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),x),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),v,y)))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),x)).
% 299.79/300.45 80719[0:SpR:21894.0,9566.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Set_Oinsert(w,x),u),y),hAPP(c_Set_Oinsert(w,x),u),v,z)),hAPP(hAPP(c_Set_Oinsert(w,x),u),y),tc_bool)*.
% 299.79/300.45 80581[0:SpR:21894.0,16776.0] || -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),u,z),v,w,x),hAPP(c_Set_Oimage(v,w,x),y),x,w)*.
% 299.79/300.45 81752[0:SpR:21893.0,5075.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),v_x),c_Set_Ovimage(u,v,w),tc_Com_Opname,x),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x)),w).
% 299.79/300.45 81750[0:SpR:21267.0,5075.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x),tc_Com_Opname,x),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x)),w).
% 299.79/300.45 82084[0:SSi:81976.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,v)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Set_Oimage(y,u,x),z,x1,x2),w)))*.
% 299.79/300.45 82928[0:SpR:21893.0,22513.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(y,w,z),hAPP(c_Set_Oimage(u,v,w),v_x)),z)*.
% 299.79/300.45 82926[0:SpR:21267.0,22513.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(y,w,z),hAPP(c_Set_Oimage(u,v,w),v_x)),z)*.
% 299.79/300.45 82917[0:SpR:354.2,22513.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,v,w,y)* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x,w,y),u),y)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(z,w,x1),u),x1)*.
% 299.79/300.45 83244[7:SpR:537.1,78357.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.45 83243[7:SpR:534.1,78357.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.45 83801[0:SpR:5899.0,59525.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_COMBS(v,w,x,y,z),t_a)* hBOOL(hAPP(c_COMBS(v,w,x1,x2,x3),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x4,c_Orderings_Otop__class_Otop(tc_fun(x5,tc_bool)),c_COMBS(v,w,x,y,z),x5)))*.
% 299.79/300.45 83800[0:SpR:5899.0,59017.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_COMBS(v,w,x,y,z),t_a)* hBOOL(hAPP(c_COMBS(v,w,x1,x2,x3),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x4,tc_bool)),x5,c_COMBS(v,w,x,y,z),x4)))*.
% 299.79/300.45 83778[7:SpR:5899.0,58968.1] || equal(c_COMBS(u,v,w,x,y),v_x) -> hBOOL(hAPP(c_COMBS(u,v,z,x1,x2),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool)),x4,c_COMBS(u,v,w,x,y),x3)))*.
% 299.79/300.45 83777[0:SpR:5899.0,58969.1] || equal(c_COMBS(u,v,w,x,y),v_Procs) -> hBOOL(hAPP(c_COMBS(u,v,z,x1,x2),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool)),x4,c_COMBS(u,v,w,x,y),x3)))*.
% 299.79/300.45 83776[7:SpR:5899.0,59476.1] || equal(c_COMBS(u,v,w,x,y),v_x) -> hBOOL(hAPP(c_COMBS(u,v,z,x1,x2),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x3,c_Orderings_Otop__class_Otop(tc_fun(x4,tc_bool)),c_COMBS(u,v,w,x,y),x4)))*.
% 299.79/300.45 83775[0:SpR:5899.0,59477.1] || equal(c_COMBS(u,v,w,x,y),v_Procs) -> hBOOL(hAPP(c_COMBS(u,v,z,x1,x2),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x3,c_Orderings_Otop__class_Otop(tc_fun(x4,tc_bool)),c_COMBS(u,v,w,x,y),x4)))*.
% 299.79/300.45 84200[7:SpL:339.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),v_x) -> .
% 299.79/300.45 84187[7:SpL:465.1,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),v_x),tc_bool),v_x) equal(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),v_x)** -> hBOOL(hAPP(hAPP(c_in(v),x),v_x)).
% 299.79/300.45 84306[0:SpL:383.1,10287.0] || equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v,w,x,y),z,x1,x,y),c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,z,x2,x,y),v,w,x,y))* -> equal(v,z) equal(x2,x1).
% 299.79/300.45 84398[0:SpR:2936.0,118.0] || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,hAPP(c_in(t_a),v_x),v,w,x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),hAPP(u,c_Orderings_Obot__class_Obot(tc_bool)),x,w),c_Fun_Ocomp(u,hAPP(c_in(t_a),v_x),v,w,x))**.
% 299.79/300.45 84930[4:SpL:5961.0,78744.0] || equal(hAPP(u,hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),x2))),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),x2,t_a).
% 299.79/300.45 84929[4:SpL:5924.0,78744.0] || equal(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2)),v),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,t_a).
% 299.79/300.45 85104[0:SpL:644.0,470.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(w,u,tc_Com_Opname),tc_Com_Opname,u)),v_Procs))*.
% 299.79/300.45 85103[0:SpL:644.0,466.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(w,u,tc_Com_Opname),v,tc_Com_Opname,u)),v_Procs))*.
% 299.79/300.45 85207[0:SpR:819.1,118.0] class_Orderings_Otop(u) || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(v,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),w,x,y),v_x,hAPP(v,c_Orderings_Otop__class_Otop(u)),y,x),c_Fun_Ocomp(v,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),w,x,y))**.
% 299.79/300.45 85263[0:SpR:1250.3,824.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Ogroup__add(u) class_Orderings_Obot(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> equal(c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x,c_HOL_Ozero__class_Ozero(u),v,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)))**.
% 299.79/300.45 85256[0:SpR:824.1,118.0] class_Orderings_Obot(u) || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),w,x,y),v_x,hAPP(v,c_Orderings_Obot__class_Obot(u)),y,x),c_Fun_Ocomp(v,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),w,x,y))**.
% 299.79/300.45 85316[0:SpL:55.1,26240.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(w,u),x),y,tc_fun(u,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(u),w),y)).
% 299.79/300.45 85448[4:SpR:78507.0,410.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,w,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,w,tc_fun(u,tc_bool)))**.
% 299.79/300.45 85828[0:Res:9066.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y))* -> hBOOL(hAPP(hAPP(c_in(w),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),u,tc_fun(w,tc_bool))))*.
% 299.79/300.45 85815[0:SpR:21894.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),c_in(u),x,y),u),z))))*.
% 299.79/300.45 85813[0:SpR:21268.0,9066.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_in(u),hAPP(c_in(u),v),x,y),u),z))))*.
% 299.79/300.45 85746[0:SpR:55.1,9066.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool)))))*.
% 299.79/300.45 86061[0:SpL:537.1,86011.0] class_Lattices_Olattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> .
% 299.79/300.45 86060[0:SpL:534.1,86011.0] class_Lattices_Oupper__semilattice(u) || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> .
% 299.79/300.45 86395[0:SpR:86109.1,59525.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(w,c_Set_Oinsert(v_x,t_a),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v))*.
% 299.79/300.45 86394[0:SpR:86109.1,59017.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(w,c_Set_Oinsert(v_x,t_a),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u))*.
% 299.79/300.45 86295[7:SpR:86109.1,58968.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u),v_Procs) equal(c_Set_Oinsert(v_x,t_a),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u))*.
% 299.79/300.45 86294[0:SpR:86109.1,58969.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u),v_Procs) equal(c_Set_Oinsert(v_x,t_a),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u))*.
% 299.79/300.45 86293[7:SpR:86109.1,59476.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v),v_Procs) equal(c_Set_Oinsert(v_x,t_a),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v))*.
% 299.79/300.45 86292[0:SpR:86109.1,59477.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v),v_Procs) equal(c_Set_Oinsert(v_x,t_a),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v))*.
% 299.79/300.45 86599[0:Res:19823.1,45899.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_Com_Opname)))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v_x)).
% 299.79/300.45 86673[0:Res:86261.1,237.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_Procs)** c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,t_a) -> equal(hAPP(u,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v_x,u,t_a,v)),v_x)**.
% 299.79/300.45 86672[0:Res:86261.1,487.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_Procs)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)))*.
% 299.79/300.45 86745[4:SpL:339.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),v_Procs) -> .
% 299.79/300.45 86732[4:SpL:465.1,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),v_x),tc_bool),v_x) equal(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(v),x),v_x)).
% 299.79/300.45 87312[7:SpR:523.1,71492.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))),x))*.
% 299.79/300.45 87311[7:SpR:460.1,71492.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),u))*.
% 299.79/300.45 87460[7:SpR:523.1,71493.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))),x,t_a)*.
% 299.79/300.45 87459[7:SpR:460.1,71493.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),u,t_a)*.
% 299.79/300.45 87513[0:SpR:769.0,118.0] || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y,z),w,hAPP(u,w),z,y),c_Fun_Ocomp(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y,z))**.
% 299.79/300.45 87590[7:SpR:523.1,71679.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))))*.
% 299.79/300.45 87589[7:SpR:460.1,71679.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))))*.
% 299.79/300.45 88311[0:Res:7227.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_COMBK(y,z,x1),v,x),u,tc_fun(x,tc_bool))))*.
% 299.79/300.45 88299[0:SpR:21894.0,7227.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_COMBK(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(u),v),c_in(u),w,x),y,z),x1,u),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.79/300.45 88297[0:SpR:21268.0,7227.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_COMBK(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(u),hAPP(c_in(u),v),w,x),y,z),x1,u),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.79/300.45 88433[0:Res:8176.1,85.0] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,y,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool)),x,tc_fun(v,tc_bool))*.
% 299.79/300.45 88407[0:SpR:56.1,8176.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(hAPP(c_Set_Oinsert(v,u),x),y,tc_fun(u,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool))*.
% 299.79/300.45 88539[0:SpL:56.1,8306.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(x,c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> c_lessequals(x,hAPP(c_Set_Oinsert(v,u),y),tc_fun(u,tc_bool))*.
% 299.79/300.45 88652[7:SpL:339.0,88086.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_x) hBOOL(c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool))* -> .
% 299.79/300.45 88639[7:SpL:465.1,88086.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oimage(u,x,y),v_x),tc_bool))* -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)).
% 299.79/300.45 88841[0:SpR:353.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(y,v),hAPP(c_Set_Oinsert(u,v),z)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),hAPP(c_Set_Oinsert(y,v),z)))*.
% 299.79/300.45 89167[0:SpL:323.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),z,w,tc_fun(v,tc_bool))),v)* -> c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,z,w,tc_fun(v,tc_bool)),v).
% 299.79/300.45 90666[0:SpL:323.0,26231.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),z,w,tc_fun(v,tc_bool))),v)* -> c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,z,w,tc_fun(v,tc_bool)),v).
% 299.79/300.45 90780[0:Res:13.2,26480.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> c_lessequals(u,c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.45 90762[0:SpL:56.1,26480.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool))*.
% 299.79/300.45 91783[0:SpR:834.1,118.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Fun_Ofun__upd(c_Fun_Ocomp(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),c_Orderings_Obot__class_Obot(u),hAPP(v,w),z,y),c_Fun_Ocomp(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z))**.
% 299.79/300.45 91926[0:SpR:79073.0,410.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,v_Procs)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,x,tc_fun(u,tc_bool)))**.
% 299.79/300.45 92078[7:SpR:79101.0,410.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_in(w),v_x),v,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_in(w),v_x),v,x,tc_fun(u,tc_bool)))**.
% 299.79/300.45 92587[7:SpL:5227.1,78178.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x) c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),v_x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),v_x,t_a).
% 299.79/300.45 92636[7:SpR:523.1,82151.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),c_Set_Oinsert(v_x,x)))*.
% 299.79/300.45 92635[7:SpR:460.1,82151.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Set_Oinsert(v_x,u)))*.
% 299.79/300.45 92786[7:SSi:92736.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(c_Set_Oinsert(v_x,x),tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v_x))*.
% 299.79/300.45 92818[0:SpR:353.0,5876.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Oinsert(w,v),z,x1,x2),hAPP(c_Set_Oinsert(u,v),x)),tc_fun(y,tc_bool))*.
% 299.79/300.45 93296[4:SpR:523.1,85556.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),x),tc_bool)*.
% 299.79/300.45 93295[4:SpR:460.1,85556.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),u),tc_bool)*.
% 299.79/300.45 93484[0:SpR:523.1,86147.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))),x))*.
% 299.79/300.45 93483[0:SpR:460.1,86147.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),u))*.
% 299.79/300.45 93635[0:SpR:523.1,86148.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))),x,t_a)*.
% 299.79/300.45 93634[0:SpR:460.1,86148.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),u,t_a)*.
% 299.79/300.45 93697[0:SpL:24914.0,7462.1] || c_lessequals(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,x),hAPP(c_Set_Oinsert(v,w),v_x)),tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,w),v_x),w) -> c_Finite__Set_Ofinite(u,w).
% 299.79/300.45 93779[0:SpR:523.1,86342.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))))*.
% 299.79/300.45 93778[0:SpR:460.1,86342.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))))*.
% 299.79/300.45 94029[0:SpR:317.0,10791.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oinsert(hAPP(u,x),w),hAPP(c_Set_Oinsert(z,w),hAPP(c_Set_Oimage(u,v,w),y))),tc_fun(w,tc_bool))*.
% 299.79/300.45 93958[0:SpR:24914.0,10791.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(w,v),tc_Com_Opname,x),hAPP(c_Set_Oinsert(w,v),v_x))),hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),v_x)),tc_fun(v,tc_bool))*.
% 299.79/300.45 94270[0:Res:14491.3,363.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Set_Oinsert(w,u),x)))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.45 696[0:Res:449.1,590.0] || hBOOL(hAPP(hAPP(hAPP(v_Q,v_x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(v_P,v_x),hAPP(v_Q,v_x),hAPP(c_Com_Ocom_OBODY,v_x),c_Suc(v_na))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(hAPP(v_P,v_x),hAPP(v_Q,v_x),hAPP(c_Com_Ocom_OBODY,v_x),c_Suc(v_na))))* -> .
% 299.79/300.45 7681[0:SSi:7656.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v),u,tc_fun(w,tc_bool))* -> equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v)).
% 299.79/300.45 7744[0:SSi:7720.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),u,tc_fun(w,tc_bool))* -> equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x)).
% 299.79/300.45 9557[0:Res:5280.2,251.1] class_Orderings_Olinorder(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),tc_fun(u,v)),w),v)*.
% 299.79/300.45 9556[0:Res:5375.2,251.1] class_Orderings_Oorder(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),tc_fun(u,v)),w),v)*.
% 299.79/300.45 9555[0:Res:5602.2,251.1] class_Orderings_Opreorder(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),tc_fun(u,v)),w),v)*.
% 299.79/300.45 9554[0:Res:111.2,251.1] class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || c_lessequals(w,x,tc_fun(u,v)) -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(x,tc_fun(u,v)),y),hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),y),v)*.
% 299.79/300.45 9552[0:Res:52.2,251.1] class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || c_lessequals(w,x,tc_fun(u,v)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,v)),y),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),y),v)*.
% 299.79/300.45 9550[0:Res:5810.2,251.1] class_Orderings_Olinorder(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),tc_fun(u,v)),w),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w),v)*.
% 299.79/300.45 9549[0:Res:6139.2,251.1] class_Orderings_Opreorder(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),tc_fun(u,v)),w),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w),v)*.
% 299.79/300.45 11711[0:SpR:130.1,9268.0] class_HOL_Ominus(u) || -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u))),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u))).
% 299.79/300.45 14164[0:SpR:329.1,176.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(x),v),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y),hAPP(c_Set_Oinsert(v,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.45 14163[0:SpR:328.1,176.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(x),u),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,y),hAPP(c_Set_Oinsert(v,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.45 14162[0:SpR:538.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.45 14160[0:SpR:599.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),u,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 14356[0:Res:474.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u),hAPP(v,x),u)*.
% 299.79/300.45 14483[0:Res:474.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u) -> c_lessequals(hAPP(v,x),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u),u)*.
% 299.79/300.45 14791[0:SpL:128.0,109.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(w,v,x),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))),tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(w,v,x),y),u,tc_fun(v,tc_bool)).
% 299.79/300.45 14789[0:SpL:128.0,109.0] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(y,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> c_lessequals(y,hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)).
% 299.79/300.45 14735[0:SpR:128.0,128.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),c_HOL_Ouminus__class_Ouminus(z,tc_fun(y,tc_bool)))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),z)),tc_fun(v,tc_bool)))*.
% 299.79/300.45 14734[0:SpR:128.0,108.1] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),y,tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(y,tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),tc_fun(v,tc_bool))*.
% 299.79/300.45 14731[0:SpR:128.0,108.1] || c_lessequals(u,hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.45 14939[0:Res:14899.2,251.1] class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),tc_fun(u,v)),w),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w),v)*.
% 299.79/300.45 15064[0:Res:15023.2,251.1] class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),tc_fun(u,v)),w),v)*.
% 299.79/300.45 16552[0:SpR:329.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_lessequals(v,w,tc_fun(x,tc_bool)) hBOOL(hAPP(hAPP(c_in(y),w),z)) -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),y,u),u)*.
% 299.79/300.45 16551[0:SpR:328.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_lessequals(v,w,tc_fun(x,tc_bool))* hBOOL(hAPP(hAPP(c_in(y),v),z))* -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),y,u),u)*.
% 299.79/300.45 16550[0:SpR:538.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),w),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),v,u),u)*.
% 299.79/300.45 16548[0:SpR:599.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool))),y)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),v,u),u)*.
% 299.79/300.45 17365[0:Res:172.2,501.0] class_Orderings_Olinorder(tc_Hoare__Mirabelle_Otriple(t_a)) || c_Finite__Set_Ofinite(u,tc_Hoare__Mirabelle_Otriple(t_a)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u),t_a)* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))) c_Hoare__Mirabelle_Otriple__valid(v,c_Finite__Set_Olinorder__class_OMax(u,tc_Hoare__Mirabelle_Otriple(t_a)),t_a).
% 299.79/300.45 17483[0:Res:171.2,501.0] class_Orderings_Olinorder(tc_Hoare__Mirabelle_Otriple(t_a)) || c_Finite__Set_Ofinite(u,tc_Hoare__Mirabelle_Otriple(t_a)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u),t_a)* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))) c_Hoare__Mirabelle_Otriple__valid(v,c_Finite__Set_Olinorder__class_OMin(u,tc_Hoare__Mirabelle_Otriple(t_a)),t_a).
% 299.79/300.45 17885[0:SpR:188.1,584.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_COMBS(x,c_Set_Ovimage(c_COMBK(v,u,y),y,u),z,x1,x2),w),hAPP(hAPP(x,w),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))))**.
% 299.79/300.45 17883[0:SpR:188.1,1103.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u))))* -> c_Hoare__Mirabelle_Ohoare__valids(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u),t_a) hBOOL(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))).
% 299.79/300.45 17867[0:SpR:188.1,415.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Fun_Ofun__upd(c_Set_Ovimage(c_COMBK(v,u,x),x,u),w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,z),c_Set_Ovimage(c_COMBK(v,u,x),x,u))**.
% 299.79/300.45 18212[0:SpR:584.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(hAPP(x,v),hAPP(y,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(x,y,z,x1,x2),u,tc_fun(x3,tc_bool)),tc_fun(x3,tc_bool))*.
% 299.79/300.45 18203[0:SpR:336.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 18189[0:SpR:584.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x)) -> c_lessequals(hAPP(c_COMBS(y,v,z,x1,x2),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(y,w),u,tc_fun(x3,tc_bool)),tc_fun(x3,tc_bool))*.
% 299.79/300.45 18180[0:SpR:337.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 18166[0:SpR:540.1,362.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.45 18165[0:SpR:539.1,362.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.45 18164[0:SpR:297.2,362.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) hBOOL(hAPP(hAPP(c_in(x),w),y)) -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.45 18155[0:SpR:299.2,362.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* hBOOL(hAPP(hAPP(c_in(x),v),y))* -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.45 18144[0:SpR:25.1,362.1] class_HOL_Ouminus(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(x,v_x),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,u)),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 18412[0:SpR:584.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(hAPP(y,v),hAPP(z,v))),hAPP(c_Set_Oimage(c_COMBS(y,z,x1,x2,x3),u,x),w)))*.
% 299.79/300.45 18403[0:SpR:336.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),u,x),w)))*.
% 299.79/300.45 18389[0:SpR:584.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x)) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(c_COMBS(z,v,x1,x2,x3),w)),hAPP(c_Set_Oimage(hAPP(z,w),u,y),x)))*.
% 299.79/300.45 18380[0:SpR:337.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u,x),w)))*.
% 299.79/300.45 18366[0:SpR:540.1,545.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,y),x)))*.
% 299.79/300.45 18365[0:SpR:539.1,545.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,y),x)))*.
% 299.79/300.45 18364[0:SpR:297.2,545.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) hBOOL(hAPP(hAPP(c_in(x),w),y)) -> hBOOL(hAPP(hAPP(c_in(z),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,z),y)))*.
% 299.79/300.45 18355[0:SpR:299.2,545.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* hBOOL(hAPP(hAPP(c_in(x),v),y))* -> hBOOL(hAPP(hAPP(c_in(z),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,z),y)))*.
% 299.79/300.45 18344[0:SpR:25.1,545.1] class_HOL_Ouminus(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_HOL_Ouminus__class_Ouminus(hAPP(y,v_x),u)),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(y,tc_fun(t_a,u)),v,x),w)))*.
% 299.79/300.45 19323[0:Res:304.3,144.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Opordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,u),u) c_lessequals(x,c_HOL_Ouminus__class_Ouminus(w,u),u) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),u),u)*.
% 299.79/300.45 19348[0:SSi:19333.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,w,tc_bool),x,tc_bool),tc_bool)* c_lessequals(y,c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,w,tc_bool),x,tc_bool),tc_bool)* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),y),v,tc_bool)*.
% 299.79/300.45 19642[0:SpL:8415.2,496.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(v_x,u)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u)),u))* c_Hoare__Mirabelle_Otriple__valid(v,v_x,t_a).
% 299.79/300.45 19701[0:SpL:181.1,19641.0] || hBOOL(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) -> hBOOL(hAPP(hAPP(c_in(v),w),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Ovimage(c_COMBK(w,v,u),u,v),x)))* c_Hoare__Mirabelle_Ohoare__valids(c_Set_Ovimage(c_COMBK(w,v,u),u,v),x,t_a).
% 299.79/300.45 19692[0:SpL:445.1,19641.0] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Fun_Ofun__upd(u,v,w,x,y),z)))* -> equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Fun_Ofun__upd(u,v,w,x,y),z),v) c_Hoare__Mirabelle_Ohoare__valids(c_Fun_Ofun__upd(u,v,w,x,y),z,t_a).
% 299.79/300.45 19876[0:SpL:104.0,3507.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))))* equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,v_x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.79/300.45 19875[0:SpL:104.0,16327.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))))* equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_Procs) -> .
% 299.79/300.45 19874[0:SpL:104.0,3499.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)))) hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.79/300.45 19870[0:SpL:104.0,13272.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.79/300.45 19869[0:SpL:104.0,3484.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),hAPP(c_Com_Ocom_OBODY,w))* -> equal(v_x,w).
% 299.79/300.45 19791[0:SpR:104.0,9569.0] || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)))),v),tc_bool)*.
% 299.79/300.45 19790[0:SpR:104.0,9568.0] || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)))),y),v),tc_bool)*.
% 299.79/300.45 19778[0:SpR:104.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(v),u),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,v_x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))))*.
% 299.79/300.45 19777[0:SpR:104.0,3317.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)))) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(v_x,u),x)))*.
% 299.79/300.45 19776[0:SpR:104.0,3305.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x),v_Procs),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))))*.
% 299.79/300.45 19772[0:SpR:104.0,2771.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)))) -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.79/300.45 19769[0:SpR:104.0,15262.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_in(t_a)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.79/300.45 19766[0:SpR:104.0,8376.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_in(tc_Com_Opname)) equal(w,v_Procs) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),w))*.
% 299.79/300.45 19765[0:SpR:104.0,8415.2] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),v_x).
% 299.79/300.45 19764[0:SpR:104.0,3291.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))),v_Procs))*.
% 299.79/300.45 19763[0:SpR:104.0,3285.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_in(tc_Com_Opname)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.79/300.45 19760[0:SpR:104.0,3279.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),v_Procs),v_x))*.
% 299.79/300.45 19988[0:SpR:64.0,353.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(u,v),x)))**.
% 299.79/300.45 19983[0:SpR:64.0,254.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(x,u),w))).
% 299.79/300.45 19971[0:SpR:64.0,9569.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Set_Oinsert(u,v)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),tc_bool)*.
% 299.79/300.45 19970[0:SpR:64.0,9568.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Set_Oinsert(u,v)),y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),tc_bool)*.
% 299.79/300.45 20075[0:SpL:8415.2,215.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(v)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__derivs(w,v_x,v) -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.79/300.45 20365[0:SpR:9987.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.79/300.45 20363[0:SpR:2095.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(u,v),w,x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.79/300.45 20359[0:SpR:2935.0,438.1] || c_Fun_Oinj__on(hAPP(c_in(t_a),v_x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_in(t_a),v_x),u,v),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))**.
% 299.79/300.45 20354[0:SpR:301.1,438.1] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),v),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.45 20321[0:SpR:414.0,438.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Fun_Ofun__upd(u,v,w,x,y),z,x1),w),v)**.
% 299.79/300.45 20308[0:SpR:8415.2,438.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),v_x),v_x)**.
% 299.79/300.45 20304[0:SpR:365.1,438.1] class_Orderings_Obot(u) || c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,w),c_Orderings_Obot__class_Obot(u)),v_x)**.
% 299.79/300.45 20303[0:SpR:397.1,438.1] class_Orderings_Otop(u) || c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,w),c_Orderings_Otop__class_Otop(u)),v_x)**.
% 299.79/300.45 20297[0:SpR:2093.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_Procs,u),v,w),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_in(tc_Com_Opname),v_x))**.
% 299.79/300.45 20295[0:SpR:3744.1,438.1] || equal(c_in(tc_Com_Opname),c_in(u)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,u),v,w),v_Procs),v_Procs)**.
% 299.79/300.45 20282[0:SpR:438.1,474.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.45 20278[0:SpR:438.1,9569.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w)),hAPP(u,x)),tc_bool)*.
% 299.79/300.45 20277[0:SpR:438.1,9568.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w)),z),hAPP(u,x)),tc_bool)*.
% 299.79/300.45 20509[0:SpR:9987.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.79/300.45 20507[0:SpR:2095.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(u,v),w,x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.79/300.45 20503[0:SpR:2935.0,99.1] || c_Fun_Oinj__on(hAPP(c_in(t_a),v_x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_in(t_a),v_x),u,v),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))**.
% 299.79/300.45 20498[0:SpR:301.1,99.1] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),v),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.45 20465[0:SpR:414.0,99.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Fun_Ofun__upd(u,v,w,x,y),z,x1),w),v)**.
% 299.79/300.45 20456[0:SpR:524.0,99.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),v),v)**.
% 299.79/300.45 20452[0:SpR:8415.2,99.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),v_x),v_x)**.
% 299.79/300.45 20448[0:SpR:365.1,99.1] class_Orderings_Obot(u) || c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,w),c_Orderings_Obot__class_Obot(u)),v_x)**.
% 299.79/300.45 20447[0:SpR:397.1,99.1] class_Orderings_Otop(u) || c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,w),c_Orderings_Otop__class_Otop(u)),v_x)**.
% 299.79/300.45 20440[0:SpR:2093.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_Procs,u),v,w),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_in(tc_Com_Opname),v_x))**.
% 299.79/300.45 20438[0:SpR:3744.1,99.1] || equal(c_in(tc_Com_Opname),c_in(u)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,u),v,w),v_Procs),v_Procs)**.
% 299.79/300.45 20424[0:SpR:99.1,474.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.45 20420[0:SpR:99.1,9569.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w)),hAPP(u,x)),tc_bool)*.
% 299.79/300.45 20419[0:SpR:99.1,9568.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w)),z),hAPP(u,x)),tc_bool)*.
% 299.79/300.45 20736[0:Res:313.1,202.1] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,w),u),tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,w),u),w) -> c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(v,w,w),u),w,w)*.
% 299.79/300.45 20725[0:SpR:8415.2,313.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(v_x,x,tc_fun(v,tc_bool)) -> c_lessequals(v_x,hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool))*.
% 299.79/300.45 20721[0:SpR:8415.2,313.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(x,v_x,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),v_x,tc_fun(w,tc_bool))*.
% 299.79/300.45 20774[0:SpR:128.0,129.1] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(x,y,v),u),tc_fun(y,tc_bool)),hAPP(c_Set_Ovimage(x,y,v),w),tc_fun(y,tc_bool))*.
% 299.79/300.45 20767[0:SpR:8415.2,129.1] || equal(v_Procs,v_x) equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(v_x,x,tc_fun(w,tc_bool)) -> c_lessequals(v_x,hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool))*.
% 299.79/300.45 20764[0:SpR:128.0,129.1] || c_lessequals(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(x,y,w),u),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(x,y,w),v),tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 20761[0:SpR:181.1,129.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),x),v))* c_lessequals(hAPP(c_Set_Ovimage(c_COMBK(x,w,y),y,w),u),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 20757[0:SpR:8415.2,129.1] || equal(v_Procs,v_x) equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(x,v_x,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),v_x,tc_fun(v,tc_bool))*.
% 299.79/300.45 20818[0:Res:19748.0,170.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),v_x,tc_Com_Opname)*.
% 299.79/300.45 20817[0:Res:19748.0,169.1] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname),tc_Com_Opname)*.
% 299.79/300.45 21027[0:SpL:317.0,62.0] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(y,w),z)),tc_fun(x,tc_bool)),x)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oimage(v,w,x),z),tc_fun(x,tc_bool)),x).
% 299.79/300.45 21017[0:SpL:317.0,390.0] || c_lessequals(u,hAPP(c_Set_Oinsert(hAPP(v,w),x),hAPP(c_Set_Oimage(v,y,x),z)),tc_fun(x,tc_bool))* -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oinsert(w,y),z),v,y,x),u,x,y)*.
% 299.79/300.45 20999[0:SpR:9987.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,v),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u),x)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,v),x)))*.
% 299.79/300.45 20997[0:SpR:2095.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w),y)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),y)))*.
% 299.79/300.45 20993[0:SpR:2935.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_in(t_a),v_x),u,v),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),u),w)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),v),hAPP(c_Set_Oimage(hAPP(c_in(t_a),v_x),u,v),w)))*.
% 299.79/300.45 20988[0:SpR:301.1,317.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),w),y)),hAPP(c_Set_Oinsert(v,x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),y)))*.
% 299.79/300.45 20955[0:SpR:414.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),z,x1),hAPP(c_Set_Oinsert(v,z),x2)),hAPP(c_Set_Oinsert(w,x1),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),z,x1),x2)))*.
% 299.79/300.45 20946[0:SpR:524.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(v,w),y)),hAPP(c_Set_Oinsert(v,x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),y)))*.
% 299.79/300.45 20942[0:SpR:8415.2,317.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(v_x,v),x)),hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(u,v,w),x)))*.
% 299.79/300.45 20938[0:SpR:365.1,317.0] class_Orderings_Obot(u) || -> equal(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),w),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,w),x)))*.
% 299.79/300.45 20937[0:SpR:397.1,317.0] class_Orderings_Otop(u) || -> equal(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,w),x)))*.
% 299.79/300.45 20929[0:SpR:2093.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),hAPP(c_Set_Oinsert(hAPP(c_in(tc_Com_Opname),v_x),v),x)),hAPP(c_Set_Oinsert(hAPP(c_in(tc_Com_Opname),v_x),w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),x)))*.
% 299.79/300.45 20927[0:SpR:3744.1,317.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),hAPP(c_Set_Oinsert(v_Procs,v),x)),hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),x)))*.
% 299.79/300.45 20917[0:SpR:8415.2,317.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),v_x)),hAPP(c_Set_Oinsert(hAPP(u,x),w),v_x))**.
% 299.79/300.45 20910[0:SpR:8415.2,317.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Set_Oinsert(u,v)) -> equal(hAPP(c_Set_Oinsert(hAPP(w,u),x),hAPP(c_Set_Oimage(w,v,x),v_x)),hAPP(c_Set_Oimage(w,v,x),v_x))**.
% 299.79/300.45 20909[0:SpR:353.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(y,v),z))),hAPP(c_Set_Oinsert(hAPP(u,y),w),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),z))))*.
% 299.79/300.45 20890[0:SpR:317.0,353.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oimage(u,y,w),z))),hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oimage(u,y,w),hAPP(c_Set_Oinsert(v,y),z))))*.
% 299.79/300.45 20878[0:SpR:317.0,63.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)),x) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(z,w),y)),tc_fun(x,tc_bool)),x)*.
% 299.79/300.45 20874[0:SpR:317.0,9569.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),c_Set_Oinsert(hAPP(u,x),w)),hAPP(c_Set_Oimage(u,v,w),y)),tc_bool)*.
% 299.79/300.45 20873[0:SpR:317.0,9568.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Set_Oinsert(hAPP(u,x),w)),x1),hAPP(c_Set_Oimage(u,v,w),y)),tc_bool)*.
% 299.79/300.45 20837[0:SpR:317.0,9569.0] || -> c_lessequals(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),y)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),c_Set_Oimage(u,x,w)),hAPP(c_Set_Oinsert(v,x),y)),tc_bool)*.
% 299.79/300.45 20836[0:SpR:317.0,9568.0] || -> c_lessequals(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),y)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Set_Oimage(u,x,w)),x1),hAPP(c_Set_Oinsert(v,x),y)),tc_bool)*.
% 299.79/300.45 21123[0:SpR:64.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),w),z)),hAPP(c_Set_Oinsert(u,v),y)))*.
% 299.79/300.45 21120[0:SpR:317.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(u,v),w),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,z,w),x1),x),x2)),hAPP(c_Set_Oimage(u,z,w),hAPP(c_Set_Oinsert(v,z),x1))))*.
% 299.79/300.45 21086[0:SpR:104.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w,x),hAPP(c_Set_Oinsert(y,w),z)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,y,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))*.
% 299.79/300.45 21046[0:SpR:99.1,20881.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(u,z),x),x1)),z))*.
% 299.79/300.45 21045[0:SpR:438.1,20881.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(u,z),x),x1)),z))*.
% 299.79/300.45 21043[0:SpR:317.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(z,v),x1),x),x2)),hAPP(c_Set_Oinsert(hAPP(u,z),w),hAPP(c_Set_Oimage(u,v,w),x1))))*.
% 299.79/300.45 21261[0:SpL:8415.2,469.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x)))* -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,v_x,w,u)),v_x)**.
% 299.79/300.45 21257[0:SpL:8415.2,469.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_x,u,x,v,w)),x)**.
% 299.79/300.45 21662[0:SpL:21267.0,332.0] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),u) -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_Com_Opname,w),u)*.
% 299.79/300.45 21640[0:SpL:21267.0,3863.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x),tc_Com_Opname,x)))*.
% 299.79/300.45 21593[0:SpL:21267.0,156.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(v,u,w),x))) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y))),x))*.
% 299.79/300.45 21418[0:SpR:21267.0,153.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(w),hAPP(c_in(w),v_x),tc_Com_Opname,x))),y))* -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Ovimage(v,w,u),y))).
% 299.79/300.45 21744[0:Rew:21267.0,21592.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(v,u),w)))* -> hBOOL(hAPP(hAPP(c_in(u),v_x),w)) equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,x),v)*.
% 299.79/300.45 21788[0:SpR:104.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))*.
% 299.79/300.45 21857[0:SpR:104.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))*.
% 299.79/300.45 21886[0:SpL:8415.2,464.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x)))* -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(x,v_x,v,w,u)),v_x)**.
% 299.79/300.45 21881[0:SpL:8415.2,464.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_x,x,u,v,w)),x)**.
% 299.79/300.45 22290[0:SpL:21893.0,332.0] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),u) -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),u)*.
% 299.79/300.45 22268[0:SpL:21893.0,3863.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x)))*.
% 299.79/300.45 22220[0:SpL:21893.0,156.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(v,u,w),x))) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y))),x))*.
% 299.79/300.45 22044[0:SpR:21893.0,153.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(w),v_x),c_in(w),tc_Com_Opname,x))),y))* -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Ovimage(v,w,u),y))).
% 299.79/300.45 22373[0:Rew:21893.0,22219.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(v,u),w)))* -> hBOOL(hAPP(hAPP(c_in(u),v_x),w)) equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,x),v)*.
% 299.79/300.45 22433[0:SpL:97.1,390.0] || c_Fun_Oinj__on(u,v,w,x) c_lessequals(y,v,tc_fun(w,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,w,x),v),c_Fun_Othe__inv__into(v,u,w,x),x,w),y,w,x)*.
% 299.79/300.45 22422[0:SpR:8415.2,97.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Fun_Oinj__on(u,v_x,v,w) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v_x,u,v,w),w,v),v_x),v_x)**.
% 299.79/300.45 22415[0:SpR:97.1,20881.0] || c_Fun_Oinj__on(u,v,w,x) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,w,x),v),y),x1)),v))*.
% 299.79/300.45 22399[0:SpR:97.1,9569.0] || c_Fun_Oinj__on(u,v,w,x) -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w)),hAPP(c_Set_Oimage(u,w,x),v)),tc_bool)*.
% 299.79/300.45 22398[0:SpR:97.1,9568.0] || c_Fun_Oinj__on(u,v,w,x) -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w)),z),hAPP(c_Set_Oimage(u,w,x),v)),tc_bool)*.
% 299.79/300.45 22489[0:SpR:104.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))),tc_Com_Opname,x),u),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))))*.
% 299.79/300.45 22667[0:SpL:158.0,390.0] || c_lessequals(u,hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1),tc_fun(y,tc_bool))* -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(w,z,x),x1),v,x,y),u,y,x)*.
% 299.79/300.45 22660[0:SpL:158.0,390.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,z,w),x1)),tc_fun(x,tc_bool))* -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(x1,c_Fun_Ocomp(v,y,w,x,z),z,x),u,x,z)*.
% 299.79/300.45 22655[0:SpL:158.0,3507.1] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(c_Fun_Ocomp(w,x,y,z,x1),x1,z))* equal(hAPP(c_Set_Oimage(w,y,z),hAPP(c_Set_Oimage(x,x1,y),v_x)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.79/300.45 22654[0:SpL:158.0,16327.1] || equal(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* equal(hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_Procs) -> .
% 299.79/300.45 22653[0:SpL:158.0,3499.1] || equal(c_in(u),c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* hBOOL(hAPP(hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.79/300.45 22649[0:SpL:158.0,13272.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.79/300.45 22648[0:SpL:158.0,3484.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Com_Ocom_OBODY)** equal(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),hAPP(c_Com_Ocom_OBODY,z))* -> equal(v_x,z).
% 299.79/300.45 22640[0:SpL:158.0,202.1] || c_Finite__Set_Ofinite(u,v) c_lessequals(u,hAPP(c_Set_Oimage(w,x,v),hAPP(c_Set_Oimage(y,v,x),u)),tc_fun(v,tc_bool))* -> c_Fun_Oinj__on(c_Fun_Ocomp(w,y,x,v,v),u,v,v)*.
% 299.79/300.45 22633[0:SpR:8415.2,158.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_x),hAPP(c_Set_Oimage(x,w,y),v_x))**.
% 299.79/300.45 22623[0:SpR:158.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(z,x1,v),x2),x),x3)),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,z,v,w,x1),x1,w),x2)))*.
% 299.79/300.45 22607[0:SpR:158.0,9569.0] || -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),x2),c_Set_Oimage(u,w,x)),hAPP(c_Set_Oimage(v,y,w),z)),tc_bool)*.
% 299.79/300.45 22606[0:SpR:158.0,9568.0] || -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Set_Oimage(u,w,x)),x2),hAPP(c_Set_Oimage(v,y,w),z)),tc_bool)*.
% 299.79/300.45 22581[0:SpR:158.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x2))))*.
% 299.79/300.45 22565[0:SpR:158.0,9569.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),x2),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w)),z),tc_bool)*.
% 299.79/300.45 22564[0:SpR:158.0,9568.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w)),x2),z),tc_bool)*.
% 299.79/300.45 22560[0:SpR:158.0,3346.1] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(c_Fun_Ocomp(w,x,y,z,x1),x1,z))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(w,y,z),hAPP(c_Set_Oimage(x,x1,y),v_x))))*.
% 299.79/300.45 22559[0:SpR:158.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y),tc_Com_Opname,x1),u),hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x))))*.
% 299.79/300.45 22558[0:SpR:158.0,3317.1] || equal(c_in(u),c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x)),hAPP(c_Set_Oinsert(v_x,u),x1)))*.
% 299.79/300.45 22557[0:SpR:158.0,3305.1] || equal(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x1),v_Procs),hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x))))*.
% 299.79/300.45 22553[0:SpR:158.0,2771.1] || equal(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x)),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.79/300.45 22549[0:SpR:158.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),hAPP(c_Set_Oinsert(x1,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))))*.
% 299.79/300.45 22548[0:SpR:158.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),t_a,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))))*.
% 299.79/300.45 22545[0:SpR:158.0,15262.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.79/300.45 22542[0:SpR:158.0,8376.2] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(tc_Com_Opname))** equal(z,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),z))*.
% 299.79/300.45 22541[0:SpR:158.0,8415.2] || equal(v_Procs,v_x) equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),v_x)**.
% 299.79/300.45 22540[0:SpR:158.0,3291.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))),v_Procs))*.
% 299.79/300.45 22539[0:SpR:158.0,3285.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),hAPP(c_Set_Oinsert(z,tc_Com_Opname),v_Procs)))*.
% 299.79/300.45 22536[0:SpR:158.0,3279.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),v_Procs),v_x))*.
% 299.79/300.45 22735[0:SpR:3294.1,545.1] || equal(c_in(t_a),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(hAPP(u,v_x),v,x),w)))*.
% 299.79/300.45 22734[0:SpR:3294.1,362.1] || equal(c_in(t_a),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),w)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.45 23033[0:SpL:131.0,3507.1] || equal(c_Set_Oinsert(u,v),c_Set_Ovimage(c_Fun_Ocomp(w,x,y,z,x1),x1,z))* equal(hAPP(c_Set_Ovimage(x,x1,y),hAPP(c_Set_Ovimage(w,y,z),v_x)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.79/300.45 23032[0:SpL:131.0,16327.1] || equal(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* equal(hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_Procs) -> .
% 299.79/300.45 23031[0:SpL:131.0,3499.1] || equal(c_in(u),c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* hBOOL(hAPP(hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.79/300.45 23027[0:SpL:131.0,13272.0] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.79/300.45 23026[0:SpL:131.0,3484.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Com_Ocom_OBODY)** equal(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),hAPP(c_Com_Ocom_OBODY,z))* -> equal(v_x,z).
% 299.79/300.45 23018[0:SpR:128.0,131.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_HOL_Ouminus__class_Ouminus(z,tc_fun(x,tc_bool))),hAPP(c_Set_Ovimage(v,y,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,w,x),z),tc_fun(w,tc_bool))))*.
% 299.79/300.45 23011[0:SpR:8415.2,131.0] || equal(v_Procs,v_x) equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x),hAPP(c_Set_Ovimage(x,y,v),v_x))**.
% 299.79/300.45 23004[0:SpR:131.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(z,w,x1),x2),x),x3)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(z,u,w,x1,v),v,x1),x2)))*.
% 299.79/300.45 22997[0:SpR:131.0,128.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(x,w,y),z),tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z),tc_fun(v,tc_bool)))*.
% 299.79/300.45 22993[0:SpR:131.0,181.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y))) equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(w,c_COMBK(v,u,z),u,x,z),z,x),y),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))**.
% 299.79/300.45 22987[0:SpR:131.0,9569.0] || -> c_lessequals(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),x2),c_Set_Ovimage(v,y,w)),hAPP(c_Set_Ovimage(u,w,x),z)),tc_bool)*.
% 299.79/300.45 22986[0:SpR:131.0,9568.0] || -> c_lessequals(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Set_Ovimage(v,y,w)),x2),hAPP(c_Set_Ovimage(u,w,x),z)),tc_bool)*.
% 299.79/300.45 22973[0:SpR:131.0,128.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),c_HOL_Ouminus__class_Ouminus(z,tc_fun(y,tc_bool)))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z),tc_fun(v,tc_bool)))*.
% 299.79/300.45 22967[0:SpR:131.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x2))))*.
% 299.79/300.45 22960[0:SpR:131.0,128.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_HOL_Ouminus__class_Ouminus(z,tc_fun(x,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),z)),tc_fun(y,tc_bool)))*.
% 299.79/300.45 22952[0:SpR:131.0,9569.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),z)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),x2),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y)),z),tc_bool)*.
% 299.79/300.45 22951[0:SpR:131.0,9568.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),z)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y)),x2),z),tc_bool)*.
% 299.79/300.45 22947[0:SpR:131.0,3346.1] || equal(c_Set_Oinsert(u,v),c_Set_Ovimage(c_Fun_Ocomp(w,x,y,z,x1),x1,z))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Ovimage(x,x1,y),hAPP(c_Set_Ovimage(w,y,z),v_x))))*.
% 299.79/300.45 22946[0:SpR:131.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y),tc_Com_Opname,x1),u),hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x))))*.
% 299.79/300.45 22945[0:SpR:131.0,3317.1] || equal(c_in(u),c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x)),hAPP(c_Set_Oinsert(v_x,u),x1)))*.
% 299.79/300.45 22944[0:SpR:131.0,3305.1] || equal(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x1),v_Procs),hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x))))*.
% 299.79/300.45 22940[0:SpR:131.0,2771.1] || equal(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x)),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.79/300.45 22935[0:SpR:131.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),hAPP(c_Set_Oinsert(x1,tc_Com_Opname),v_Procs)),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))))*.
% 299.79/300.45 22934[0:SpR:131.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),t_a,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))))*.
% 299.79/300.45 22931[0:SpR:131.0,15262.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.79/300.45 22928[0:SpR:131.0,8376.2] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(tc_Com_Opname))** equal(z,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),z))*.
% 299.79/300.45 22927[0:SpR:131.0,8415.2] || equal(v_Procs,v_x) equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),v_x)**.
% 299.79/300.45 22926[0:SpR:131.0,3291.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))),v_Procs))*.
% 299.79/300.45 22925[0:SpR:131.0,3285.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),hAPP(c_Set_Oinsert(z,tc_Com_Opname),v_Procs)))*.
% 299.79/300.45 22922[0:SpR:131.0,3279.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),v_Procs),v_x))*.
% 299.79/300.45 23135[0:SpL:23.0,95.0] || c_Fun_Oinj__on(c_Fun_Ocomp(u,c_Fun_Ocomp(v,w,x,y,z),y,x1,z),x2,z,x1)* -> c_Fun_Oinj__on(c_Fun_Ocomp(u,v,y,x1,x),hAPP(c_Set_Oimage(w,z,x),x2),x,x1)*.
% 299.79/300.45 23132[0:SpL:23.0,95.0] || c_Fun_Oinj__on(c_Fun_Ocomp(c_Fun_Ocomp(u,v,w,x,y),z,y,x,x1),x2,x1,x)* -> c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(c_Fun_Ocomp(v,z,y,w,x1),x1,w),x2),w,x)*.
% 299.79/300.45 23198[0:SpL:188.1,3487.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.45 23403[0:SpL:460.1,3698.2] || class_Lattices_Olattice(t_b) equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.45 23397[0:SpL:460.1,3493.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_in(tc_Com_Opname)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))* -> .
% 299.79/300.45 23384[0:SpR:460.1,7253.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))))*.
% 299.79/300.45 23369[0:SpR:460.1,3339.1] || class_Lattices_Olattice(t_b) equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)) -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),v,w),u)**.
% 299.79/300.45 23368[0:SpR:460.1,3316.1] || class_Lattices_Olattice(t_b) equal(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.79/300.45 23365[0:SpR:460.1,648.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,u),v_Procs)))*.
% 299.79/300.45 23358[0:SpR:460.1,21141.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),t_a,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))))*.
% 299.79/300.45 23356[0:SpR:460.1,11030.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.79/300.45 23355[0:SpR:460.1,10090.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.45 23350[0:SpR:460.1,3284.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))))*.
% 299.79/300.45 23345[2:SpR:460.1,15483.1] || class_Lattices_Olattice(t_b) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool))*.
% 299.79/300.45 23343[0:SpR:460.1,15482.1] || class_Lattices_Olattice(t_b) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_fun(t_a,tc_bool)),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool))*.
% 299.79/300.45 23340[0:SpR:460.1,651.0] || class_Lattices_Olattice(t_b) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.45 23581[0:SpL:523.1,3698.2] class_Lattices_Olattice(u) || equal(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x))* equal(c_Com_Ocom_OBODY,v) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.45 23575[0:SpL:523.1,3493.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_in(tc_Com_Opname)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> .
% 299.79/300.45 23515[0:SpR:523.1,7253.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))))*.
% 299.79/300.45 23500[0:SpR:523.1,3339.1] class_Lattices_Olattice(u) || equal(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x)) -> equal(c_Fun_Ofun__upd(v,v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)),y,z),v)**.
% 299.79/300.45 23499[0:SpR:523.1,3316.1] class_Lattices_Olattice(u) || equal(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.79/300.45 23496[0:SpR:523.1,648.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x),tc_Com_Opname,v),v_Procs)))*.
% 299.79/300.45 23489[0:SpR:523.1,21141.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),t_a,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))))*.
% 299.79/300.45 23487[0:SpR:523.1,11030.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.79/300.45 23486[0:SpR:523.1,10090.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.45 23481[0:SpR:523.1,3284.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))))*.
% 299.79/300.45 23476[2:SpR:523.1,15483.1] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool))*.
% 299.79/300.45 23474[0:SpR:523.1,15482.1] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_fun(t_a,tc_bool)),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool))*.
% 299.79/300.45 23471[0:SpR:523.1,651.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_Com_Opname,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.45 24454[0:Res:124.0,208.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),w),x,tc_fun(u,tc_bool))))* c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),w),x,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))*.
% 299.79/300.45 24766[0:SpR:614.2,415.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u),y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))**.
% 299.79/300.45 24966[0:SpR:23902.1,317.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),v),x)),hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),x)))*.
% 299.79/300.45 25433[0:SpL:512.0,3698.2] || equal(u,c_Set_Oimage(hAPP(c_COMBB(v,w,x,y),z),y,x))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(z,y,w),v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.45 25427[0:SpL:512.0,3493.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_in(tc_Com_Opname))** equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))* -> .
% 299.79/300.45 25372[0:SpR:512.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),x2))))*.
% 299.79/300.45 25352[0:SpR:512.0,3339.1] || equal(u,c_Set_Oimage(hAPP(c_COMBB(v,w,x,y),z),y,x))* -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(z,y,w),v_x)),x1,x2),u)**.
% 299.79/300.45 25351[0:SpR:512.0,3316.1] || equal(c_in(u),c_Set_Oimage(hAPP(c_COMBB(v,w,x,y),z),y,x))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(z,y,w),v_x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.79/300.45 25348[0:SpR:512.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,z,w),v_x))),hAPP(c_Set_Oimage(c_Set_Oimage(hAPP(c_COMBB(v,w,x,z),y),z,x),tc_Com_Opname,u),v_Procs)))*.
% 299.79/300.45 25340[0:SpR:512.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),t_a,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x))))*.
% 299.79/300.45 25338[0:SpR:512.0,11030.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))*.
% 299.79/300.45 25337[0:SpR:512.0,10090.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.45 25331[0:SpR:512.0,3284.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(z),v_Procs),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x))))*.
% 299.79/300.45 25326[2:SpR:512.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),tc_bool))*.
% 299.79/300.45 25324[0:SpR:512.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),tc_bool))*.
% 299.79/300.45 25321[0:SpR:512.0,651.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oimage(hAPP(c_COMBB(u,v,w,y),x),y,w),tc_Com_Opname,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.45 25309[0:SpR:512.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),z,x1),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_Procs))))*.
% 299.79/300.45 25706[0:Res:176.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),w),hAPP(c_Set_Oinsert(hAPP(v,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,y),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(y,x,t_a)*.
% 299.79/300.45 25964[0:SpL:339.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),v_Procs) -> .
% 299.79/300.45 25963[0:SpL:339.0,3929.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.79/300.45 25896[0:SpR:339.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x,tc_fun(y,tc_bool)),z),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z)),tc_bool)*.
% 299.79/300.45 25877[0:SpR:339.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),z,x1,x2),x))*.
% 299.79/300.45 25858[0:SpR:339.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),x)),tc_Com_Opname,u),u)*.
% 299.79/300.45 25857[0:SpR:339.0,23902.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.45 26246[0:SpL:338.0,215.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),w),hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(v)),y)),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.79/300.45 26245[0:SpL:338.0,363.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),y,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),y,tc_fun(u,tc_bool)).
% 299.79/300.45 26131[0:SpR:338.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(u,v),w,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),hAPP(c_Set_Oinsert(u,v),z)),tc_bool)*.
% 299.79/300.45 26114[0:SpR:338.0,364.1] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(y,v),x)),tc_fun(v,tc_bool))*.
% 299.79/300.45 26108[0:SpR:338.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),y),c_Set_Oinsert(w,u),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))*.
% 299.79/300.45 26061[0:SpR:338.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,u),z)),hAPP(c_Set_Oinsert(y,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z)),tc_bool)*.
% 299.79/300.45 26058[0:SpR:338.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z,u),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.45 26042[0:SpR:338.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),z,x1,x2),hAPP(c_Set_Oinsert(u,v),x)))*.
% 299.79/300.45 26358[0:SpL:104.0,85.0] || c_lessequals(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),tc_fun(x,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),w,tc_fun(x,tc_bool))*.
% 299.79/300.45 26503[0:SpR:104.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* -> c_lessequals(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)).
% 299.79/300.45 26971[0:MRR:26958.2,418.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool))))* c_lessequals(w,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> .
% 299.79/300.45 27082[0:Res:176.0,280.1] || hBOOL(hAPP(hAPP(u,v),w)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Ovimage(x,y,z),hAPP(c_Set_Oinsert(hAPP(x,v),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))),u,y,tc_fun(x1,tc_bool)),w))*.
% 299.79/300.45 27140[0:SpR:302.1,450.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w,x)))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),w),v),t_a)*.
% 299.79/300.45 27391[0:Res:168.0,470.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x),t_a) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x)),v,w,tc_Hoare__Mirabelle_Otriple(t_a))),x))*.
% 299.79/300.45 27395[1:MRR:21911.0,27381.0] || -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v_P,v_x),v_P,tc_Com_Opname,u))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v_P,v_x),v_P,tc_Com_Opname,u))),t_a)*.
% 299.79/300.45 27396[1:MRR:21909.0,27381.0] || -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Ocom_OBODY,v_x),c_Com_Ocom_OBODY,tc_Com_Opname,u))),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Ocom_OBODY,v_x),c_Com_Ocom_OBODY,tc_Com_Opname,u))),t_a)*.
% 299.79/300.45 27397[1:MRR:21908.0,27381.0] || -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v_Q,v_x),v_Q,tc_Com_Opname,u))),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v_Q,v_x),v_Q,tc_Com_Opname,u))),hAPP(v_Q,v_x)),t_a)*.
% 299.79/300.45 27451[0:Res:168.0,466.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x),t_a) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x)),w,tc_Hoare__Mirabelle_Otriple(t_a))),x))*.
% 299.79/300.45 27455[1:MRR:21285.0,27441.0] || -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_P,hAPP(v_P,v_x),tc_Com_Opname,u))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_P,hAPP(v_P,v_x),tc_Com_Opname,u))),t_a)*.
% 299.79/300.45 27456[1:MRR:21283.0,27441.0] || -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,v_x),tc_Com_Opname,u))),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,v_x),tc_Com_Opname,u))),t_a)*.
% 299.79/300.45 27457[1:MRR:21282.0,27441.0] || -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_Q,hAPP(v_Q,v_x),tc_Com_Opname,u))),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v_Q,hAPP(v_Q,v_x),tc_Com_Opname,u))),hAPP(v_Q,v_x)),t_a)*.
% 299.79/300.45 27625[0:SpR:23840.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u,x),w),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.45 27609[0:SpR:23682.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,x),v),v)**.
% 299.79/300.45 27539[0:SpR:8385.1,373.2] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oinsert(v_x,tc_Com_Opname),v,x),u),u)**.
% 299.79/300.45 27530[0:SpR:373.2,9567.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Hilbert__Choice_Oinv__into(w,x,u,y),z,tc_fun(x1,tc_bool)),hAPP(x,v)),v,tc_bool)*.
% 299.79/300.45 27519[0:SpR:373.2,5875.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(v,z),c_Hilbert__Choice_Oinv__into(w,x,u,y),x1,x2,x3),hAPP(x,v)))*.
% 299.79/300.45 27778[0:SpR:23840.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u,x),w),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.45 27762[0:SpR:23682.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,x),v),v)**.
% 299.79/300.45 27691[0:SpR:8385.1,71.2] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oinsert(v_x,tc_Com_Opname),v,x),u),u)**.
% 299.79/300.45 27682[0:SpR:71.2,9567.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Fun_Othe__inv__into(w,x,u,y),z,tc_fun(x1,tc_bool)),hAPP(x,v)),v,tc_bool)*.
% 299.79/300.45 27670[0:SpR:71.2,5875.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(v,z),c_Fun_Othe__inv__into(w,x,u,y),x1,x2,x3),hAPP(x,v)))*.
% 299.79/300.45 27849[7:SpR:523.1,27219.1] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_fun(t_a,tc_bool)),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool))*.
% 299.79/300.45 27848[7:SpR:460.1,27219.1] || class_Lattices_Olattice(t_b) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_fun(t_a,tc_bool)),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool))*.
% 299.79/300.45 27949[0:Res:468.0,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,w,x,y,z)))* -> equal(hAPP(c_Set_Oimage(w,y,z),v),hAPP(c_Set_Oimage(x,y,z),v)) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,x1,u,y)))*.
% 299.79/300.45 27948[0:Res:468.0,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,w,x,y,z)))* -> equal(hAPP(c_Set_Oimage(w,y,z),v),hAPP(c_Set_Oimage(x,y,z),v)) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,v,u,y)))*.
% 299.79/300.45 27947[0:Res:468.0,454.0] || -> equal(hAPP(c_Set_Oimage(u,tc_Hoare__Mirabelle_Otriple(t_a),v),w),hAPP(c_Set_Oimage(x,tc_Hoare__Mirabelle_Otriple(t_a),v),w)) c_Hoare__Mirabelle_Ohoare__valids(w,y,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(w,y),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,u,x,tc_Hoare__Mirabelle_Otriple(t_a),v),t_a)*.
% 299.79/300.45 27927[0:Res:468.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) -> equal(hAPP(c_Set_Oimage(w,u,x),v),hAPP(c_Set_Oimage(y,u,x),v)) c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,w,y,u,x),u)*.
% 299.79/300.45 27926[0:Res:468.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) -> equal(hAPP(c_Set_Oimage(w,u,x),v),hAPP(c_Set_Oimage(y,u,x),v)) c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,w,y,u,x),c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.79/300.45 27996[0:SpR:523.1,27381.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.45 27995[0:SpR:460.1,27381.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,u)),v_Procs))*.
% 299.79/300.45 28226[0:SpL:465.1,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(v),x),v_x)).
% 299.79/300.45 28225[0:SpL:465.1,3929.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),v_x)) equal(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),z)* -> hBOOL(hAPP(hAPP(c_in(v),x),v_x)) hBOOL(hAPP(z,v_x))*.
% 299.79/300.45 28191[0:SpR:465.1,9567.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1,tc_fun(x2,tc_bool)),w),hAPP(c_Set_Oimage(x,u,z),w),tc_bool)*.
% 299.79/300.45 28173[0:SpR:465.1,5875.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oimage(x,u,y),w),z),c_Set_Oimage(c_Fun_Ofun__upd(x,v,x1,u,y),u,y),x2,x3,x4),w))*.
% 299.79/300.45 28162[0:SpR:465.1,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),v_x)) c_lessequals(hAPP(c_Set_Oimage(x,v,y),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(x,w,z,v,y),v,y),tc_Com_Opname,u),u)*.
% 299.79/300.45 28161[0:SpR:465.1,23902.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) equal(hAPP(hAPP(c_Set_Oimage(u,x,y),v_x),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.45 28129[0:SpR:465.1,21143.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))) hBOOL(hAPP(hAPP(c_Set_Oimage(v,t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Fun_Ofun__upd(v,u,x,t_a,w),v_x)))*.
% 299.79/300.45 28127[0:SpR:465.1,21131.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))) hBOOL(hAPP(hAPP(c_Set_Oimage(w,tc_Com_Opname,x),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),hAPP(c_Fun_Ofun__upd(w,u,y,tc_Com_Opname,x),v_x)))*.
% 299.79/300.45 28126[0:SpR:465.1,20881.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x))) hBOOL(hAPP(hAPP(c_Set_Oimage(y,u,z),hAPP(c_Set_Oinsert(w,u),x)),hAPP(c_Fun_Ofun__upd(y,v,x1,u,z),w)))*.
% 299.79/300.45 28299[0:SpR:523.1,27441.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.45 28298[0:SpR:460.1,27441.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_Com_Opname,u)),v_Procs))*.
% 299.79/300.45 28544[0:SpR:9925.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Fun_Ofun__upd(v,w,c_Orderings_Otop__class_Otop(tc_bool),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,y,z,x),w,c_Orderings_Otop__class_Otop(tc_bool),x,z))*.
% 299.79/300.45 28520[0:SpR:23682.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Fun_Ofun__upd(u,v,w,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,y,z,x),v,w,x,z))*.
% 299.79/300.45 28447[0:SpR:8385.1,118.0] || equal(u,v_Procs) -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_x,tc_Com_Opname),c_Fun_Ofun__upd(v,w,u,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_x,tc_Com_Opname),v,y,z,x),w,u,x,z))*.
% 299.79/300.45 28758[0:SpR:523.1,28031.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.45 28757[0:SpR:460.1,28031.0] || class_Lattices_Olattice(t_b) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,u),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.45 28913[0:SpR:523.1,28334.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.45 28912[0:SpR:460.1,28334.0] || class_Lattices_Olattice(t_b) -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_Com_Opname,u),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.45 29166[0:SpL:537.1,3506.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))* -> .
% 299.79/300.45 29150[0:SpR:3294.1,537.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(tc_bool)),v))**.
% 299.79/300.45 29145[0:SpR:584.0,537.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z)),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,z)),x1)))*.
% 299.79/300.45 29103[0:SpR:8415.2,537.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v_x,v)),w),hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))**.
% 299.79/300.45 29031[0:SpR:537.1,9566.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))),x),tc_bool)*.
% 299.79/300.45 28990[0:SpR:537.1,24020.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),v_x),v_x)**.
% 299.79/300.45 29261[0:SSi:29185.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),x)** -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)).
% 299.79/300.45 29262[0:SSi:29137.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x))**.
% 299.79/300.45 29263[0:SSi:29136.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x))**.
% 299.79/300.45 29266[0:SSi:29080.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),x)**.
% 299.79/300.45 29691[0:SpL:534.1,3506.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))* -> .
% 299.79/300.45 29675[0:SpR:3294.1,534.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(tc_bool)),v))**.
% 299.79/300.45 29670[0:SpR:584.0,534.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z)),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,z)),x1)))*.
% 299.79/300.45 29627[0:SpR:8415.2,534.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v_x,v)),w),hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))**.
% 299.79/300.45 29553[0:SpR:534.1,9566.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))),x),tc_bool)*.
% 299.79/300.45 29512[0:SpR:534.1,24020.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),v_x),v_x)**.
% 299.79/300.45 29770[0:Obv:29550.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))**.
% 299.79/300.45 30270[0:SpR:8415.2,536.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(v_x,w)),hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))**.
% 299.79/300.45 30260[0:SpR:3294.1,536.1] class_Lattices_Olattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(tc_bool)))**.
% 299.79/300.45 30255[0:SpR:584.0,536.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(x,v))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v)))*.
% 299.79/300.45 30096[0:SpR:536.1,474.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z,v),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.45 30077[0:SpR:536.1,9566.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)),tc_bool)*.
% 299.79/300.45 30420[0:Obv:30234.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))**.
% 299.79/300.45 30432[0:SSi:30247.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v))**.
% 299.79/300.45 30433[0:SSi:30246.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v))**.
% 299.79/300.45 30434[0:SSi:30130.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w)),x)**.
% 299.79/300.45 30474[0:SSi:30473.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)))*.
% 299.79/300.45 30834[0:SpR:8415.2,535.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(v_x,w)),hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))**.
% 299.79/300.45 30824[0:SpR:3294.1,535.1] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Obot__class_Obot(tc_bool)))**.
% 299.79/300.45 30819[0:SpR:584.0,535.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(x,v))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v)))*.
% 299.79/300.45 30652[0:SpR:535.1,474.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z,v),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.45 30633[0:SpR:535.1,9566.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)),tc_bool)*.
% 299.79/300.45 30981[0:Obv:30864.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x))** -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),u).
% 299.79/300.45 30983[0:Obv:30795.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))**.
% 299.79/300.45 30987[0:Obv:30645.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))**.
% 299.79/300.45 31305[0:Res:468.0,356.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(y,v,w),x))* equal(hAPP(c_Set_Oimage(c_COMBK(z,x1,v),v,x1),x),hAPP(c_Set_Oinsert(z,x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))**.
% 299.79/300.45 31275[0:Res:545.1,356.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(c_Set_Oimage(c_COMBK(x,y,z),z,y),hAPP(c_Set_Oimage(x1,u,z),w)),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.45 31245[0:SpL:584.0,356.0] || hBOOL(hAPP(c_COMBS(c_in(u),v,w,x,y),z))* -> equal(hAPP(c_Set_Oimage(c_COMBK(x1,x2,u),u,x2),hAPP(v,z)),hAPP(c_Set_Oinsert(x1,x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))))**.
% 299.79/300.45 31399[0:SpL:11176.1,449.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,x)))* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),t_a)*.
% 299.79/300.45 31506[0:SpL:131.0,24254.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.79/300.45 31505[0:SpL:158.0,24254.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.79/300.45 31487[0:SpL:104.0,24254.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.79/300.45 31830[7:SpL:339.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),v_x) -> .
% 299.79/300.45 31818[7:SpL:465.1,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),v_x),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),v_x)** -> hBOOL(hAPP(hAPP(c_in(v),x),v_x)).
% 299.79/300.45 31992[0:SpR:395.0,383.1] || -> equal(u,v) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(c_Fun_Ofun__upd(w,v,x,y,z),u,x1,y,z),v,x2,y,z),c_Fun_Ofun__upd(c_Fun_Ofun__upd(w,v,x2,y,z),u,x1,y,z))**.
% 299.79/300.45 32048[0:SpR:3229.1,151.2] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> hBOOL(hAPP(hAPP(c_in(v),v_x),x)) hBOOL(hAPP(hAPP(u,v_x),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool))))*.
% 299.79/300.45 32092[0:SpR:3229.1,340.2] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* c_lessequals(w,x,tc_fun(v,tc_bool))* c_lessequals(v_x,x,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(u,v_x),x,tc_fun(v,tc_bool))*.
% 299.79/300.45 32087[0:SpR:3229.1,340.2] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) c_lessequals(v_x,w,tc_fun(v,tc_bool)) c_lessequals(x,w,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(hAPP(u,v_x),x),w,tc_fun(v,tc_bool))*.
% 299.79/300.45 32312[0:SpL:338.0,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),z),x))* -> hBOOL(hAPP(u,z))*.
% 299.79/300.45 32285[0:SpL:3229.1,477.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(u,v_x),x,v)))* hBOOL(hAPP(hAPP(c_in(v),y),w))* -> hBOOL(hAPP(x,y))*.
% 299.79/300.45 32280[0:SpL:3229.1,477.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(u,v_x),x),w,v)))* hBOOL(hAPP(hAPP(c_in(v),y),v_x))* -> hBOOL(hAPP(w,y))*.
% 299.79/300.45 32406[0:Rew:331.0,32341.2] || hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),u))* hBOOL(hAPP(hAPP(c_in(u),y),v))* -> hBOOL(y).
% 299.79/300.45 32496[0:SpL:339.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),z),y))* -> hBOOL(hAPP(u,z))*.
% 299.79/300.45 32465[0:SpL:3229.1,476.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(u,v_x),x,v)))* hBOOL(hAPP(hAPP(c_in(v),y),v_x))* -> hBOOL(hAPP(x,y))*.
% 299.79/300.45 32460[0:SpL:3229.1,476.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(u,v_x),x),w,v)))* hBOOL(hAPP(hAPP(c_in(v),y),x))* -> hBOOL(hAPP(w,y))*.
% 299.79/300.45 32584[0:Rew:331.0,32521.2] || hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),u))* hBOOL(hAPP(hAPP(c_in(u),y),w))* -> hBOOL(y).
% 299.79/300.45 32658[0:SpR:131.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)))),v_Procs))*.
% 299.79/300.45 32657[0:SpR:158.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))),v_Procs))*.
% 299.79/300.45 32639[0:SpR:104.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),tc_Com_Opname,w),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))),v_Procs))*.
% 299.79/300.45 32716[0:SpR:537.1,32669.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))))*.
% 299.79/300.45 32715[0:SpR:534.1,32669.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))))*.
% 299.79/300.45 32825[0:SSi:32824.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,v,tc_fun(t_a,tc_bool)) c_lessequals(v,w,tc_fun(t_a,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(u,v_x),tc_bool),tc_bool),hAPP(u,v_x))**.
% 299.79/300.45 32987[0:SpR:23912.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(v,x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,x),w))**.
% 299.79/300.45 32958[0:SpR:351.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oimage(c_COMBK(x,z,x1),u,y),w)),hAPP(c_Set_Oimage(c_COMBK(x,z,x1),u,y),w))**.
% 299.79/300.45 32934[0:SpR:3229.1,475.1] || equal(u,v) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> equal(hAPP(c_Set_Oinsert(hAPP(u,v_x),y),hAPP(c_Set_Oimage(v,w,y),x)),hAPP(c_Set_Oimage(v,w,y),x))**.
% 299.79/300.45 33078[0:SpL:3229.1,94.1] || equal(u,c_Set_Oimage(v,w,x))* c_Fun_Oinj__on(v,v_x,w,x) c_Fun_Oinj__on(y,hAPP(u,v_x),x,z)* -> c_Fun_Oinj__on(c_Fun_Ocomp(y,v,x,z,w),v_x,w,z)*.
% 299.79/300.45 33088[0:MRR:33074.1,96.1] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(y,v,w,z) -> c_Fun_Oinj__on(c_Fun_Ocomp(y,c_Fun_Othe__inv__into(v,u,w,x),w,z,x),hAPP(c_Set_Oimage(u,w,x),v),x,z)*.
% 299.79/300.45 33314[0:SpR:131.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.45 33313[0:SpR:158.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.45 33295[0:SpR:104.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),tc_Com_Opname,w),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.45 33600[0:SpR:131.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(v,w,x),hAPP(c_Set_Ovimage(y,x,z),v_x)),c_Set_Ovimage(c_Fun_Ocomp(y,v,x,z,w),w,z),tc_Com_Opname,x1)))*.
% 299.79/300.45 33599[0:SpR:158.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,z,w),v_x)),c_Set_Oimage(c_Fun_Ocomp(v,y,w,x,z),z,x),tc_Com_Opname,x1)))*.
% 299.79/300.45 33581[0:SpR:104.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),tc_Com_Opname,x)))*.
% 299.79/300.45 33691[0:SpR:131.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y),hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x)),tc_Com_Opname,x1)))*.
% 299.79/300.45 33690[0:SpR:158.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y),hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x)),tc_Com_Opname,x1)))*.
% 299.79/300.45 33672[0:SpR:104.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_Com_Opname,x)))*.
% 299.79/300.45 33782[7:SpL:131.0,31886.1] || equal(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* equal(hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_x) -> .
% 299.79/300.45 33781[7:SpL:158.0,31886.1] || equal(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* equal(hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_x) -> .
% 299.79/300.45 33763[7:SpL:104.0,31886.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))))* equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_x) -> .
% 299.79/300.45 34415[0:SpL:24914.0,515.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v_x),y),z))* -> equal(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Hoare__Mirabelle_Otriple_Otriple(u),tc_Com_Opname,x1),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v_x)))*.
% 299.79/300.45 34345[0:SpL:24914.0,296.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),w,u) -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),w,u)*.
% 299.79/300.45 34343[0:SpL:24914.0,312.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),c_Orderings_Obot__class_Obot(u)) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.45 34310[0:SpL:24914.0,278.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(v),tc_Com_Opname,w),hAPP(c_in(v),v_x))))* hBOOL(hAPP(hAPP(c_in(v),v_x),x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,y,u,v)))*.
% 299.79/300.45 34309[0:SpL:24914.0,277.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(v),tc_Com_Opname,w),hAPP(c_in(v),v_x))))* hBOOL(hAPP(hAPP(c_in(v),v_x),x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,x,u,v)))*.
% 299.79/300.45 34291[0:SpL:24914.0,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,w),hAPP(c_in(u),v_x)),u)*.
% 299.79/300.45 34290[0:SpL:24914.0,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Finite__Set_Ofinite(v,u) -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,w),hAPP(c_in(u),v_x)),c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.79/300.45 34265[0:SpL:24914.0,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),u)) -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(u,v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,w),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x)),t_a)*.
% 299.79/300.45 34118[0:SpR:24914.0,294.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),u)* -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x),u).
% 299.79/300.45 34101[0:SpR:24914.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,x),hAPP(u,v_x)),v),y)),hAPP(c_Set_Oinsert(hAPP(u,v_x),w),hAPP(c_Set_Oimage(u,v,w),y)))*.
% 299.79/300.45 34095[0:SpR:24914.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x),hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x))),tc_bool)*.
% 299.79/300.45 34086[0:SpR:24914.0,353.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,x),hAPP(c_Set_Oinsert(u,v),v_x)))),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(u,v),v_x)))**.
% 299.79/300.45 34050[0:SpR:24914.0,254.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(w,u),tc_Com_Opname,x),hAPP(c_Set_Oinsert(w,u),v_x))))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),v_x))).
% 299.79/300.45 34027[0:SpR:24914.0,8369.1] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),tc_Com_Opname,w),hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),v_x))),v))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),v_x)).
% 299.79/300.45 33971[0:SpR:24914.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,x),hAPP(c_in(u),v_x))),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.45 33907[0:SpR:24914.0,341.0] || -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_fun(u,tc_bool))*.
% 299.79/300.45 34575[0:SpR:55.1,7539.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(y,u),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool))),tc_fun(u,tc_bool))*.
% 299.79/300.45 34909[0:SpR:131.0,28053.1] || equal(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x)),u,tc_Com_Opname,x1)))*.
% 299.79/300.45 34908[0:SpR:158.0,28053.1] || equal(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x)),u,tc_Com_Opname,x1)))*.
% 299.79/300.45 34890[0:SpR:104.0,28053.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),u,tc_Com_Opname,x)))*.
% 299.79/300.45 34988[0:SpR:131.0,28356.1] || equal(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x)),tc_Com_Opname,x1)))*.
% 299.79/300.45 34987[0:SpR:158.0,28356.1] || equal(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x)),tc_Com_Opname,x1)))*.
% 299.79/300.45 34969[0:SpR:104.0,28356.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_Com_Opname,x)))*.
% 299.79/300.45 35432[0:SpL:410.0,519.0] || hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),z))* -> hBOOL(hAPP(hAPP(x,u),z)) hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool)),z)).
% 299.79/300.45 35263[0:SpR:3586.1,410.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(x,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,x,u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,x,u,tc_fun(w,tc_bool)))**.
% 299.79/300.45 35262[7:SpR:27278.1,410.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(x,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,x,u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,x,u,tc_fun(w,tc_bool)))**.
% 299.79/300.45 35253[0:SpR:8498.1,410.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(x,y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,x,v,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,x,v,tc_fun(w,tc_bool)))**.
% 299.79/300.45 35236[0:SpR:410.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,y,tc_fun(u,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(z,y),w),x,y,tc_fun(u,tc_bool))))*.
% 299.79/300.45 35534[0:SpL:113.0,103.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),x),v) c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(y,x,tc_fun(w,tc_bool))),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),y),v).
% 299.79/300.45 35533[0:SpL:113.0,147.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y))) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),c_HOL_Ominus__class_Ominus(z,y,tc_fun(x,tc_bool)))))* -> .
% 299.79/300.45 35545[0:Rew:6.0,35500.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool))),hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y))**.
% 299.79/300.45 36196[0:Res:8376.2,516.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(u),v_x),v)) hBOOL(hAPP(hAPP(c_in(u),v_x),w)).
% 299.79/300.45 36199[0:Rew:8415.2,36173.4,8415.2,36173.3] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))* -> hBOOL(hAPP(v_x,v)) hBOOL(hAPP(v_x,w)).
% 299.79/300.45 36859[0:SpR:66.0,67.0] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),y,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),y),tc_fun(w,tc_bool)))**.
% 299.79/300.45 36981[0:Res:19747.0,375.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,v),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool)),tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.45 36978[0:Res:1145.0,375.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),z,x1),tc_Com_Opname,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 37149[0:Res:19747.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,v)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oimage(y,u,x),w),tc_fun(x,tc_bool)),tc_fun(x,tc_bool))))*.
% 299.79/300.45 37144[0:Res:1145.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_Set_Oimage(y,u,x),w),z,x1),tc_Com_Opname,tc_fun(x,tc_bool))))*.
% 299.79/300.45 37465[0:SpR:205.1,7253.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),z))*.
% 299.79/300.45 37441[0:SpR:205.1,21126.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,tc_Com_Opname) equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),v_Procs) -> hBOOL(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_Com_Opname),v_x)))*.
% 299.79/300.45 37918[0:Res:37799.1,477.0] || hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u))* hBOOL(hAPP(hAPP(c_in(u),y),v))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),y))*.
% 299.79/300.45 37917[0:Res:37799.1,476.0] || hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u))* hBOOL(hAPP(hAPP(c_in(u),y),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),y))*.
% 299.79/300.45 38228[0:Res:13.2,437.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,y,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool)),w)*.
% 299.79/300.45 38200[0:SpR:80.0,13.2] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.45 38262[0:SpR:87.1,201.3] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u),w,u,u),u)*.
% 299.79/300.45 38261[0:SpR:88.1,201.3] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v,u)),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,u,u),u)*.
% 299.79/300.45 38418[0:Res:16753.1,493.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** equal(hAPP(c_Set_Oimage(x,u,u),v),hAPP(c_Set_Oimage(x,u,u),w))* -> equal(v,w).
% 299.79/300.45 38653[0:SpL:584.0,184.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(v,w,u),x,y,z),x1))* c_Fun_Oinj__on(v,x1,w,u) -> equal(hAPP(v,hAPP(c_Fun_Othe__inv__into(x1,v,w,u),x1)),x1)**.
% 299.79/300.45 38940[0:SpR:354.2,16776.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,w,y),u),c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),u,w,y)*.
% 299.79/300.45 39016[0:MRR:38956.2,20734.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,w,y),u),c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),u,w,y)*.
% 299.79/300.45 39219[0:SpR:533.0,538.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v)))*.
% 299.79/300.45 39857[0:Rew:533.0,39643.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w)))*.
% 299.79/300.45 39613[0:SpR:532.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z))))*.
% 299.79/300.45 39935[0:Rew:39934.1,20341.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),y),y)**.
% 299.79/300.45 40458[0:Res:1013.1,529.0] || hBOOL(hAPP(v_G,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v))),w)))* -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_na),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),hAPP(c_Com_Ocom_OBODY,v)),w),t_a).
% 299.79/300.45 40791[4:Res:247.4,40171.0] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(v,tc_bool),tc_bool)* -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) hBOOL(c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.79/300.45 40790[4:Res:248.4,40171.0] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMin(u,tc_bool),tc_bool)* -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) hBOOL(c_Finite__Set_Olinorder__class_OMin(v,tc_bool)).
% 299.79/300.45 40944[0:Res:31533.0,479.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))*.
% 299.79/300.45 40943[0:Res:27443.0,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,z,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),z)))*.
% 299.79/300.45 40942[0:Res:28312.0,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w)))*.
% 299.79/300.45 40940[0:Res:27383.0,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,z,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),z)))*.
% 299.79/300.45 40939[0:Res:28009.0,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w)))*.
% 299.79/300.45 40926[0:Res:23946.1,479.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,w,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w)))*.
% 299.79/300.45 40918[0:Res:15261.0,479.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v,u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v)))*.
% 299.79/300.45 40949[0:Rew:339.0,40891.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,w),x),y,u,w)),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y))))*.
% 299.79/300.45 40950[0:Rew:339.0,40882.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),w,u,tc_Com_Opname)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w))))*.
% 299.79/300.45 41225[0:Res:31533.0,478.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs)))*.
% 299.79/300.45 41224[0:Res:27443.0,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),z),v_Procs)))*.
% 299.79/300.45 41223[0:Res:28312.0,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.79/300.45 41221[0:Res:27383.0,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),z),v_Procs)))*.
% 299.79/300.45 41220[0:Res:28009.0,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.79/300.45 41207[0:Res:23946.1,478.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_x,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)))*.
% 299.79/300.45 41199[0:Res:15261.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))))*.
% 299.79/300.45 41172[0:Res:267.0,478.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(v,w),y),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(v,w),y))))*.
% 299.79/300.45 41163[0:Res:658.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))))*.
% 299.79/300.45 41406[0:Res:254.1,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),w),y))* -> hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(z,u),x,tc_fun(u,tc_bool))))*.
% 299.79/300.45 41253[0:SpL:659.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.45 41487[4:SpR:339.0,38236.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_Com_Opname,tc_bool))*.
% 299.79/300.45 41475[4:SpR:465.1,38236.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oimage(u,x,y),v_x),tc_Com_Opname,tc_bool))*.
% 299.79/300.45 41743[0:Res:1013.1,494.1] || hBOOL(hAPP(v_G,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v),w)))* hBOOL(hAPP(hAPP(u,x),y))* c_Natural_Oevaln(v,y,v_na,z)* -> hBOOL(hAPP(hAPP(w,x),z))*.
% 299.79/300.45 42209[0:Obv:42075.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u)),x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u))**.
% 299.79/300.45 42210[0:Obv:42058.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u),x,u) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u),x)**.
% 299.79/300.45 42215[0:SSi:42166.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) c_Finite__Set_Ofinite(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(x,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v)* -> c_Finite__Set_Ofinite(x,v).
% 299.79/300.45 42216[0:SSi:42157.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v,hAPP(c_Set_Oinsert(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),u),tc_fun(tc_Com_Opname,tc_bool),tc_fun(tc_Com_Opname,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))** -> .
% 299.79/300.45 42218[0:SSi:42061.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(hAPP(c_in(tc_Com_Opname),v_x),tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v_Procs))*.
% 299.79/300.45 42219[0:SSi:42047.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v,hAPP(c_Set_Oinsert(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),u),tc_fun(tc_Com_Opname,tc_bool),tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.79/300.45 42378[4:SSi:42347.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v_x))*.
% 299.79/300.45 42478[0:SpL:10463.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x,y)),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(c_Set_Oimage(u,x,y),v),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x,y),v)).
% 299.79/300.45 42477[0:SpL:9911.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,y)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Set_Oimage(u,x,y),v),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,y),v)).
% 299.79/300.45 42437[0:SpL:10463.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),u,x,y)),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x,y),v),hAPP(c_Set_Oimage(u,x,y),v)).
% 299.79/300.45 42436[0:SpL:9911.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,x,y)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,y),v),hAPP(c_Set_Oimage(u,x,y),v)).
% 299.79/300.45 42619[4:SSi:42573.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),x))*.
% 299.79/300.45 43187[4:SSi:43167.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),x,t_a)*.
% 299.79/300.45 44329[0:Res:11029.0,268.0] || hBOOL(hAPP(hAPP(c_in(t_a),u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* equal(hAPP(w,v_x),hAPP(w,u))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),t_a,x)* -> equal(v_x,u).
% 299.79/300.45 44328[0:Res:9258.0,268.0] || hBOOL(hAPP(hAPP(c_in(t_a),u),v))* equal(hAPP(w,v_x),hAPP(w,u))* c_Fun_Oinj__on(w,v,t_a,x)* -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool)) equal(v_x,u).
% 299.79/300.45 44321[0:Res:3283.1,268.0] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(c_in(u),v),v_Procs))* equal(hAPP(w,v_x),hAPP(w,v))* c_Fun_Oinj__on(w,v_Procs,u,x)* -> equal(v_x,v).
% 299.79/300.45 44299[0:Res:678.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_in(tc_Com_Opname),v_x)))* equal(hAPP(w,v_Procs),hAPP(w,v))* c_Fun_Oinj__on(w,hAPP(c_in(tc_Com_Opname),v_x),u,x)* -> equal(v_Procs,v).
% 299.79/300.45 44783[0:Res:526.1,593.0] || hBOOL(hAPP(v_Procs,u)) c_Hoare__Mirabelle_Otriple__valid(v,v_n(v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,u)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u))),hAPP(v_Q,u)),t_a)*.
% 299.79/300.45 44866[0:SSi:44823.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v_x))*.
% 299.79/300.45 45345[0:Res:526.1,487.1] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x))* hBOOL(hAPP(y,x))* -> hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,y,u)))* hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,y,u)))*.
% 299.79/300.45 45452[0:Res:45357.1,280.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(w,v),x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),w,u,tc_fun(y,tc_bool)),x))*.
% 299.79/300.45 45500[0:Res:526.1,237.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),x))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(u,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(x,u,w,v)),x)**.
% 299.79/300.45 45889[0:Res:3346.1,482.2] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,v)))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,x,v)))* -> hBOOL(hAPP(x,u))*.
% 299.79/300.45 45883[0:Res:8366.1,482.2] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_Procs)** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,tc_Com_Opname)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,tc_Com_Opname)))* -> hBOOL(hAPP(w,v_x)).
% 299.79/300.45 46643[4:SpL:523.1,46565.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)))* -> .
% 299.79/300.45 46642[4:SpL:460.1,46565.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))* -> .
% 299.79/300.45 46955[0:MRR:46924.0,264.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))*.
% 299.79/300.45 47266[0:MRR:47181.0,264.0] || c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),tc_fun(v,tc_bool)).
% 299.79/300.45 48164[4:SpR:131.0,39023.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))),x2))*.
% 299.79/300.45 48163[4:SpR:158.0,39023.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))),x2))*.
% 299.79/300.45 48144[4:SpR:104.0,39023.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))),y))*.
% 299.79/300.45 48279[4:SpR:131.0,39064.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(z,x1),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))),x2,t_a)*.
% 299.79/300.45 48278[4:SpR:158.0,39064.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(z,x1),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))),x2,t_a)*.
% 299.79/300.45 48259[4:SpR:104.0,39064.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))),y,t_a)*.
% 299.79/300.45 48473[0:MRR:48472.0,267.0] || c_Fun_Oinj__on(c_COMBK(u,v,w),hAPP(c_Set_Oinsert(x,w),y),w,v)* -> equal(c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.79/300.45 48620[0:SpR:197.1,115.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),w)*.
% 299.79/300.45 49347[0:Res:49314.1,479.1] || hBOOL(hAPP(u,v_x)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w)))*.
% 299.79/300.45 49346[0:Res:49314.1,478.1] || hBOOL(hAPP(u,v_x)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.79/300.45 51109[0:MRR:51099.1,648.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v_Procs)))* equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v),v_x) -> equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)).
% 299.79/300.45 51377[0:SpR:131.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),hAPP(hAPP(c_Set_Oinsert(z,t_a),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.45 51376[0:SpR:158.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),hAPP(hAPP(c_Set_Oinsert(z,t_a),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.45 51357[0:SpR:104.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),hAPP(hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.45 51844[4:SpR:24914.0,40792.1] || c_lessequals(v_x,hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(v,w),u),tc_Com_Opname,x),hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x))),tc_bool)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),u),v_x)).
% 299.79/300.45 52818[0:SpR:24019.2,545.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(v_x,u,w),v)))*.
% 299.79/300.45 52814[0:SpR:24019.2,362.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.45 53041[0:SpR:23955.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)),w))* -> hBOOL(hAPP(hAPP(c_in(x),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,x),w)))*.
% 299.79/300.45 53037[0:SpR:23955.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)),w))* -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.45 53173[0:SpR:23958.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)),w))* -> hBOOL(hAPP(hAPP(c_in(x),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,x),w)))*.
% 299.79/300.45 53169[0:SpR:23958.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)),w))* -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.45 53427[0:SpR:33303.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,x),v_x),tc_Com_Opname),u,w),v)))*.
% 299.79/300.45 53423[0:SpR:33303.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),v_x),tc_Com_Opname),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.45 53761[0:Res:7226.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_Option_Othe(v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(c_Option_Othe(v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u),x,u)*.
% 299.79/300.45 53760[0:Res:7226.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_Option_Othe(v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u) -> c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(c_Option_Othe(v),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u),u)*.
% 299.79/300.45 54114[0:SpR:52997.1,545.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,x),u,w),v)))*.
% 299.79/300.45 54110[0:SpR:52997.1,362.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_Procs,w),u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.45 54324[0:SpR:54251.0,55.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)))) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),w),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w))**.
% 299.79/300.45 54727[0:SpR:13749.2,545.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,x),w)))*.
% 299.79/300.45 54723[0:SpR:13749.2,362.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 55201[0:SpR:14043.2,545.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,x),w)))*.
% 299.79/300.45 55197[0:SpR:14043.2,362.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 55995[0:SpL:523.1,55174.1] class_Lattices_Olattice(u) || equal(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)))* -> .
% 299.79/300.45 55994[0:SpL:460.1,55174.1] || class_Lattices_Olattice(t_b) equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))* -> .
% 299.79/300.45 55913[0:SpL:523.1,55174.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool),hAPP(x,v_x))* -> .
% 299.79/300.45 55912[0:SpL:460.1,55174.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool),hAPP(u,v_x))* -> .
% 299.79/300.45 56205[0:SpR:30368.2,545.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y),x)))*.
% 299.79/300.45 56201[0:SpR:30368.2,362.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 56647[0:SpR:30928.2,545.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y),x)))*.
% 299.79/300.45 56643[0:SpR:30928.2,362.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 57729[0:Res:4122.3,251.1] class_Lattices_Oboolean__algebra(tc_fun(u,v)) class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || equal(c_Orderings_Otop__class_Otop(tc_fun(u,v)),w) -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,v)),x),hAPP(w,x),v)*.
% 299.79/300.45 57970[0:SpL:131.0,55910.1] || equal(c_COMBK(u,v,w),c_Set_Ovimage(c_Fun_Ocomp(x,y,z,x1,x2),x2,x1))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(c_Set_Ovimage(y,x2,z),hAPP(c_Set_Ovimage(x,z,x1),v_x)))* -> .
% 299.79/300.45 57969[0:SpL:158.0,55910.1] || equal(c_COMBK(u,v,w),c_Set_Oimage(c_Fun_Ocomp(x,y,z,x1,x2),x2,x1))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(c_Set_Oimage(x,z,x1),hAPP(c_Set_Oimage(y,x2,z),v_x)))* -> .
% 299.79/300.45 57950[0:SpL:104.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(y,v_x,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))) -> .
% 299.79/300.45 58127[0:SpL:131.0,55992.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_COMBK(z,x1,x2))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_bool),z)* -> .
% 299.79/300.45 58126[0:SpL:158.0,55992.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_COMBK(z,x1,x2))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_bool),z)* -> .
% 299.79/300.45 58107[0:SpL:104.0,55992.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),tc_bool),w)* -> .
% 299.79/300.45 58485[0:SpL:339.0,58248.0] || equal(c_COMBK(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),x,y),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),tc_fun(t_a,tc_bool)))** -> .
% 299.79/300.45 58472[0:SpL:465.1,58248.0] || equal(c_COMBK(hAPP(c_Set_Oimage(u,v,w),v_x),x,y),c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(c_Fun_Ofun__upd(u,z,x1,v,w),v,w),tc_fun(t_a,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(v),z),v_x)).
% 299.79/300.45 58593[0:SpR:21893.0,10771.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Set_Oinsert(v,u),w),v_x),hAPP(c_Set_Oinsert(v,u),w),tc_Com_Opname,x)),w))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),w),v_x)).
% 299.79/300.45 58592[0:SpR:21267.0,10771.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(v,u),w),hAPP(hAPP(c_Set_Oinsert(v,u),w),v_x),tc_Com_Opname,x)),w))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),w),v_x)).
% 299.79/300.45 59055[0:Res:35463.0,15629.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname),u,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname),u,tc_fun(v,tc_bool)),w)))*.
% 299.79/300.45 59054[0:Res:35464.0,15629.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname),t_a,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname),t_a,tc_fun(v,tc_bool)),w)))*.
% 299.79/300.45 58943[0:Res:44824.0,15629.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)))*.
% 299.79/300.45 58941[4:Res:40372.0,15629.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x)))*.
% 299.79/300.45 58940[0:Res:44716.0,15629.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w),x)))*.
% 299.79/300.45 58938[4:Res:40371.0,15629.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v)),w),x)))*.
% 299.79/300.45 58866[0:Res:676.0,15629.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_in(tc_Com_Opname),v_x)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_in(tc_Com_Opname),v_x)),w)))*.
% 299.79/300.45 58865[0:Res:675.0,15629.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),v),w)))*.
% 299.79/300.45 58806[0:SpL:317.0,15629.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)))* -> hBOOL(hAPP(c_Set_Oinsert(hAPP(u,x),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Set_Oinsert(hAPP(u,x),w),z)))*.
% 299.79/300.45 58760[0:SpL:329.1,15629.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x)))*.
% 299.79/300.45 58750[0:SpL:538.0,15629.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))*.
% 299.79/300.45 58680[0:SpL:317.0,15629.0] || hBOOL(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),y)))* -> hBOOL(hAPP(c_Set_Oimage(u,x,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Set_Oimage(u,x,w),z)))*.
% 299.79/300.45 59564[0:Res:35463.0,15857.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname),u,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname),u,tc_fun(v,tc_bool)),x)))*.
% 299.79/300.45 59563[0:Res:35464.0,15857.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname),t_a,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_in(tc_Com_Opname),t_a,tc_fun(v,tc_bool)),x)))*.
% 299.79/300.45 59451[0:Res:44824.0,15857.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),y)))*.
% 299.79/300.45 59449[4:Res:40372.0,15857.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),y)))*.
% 299.79/300.45 59448[0:Res:44716.0,15857.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w),y)))*.
% 299.79/300.45 59446[4:Res:40371.0,15857.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v)),w),y)))*.
% 299.79/300.45 59374[0:Res:676.0,15857.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_in(tc_Com_Opname),v_x)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_in(tc_Com_Opname),v_x)),x)))*.
% 299.79/300.45 59373[0:Res:675.0,15857.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),v),x)))*.
% 299.79/300.45 59314[0:SpL:317.0,15857.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)))* -> hBOOL(hAPP(c_Set_Oinsert(hAPP(u,x),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Set_Oinsert(hAPP(u,x),w),x1)))*.
% 299.79/300.45 59268[0:SpL:329.1,15857.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(v) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y)))*.
% 299.79/300.45 59258[0:SpL:538.0,15857.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)))*.
% 299.79/300.45 59188[0:SpL:317.0,15857.0] || hBOOL(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),y)))* -> hBOOL(hAPP(c_Set_Oimage(u,x,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Set_Oimage(u,x,w),x1)))*.
% 299.79/300.45 59927[0:Obv:59848.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))** -> c_lessequals(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u).
% 299.79/300.45 59928[0:Obv:59847.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u),x)** -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u),x,u).
% 299.79/300.45 60239[0:SpL:131.0,58170.1] || equal(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_x)),tc_bool),x1,x2),u)* -> .
% 299.79/300.45 60238[0:SpL:158.0,58170.1] || equal(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_x)),tc_bool),x1,x2),u)* -> .
% 299.79/300.45 60219[0:SpL:104.0,58170.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)))) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_bool),x,y),u)* -> .
% 299.79/300.45 60438[7:Res:58968.1,501.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.45 60423[7:Res:58968.1,255.0] || equal(hAPP(c_in(u),v),v_x) c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w),y,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),y)).
% 299.79/300.45 60374[7:SpR:2097.1,58968.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(w,x),u),w))* equal(c_Set_Oinsert(w,x),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(w,x),u)).
% 299.79/300.45 60463[0:SpR:5882.1,545.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),y,z,x1,x2),v,x),w)))*.
% 299.79/300.45 60459[0:SpR:5882.1,362.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.79/300.45 60551[0:Res:58969.1,501.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Procs) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.45 60536[0:Res:58969.1,255.0] || equal(hAPP(c_in(u),v),v_Procs) c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w),y,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),y)).
% 299.79/300.45 60487[0:SpR:2097.1,58969.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(w,x),u),w))* equal(c_Set_Oinsert(w,x),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(w,x),u)).
% 299.79/300.45 60624[7:Res:59476.1,501.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.45 60609[7:Res:59476.1,255.0] || equal(hAPP(c_in(u),v),v_x) c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x),y,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),y)).
% 299.79/300.45 60560[7:SpR:2097.1,59476.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),v),w))* equal(c_Set_Oinsert(w,x),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),v)).
% 299.79/300.45 60697[0:Res:59477.1,501.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Procs) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.45 60682[0:Res:59477.1,255.0] || equal(hAPP(c_in(u),v),v_Procs) c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x),y,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),y)).
% 299.79/300.45 60633[0:SpR:2097.1,59477.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),v),w))* equal(c_Set_Oinsert(w,x),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),v)).
% 299.79/300.45 60882[0:Res:59017.1,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x),v)),t_a)* -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x),t_a)* c_Hoare__Mirabelle_Otriple__valid(u,x,t_a).
% 299.79/300.45 60867[0:Res:59017.1,255.0] || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(c_in(w),x),u),y,tc_fun(w,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(z,hAPP(c_in(w),x),t_a)* hBOOL(hAPP(hAPP(c_in(w),x),y)).
% 299.79/300.45 60818[0:SpR:2097.1,59017.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(w,x),u),w))* -> c_Hoare__Mirabelle_Ohoare__valids(y,c_Set_Oinsert(w,x),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(w,x),u)).
% 299.79/300.45 60955[0:Res:59525.1,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x),w)),t_a)* -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x),t_a)* c_Hoare__Mirabelle_Otriple__valid(u,x,t_a).
% 299.79/300.45 60940[0:Res:59525.1,255.0] || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(w),x),v),y,tc_fun(w,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(z,hAPP(c_in(w),x),t_a)* hBOOL(hAPP(hAPP(c_in(w),x),y)).
% 299.79/300.45 60891[0:SpR:2097.1,59525.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),v),w))* -> c_Hoare__Mirabelle_Ohoare__valids(y,c_Set_Oinsert(w,x),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),v)).
% 299.79/300.45 61785[0:SpR:11167.1,545.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(x,y),c_Set_Oinsert(v_x,tc_Com_Opname)),u,w),v)))*.
% 299.79/300.45 61781[0:SpR:11167.1,362.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Set_Oinsert(w,x),c_Set_Oinsert(v_x,tc_Com_Opname)),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 61931[0:SpL:188.1,15487.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.79/300.45 62165[0:Res:23754.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs),u),v_x,u)*.
% 299.79/300.45 62164[0:Res:23754.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs),u) -> c_lessequals(v_x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs),u),u)*.
% 299.79/300.45 62436[0:Obv:62308.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(x,w,u) equal(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)) -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),u)*.
% 299.79/300.45 62750[0:Obv:62643.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(x,w,u) c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),u)* -> equal(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)).
% 299.79/300.45 63460[0:Res:4719.2,251.1] class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || c_lessequals(w,x,tc_fun(u,v)) -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),tc_fun(u,v)),y),hAPP(x,y),v)*.
% 299.79/300.45 63785[0:SSi:63668.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool)),y)* hBOOL(hAPP(hAPP(c_in(x),z),v))* -> c_lessequals(hAPP(w,z),y,tc_fun(u,tc_bool))*.
% 299.79/300.45 63786[0:SSi:63667.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(hAPP(c_Set_Oimage(v,w,u),x),y)* hBOOL(hAPP(hAPP(c_in(w),z),x))* -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,z)),y))*.
% 299.79/300.45 63791[0:MRR:63790.2,24483.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),x)* -> c_lessequals(v,hAPP(c_Set_Oinsert(w,u),x),tc_fun(u,tc_bool))*.
% 299.79/300.45 63880[0:Res:4804.2,251.1] class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || c_lessequals(w,x,tc_fun(u,v)) -> c_lessequals(hAPP(w,y),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(x,tc_fun(u,v)),tc_fun(u,v)),y),v)*.
% 299.79/300.45 63972[0:SpR:647.0,35.2] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) c_lessequals(u,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),tc_fun(tc_Com_Opname,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)**.
% 299.79/300.45 63961[0:SpR:647.0,151.2] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v))) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.79/300.45 64245[0:SpR:584.0,646.1] || c_Fun_Oinj__on(c_COMBS(u,v,w,x,y),v_Procs,tc_Com_Opname,z) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_COMBS(u,v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(u,v_x),hAPP(v,v_x))),v_x)**.
% 299.79/300.45 64244[0:SpR:586.0,646.1] || c_Fun_Oinj__on(hAPP(c_COMBB(u,v,w,x),y),v_Procs,tc_Com_Opname,z) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_COMBB(u,v,w,x),y),tc_Com_Opname,z),hAPP(u,hAPP(y,v_x))),v_x)**.
% 299.79/300.45 64243[0:SpR:585.0,646.1] || c_Fun_Oinj__on(hAPP(c_COMBC(u,v,w,x),y),v_Procs,tc_Com_Opname,z) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_COMBC(u,v,w,x),y),tc_Com_Opname,z),hAPP(hAPP(u,v_x),y)),v_x)**.
% 299.79/300.45 64205[0:SpR:331.0,646.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_Com_Opname,v),v_x),v_x)**.
% 299.79/300.45 64194[0:SpR:34428.0,646.1] || c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_Com_Opname,v),v_x),v_x)**.
% 299.79/300.45 64166[0:SpR:646.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(v,v_x)),y)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Fun_Othe__inv__into(v_Procs,v,tc_Com_Opname,w),x,u),u)*.
% 299.79/300.45 64158[0:SpR:646.1,176.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),hAPP(c_Set_Ovimage(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,x),hAPP(c_Set_Oinsert(v_x,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 64412[0:SpR:584.0,645.1] || c_Fun_Oinj__on(c_COMBS(u,v,w,x,y),v_Procs,tc_Com_Opname,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(u,v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(u,v_x),hAPP(v,v_x))),v_x)**.
% 299.79/300.45 64411[0:SpR:586.0,645.1] || c_Fun_Oinj__on(hAPP(c_COMBB(u,v,w,x),y),v_Procs,tc_Com_Opname,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_COMBB(u,v,w,x),y),tc_Com_Opname,z),hAPP(u,hAPP(y,v_x))),v_x)**.
% 299.79/300.45 64410[0:SpR:585.0,645.1] || c_Fun_Oinj__on(hAPP(c_COMBC(u,v,w,x),y),v_Procs,tc_Com_Opname,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_COMBC(u,v,w,x),y),tc_Com_Opname,z),hAPP(hAPP(u,v_x),y)),v_x)**.
% 299.79/300.45 64361[0:SpR:34428.0,645.1] || c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),tc_Com_Opname,v),v_x),v_x)**.
% 299.79/300.45 64333[0:SpR:645.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(v,v_x)),y)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),x,u),u)*.
% 299.79/300.45 64325[0:SpR:645.1,176.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),hAPP(c_Set_Ovimage(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,x),hAPP(c_Set_Oinsert(v_x,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.45 64590[0:SpR:26782.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) -> hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),x,tc_fun(y,tc_bool)),u,w),v)))*.
% 299.79/300.45 64586[0:SpR:26782.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,tc_fun(x,tc_bool)),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 64817[0:SpR:28747.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),tc_Com_Opname,y),tc_Com_Opname),u,w),v)))*.
% 299.79/300.45 64813[0:SpR:28747.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 64937[0:SpR:28748.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),tc_Com_Opname,y),tc_Com_Opname),u,w),v)))*.
% 299.79/300.45 64933[0:SpR:28748.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 65057[0:SpR:28902.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,y),tc_Com_Opname),u,w),v)))*.
% 299.79/300.45 65053[0:SpR:28902.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 65177[0:SpR:28903.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,y),tc_Com_Opname),u,w),v)))*.
% 299.79/300.45 65173[0:SpR:28903.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.45 66722[0:SpR:1188.2,361.2] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),c_HOL_Ozero__class_Ozero(u)),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),w,v),v)*.
% 299.79/300.45 66703[0:SpR:1188.2,176.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.45 67477[0:SpR:1189.2,361.2] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),c_HOL_Ozero__class_Ozero(u)),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),w,v),v)*.
% 299.79/300.45 67458[0:SpR:1189.2,176.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))*.
% 299.79/300.45 69726[0:SSi:69712.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))).
% 299.79/300.45 69727[0:SSi:69711.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))).
% 299.79/300.45 69753[0:Res:66670.2,251.1] class_Lattices_Olattice(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),tc_fun(u,v)),w),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w),v)*.
% 299.79/300.45 70320[0:Res:70279.2,251.1] class_Lattices_Olattice(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),tc_fun(u,v)),w),v)*.
% 299.79/300.45 70364[0:SpL:55.1,12983.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w),x,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v),x)) c_Hoare__Mirabelle_Otriple__valid(u,v,t_a).
% 299.79/300.45 70904[0:SpL:532.0,6582.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),w)** -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),w,tc_fun(u,tc_bool)).
% 299.79/300.45 71060[0:SpR:533.0,7568.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y))),tc_fun(u,tc_bool))*.
% 299.79/300.45 71249[0:SpR:338.0,7538.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(y,u),w))),tc_fun(u,tc_bool))*.
% 299.79/300.45 71625[7:SpR:71455.1,118.0] || equal(u,v_x) -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),c_Fun_Ofun__upd(v,w,u,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),v,y,z,x),w,u,x,z))*.
% 299.79/300.45 71600[7:SpR:71455.1,71.2] || equal(u,v_x) hBOOL(hAPP(hAPP(c_in(v),u),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oinsert(v_x,t_a),v,x),u),u)**.
% 299.79/300.45 71599[7:SpR:71455.1,373.2] || equal(u,v_x) hBOOL(hAPP(hAPP(c_in(v),u),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oinsert(v_x,t_a),v,x),u),u)**.
% 299.79/300.45 72085[0:SpR:532.0,7830.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w))),tc_fun(u,tc_bool))*.
% 299.79/300.45 72971[7:Rew:339.0,72966.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,t_a),v_x),w,u,t_a)),hAPP(c_Set_Oinsert(v,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v_x),w))))*.
% 299.79/300.45 73067[7:Res:71608.1,482.2] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x)** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)))* -> hBOOL(hAPP(w,v_x)).
% 299.79/300.45 74298[7:SpL:71835.1,477.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,w,u)))* hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(hAPP(w,x))*.
% 299.79/300.45 74213[7:SpL:71835.1,477.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(v_x,w),v,u)))* hBOOL(hAPP(hAPP(c_in(u),x),v_x))* -> hBOOL(hAPP(v,x))*.
% 299.79/300.45 74212[7:SpL:71835.1,476.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(v_x,w),v,u)))* hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(hAPP(v,x))*.
% 299.79/300.45 74185[7:SpL:71835.1,94.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_Fun_Oinj__on(u,v_x,v,w) c_Fun_Oinj__on(x,v_x,w,y) -> c_Fun_Oinj__on(c_Fun_Ocomp(x,u,w,y,v),v_x,v,y)*.
% 299.79/300.45 73610[7:SpR:71835.1,475.1] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(c_Set_Oinsert(v_x,x),hAPP(c_Set_Oimage(u,v,x),w)),hAPP(c_Set_Oimage(u,v,x),w))**.
% 299.79/300.45 73244[7:SpR:71835.1,340.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) c_lessequals(v_x,v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(v_x,w),v,tc_fun(u,tc_bool))*.
% 299.79/300.45 75401[0:SpR:24914.0,7820.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),u)*.
% 299.79/300.45 75611[0:Obv:75505.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),x) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),x,u)*.
% 299.79/300.45 75612[0:Obv:75504.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),x,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),x).
% 299.79/300.45 76082[0:Obv:75959.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),w) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),w,u)*.
% 299.79/300.45 76083[0:Obv:75958.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),w,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),w).
% 299.79/300.45 76154[0:SpR:9915.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_COMBS(c_Set_Ovimage(y,z,w),x1,x2,x3,x4),v,u),u)*.
% 299.79/300.45 76146[0:SpR:9915.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Ovimage(c_COMBS(c_Set_Ovimage(w,x,v),y,z,x1,x2),u,x3),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x3),c_Orderings_Obot__class_Obot(tc_fun(x3,tc_bool))))))*.
% 299.79/300.45 76274[0:SpR:10469.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_COMBS(c_Set_Oimage(y,w,z),x1,x2,x3,x4),v,u),u)*.
% 299.79/300.45 76266[0:SpR:10469.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Ovimage(c_COMBS(c_Set_Oimage(w,v,x),y,z,x1,x2),u,x3),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x3),c_Orderings_Obot__class_Obot(tc_fun(x3,tc_bool))))))*.
% 299.79/300.45 76404[0:SpR:10470.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_COMBS(c_Set_Ovimage(y,z,w),x1,x2,x3,x4),v,u),u)*.
% 299.79/300.45 76396[0:SpR:10470.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Ovimage(c_COMBS(c_Set_Ovimage(w,x,v),y,z,x1,x2),u,x3),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x3),c_Orderings_Obot__class_Obot(tc_fun(x3,tc_bool))))))*.
% 299.79/300.45 76532[0:SpR:24914.0,29199.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),u)*.
% 299.79/300.45 77181[7:SpL:537.1,74788.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),x)* -> hBOOL(x)*.
% 299.79/300.45 77180[7:SpL:534.1,74788.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),x)* -> hBOOL(x)*.
% 299.79/300.45 77347[0:Res:2399.2,18625.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))* c_lessequals(hAPP(v,w),hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),w),tc_bool)*.
% 299.79/300.45 77465[7:SpR:71894.1,118.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_Fun_Ocomp(v_x,c_Fun_Ofun__upd(u,v,c_Orderings_Obot__class_Obot(tc_bool),w,x),x,y,w),c_Fun_Ofun__upd(c_Fun_Ocomp(v_x,u,x,y,w),v,v_x,w,y))*.
% 299.79/300.45 77905[0:Res:153.1,5892.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(c_Set_Ovimage(v,w,u),x))),x))* -> hBOOL(hAPP(c_COMBS(c_in(y),c_in(w),z,x1,x2),hAPP(c_Set_Ovimage(v,w,u),x)))*.
% 299.79/300.45 78425[7:SpL:78167.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,y),u,tc_fun(w,tc_bool))))*.
% 299.79/300.45 78502[4:Res:77988.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)))* equal(hAPP(w,v_x),hAPP(w,v))* c_Fun_Oinj__on(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,x)* -> equal(v_x,v).
% 299.79/300.45 78699[4:Res:78665.1,184.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)),v_x)** c_Fun_Oinj__on(w,y,x,u) -> equal(hAPP(w,hAPP(c_Fun_Othe__inv__into(y,w,x,u),v)),v)**.
% 299.79/300.45 78871[0:SpR:24914.0,11064.1] || c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),v_x),y,tc_fun(w,tc_bool)),w)*.
% 299.79/300.45 78963[0:SpR:223.1,15630.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(x,y)) -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,y,u,x1),u,x1),w),x2,x,x1)))*.
% 299.79/300.45 79068[0:Res:78077.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))* equal(hAPP(x,v_Procs),hAPP(x,v))* c_Fun_Oinj__on(x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,y)* -> equal(v_Procs,v).
% 299.79/300.45 79096[7:Res:78199.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_in(w),v_x)))* equal(hAPP(x,v_x),hAPP(x,v))* c_Fun_Oinj__on(x,hAPP(c_in(w),v_x),u,y)* -> equal(v_x,v).
% 299.79/300.45 79183[0:SpR:223.1,15858.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(x,y)) -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x1,v,y,u,x2),u,x2),w),x,x2)))*.
% 299.79/300.45 80254[0:SpL:21268.0,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_in(t_a),v_x),hAPP(hAPP(c_in(t_a),v_x),v),u,w),v_x),tc_bool))* hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)) -> .
% 299.79/300.45 80253[0:SpL:21268.0,46309.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool)* hBOOL(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),x,y))* -> hBOOL(w).
% 299.79/300.45 80219[0:SpL:21268.0,11894.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_in(v),w),hAPP(hAPP(c_in(v),w),x),u,y),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** hBOOL(hAPP(hAPP(c_in(v),w),x)) -> .
% 299.79/300.45 80190[7:SpL:21268.0,27284.0] || equal(hAPP(c_Set_Ovimage(u,v,w),x),v_x) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),x),y,z),hAPP(u,v_x)))*.
% 299.79/300.45 80189[0:SpL:21268.0,4439.0] || equal(hAPP(c_Set_Ovimage(u,v,w),x),v_Procs) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),x),y,z),hAPP(u,v_x)))*.
% 299.79/300.45 80148[0:SpL:21268.0,363.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),w),y,z),x,tc_fun(v,tc_bool))*.
% 299.79/300.45 79985[0:SpR:28334.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),v_Procs,w,x)),v_Procs)**.
% 299.79/300.45 79980[0:SpR:28031.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),v_Procs,w,x)),v_Procs)**.
% 299.79/300.45 79956[0:SpR:9915.0,21268.0] || -> equal(hAPP(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_Orderings_Otop__class_Otop(tc_bool),x2,x3)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.45 79943[0:SpR:10470.0,21268.0] || -> equal(hAPP(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_Orderings_Obot__class_Obot(tc_bool),x2,x3)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.45 79941[0:SpR:10469.0,21268.0] || -> equal(hAPP(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),c_Orderings_Obot__class_Obot(tc_bool),x2,x3)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.45 79931[0:SpR:584.0,21268.0] || -> equal(hAPP(hAPP(u,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(u,v),hAPP(c_COMBS(u,x,y,z,x1),v),w,x2)),hAPP(c_COMBS(u,x,y,z,x1),v))**.
% 299.79/300.45 79814[0:SpR:21268.0,7538.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),hAPP(c_Set_Oinsert(v,w),x)),tc_fun(w,tc_bool))*.
% 299.79/300.45 79730[0:SpR:21268.0,37923.1] || hBOOL(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),u,x))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)))*.
% 299.79/300.45 79724[0:SpR:21268.0,9935.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),u,x),tc_bool)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.79/300.45 79615[0:SpR:21268.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(x,y),w,z)),x1))* -> c_lessequals(hAPP(x,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,x,v,u),u)*.
% 299.79/300.45 79538[0:SpR:21268.0,364.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),hAPP(c_Set_Oinsert(w,x),y),v,z),tc_fun(x,tc_bool))* -> c_lessequals(u,hAPP(c_Set_Oinsert(w,x),y),tc_fun(x,tc_bool)).
% 299.79/300.45 79532[0:SpR:21268.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(w,x),v,y)),hAPP(c_Set_Ovimage(w,u,z),hAPP(c_Set_Oinsert(hAPP(w,x),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.45 79525[0:SpR:21268.0,212.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,x),u),hAPP(hAPP(c_Set_Oinsert(w,x),u),y),v,z)))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),u),y)).
% 299.79/300.45 79391[0:SpR:21268.0,21126.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,tc_Com_Opname,w),hAPP(c_Set_Oimage(v,tc_Com_Opname,w),x),u,y),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),x),hAPP(v,v_x))).
% 299.79/300.45 79373[0:SpR:21268.0,679.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),u,w),v_Procs,tc_fun(tc_Com_Opname,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),v_Procs,tc_fun(tc_Com_Opname,tc_bool)).
% 299.79/300.45 81449[0:SpL:21894.0,70070.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),v),hAPP(c_in(t_a),v_x),u,w),v_x),tc_bool))* hBOOL(hAPP(hAPP(c_in(t_a),v_x),v)) -> .
% 299.79/300.45 81448[0:SpL:21894.0,46309.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool)* hBOOL(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x,y))* -> hBOOL(w).
% 299.79/300.45 81414[0:SpL:21894.0,11894.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_in(v),w),x),hAPP(c_in(v),w),u,y),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** hBOOL(hAPP(hAPP(c_in(v),w),x)) -> .
% 299.79/300.45 81385[7:SpL:21894.0,27284.0] || equal(hAPP(c_Set_Ovimage(u,v,w),x),v_x) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x),c_Set_Ovimage(u,v,w),y,z),hAPP(u,v_x)))*.
% 299.79/300.45 81384[0:SpL:21894.0,4439.0] || equal(hAPP(c_Set_Ovimage(u,v,w),x),v_Procs) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x),c_Set_Ovimage(u,v,w),y,z),hAPP(u,v_x)))*.
% 299.79/300.45 81343[0:SpL:21894.0,363.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(u,v),y,z),x,tc_fun(v,tc_bool))*.
% 299.79/300.45 81179[0:SpR:28334.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),w,x)),v_Procs)**.
% 299.79/300.45 81174[0:SpR:28031.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),w,x)),v_Procs)**.
% 299.79/300.45 81150[0:SpR:9915.0,21894.0] || -> equal(hAPP(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.45 81137[0:SpR:10470.0,21894.0] || -> equal(hAPP(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.45 81135[0:SpR:10469.0,21894.0] || -> equal(hAPP(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),x2,x3)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.45 81125[0:SpR:584.0,21894.0] || -> equal(hAPP(hAPP(u,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_COMBS(u,x,y,z,x1),v),hAPP(u,v),w,x2)),hAPP(c_COMBS(u,x,y,z,x1),v))**.
% 299.79/300.45 81008[0:SpR:21894.0,7538.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),hAPP(c_Set_Oinsert(v,w),x)),tc_fun(w,tc_bool))*.
% 299.79/300.45 80924[0:SpR:21894.0,37923.1] || hBOOL(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,x))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)))*.
% 299.79/300.45 80918[0:SpR:21894.0,9935.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,x),tc_bool)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.79/300.45 80809[0:SpR:21894.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(x,y),x,w,z)),x1))* -> c_lessequals(hAPP(x,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,x,v,u),u)*.
% 299.79/300.45 80731[0:SpR:21894.0,364.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,x),y),c_Set_Oinsert(w,x),v,z),tc_fun(x,tc_bool))* -> c_lessequals(u,hAPP(c_Set_Oinsert(w,x),y),tc_fun(x,tc_bool)).
% 299.79/300.45 80725[0:SpR:21894.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(w,x),w,v,y)),hAPP(c_Set_Ovimage(w,u,z),hAPP(c_Set_Oinsert(hAPP(w,x),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.45 80718[0:SpR:21894.0,212.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Set_Oinsert(w,x),u),y),hAPP(c_Set_Oinsert(w,x),u),v,z)))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),u),y)).
% 299.79/300.45 80584[0:SpR:21894.0,21126.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,tc_Com_Opname,w),x),c_Set_Oimage(v,tc_Com_Opname,w),u,y),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),x),hAPP(v,v_x))).
% 299.79/300.45 80566[0:SpR:21894.0,679.1] || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),c_Set_Oinsert(v_x,tc_Com_Opname),u,w),v_Procs,tc_fun(tc_Com_Opname,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),v_Procs,tc_fun(tc_Com_Opname,tc_bool)).
% 299.79/300.45 81746[0:SpR:24914.0,5075.1] || c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Ovimage(u,v,w),v_x)),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x)),w).
% 299.79/300.45 81916[0:SpR:128.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Ovimage(v,w,x),z,x1,x2),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))),u)*.
% 299.79/300.45 82079[0:Obv:81980.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),hAPP(v,z)) -> c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),hAPP(v,z),u)*.
% 299.79/300.45 82080[0:Obv:81979.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),hAPP(v,z),u)* -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),hAPP(v,z)).
% 299.79/300.45 82169[7:SpR:78597.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),c_Fun_Ofun__upd(u,v,c_Set_Oinsert(v_x,w),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),u,y,z,x),v,c_Set_Oinsert(v_x,w),x,z))*.
% 299.79/300.45 82388[0:SpR:128.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Ovimage(v,w,x),z,x1,x2),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))),u)*.
% 299.79/300.45 82855[7:Res:77991.0,479.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),v_x),y,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,x),v_x)),y)))*.
% 299.79/300.45 82854[7:Res:77991.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oinsert(x,y),v_x),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,y),v_x))))*.
% 299.79/300.45 82924[0:SpR:24914.0,22513.1] || c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(y,w,z),hAPP(c_Set_Oimage(u,v,w),v_x)),z)*.
% 299.79/300.45 83050[0:SpR:5924.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(hAPP(y,w),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_COMBS(y,c_COMBK(z,x1,x2),x3,x4,x5),v,u),u)*.
% 299.79/300.45 83034[0:SpR:5924.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_COMBS(w,c_COMBK(x,y,z),x1,x2,x3),u,x4),hAPP(c_Set_Oinsert(hAPP(hAPP(w,v),x),x4),c_Orderings_Obot__class_Obot(tc_fun(x4,tc_bool))))))*.
% 299.79/300.45 82975[0:SpR:5924.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(u,v_x),v),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_COMBS(u,c_COMBK(v,w,x),y,z,x1)),c_COMBS(u,c_COMBK(v,w,x),y,z,x1))**.
% 299.79/300.45 83158[0:Rew:5924.0,83049.0] || -> equal(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(u,w),x),c_COMBS(u,c_COMBK(x,y,z),x1,x2,x3),v,x4)),x),hAPP(hAPP(u,w),x))**.
% 299.79/300.45 83159[0:Rew:5924.0,83048.0] || -> equal(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_COMBS(u,c_COMBK(w,x,y),z,x1,x2),hAPP(hAPP(u,x3),w),v,x4)),w),hAPP(hAPP(u,x3),w))**.
% 299.79/300.45 83377[0:SpR:5961.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(y,hAPP(z,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_COMBS(c_COMBK(y,x1,x2),z,x3,x4,x5),v,u),u)*.
% 299.79/300.46 83365[0:SpR:5961.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_COMBS(c_COMBK(w,x,y),z,x1,x2,x3),u,x4),hAPP(c_Set_Oinsert(hAPP(w,hAPP(z,v)),x4),c_Orderings_Obot__class_Obot(tc_fun(x4,tc_bool))))))*.
% 299.79/300.46 83305[0:SpR:5961.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,hAPP(v,v_x)),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_COMBS(c_COMBK(u,w,x),v,y,z,x1)),c_COMBS(c_COMBK(u,w,x),v,y,z,x1))**.
% 299.79/300.46 83468[0:Rew:5961.0,83376.0] || -> equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(u,hAPP(v,x)),c_COMBS(c_COMBK(u,y,z),v,x1,x2,x3),w,x4))),hAPP(u,hAPP(v,x)))**.
% 299.79/300.46 83469[0:Rew:5961.0,83375.0] || -> equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_COMBS(c_COMBK(u,x,y),v,z,x1,x2),hAPP(u,hAPP(v,x3)),w,x4))),hAPP(u,hAPP(v,x3)))**.
% 299.79/300.46 83879[0:SpL:5899.0,15629.0] || hBOOL(hAPP(c_COMBS(u,v,w,x,y),z))* -> hBOOL(hAPP(c_COMBS(u,v,x1,x2,x3),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x4,tc_bool)),x5,c_COMBS(u,v,x1,x2,x3),x4)))*.
% 299.79/300.46 83878[0:SpL:5899.0,15857.0] || hBOOL(hAPP(c_COMBS(u,v,w,x,y),z))* -> hBOOL(hAPP(c_COMBS(u,v,x1,x2,x3),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x4,c_Orderings_Otop__class_Otop(tc_fun(x5,tc_bool)),c_COMBS(u,v,x1,x2,x3),x5)))*.
% 299.79/300.46 83759[0:SpR:5899.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(c_COMBS(y,z,x1,x2,x3),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_COMBS(y,z,x4,x5,x6),v,u),u)*.
% 299.79/300.46 83743[0:SpR:5899.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_COMBS(w,x,y,z,x1),u,x2),hAPP(c_Set_Oinsert(hAPP(c_COMBS(w,x,x3,x4,x5),v),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))))))*.
% 299.79/300.46 84195[7:SpL:537.1,78767.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> .
% 299.79/300.46 84194[7:SpL:534.1,78767.0] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> .
% 299.79/300.46 85011[0:Res:84957.0,479.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,x),v),y,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,x),v)),y)))*.
% 299.79/300.46 85010[0:Res:84957.0,478.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(v,y),v),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(v,y),v))))*.
% 299.79/300.46 84981[0:SpR:24914.0,84957.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),hAPP(c_in(u),v_x)),w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),hAPP(c_in(u),v_x)))))*.
% 299.79/300.46 85102[0:SpL:644.0,473.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBK(w,u,tc_Com_Opname),tc_Com_Opname,u),v)),v_Procs))*.
% 299.79/300.46 85209[0:SpR:819.1,383.1] class_Orderings_Otop(u) || -> equal(v,v_x) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,w,x,y),v_x,c_Orderings_Otop__class_Otop(u),x,y),c_Fun_Ofun__upd(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,w,x,y))**.
% 299.79/300.46 85258[0:SpR:824.1,383.1] class_Orderings_Obot(u) || -> equal(v,v_x) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,w,x,y),v_x,c_Orderings_Obot__class_Obot(u),x,y),c_Fun_Ofun__upd(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,w,x,y))**.
% 299.79/300.46 85470[4:SpR:78507.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v),x)),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),x)))*.
% 299.79/300.46 85469[4:SpR:78507.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,u),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))**.
% 299.79/300.46 85468[4:SpR:78507.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,u),v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))**.
% 299.79/300.46 85950[0:Res:15858.1,13582.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(x,z),x1),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),z)),v))* -> .
% 299.79/300.46 85947[0:Res:15630.1,13582.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(x,y),z),x1,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),y)),v))* -> .
% 299.79/300.46 86283[0:SpR:86109.1,118.0] || equal(u,v_Procs) -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),c_Fun_Ofun__upd(v,w,u,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),v,y,z,x),w,u,x,z))*.
% 299.79/300.46 86253[0:SpR:86109.1,71.2] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oinsert(v_x,t_a),v,x),u),u)**.
% 299.79/300.46 86252[0:SpR:86109.1,373.2] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oinsert(v_x,t_a),v,x),u),u)**.
% 299.79/300.46 86661[0:Res:86261.1,482.2] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_Procs)** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)))* -> hBOOL(hAPP(w,v_x)).
% 299.79/300.46 86740[4:SpL:537.1,86106.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> .
% 299.79/300.46 86739[4:SpL:534.1,86106.0] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> .
% 299.79/300.46 87096[0:Rew:321.0,86980.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,w,y),u),hAPP(c_Set_Oimage(x,w,y),v),tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.46 87321[7:SpR:339.0,71492.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),x))*.
% 299.79/300.46 87308[7:SpR:465.1,71492.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_x)** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oimage(u,x,y),v_x)),z))*.
% 299.79/300.46 87469[7:SpR:339.0,71493.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),x,t_a)*.
% 299.79/300.46 87456[7:SpR:465.1,71493.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_x)** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oimage(u,x,y),v_x)),z,t_a)*.
% 299.79/300.46 87515[0:SpR:769.0,383.1] || -> equal(u,v) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),u,x,y,z),v,v,y,z),c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),u,x,y,z))**.
% 299.79/300.46 87599[7:SpR:339.0,71679.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.46 87586[7:SpR:465.1,71679.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_x)** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(c_Set_Oimage(u,x,y),v_x)))*.
% 299.79/300.46 88326[0:Res:7227.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(c_COMBK(v,w,x),y,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,z)),u))* c_Hoare__Mirabelle_Otriple__valid(z,v,t_a)*.
% 299.79/300.46 88647[7:SpL:537.1,88086.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) hBOOL(c_HOL_Ominus__class_Ominus(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool))* -> .
% 299.79/300.46 88646[7:SpL:534.1,88086.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) hBOOL(c_HOL_Ominus__class_Ominus(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool))* -> .
% 299.79/300.46 88859[0:SpR:130.1,14196.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x,y),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),v_x))*.
% 299.79/300.46 89364[7:SpR:78590.1,317.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,v),x)),hAPP(c_Set_Oinsert(u,w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),x)))*.
% 299.79/300.46 89363[7:SpR:78590.1,99.1] || equal(c_Set_Oinsert(v_x,t_a),u) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v,w),u),u)**.
% 299.79/300.46 89362[7:SpR:78590.1,438.1] || equal(c_Set_Oinsert(v_x,t_a),u) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v,w),u),u)**.
% 299.79/300.46 89696[7:Res:89344.1,268.0] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(t_a),v),u))* equal(hAPP(w,v_x),hAPP(w,v))* c_Fun_Oinj__on(w,u,t_a,x)* -> equal(v_x,v).
% 299.79/300.46 89856[0:SpR:26183.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y,z),hAPP(c_Set_Oinsert(x1,u),v)),hAPP(hAPP(c_Set_Oinsert(x1,u),v),hAPP(w,hAPP(c_Set_Oinsert(x1,u),v))))*.
% 299.79/300.46 89855[0:SpR:26183.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y,z),hAPP(c_Set_Oinsert(x1,v),w)),hAPP(hAPP(u,hAPP(c_Set_Oinsert(x1,v),w)),hAPP(c_Set_Oinsert(x1,v),w)))*.
% 299.79/300.46 89789[0:SpR:26183.0,21894.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,u),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,y)),hAPP(c_Set_Oinsert(x,u),v))**.
% 299.79/300.46 89788[0:SpR:26183.0,21268.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(x,u),v),w,y)),hAPP(c_Set_Oinsert(x,u),v))**.
% 299.79/300.46 90154[4:SpR:78660.1,317.0] || equal(hAPP(u,v_x),v_x) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,v),x)),hAPP(c_Set_Oinsert(u,w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),x)))*.
% 299.79/300.46 90153[4:SpR:78660.1,99.1] || equal(hAPP(u,v_x),v_x) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v,w),u),u)**.
% 299.79/300.46 90152[4:SpR:78660.1,438.1] || equal(hAPP(u,v_x),v_x) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v,w),u),u)**.
% 299.79/300.46 90840[4:Res:90134.1,268.0] || equal(hAPP(u,v_x),v_x) hBOOL(hAPP(hAPP(c_in(t_a),v),u))* equal(hAPP(w,v_x),hAPP(w,v))* c_Fun_Oinj__on(w,u,t_a,x)* -> equal(v_x,v).
% 299.79/300.46 91353[0:Rew:91288.1,91101.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),w),y)),hAPP(c_Set_Oinsert(v,x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),y)))*.
% 299.79/300.46 91354[0:Rew:91288.1,91100.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),v),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.46 91355[0:Rew:91288.1,91099.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),v),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.46 91828[4:SpL:297.2,78747.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname),u)* equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)).
% 299.79/300.46 91947[0:SpR:79073.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),v),y)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),y)))*.
% 299.79/300.46 91946[0:SpR:79073.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_Procs,u),v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))**.
% 299.79/300.46 91945[0:SpR:79073.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_Procs,u),v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))**.
% 299.79/300.46 92100[7:SpR:79101.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),hAPP(c_Set_Oinsert(hAPP(c_in(x),v_x),v),y)),hAPP(c_Set_Oinsert(hAPP(c_in(x),v_x),w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,w),y)))*.
% 299.79/300.46 92099[7:SpR:79101.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,u),v,w),hAPP(c_in(x),v_x)),hAPP(c_in(x),v_x))**.
% 299.79/300.46 92098[7:SpR:79101.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,u),v,w),hAPP(c_in(x),v_x)),hAPP(c_in(x),v_x))**.
% 299.79/300.46 92577[0:SpR:5227.1,5227.1] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x) c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,y),z,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),x1)* -> equal(c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(y,c_Suc(w),z,x1)),c_Suc(w)).
% 299.79/300.46 92645[7:SpR:339.0,82151.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Set_Oinsert(v_x,x)))*.
% 299.79/300.46 92632[7:SpR:465.1,82151.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(u,x,y),v_x),c_Set_Oinsert(v_x,z)))*.
% 299.79/300.46 93305[4:SpR:339.0,85556.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),x),tc_bool)*.
% 299.79/300.46 93292[4:SpR:465.1,85556.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) c_lessequals(v_x,hAPP(hAPP(c_Set_Oimage(u,x,y),v_x),z),tc_bool)*.
% 299.79/300.46 93493[0:SpR:339.0,86147.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),x))*.
% 299.79/300.46 93480[0:SpR:465.1,86147.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oimage(u,x,y),v_x)),z))*.
% 299.79/300.46 93644[0:SpR:339.0,86148.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),x,t_a)*.
% 299.79/300.46 93631[0:SpR:465.1,86148.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Set_Oimage(u,x,y),v_x)),z,t_a)*.
% 299.79/300.46 93788[0:SpR:339.0,86342.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.46 93775[0:SpR:465.1,86342.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),hAPP(c_Set_Oimage(u,x,y),v_x)))*.
% 299.79/300.46 94160[0:Res:14364.3,251.1] class_Orderings_Olinorder(tc_fun(u,v)) class_HOL_Oord(v) || hBOOL(hAPP(w,x)) c_Finite__Set_Ofinite(w,tc_fun(u,v)) -> c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(w,tc_fun(u,v)),y),hAPP(x,y),v)*.
% 299.79/300.46 94159[0:Res:14364.3,8306.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))*.
% 299.79/300.46 94146[0:Res:14364.3,431.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_Fun_Oinj__on(x,w,u,y)* -> c_Fun_Oinj__on(x,c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),u,y)*.
% 299.79/300.46 94285[0:Res:14491.3,251.1] class_Orderings_Olinorder(tc_fun(u,v)) class_HOL_Oord(v) || hBOOL(hAPP(w,x)) c_Finite__Set_Ofinite(w,tc_fun(u,v)) -> c_lessequals(hAPP(x,y),hAPP(c_Finite__Set_Olinorder__class_OMax(w,tc_fun(u,v)),y),v)*.
% 299.79/300.46 94269[0:Res:14491.3,214.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Set_Oinsert(w,u),x)))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),w),c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool))))*.
% 299.79/300.46 94262[0:Res:14491.3,2092.0] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) || hBOOL(hAPP(u,v_Procs)) c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Finite__Set_Olinorder__class_OMax(u,tc_fun(tc_Com_Opname,tc_bool))),c_Finite__Set_Olinorder__class_OMax(u,tc_fun(tc_Com_Opname,tc_bool)))**.
% 299.79/300.46 94251[0:Res:14491.3,431.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_Fun_Oinj__on(x,c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),u,y)* -> c_Fun_Oinj__on(x,w,u,y)*.
% 299.79/300.46 4323[0:SpR:297.2,687.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname),u)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname)).
% 299.79/300.46 4322[0:SpR:297.2,686.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname),u)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname)).
% 299.79/300.46 4385[0:Res:687.1,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,hAPP(c_Set_Oinsert(u,v),w),tc_Com_Opname)))* equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,hAPP(c_Set_Oinsert(u,v),w),tc_Com_Opname),u).
% 299.79/300.46 4384[0:Res:686.1,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,hAPP(c_Set_Oinsert(u,v),w),tc_Com_Opname)))* equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,hAPP(c_Set_Oinsert(u,v),w),tc_Com_Opname),u).
% 299.79/300.46 6664[0:SpR:329.1,1103.1] || c_lessequals(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u)),tc_fun(w,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),t_a) hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u))).
% 299.79/300.46 9562[0:Res:4801.2,251.1] class_Orderings_Otop(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(w,x),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(u,v)),tc_fun(u,v)),tc_fun(u,v)),x),v)*.
% 299.79/300.46 9525[0:Res:4834.2,251.1] class_Orderings_Obot(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(u,v)),tc_fun(u,v)),tc_fun(u,v)),w),hAPP(x,w),v)*.
% 299.79/300.46 10856[0:SpR:353.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),hAPP(c_Set_Oinsert(x1,v),x2)),hAPP(hAPP(c_Set_Oinsert(x1,v),hAPP(c_Set_Oinsert(u,v),x2)),hAPP(w,hAPP(c_Set_Oinsert(x1,v),x2))))*.
% 299.79/300.46 10855[0:SpR:353.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oinsert(v,w),x,y,z),hAPP(c_Set_Oinsert(x1,w),x2)),hAPP(hAPP(u,hAPP(c_Set_Oinsert(x1,w),x2)),hAPP(c_Set_Oinsert(x1,w),hAPP(c_Set_Oinsert(v,w),x2))))*.
% 299.79/300.46 12811[0:Res:49.2,430.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(v,c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) c_lessequals(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))* -> c_lessequals(v,w,tc_fun(u,tc_bool)).
% 299.79/300.46 12788[0:Res:47.2,430.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)) c_lessequals(v,w,tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))*.
% 299.79/300.46 14787[0:SpL:128.0,70.0] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Ovimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.79/300.46 16594[0:Res:361.2,251.1] class_Complete__Lattice_Ocomplete__lattice(tc_fun(u,v)) class_HOL_Oord(v) || hBOOL(hAPP(hAPP(c_in(w),x),y)) -> c_lessequals(hAPP(hAPP(z,x),x1),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,z,w,tc_fun(u,v)),x1),v)*.
% 299.79/300.46 18183[0:SpR:329.1,362.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) hBOOL(hAPP(hAPP(c_in(x),v),y)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.46 18182[0:SpR:328.1,362.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(x),u),y))* -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.46 18181[0:SpR:538.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.46 18178[0:SpR:599.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),x)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.46 18425[0:Res:545.1,454.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oimage(x,u,tc_Hoare__Mirabelle_Otriple(t_a)),w),y,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oimage(x,u,tc_Hoare__Mirabelle_Otriple(t_a)),w),y),hAPP(x,v),t_a)*.
% 299.79/300.46 18383[0:SpR:329.1,545.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) hBOOL(hAPP(hAPP(c_in(x),v),y)) -> hBOOL(hAPP(hAPP(c_in(z),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,z),y)))*.
% 299.79/300.46 18382[0:SpR:328.1,545.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(x),u),y))* -> hBOOL(hAPP(hAPP(c_in(z),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,z),y)))*.
% 299.79/300.46 18381[0:SpR:538.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),z)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),u,x),w)))*.
% 299.79/300.46 18378[0:SpR:599.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),x)) -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),u,y),x)))*.
% 299.79/300.46 18593[0:Res:153.1,454.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),u),x),y,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),u),x),y),w,t_a)*.
% 299.79/300.46 19351[0:SSi:19307.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(y,v,w,z)* -> c_Fun_Oinj__on(y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),w,z)*.
% 299.79/300.46 19352[0:SSi:19285.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),v,tc_fun(w,tc_bool))*.
% 299.79/300.46 19661[0:Res:149.1,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)))),c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.46 19656[0:Res:1157.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oimage(c_COMBK(v,w,x),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))),hAPP(c_Set_Oimage(c_COMBK(v,w,x),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs)))* c_Hoare__Mirabelle_Otriple__valid(u,v,t_a).
% 299.79/300.46 19700[0:SpL:188.1,19641.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Ovimage(c_COMBK(v,u,w),w,u),x)))* hBOOL(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Ovimage(c_COMBK(v,u,w),w,u),x,t_a).
% 299.79/300.46 19838[0:SpR:104.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w,x,y,z),x1),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,x1,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),hAPP(w,x1)))*.
% 299.79/300.46 19837[0:SpR:104.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))),x,y,z),x1),hAPP(hAPP(u,x1),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,x1,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))))*.
% 299.79/300.46 19829[0:SpR:104.0,584.0] || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),c_HOL_Ouminus__class_Ouminus(z,tc_fun(u,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(z,hAPP(v,c_HOL_Ouminus__class_Ouminus(z,tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))*.
% 299.79/300.46 20360[0:SpR:303.1,438.1] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.46 20347[0:SpR:11177.1,438.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),u),u)**.
% 299.79/300.46 20315[0:SpR:300.1,438.1] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w),x),x)**.
% 299.79/300.46 20311[0:SpR:3586.1,438.1] || equal(hAPP(c_in(u),v),v_Procs) c_Fun_Oinj__on(c_Set_Oinsert(v,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v,u),w,x),v_x),v_x)**.
% 299.79/300.46 20292[0:SpR:9493.1,438.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v,w),u),u)**.
% 299.79/300.46 20290[0:SpR:8498.1,438.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) c_Fun_Oinj__on(c_Set_Oinsert(w,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(w,v),x,y),u),u)**.
% 299.79/300.46 20504[0:SpR:303.1,99.1] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.46 20491[0:SpR:11177.1,99.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),u),u)**.
% 299.79/300.46 20459[0:SpR:300.1,99.1] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w),x),x)**.
% 299.79/300.46 20455[0:SpR:3586.1,99.1] || equal(hAPP(c_in(u),v),v_Procs) c_Fun_Oinj__on(c_Set_Oinsert(v,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v,u),w,x),v_x),v_x)**.
% 299.79/300.46 20435[0:SpR:9493.1,99.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v,w),u),u)**.
% 299.79/300.46 20433[0:SpR:8498.1,99.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) c_Fun_Oinj__on(c_Set_Oinsert(w,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(w,v),x,y),u),u)**.
% 299.79/300.46 20770[0:SpR:188.1,129.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(w,x,tc_fun(u,tc_bool))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Ovimage(c_COMBK(v,u,y),y,u),x),tc_fun(y,tc_bool))*.
% 299.79/300.46 20766[0:SpR:196.1,129.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool))* -> c_lessequals(x,hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool))*.
% 299.79/300.46 21016[0:SpL:317.0,447.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),y)),w)* c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,x),y),x,w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,x),y),x).
% 299.79/300.46 21001[0:SpR:10090.1,317.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),v),x)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),x)))*.
% 299.79/300.46 20994[0:SpR:303.1,317.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),y)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),y)))*.
% 299.79/300.46 20983[0:SpR:11176.1,317.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oinsert(u,w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),y)))*.
% 299.79/300.46 20981[0:SpR:11177.1,317.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),hAPP(c_Set_Oinsert(u,w),y)),hAPP(c_Set_Oinsert(u,x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),y)))*.
% 299.79/300.46 20949[0:SpR:300.1,317.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w),y)))*.
% 299.79/300.46 20945[0:SpR:3586.1,317.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,x),hAPP(c_Set_Oinsert(v_x,w),y)),hAPP(c_Set_Oinsert(v_x,x),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,x),y)))*.
% 299.79/300.46 20924[0:SpR:9493.1,317.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(u,v),x)),hAPP(c_Set_Oinsert(u,w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),x)))*.
% 299.79/300.46 20922[0:SpR:8498.1,317.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(w,v),x,y),hAPP(c_Set_Oinsert(u,x),z)),hAPP(c_Set_Oinsert(u,y),hAPP(c_Set_Oimage(c_Set_Oinsert(w,v),x,y),z)))*.
% 299.79/300.46 20901[0:SpR:317.0,10931.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x),t_a) hBOOL(hAPP(hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(y,w),x)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x))))*.
% 299.79/300.46 20852[0:SpR:317.0,196.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(u,x),w),hAPP(c_Set_Oimage(u,v,w),y))),hAPP(c_Set_Oinsert(x,v),y))**.
% 299.79/300.46 20846[0:SpR:317.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* -> hBOOL(hAPP(hAPP(c_in(y),hAPP(z,v)),hAPP(c_Set_Oinsert(hAPP(z,w),y),hAPP(c_Set_Oimage(z,u,y),x))))*.
% 299.79/300.46 20839[0:SpR:317.0,98.1] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),x),w,y)* -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(hAPP(u,v),y),hAPP(c_Set_Oimage(u,w,y),x)),y),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(v,w),x),w))*.
% 299.79/300.46 21636[0:SpL:21267.0,62.0] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),v_x),tc_fun(w,tc_bool)),w) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),v_x),tc_Com_Opname,x),tc_fun(w,tc_bool)),w)*.
% 299.79/300.46 21573[0:SpL:21267.0,357.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v)* c_lessequals(y,hAPP(c_Set_Oimage(u,v,w),v_x),tc_fun(w,tc_bool))* -> c_Finite__Set_Ofinite(y,w).
% 299.79/300.46 21560[0:SpL:21267.0,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),u))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),tc_Com_Opname,w),t_a)*.
% 299.79/300.46 21464[0:SpR:21267.0,9569.0] || -> c_lessequals(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_Com_Opname,w),x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),x),tc_bool)*.
% 299.79/300.46 21379[0:SpR:21267.0,63.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),v_x),tc_Com_Opname,x),tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),v_x),tc_fun(w,tc_bool)),w).
% 299.79/300.46 21378[0:SpR:21267.0,446.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),v_x),tc_Com_Opname,x),tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,w),u),hAPP(c_Set_Oinsert(v,w),v_x),tc_fun(w,tc_bool)).
% 299.79/300.46 21294[0:SpR:21267.0,446.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),x,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(u,v),v_x),hAPP(c_Set_Oinsert(u,v),x),tc_fun(v,tc_bool)).
% 299.79/300.46 21738[0:Rew:584.0,21381.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),tc_Com_Opname,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),u)*.
% 299.79/300.46 21739[0:Rew:584.0,21380.1] class_Lattices_Olattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),tc_Com_Opname,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),u)*.
% 299.79/300.46 22264[0:SpL:21893.0,62.0] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),v_x),tc_fun(w,tc_bool)),w) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),v_x),c_Set_Oinsert(v,w),tc_Com_Opname,x),tc_fun(w,tc_bool)),w)*.
% 299.79/300.46 22200[0:SpL:21893.0,357.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v)* c_lessequals(y,hAPP(c_Set_Oimage(u,v,w),v_x),tc_fun(w,tc_bool))* -> c_Finite__Set_Ofinite(y,w).
% 299.79/300.46 22187[0:SpL:21893.0,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),u))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,w),t_a)*.
% 299.79/300.46 22090[0:SpR:21893.0,9569.0] || -> c_lessequals(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),x),tc_bool)*.
% 299.79/300.46 22005[0:SpR:21893.0,63.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),v_x),c_Set_Oinsert(v,w),tc_Com_Opname,x),tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),v_x),tc_fun(w,tc_bool)),w).
% 299.79/300.46 22004[0:SpR:21893.0,446.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),v_x),c_Set_Oinsert(v,w),tc_Com_Opname,x),tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,w),u),hAPP(c_Set_Oinsert(v,w),v_x),tc_fun(w,tc_bool)).
% 299.79/300.46 21920[0:SpR:21893.0,446.1] || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),x,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(u,v),v_x),hAPP(c_Set_Oinsert(u,v),x),tc_fun(v,tc_bool)).
% 299.79/300.46 22367[0:Rew:584.0,22007.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),u)*.
% 299.79/300.46 22368[0:Rew:584.0,22006.1] class_Lattices_Olattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),u)*.
% 299.79/300.46 22409[0:SpR:97.1,545.1] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(u,w,x),v)))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(v,u,w,x),y)),v))*.
% 299.79/300.46 22438[0:MRR:22403.1,96.1] || c_Fun_Oinj__on(u,v,w,x) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,w,x),v),c_Fun_Othe__inv__into(v,u,w,x),x,w),w,x),v),hAPP(c_Set_Oimage(u,w,x),v))**.
% 299.79/300.46 22639[0:SpL:158.0,193.1] || c_Finite__Set_Ofinite(u,v) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(w,x,y),hAPP(c_Set_Oimage(z,v,x),u)),y),c_Finite__Set_Ocard(u,v))** -> c_Fun_Oinj__on(c_Fun_Ocomp(w,z,x,y,v),u,v,y)*.
% 299.79/300.46 22624[0:SpR:158.0,196.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z)),hAPP(c_Set_Oimage(x,y,v),z))**.
% 299.79/300.46 22617[0:SpR:158.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* -> hBOOL(hAPP(hAPP(c_in(z),hAPP(x1,v)),hAPP(c_Set_Oimage(c_Fun_Ocomp(x1,w,u,z,x),x,z),y)))*.
% 299.79/300.46 22592[0:SpR:158.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1,x2,x3),x4),hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x4)),hAPP(z,x4)))*.
% 299.79/300.46 22591[0:SpR:158.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1,x2,x3),x4),hAPP(hAPP(u,x4),hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),x4))))*.
% 299.79/300.46 22840[0:SpR:158.0,3294.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(t_a))** -> equal(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 22826[0:SpR:104.0,3294.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_in(t_a)) -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 23040[0:SpL:131.0,156.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_Fun_Ocomp(w,x,y,z,u),u,z),x1)))* -> hBOOL(hAPP(hAPP(c_in(y),hAPP(x,v)),hAPP(c_Set_Ovimage(w,y,z),x1)))*.
% 299.79/300.46 23010[0:SpR:196.1,131.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,x,v,w,y),y,w),hAPP(c_Set_Oimage(u,v,w),z)),hAPP(c_Set_Ovimage(x,y,v),z))**.
% 299.79/300.46 22998[0:SpR:131.0,153.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Ovimage(x,u,y),z)))* -> hBOOL(hAPP(hAPP(c_in(x1),w),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,v,u,y,x1),x1,y),z)))*.
% 299.79/300.46 22994[0:SpR:131.0,188.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y))) -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(w,c_COMBK(v,u,z),u,x,z),z,x),y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))**.
% 299.79/300.46 22975[0:SpR:131.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1,x2,x3),x4),hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x4)),hAPP(z,x4)))*.
% 299.79/300.46 22974[0:SpR:131.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1,x2,x3),x4),hAPP(hAPP(u,x4),hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),x4))))*.
% 299.79/300.46 22937[0:SpR:131.0,3294.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(t_a))** -> equal(hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 23221[0:SpL:131.0,3487.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.46 23220[0:SpL:158.0,3487.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.46 23206[0:SpL:104.0,3487.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.46 23298[0:SpL:131.0,3489.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(tc_Com_Opname))** hBOOL(hAPP(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.79/300.46 23297[0:SpL:158.0,3489.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_in(tc_Com_Opname))** hBOOL(hAPP(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.79/300.46 23283[0:SpL:104.0,3489.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_in(tc_Com_Opname)) hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.79/300.46 23407[0:SpL:460.1,3507.1] || class_Lattices_Olattice(t_b) equal(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.79/300.46 23406[0:SpL:460.1,16327.1] || class_Lattices_Olattice(t_b) equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_Procs) -> .
% 299.79/300.46 23405[0:SpL:460.1,3499.1] || class_Lattices_Olattice(t_b) equal(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.79/300.46 23399[0:SpL:460.1,13272.0] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u)* -> hBOOL(hAPP(u,v_x))*.
% 299.79/300.46 23398[0:SpL:460.1,3484.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(c_Com_Ocom_OBODY,u))* -> equal(v_x,u).
% 299.79/300.46 23389[0:SpR:460.1,20881.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,v),hAPP(c_Set_Oinsert(v_x,u),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))))*.
% 299.79/300.46 23378[0:SpR:460.1,9569.0] || class_Lattices_Olattice(t_b) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)),v_x),tc_bool)*.
% 299.79/300.46 23377[0:SpR:460.1,9568.0] || class_Lattices_Olattice(t_b) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)),v),v_x),tc_bool)*.
% 299.79/300.46 23373[0:SpR:460.1,3346.1] || class_Lattices_Olattice(t_b) equal(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))))*.
% 299.79/300.46 23372[0:SpR:460.1,21126.1] || class_Lattices_Olattice(t_b) equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,v),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))))*.
% 299.79/300.46 23371[0:SpR:460.1,3317.1] || class_Lattices_Olattice(t_b) equal(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(c_Set_Oinsert(v_x,u),v)))*.
% 299.79/300.46 23370[0:SpR:460.1,3305.1] || class_Lattices_Olattice(t_b) equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))))*.
% 299.79/300.46 23366[0:SpR:460.1,2771.1] || class_Lattices_Olattice(t_b) equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.79/300.46 23361[0:SpR:460.1,21131.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))))*.
% 299.79/300.46 23360[0:SpR:460.1,21143.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),t_a,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))))*.
% 299.79/300.46 23357[0:SpR:460.1,15262.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.79/300.46 23354[0:SpR:460.1,8376.2] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_in(tc_Com_Opname)) equal(u,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),u))*.
% 299.79/300.46 23353[0:SpR:460.1,8415.2] || class_Lattices_Olattice(t_b) equal(v_Procs,v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),v_x)**.
% 299.79/300.46 23352[0:SpR:460.1,3291.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),v_Procs))*.
% 299.79/300.46 23351[0:SpR:460.1,3285.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs)))*.
% 299.79/300.46 23348[0:SpR:460.1,3279.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),v_Procs),v_x))*.
% 299.79/300.46 23585[0:SpL:523.1,3507.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),x),y))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(x,v_x)),hAPP(y,v_x)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.79/300.46 23584[0:SpL:523.1,16327.1] class_Lattices_Olattice(u) || equal(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(v,v_Procs) -> .
% 299.79/300.46 23583[0:SpL:523.1,3499.1] class_Lattices_Olattice(u) || equal(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.79/300.46 23577[0:SpL:523.1,13272.0] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.79/300.46 23576[0:SpL:523.1,3484.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),hAPP(c_Com_Ocom_OBODY,x))* -> equal(v_x,x).
% 299.79/300.46 23534[0:SpR:8415.2,523.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(v_x,v_x)),hAPP(v_x,v_x))**.
% 299.79/300.46 23529[0:SpR:8415.2,523.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v_x,v_x)),hAPP(v,v_x)),hAPP(hAPP(v_x,v),v_x))**.
% 299.79/300.46 23520[0:SpR:523.1,20881.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x,y),hAPP(c_Set_Oinsert(v_x,x),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))))*.
% 299.79/300.46 23509[0:SpR:523.1,9569.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w)),v_x),tc_bool)*.
% 299.79/300.46 23508[0:SpR:523.1,9568.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w)),y),v_x),tc_bool)*.
% 299.79/300.46 23504[0:SpR:523.1,3346.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),x),y)) -> hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(x,v_x)),hAPP(y,v_x))))*.
% 299.79/300.46 23503[0:SpR:523.1,21126.1] class_Lattices_Olattice(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x),tc_Com_Opname,y),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x))))*.
% 299.79/300.46 23502[0:SpR:523.1,3317.1] class_Lattices_Olattice(u) || equal(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)),hAPP(c_Set_Oinsert(v_x,v),y)))*.
% 299.79/300.46 23501[0:SpR:523.1,3305.1] class_Lattices_Olattice(u) || equal(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,y),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x))))*.
% 299.79/300.46 23497[0:SpR:523.1,2771.1] class_Lattices_Olattice(u) || equal(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x)) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))*.
% 299.79/300.46 23492[0:SpR:523.1,21131.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_Com_Opname,x),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))))*.
% 299.79/300.46 23491[0:SpR:523.1,21143.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),t_a,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))))*.
% 299.79/300.46 23488[0:SpR:523.1,15262.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.79/300.46 23485[0:SpR:523.1,8376.2] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_in(tc_Com_Opname)) equal(x,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),x))*.
% 299.79/300.46 23484[0:SpR:523.1,8415.2] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),v_x)**.
% 299.79/300.46 23483[0:SpR:523.1,3291.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))),v_Procs))*.
% 299.79/300.46 23482[0:SpR:523.1,3285.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)))*.
% 299.79/300.46 23479[0:SpR:523.1,3279.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),v_Procs),v_x))*.
% 299.79/300.46 24156[0:SpR:542.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),w),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)))*.
% 299.79/300.46 24138[0:SpR:542.0,9569.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_bool)*.
% 299.79/300.46 24137[0:SpR:542.0,9568.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_bool)*.
% 299.79/300.46 24134[0:SpR:542.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v))**.
% 299.79/300.46 24378[0:SpL:393.1,390.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))* -> equal(x,c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(x,c_COMBK(v,w,y),y,w),u,w,y)*.
% 299.79/300.46 24336[0:SpR:393.1,20881.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(w,x,v),v,x),y,z),hAPP(c_Set_Oinsert(u,y),x1)),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))))*.
% 299.79/300.46 24320[0:SpR:393.1,9569.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) c_lessequals(hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),c_Set_Oimage(c_COMBK(w,x,v),v,x)),u),tc_bool)*.
% 299.79/300.46 24319[0:SpR:393.1,9568.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) c_lessequals(hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Oimage(c_COMBK(w,x,v),v,x)),z),u),tc_bool)*.
% 299.79/300.46 24435[0:SpL:353.0,208.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),y)),tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),x),u)) c_lessequals(u,hAPP(c_Set_Oinsert(v,w),y),tc_fun(w,tc_bool)).
% 299.79/300.46 24788[0:SpR:614.2,20881.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,y),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u),x),x1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u)))*.
% 299.79/300.46 24770[0:SpR:614.2,9569.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u)),tc_bool)*.
% 299.79/300.46 24769[0:SpR:614.2,9568.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u))),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u)),tc_bool)*.
% 299.79/300.46 24906[0:SpL:8415.2,467.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x))) -> equal(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),v_x)),v_x)**.
% 299.79/300.46 24899[0:SpL:8415.2,467.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_x,u,v,w),x)),x)**.
% 299.79/300.46 25134[0:Res:252.1,121.0] || c_Natural_Oevaln(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,w,x,y),y,z) -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),x),w),t_a)* c_Natural_Oevaln(c_Com_Ocom_OSemi(x,u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(v,w,x,y),y,z)*.
% 299.79/300.46 25442[0:SpL:512.0,390.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,z,w),x1)),tc_fun(x,tc_bool))* -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(x1,hAPP(c_COMBB(v,w,x,z),y),z,x),u,x,z)*.
% 299.79/300.46 25437[0:SpL:512.0,3507.1] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(hAPP(c_COMBB(w,x,y,z),x1),z,y))* equal(hAPP(c_Set_Oimage(w,x,y),hAPP(c_Set_Oimage(x1,z,x),v_x)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.79/300.46 25436[0:SpL:512.0,16327.1] || equal(u,c_Set_Oimage(hAPP(c_COMBB(v,w,x,y),z),y,x))* equal(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(z,y,w),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_Procs) -> .
% 299.79/300.46 25435[0:SpL:512.0,3499.1] || equal(c_in(u),c_Set_Oimage(hAPP(c_COMBB(v,w,x,y),z),y,x))* hBOOL(hAPP(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(z,y,w),v_x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.79/300.46 25429[0:SpL:512.0,13272.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,y),x),y,w),z)* -> hBOOL(hAPP(z,v_x))*.
% 299.79/300.46 25428[0:SpL:512.0,3484.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_Com_Ocom_OBODY)** equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),hAPP(c_Com_Ocom_OBODY,z))* -> equal(v_x,z).
% 299.79/300.46 25420[0:SpL:512.0,202.1] || c_Finite__Set_Ofinite(u,v) c_lessequals(u,hAPP(c_Set_Oimage(w,x,v),hAPP(c_Set_Oimage(y,v,x),u)),tc_fun(v,tc_bool))* -> c_Fun_Oinj__on(hAPP(c_COMBB(w,x,v,v),y),u,v,v)*.
% 299.79/300.46 25406[0:SpR:8415.2,512.0] || equal(v_Procs,v_x) equal(c_COMBB(u,v,w,x),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(v_x,x,v),y)),hAPP(c_Set_Oimage(v_x,x,w),y))**.
% 299.79/300.46 25377[0:SpR:512.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),x2))))*.
% 299.79/300.46 25361[0:SpR:512.0,9569.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),x2),c_Set_Oimage(hAPP(c_COMBB(u,v,w,y),x),y,w)),z),tc_bool)*.
% 299.79/300.46 25360[0:SpR:512.0,9568.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Set_Oimage(hAPP(c_COMBB(u,v,w,y),x),y,w)),x2),z),tc_bool)*.
% 299.79/300.46 25356[0:SpR:512.0,3346.1] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(hAPP(c_COMBB(w,x,y,z),x1),z,y))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(w,x,y),hAPP(c_Set_Oimage(x1,z,x),v_x))))*.
% 299.79/300.46 25355[0:SpR:512.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(hAPP(c_COMBB(v,w,x,y),z),y,x),tc_Com_Opname,x1),u),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(z,y,w),v_x))))*.
% 299.79/300.46 25354[0:SpR:512.0,3317.1] || equal(c_in(u),c_Set_Oimage(hAPP(c_COMBB(v,w,x,y),z),y,x))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(z,y,w),v_x)),hAPP(c_Set_Oinsert(v_x,u),x1)))*.
% 299.79/300.46 25353[0:SpR:512.0,3305.1] || equal(u,c_Set_Oimage(hAPP(c_COMBB(v,w,x,y),z),y,x))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x1),v_Procs),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(z,y,w),v_x))))*.
% 299.79/300.46 25349[0:SpR:512.0,2771.1] || equal(u,c_Set_Oimage(hAPP(c_COMBB(v,w,x,y),z),y,x))* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(z,y,w),v_x)),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.79/300.46 25343[0:SpR:512.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),tc_Com_Opname,z),hAPP(c_Set_Oinsert(x1,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x))))*.
% 299.79/300.46 25342[0:SpR:512.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),t_a,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x))))*.
% 299.79/300.46 25339[0:SpR:512.0,15262.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.79/300.46 25336[0:SpR:512.0,8376.2] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_in(tc_Com_Opname))** equal(z,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),z))*.
% 299.79/300.46 25335[0:SpR:512.0,8415.2] || equal(v_Procs,v_x) equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),v_x)**.
% 299.79/300.46 25334[0:SpR:512.0,3291.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x))),v_Procs))*.
% 299.79/300.46 25333[0:SpR:512.0,3285.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),hAPP(c_Set_Oinsert(z,tc_Com_Opname),v_Procs)))*.
% 299.79/300.46 25329[0:SpR:512.0,3279.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),v_Procs),v_x))*.
% 299.79/300.46 25716[0:Res:153.1,455.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),u),x),t_a)* c_Hoare__Mirabelle_Otriple__valid(z,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(y,z),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(z,w,t_a)*.
% 299.79/300.46 25715[0:Res:545.1,455.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Hoare__Mirabelle_Ohoare__valids(x,hAPP(c_Set_Oimage(y,u,tc_Hoare__Mirabelle_Otriple(t_a)),w),t_a)* c_Hoare__Mirabelle_Otriple__valid(z,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(x,z),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(z,hAPP(y,v),t_a)*.
% 299.79/300.46 25973[0:SpL:339.0,3698.2] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x)))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.46 25967[0:SpL:339.0,3493.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_in(tc_Com_Opname)) equal(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> .
% 299.79/300.46 25895[0:SpR:339.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z))))*.
% 299.79/300.46 25863[0:SpR:339.0,3339.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x))) -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),y,z),u)**.
% 299.79/300.46 25862[0:SpR:339.0,3316.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x))) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.79/300.46 25859[0:SpR:339.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),x)),tc_Com_Opname,u),v_Procs)))*.
% 299.79/300.46 25851[0:SpR:339.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),t_a,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.46 25849[0:SpR:339.0,11030.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.79/300.46 25848[0:SpR:339.0,10090.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.46 25842[0:SpR:339.0,3284.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.46 25837[2:SpR:339.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool))*.
% 299.79/300.46 25835[0:SpR:339.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),tc_fun(t_a,tc_bool)),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool))*.
% 299.79/300.46 25832[0:SpR:339.0,651.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),tc_Com_Opname,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.46 25829[0:SpR:339.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x,y),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_Procs))))*.
% 299.79/300.46 26202[0:SpR:542.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x))),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))**.
% 299.79/300.46 26298[0:Rew:26297.1,25898.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y)* -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z)),z)**.
% 299.79/300.46 26526[0:Res:84.1,325.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool))* -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y),tc_fun(u,tc_bool)).
% 299.79/300.46 26525[0:Res:84.1,324.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool))* -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y),tc_fun(u,tc_bool)).
% 299.79/300.46 26521[0:Res:84.1,430.0] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),y,tc_fun(w,tc_bool))* -> c_lessequals(u,y,tc_fun(w,tc_bool))*.
% 299.79/300.46 26499[0:SpR:542.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),tc_fun(w,tc_bool))* -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),tc_fun(w,tc_bool)).
% 299.79/300.46 26549[0:SSi:26541.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* c_lessequals(y,u,tc_fun(w,tc_bool))* -> c_lessequals(y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),tc_fun(w,tc_bool))*.
% 299.79/300.46 26868[0:SpL:56.1,148.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(u),x),c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(u),x),hAPP(c_Set_Oinsert(v,u),y)))*.
% 299.79/300.46 26879[0:Rew:56.1,26851.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,u),v_x),c_Set_Oinsert(v,u),tc_Com_Opname,x),w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v_x,w,tc_fun(u,tc_bool)))**.
% 299.79/300.46 26880[0:Rew:56.1,26850.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v,u),v_x),tc_Com_Opname,x),w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v_x,w,tc_fun(u,tc_bool)))**.
% 299.79/300.46 26950[0:Res:424.2,430.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(x,w,tc_fun(u,tc_bool))* c_lessequals(w,y,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,u),x),y,tc_fun(u,tc_bool))*.
% 299.79/300.46 26970[0:SSi:26964.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(x,w,tc_fun(u,tc_bool))* c_lessequals(y,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool))* -> c_lessequals(y,w,tc_fun(u,tc_bool))*.
% 299.79/300.46 27019[0:Rew:9.0,26996.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),hAPP(c_Set_Ovimage(y,x,z),hAPP(c_Set_Oinsert(x1,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))))))* -> equal(hAPP(y,hAPP(w,v)),x1).
% 299.79/300.46 27120[0:Res:687.1,280.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(w,v),x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,v_Procs,hAPP(c_in(u),v),tc_Com_Opname),w,u,tc_fun(z,tc_bool)),x))*.
% 299.79/300.46 27119[0:Res:686.1,280.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(w,v),x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,y,hAPP(c_in(u),v),tc_Com_Opname),w,u,tc_fun(z,tc_bool)),x))*.
% 299.79/300.46 27117[0:Res:171.2,280.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(hAPP(w,c_Finite__Set_Olinorder__class_OMin(v,u)),x)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,u,tc_fun(y,tc_bool)),x))*.
% 299.79/300.46 27116[0:Res:172.2,280.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(hAPP(w,c_Finite__Set_Olinorder__class_OMax(v,u)),x)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,u,tc_fun(y,tc_bool)),x))*.
% 299.79/300.46 27092[0:Res:153.1,280.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* hBOOL(hAPP(hAPP(y,w),z))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Ovimage(v,x1,u),x),y,x1,tc_fun(x2,tc_bool)),z))*.
% 299.79/300.46 27091[0:Res:545.1,280.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(x,hAPP(y,v)),z))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(y,u,x1),w),x,x1,tc_fun(x2,tc_bool)),z))*.
% 299.79/300.46 27084[0:Res:510.1,280.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(x,v),y))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z),x,u,tc_fun(x1,tc_bool)),y))*.
% 299.79/300.46 27083[0:Res:511.1,280.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(x,v),y))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),w),x,u,tc_fun(x1,tc_bool)),y))*.
% 299.79/300.46 27174[0:SpR:540.1,450.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x)))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Lattices_Oupper__semilattice__class_Osup(u)),w),v),t_a).
% 299.79/300.46 27173[0:SpR:539.1,450.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x)))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Lattices_Oupper__semilattice__class_Osup(u)),w),v),t_a).
% 299.79/300.46 27158[0:SpR:9936.1,450.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x))) c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),w),v),t_a)*.
% 299.79/300.46 27633[0:SpR:9925.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),v)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u,x),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.46 27614[0:SpR:24020.1,373.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(hAPP(u,v_x),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(u,v_x),v,x),v_x),v_x)**.
% 299.79/300.46 27606[0:SpR:9924.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),w,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,x),c_Orderings_Otop__class_Otop(tc_bool)),v)*.
% 299.79/300.46 27569[0:SpR:525.1,373.2] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),w),w)**.
% 299.79/300.46 27537[0:SpR:2097.1,373.2] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),u),x)) c_Fun_Oinj__on(c_Set_Oinsert(v,y),x,w,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,c_Set_Oinsert(v,y),w,z),u),u)**.
% 299.79/300.46 27518[0:SpR:373.2,415.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(c_Fun_Ofun__upd(c_Hilbert__Choice_Oinv__into(w,x,u,y),hAPP(x,v),v,z,x1),c_Hilbert__Choice_Oinv__into(w,x,u,y))**.
% 299.79/300.46 27786[0:SpR:9925.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),v)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),v,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u,x),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.46 27767[0:SpR:24020.1,71.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(hAPP(u,v_x),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(u,v_x),v,x),v_x),v_x)**.
% 299.79/300.46 27759[0:SpR:9924.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),w,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,x),c_Orderings_Otop__class_Otop(tc_bool)),v)*.
% 299.79/300.46 27722[0:SpR:525.1,71.2] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),w),w)**.
% 299.79/300.46 27689[0:SpR:2097.1,71.2] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),u),x)) c_Fun_Oinj__on(c_Set_Oinsert(v,y),x,w,z) -> equal(hAPP(c_Fun_Othe__inv__into(x,c_Set_Oinsert(v,y),w,z),u),u)**.
% 299.79/300.46 27669[0:SpR:71.2,415.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(c_Fun_Ofun__upd(c_Fun_Othe__inv__into(w,x,u,y),hAPP(x,v),v,z,x1),c_Fun_Othe__inv__into(w,x,u,y))**.
% 299.79/300.46 27855[7:SpR:339.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),tc_fun(t_a,tc_bool)),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool))*.
% 299.79/300.46 27925[0:Res:468.0,255.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(c_Set_Oimage(x,w,y),u),hAPP(c_Set_Oimage(z,w,y),u)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,x,z,w,y)),v))*.
% 299.79/300.46 28002[0:SpR:339.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.46 28235[0:SpL:465.1,3698.2] || equal(u,c_Set_Oimage(c_Fun_Ofun__upd(v,w,x,y,z),y,z))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(c_Set_Oimage(v,y,z),v_x),c_Com_Ocom_OSKIP) -> hBOOL(hAPP(hAPP(c_in(y),w),v_x)).
% 299.79/300.46 28229[0:SpL:465.1,3493.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_in(tc_Com_Opname))** equal(hAPP(c_Set_Oimage(u,x,y),v_x),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)).
% 299.79/300.46 28190[0:SpR:465.1,7253.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1,x2),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),hAPP(c_Set_Oimage(x,u,z),w)))*.
% 299.79/300.46 28167[0:SpR:465.1,3339.1] || equal(u,c_Set_Oimage(c_Fun_Ofun__upd(v,w,x,y,z),y,z))* -> hBOOL(hAPP(hAPP(c_in(y),w),v_x)) equal(c_Fun_Ofun__upd(u,v_x,hAPP(c_Set_Oimage(v,y,z),v_x),x1,x2),u)**.
% 299.79/300.46 28166[0:SpR:465.1,3316.1] || equal(c_in(u),c_Set_Oimage(c_Fun_Ofun__upd(v,w,x,y,z),y,z))* -> hBOOL(hAPP(hAPP(c_in(y),w),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(v,y,z),v_x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.79/300.46 28163[0:SpR:465.1,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Set_Oimage(x,u,y),v_x)),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(x,v,z,u,y),u,y),tc_Com_Opname,w),v_Procs)))*.
% 299.79/300.46 28157[0:SpR:465.1,27381.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,u,x),v_x),c_Set_Oimage(c_Fun_Ofun__upd(w,v,y,u,x),u,x),tc_Com_Opname,z)),v_Procs))*.
% 299.79/300.46 28153[0:SpR:465.1,21141.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),t_a,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),hAPP(c_Set_Oimage(w,u,y),v_x)))*.
% 299.79/300.46 28151[0:SpR:465.1,11030.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(u,x,y),v_x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))*.
% 299.79/300.46 28150[0:SpR:465.1,10090.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) equal(hAPP(hAPP(c_Set_Oimage(u,x,y),v_x),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.46 28144[0:SpR:465.1,3284.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(c_in(z),v_Procs),hAPP(c_Set_Oimage(u,x,y),v_x)))*.
% 299.79/300.46 28139[2:SpR:465.1,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,x,y),v_x),tc_bool)).
% 299.79/300.46 28137[0:SpR:465.1,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,x,y),v_x),tc_bool)).
% 299.79/300.46 28136[7:SpR:465.1,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,x,y),v_x),tc_bool)).
% 299.79/300.46 28133[0:SpR:465.1,651.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_lessequals(hAPP(c_Set_Oimage(w,u,x),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(w,v,y,u,x),u,x),tc_Com_Opname,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.46 28120[0:SpR:465.1,21130.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_Procs)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),z,x1),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_Set_Oimage(w,u,y),v_Procs)))*.
% 299.79/300.46 28255[0:Rew:9.0,28254.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Fun_Ocomp(c_Fun_Ocomp(z,x1,x2,x,x3),x4,x3,x,y))* -> equal(hAPP(u,hAPP(v,x5)),hAPP(z,hAPP(x1,hAPP(x4,x5))))*.
% 299.79/300.46 28256[0:Rew:9.0,28253.1] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Fun_Ocomp(z,c_Fun_Ocomp(x1,x2,x3,x4,y),x4,x,y))* -> equal(hAPP(u,hAPP(v,x5)),hAPP(z,hAPP(x1,hAPP(x2,x5))))*.
% 299.79/300.46 28305[0:SpR:339.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.46 28295[0:SpR:465.1,27441.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),hAPP(c_Set_Oimage(w,u,y),v_x),tc_Com_Opname,z)),v_Procs))*.
% 299.79/300.46 28563[0:SpR:21893.0,118.0] || -> equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,w,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,x),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,z,x1,y),w,hAPP(u,v_x),y,x1))*.
% 299.79/300.46 28562[0:SpR:21267.0,118.0] || -> equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,x),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,z,x1,y),w,hAPP(u,v_x),y,x1))*.
% 299.79/300.46 28525[0:SpR:24020.1,118.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(c_Fun_Ocomp(hAPP(u,v_x),c_Fun_Ofun__upd(v,w,v_x,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(u,v_x),v,y,z,x),w,v_x,x,z))*.
% 299.79/300.46 28517[0:SpR:9924.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_Fun_Ofun__upd(u,v,w,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,y,z,x),v,c_Orderings_Otop__class_Otop(tc_bool),x,z))*.
% 299.79/300.46 28479[0:SpR:525.1,118.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Fun_Ofun__upd(w,x,v,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,z,x1,y),x,v,y,x1))*.
% 299.79/300.46 28445[0:SpR:2097.1,118.0] || hBOOL(hAPP(u,v)) -> equal(c_Fun_Ocomp(c_Set_Oinsert(v,w),c_Fun_Ofun__upd(x,y,u,z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v,w),x,x1,x2,z),y,u,z,x2))*.
% 299.79/300.46 28764[0:SpR:339.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.46 28754[0:SpR:465.1,28031.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,u,x),v_x),c_Set_Oimage(c_Fun_Ofun__upd(w,v,y,u,x),u,x),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.46 28919[0:SpR:339.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.46 28909[0:SpR:465.1,28334.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),hAPP(c_Set_Oimage(w,u,y),v_x),tc_Com_Opname,z),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.46 29164[0:SpL:537.1,16217.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> .
% 299.79/300.46 29163[0:SpL:537.1,3929.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.79/300.46 29052[0:SpR:537.1,9567.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,tc_fun(y,tc_bool)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)),tc_bool)*.
% 299.79/300.46 29030[0:SpR:537.1,5875.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),z,x1,x2),x))*.
% 299.79/300.46 29011[0:SpR:537.1,683.1] class_Lattices_Olattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),tc_Com_Opname,v),v)*.
% 299.79/300.46 29010[0:SpR:537.1,23902.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.46 29268[0:SSi:29192.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),v,z)* -> c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v,z).
% 299.79/300.46 29269[0:SSi:29048.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) c_Finite__Set_Ofinite(x,u) -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),u)*.
% 299.79/300.46 29403[7:SpR:27278.1,317.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,x),hAPP(c_Set_Oinsert(v_x,w),y)),hAPP(c_Set_Oinsert(v_x,x),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,x),y)))*.
% 299.79/300.46 29402[7:SpR:27278.1,99.1] || equal(hAPP(c_in(u),v),v_x) c_Fun_Oinj__on(c_Set_Oinsert(v,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v,u),w,x),v_x),v_x)**.
% 299.79/300.46 29401[7:SpR:27278.1,438.1] || equal(hAPP(c_in(u),v),v_x) c_Fun_Oinj__on(c_Set_Oinsert(v,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v,u),w,x),v_x),v_x)**.
% 299.79/300.46 29689[0:SpL:534.1,16217.0] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> .
% 299.79/300.46 29688[0:SpL:534.1,3929.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.79/300.46 29575[0:SpR:534.1,9567.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,tc_fun(y,tc_bool)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)),tc_bool)*.
% 299.79/300.46 29552[0:SpR:534.1,5875.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),z,x1,x2),x))*.
% 299.79/300.46 29533[0:SpR:534.1,683.1] class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),tc_Com_Opname,v),v)*.
% 299.79/300.46 29532[0:SpR:534.1,23902.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.46 29773[0:Obv:29584.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,u) c_lessequals(y,x,u) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),x,u)*.
% 299.79/300.46 30099[0:SpR:536.1,9567.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z)),tc_bool)*.
% 299.79/300.46 30076[0:SpR:536.1,5875.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))*.
% 299.79/300.46 30075[0:SpR:536.1,415.0] class_Lattices_Olattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)),y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.79/300.46 30443[0:SSi:30313.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),v,z)* -> c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y),v,z).
% 299.79/300.46 30444[0:SSi:30095.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v) -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),x)),v)*.
% 299.79/300.46 30655[0:SpR:535.1,9567.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z)),tc_bool)*.
% 299.79/300.46 30632[0:SpR:535.1,5875.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))*.
% 299.79/300.46 30631[0:SpR:535.1,415.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)),y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))**.
% 299.79/300.46 30994[0:Obv:30666.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y),w,u) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)),w,u)*.
% 299.79/300.46 31266[0:Res:176.0,356.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(c_Set_Ovimage(x,w,y),hAPP(c_Set_Oinsert(hAPP(x,z),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.79/300.46 31364[0:Res:23961.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs)))* c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.79/300.46 31377[0:SpL:302.1,449.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,x)))* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),t_a)*.
% 299.79/300.46 31480[0:SpL:523.1,24254.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.79/300.46 31479[0:SpL:460.1,24254.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.79/300.46 31544[0:Res:168.0,473.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x),t_a) hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x)))),x))*.
% 299.79/300.46 31825[7:SpL:537.1,31778.0] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> .
% 299.79/300.46 31824[7:SpL:534.1,31778.0] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> .
% 299.79/300.46 31972[0:SpR:383.1,3339.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),z) -> equal(v_x,v) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v_x,hAPP(z,v_x),x,y),v,w,x,y),c_Fun_Ofun__upd(u,v,w,x,y))**.
% 299.79/300.46 32131[0:SpR:3294.1,340.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_lessequals(v_x,v,tc_fun(u,tc_bool)) c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v,tc_fun(u,tc_bool))* -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),v,tc_fun(u,tc_bool)).
% 299.79/300.46 32126[0:SpR:584.0,340.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(hAPP(x,u),v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,y,z,x1),u),v,tc_fun(w,tc_bool))*.
% 299.79/300.46 32372[0:Res:8366.1,477.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(tc_Com_Opname),v_x),u),v_Procs)** hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),x))*.
% 299.79/300.46 32552[0:Res:8366.1,476.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(tc_Com_Opname),v_x),u),v_Procs)** hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),x))*.
% 299.79/300.46 32504[0:SpL:3294.1,476.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Orderings_Obot__class_Obot(tc_bool),v,u)))* hBOOL(hAPP(hAPP(c_in(u),w),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))))* -> hBOOL(hAPP(v,w))*.
% 299.79/300.46 32499[0:SpL:584.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),x1),u,v)))* hBOOL(hAPP(hAPP(c_in(v),x2),hAPP(w,x1)))* -> hBOOL(hAPP(u,x2))*.
% 299.79/300.46 32490[0:SpL:600.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,v)))* hBOOL(hAPP(hAPP(c_in(v),y),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool))))* -> hBOOL(hAPP(u,y))*.
% 299.79/300.46 32632[0:SpR:523.1,31533.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)))),v_Procs))*.
% 299.79/300.46 32631[0:SpR:460.1,31533.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))),v_Procs))*.
% 299.79/300.46 33002[0:SpR:23840.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) -> equal(hAPP(c_Set_Oinsert(w,x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u,x),v)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u,x),v))**.
% 299.79/300.46 32949[0:SpR:10463.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),u,x),w)),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),u,x),w))**.
% 299.79/300.46 32948[0:SpR:9911.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),u,x),w)),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),u,x),w))**.
% 299.79/300.46 32894[0:SpR:97.1,475.1] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(u,w,x),v)))* -> equal(hAPP(c_Set_Oinsert(hAPP(c_Fun_Othe__inv__into(v,u,w,x),y),w),v),v)**.
% 299.79/300.46 32868[0:SpR:475.1,474.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(y,v),z),x1,x),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.79/300.46 32848[0:SpR:475.1,9566.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oimage(x,u,y),w),hAPP(hAPP(c_Set_Oinsert(z,x1),c_Set_Oinsert(hAPP(x,v),y)),hAPP(c_Set_Oimage(x,u,y),w)),tc_bool)*.
% 299.79/300.46 33288[0:SpR:523.1,32668.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.46 33287[0:SpR:460.1,32668.0] || class_Lattices_Olattice(t_b) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.46 33408[0:Res:149.1,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),w),v))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,x)),u))* c_Hoare__Mirabelle_Otriple__valid(x,w,t_a)*.
% 299.79/300.46 33389[0:SpL:3229.1,453.0] || equal(u,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v))* hBOOL(hAPP(u,v_x))* c_Hoare__Mirabelle_Ohoare__valids(w,v_x,t_a) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x)),w))* c_Hoare__Mirabelle_Otriple__valid(x,v,t_a)*.
% 299.79/300.46 33384[0:SpL:3229.1,453.0] || equal(u,c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(hAPP(u,v_x),v))* c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x)),w))* c_Hoare__Mirabelle_Otriple__valid(x,v_x,t_a).
% 299.79/300.46 33517[0:SpL:61.1,521.0] || c_Finite__Set_Ofinite(u,v) equal(c_Suc(w),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(x,v),u),v))* -> equal(w,c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v))*.
% 299.79/300.46 33574[0:SpR:523.1,28704.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x),tc_Com_Opname,y)))*.
% 299.79/300.46 33573[0:SpR:460.1,28704.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,v)))*.
% 299.79/300.46 33665[0:SpR:523.1,28859.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)),tc_Com_Opname,y)))*.
% 299.79/300.46 33664[0:SpR:460.1,28859.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_Com_Opname,v)))*.
% 299.79/300.46 33756[7:SpL:523.1,31886.1] class_Lattices_Olattice(u) || equal(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(v,v_x) -> .
% 299.79/300.46 33755[7:SpL:460.1,31886.1] || class_Lattices_Olattice(t_b) equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_x) -> .
% 299.79/300.46 34387[0:SpL:24914.0,332.0] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),u) -> c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),u)*.
% 299.79/300.46 34361[0:SpL:24914.0,3863.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) -> hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x))))*.
% 299.79/300.46 34300[0:SpL:24914.0,156.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(v,u,w),x))) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x)))),x))*.
% 299.79/300.46 34162[0:SpR:24914.0,584.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,z),hAPP(u,v_x))),hAPP(hAPP(u,v_x),hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,z),hAPP(u,v_x)))))**.
% 299.79/300.46 34160[0:SpR:24914.0,584.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,z),hAPP(v,v_x))),hAPP(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,z),hAPP(v,v_x))),hAPP(v,v_x)))**.
% 299.79/300.46 34074[0:SpR:24914.0,153.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(w),tc_Com_Opname,x),hAPP(c_in(w),v_x)))),y))* -> hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Ovimage(v,w,u),y))).
% 299.79/300.46 34523[0:Rew:24914.0,34299.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oinsert(v,u),w)))* -> hBOOL(hAPP(hAPP(c_in(u),v_x),w)) equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,x),hAPP(c_in(u),v_x)),v)*.
% 299.79/300.46 34664[0:SpL:55.1,7600.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(w,v),x),y,tc_fun(v,tc_bool))),v)* -> hBOOL(hAPP(hAPP(c_in(v),w),y)) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)),v).
% 299.79/300.46 34661[0:SpL:55.1,360.0] || c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,w),x),y,tc_fun(w,tc_bool)),w,z)* -> hBOOL(hAPP(hAPP(c_in(w),v),y)) c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),w,z).
% 299.79/300.46 34656[0:SpL:55.1,4382.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(v),u),x)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),v_x)) equal(u,v_x).
% 299.79/300.46 34585[0:SpR:55.1,19436.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),w),v)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(w,tc_Com_Opname),u),v,tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.79/300.46 34584[0:SpR:55.1,7460.1] || c_lessequals(v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),w),v)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(w,tc_Com_Opname),u),v,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.79/300.46 34795[7:SpL:55.1,27282.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)),v_x)** -> hBOOL(hAPP(hAPP(c_in(v),u),x)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),v_x)) equal(u,v_x).
% 299.79/300.46 34883[0:SpR:523.1,28053.1] class_Lattices_Olattice(u) || equal(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)),v,tc_Com_Opname,y)))*.
% 299.79/300.46 34882[0:SpR:460.1,28053.1] || class_Lattices_Olattice(t_b) equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),u,tc_Com_Opname,v)))*.
% 299.79/300.46 34962[0:SpR:523.1,28356.1] class_Lattices_Olattice(u) || equal(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)),tc_Com_Opname,y)))*.
% 299.79/300.46 34961[0:SpR:460.1,28356.1] || class_Lattices_Olattice(t_b) equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_Com_Opname,v)))*.
% 299.79/300.46 35437[0:SpL:410.0,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),y,w,tc_fun(z,tc_bool)),u,z)))* hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(y,v)))* -> hBOOL(hAPP(u,x1))*.
% 299.79/300.46 35364[0:SpR:23912.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(x,tc_bool))))*.
% 299.79/300.46 35335[0:SpR:351.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_COMBK(x,y,z),v,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBK(x,y,z),v,tc_fun(x1,tc_bool))))*.
% 299.79/300.46 35310[0:SpR:3229.1,410.0] || equal(u,v) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,w),x),v,w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(u,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,w,tc_fun(y,tc_bool))))*.
% 299.79/300.46 35274[0:SpR:27043.1,410.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,v_Procs)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,v,w,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,v,w,tc_fun(u,tc_bool)))**.
% 299.79/300.46 35261[0:SpR:3229.1,410.0] || equal(u,c_Set_Oinsert(v,w)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(u,v_x),x,w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,x,w,tc_fun(y,tc_bool))))*.
% 299.79/300.46 35256[0:SpR:369.0,410.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),y),v,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),y),v,x,tc_fun(u,tc_bool)))**.
% 299.79/300.46 35215[0:SpR:410.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),y,w,tc_fun(z,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x1,u),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.79/300.46 35441[0:SSi:35249.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(t_a,tc_bool)),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(x,u),v_x)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(t_a,tc_bool)),v_x)))*.
% 299.79/300.46 35513[0:SpR:3229.1,113.0] || equal(u,c_Set_Ovimage(v,w,x)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),c_HOL_Ominus__class_Ominus(v_x,y,tc_fun(x,tc_bool))))*.
% 299.79/300.46 35498[0:SpR:3229.1,113.0] || equal(u,c_Set_Ovimage(v,w,x)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(v,w,x),y),hAPP(u,v_x),tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),c_HOL_Ominus__class_Ominus(y,v_x,tc_fun(x,tc_bool))))*.
% 299.79/300.46 35543[0:SSi:35492.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Ovimage(u,t_a,v),w),v_x),hAPP(hAPP(c_Set_Ovimage(u,t_a,v),x),v_x),tc_bool),hAPP(hAPP(c_Set_Ovimage(u,t_a,v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool))),v_x))**.
% 299.79/300.46 35636[0:SpR:3229.1,89.0] || equal(u,c_Set_Oimage(v,w,x)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,hAPP(c_COMBB(y,x,tc_fun(z,tc_bool),w),v),w,tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(u,v_x),y,x,tc_fun(z,tc_bool)))*.
% 299.79/300.46 35626[0:SpR:3229.1,89.0] || equal(u,c_COMBB(v,w,tc_fun(x,tc_bool),y)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(u,v_x),y,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v_x,y,w),z),v,w,tc_fun(x,tc_bool)))*.
% 299.79/300.46 35906[0:Rew:97.1,35903.1] || c_Fun_Oinj__on(u,v,w,x) -> hBOOL(hAPP(hAPP(c_in(w),y),v)) c_Fun_Oinj__on(c_Fun_Ofun__upd(c_Fun_Othe__inv__into(v,u,w,x),z,y,x,w),hAPP(c_Set_Oimage(u,w,x),v),x,w)*.
% 299.79/300.46 36776[0:SpL:67.0,103.1] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,v),u),tc_fun(v,tc_bool)),v)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v)*.
% 299.79/300.46 36731[0:SpR:67.0,114.1] || c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)),x,y)* -> c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),z),tc_fun(x,tc_bool)),x,y)*.
% 299.79/300.46 36894[0:SpL:66.0,147.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(w,u),y),tc_fun(u,tc_bool))))* -> .
% 299.79/300.46 37014[0:SSi:37004.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z,x1,x2,x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))),tc_fun(y,tc_bool))*.
% 299.79/300.46 37187[0:SSi:37174.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,v)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z,x1,x2,x3),hAPP(c_Set_Oimage(y,u,x),w))))*.
% 299.79/300.46 38223[0:Res:13.2,18625.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,y,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool)),z),hAPP(c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),z),tc_bool)*.
% 299.79/300.46 38217[0:SpR:10.0,13.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)) c_lessequals(w,x,tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(x,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.46 38339[0:SSi:38321.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),u),v))* c_Finite__Set_Ofinite(v,tc_bool) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,v,tc_bool,tc_bool),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.46 38423[7:MRR:38409.3,27297.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) equal(hAPP(c_Set_Oimage(v,u,w),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),hAPP(c_Set_Oimage(v,u,w),v_x))** c_Fun_Oinj__on(v,c_Orderings_Obot__class_Obot(tc_bool),u,w) -> .
% 299.79/300.46 38671[0:Res:8376.2,184.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Oimage(v,w,u),x),v_Procs) c_Fun_Oinj__on(v,x,w,u) -> equal(hAPP(v,hAPP(c_Fun_Othe__inv__into(x,v,w,u),v_x)),v_x)**.
% 299.79/300.46 38999[0:SpL:354.2,357.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,v,w,y)* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x,w,y),u),y)* c_lessequals(z,u,tc_fun(w,tc_bool))* -> c_Finite__Set_Ofinite(z,w).
% 299.79/300.46 38968[0:SpR:354.2,7253.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),u))*.
% 299.79/300.46 38943[0:SpR:354.2,21126.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,tc_Com_Opname) equal(hAPP(c_Set_Oimage(x,w,tc_Com_Opname),u),v_Procs) -> hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v,x,w,tc_Com_Opname),v_x)))*.
% 299.79/300.46 39254[0:SpR:3229.1,533.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(u,v_x),w)),x),hAPP(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))**.
% 299.79/300.46 39111[2:SpR:533.0,4250.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Com_Ocom_OBODY) -> c_Com_OWT(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))*.
% 299.79/300.46 39100[0:SpR:533.0,3282.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))*.
% 299.79/300.46 39099[7:SpR:533.0,27207.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))*.
% 299.79/300.46 39795[0:SpR:3229.1,532.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(u,v_x),x)),hAPP(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))*.
% 299.79/300.46 40193[0:Res:399.1,437.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),v),w)* -> c_Finite__Set_Ofinite(hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),u),w)*.
% 299.79/300.46 40460[0:Res:1012.1,529.0] || hBOOL(hAPP(v_G,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v))),w)))* -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(c_Suc(v_na)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),hAPP(c_Com_Ocom_OBODY,v)),w),t_a).
% 299.79/300.46 40707[0:Res:530.1,522.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(c_Suc(u)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),y),v) -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),v)*.
% 299.79/300.46 40932[0:Res:168.0,479.1] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,w)))* -> c_Hoare__Mirabelle_Ohoare__valids(v,w,t_a) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,x,u,tc_Hoare__Mirabelle_Otriple(t_a))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),x)))*.
% 299.79/300.46 40902[0:Res:3284.1,479.1] || equal(c_in(tc_Com_Opname),u) hBOOL(hAPP(v,v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(u,v_x),x,v,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(u,v_x)),x)))*.
% 299.79/300.46 41213[0:Res:168.0,478.1] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,w)))* -> c_Hoare__Mirabelle_Ohoare__valids(v,w,t_a) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,w,u,tc_Hoare__Mirabelle_Otriple(t_a))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),x),w)))*.
% 299.79/300.46 41183[0:Res:3284.1,478.1] || equal(c_in(tc_Com_Opname),u) hBOOL(hAPP(v,v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(u,v_x),v,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(u,v_x))))*.
% 299.79/300.46 41395[0:SpL:584.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(c_COMBS(c_in(x),y,z,x1,x2),v))* -> hBOOL(hAPP(hAPP(c_in(x),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool))))*.
% 299.79/300.46 41338[0:SpL:23912.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),y),v)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,tc_fun(x,tc_bool))))*.
% 299.79/300.46 41305[0:SpL:351.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),z)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBK(z,x1,x2),u,tc_fun(x,tc_bool))))*.
% 299.79/300.46 41303[0:SpL:456.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(v,w)),x))* hBOOL(hAPP(hAPP(c_in(y),z),v))* -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Option_Othe(w),u,tc_fun(y,tc_bool))))*.
% 299.79/300.46 41482[4:SpR:537.1,38236.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_Com_Opname,tc_bool))*.
% 299.79/300.46 41481[4:SpR:534.1,38236.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_Com_Opname,tc_bool))*.
% 299.79/300.46 41745[0:Res:1012.1,494.1] || hBOOL(hAPP(v_G,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v),w)))* hBOOL(hAPP(hAPP(u,x),y))* c_Natural_Oevaln(v,y,c_Suc(v_na),z)* -> hBOOL(hAPP(hAPP(w,x),z))*.
% 299.79/300.46 41735[0:SpL:24020.1,494.1] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,v_x,t_a) c_Natural_Oevaln(v_x,w,x,y)* -> hBOOL(hAPP(hAPP(v_x,v),y))*.
% 299.79/300.46 41724[0:SpL:24020.1,494.1] || equal(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(v_x,u),v))* c_Hoare__Mirabelle_Otriple__valid(w,hAPP(v_x,x),t_a)* c_Natural_Oevaln(v_x,v,w,y)* -> hBOOL(hAPP(hAPP(x,u),y))*.
% 299.79/300.46 41748[0:Rew:10463.0,41736.4] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),c_in(t_a)) hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,c_Orderings_Obot__class_Obot(tc_bool),t_a)* c_Natural_Oevaln(v_x,w,x,y)* -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),y))*.
% 299.79/300.46 41995[0:Res:82.0,437.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),w) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),w)*.
% 299.79/300.46 42093[0:SpR:180.2,88.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) || c_Finite__Set_Ofinite(v,u) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u),u),u),v),u,u),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.46 42086[0:SpR:180.2,7253.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),z,hAPP(c_Set_Oinsert(w,u),v),u,u)))*.
% 299.79/300.46 42212[0:Obv:42163.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u),y,u)* -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u),y,u).
% 299.79/300.46 42213[0:Obv:42098.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u),u) -> c_lessequals(w,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(y,u),v),u,u),u)*.
% 299.79/300.46 42214[0:Obv:42052.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u),u),v),u,u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u))**.
% 299.79/300.46 42220[0:SSi:42156.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v,hAPP(c_Set_Oinsert(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),u),tc_fun(tc_Com_Opname,tc_bool),tc_fun(tc_Com_Opname,tc_bool)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.79/300.46 42221[0:SSi:42155.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v,hAPP(c_Set_Oinsert(v_Procs,tc_fun(tc_Com_Opname,tc_bool)),u),tc_fun(tc_Com_Opname,tc_bool),tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.46 42224[0:SSi:42123.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(w,x),hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,hAPP(c_Set_Oinsert(w,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),x),tc_bool)*.
% 299.79/300.46 42225[0:SSi:42110.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> c_lessequals(v_Procs,hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(c_Set_Oinsert(v_x,tc_Com_Opname),tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v_Procs),tc_bool)*.
% 299.79/300.46 42280[0:Rew:42279.1,42223.1] || c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v,hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),tc_fun(tc_Com_Opname,tc_bool)),u),tc_fun(tc_Com_Opname,tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.79/300.46 42677[0:SpR:161.0,510.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y),x,tc_fun(u,tc_bool))))*.
% 299.79/300.46 42676[0:SpR:161.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w),x,tc_fun(u,tc_bool))))*.
% 299.79/300.46 42764[0:Rew:161.0,42721.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),x),w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),w,tc_fun(u,tc_bool)))**.
% 299.79/300.46 42765[0:Rew:161.0,42706.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))),x,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)))**.
% 299.79/300.46 42942[0:SpR:486.1,538.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool))),hAPP(y,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)))**.
% 299.79/300.46 43495[0:SpR:507.0,510.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))))*.
% 299.79/300.46 43494[0:SpR:507.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),y))))*.
% 299.79/300.46 43717[0:SpR:162.0,510.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))))*.
% 299.79/300.46 43716[0:SpR:162.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),y))))*.
% 299.79/300.46 44343[0:Res:3282.1,268.0] || equal(hAPP(c_in(u),v),v_Procs)** hBOOL(hAPP(hAPP(c_in(u),w),v_x))* equal(hAPP(x,v),hAPP(x,w))* c_Fun_Oinj__on(x,v_x,u,y)* -> equal(v,w).
% 299.79/300.46 44342[7:Res:27207.1,268.0] || equal(hAPP(c_in(u),v),v_x)** hBOOL(hAPP(hAPP(c_in(u),w),v_x))* equal(hAPP(x,v),hAPP(x,w))* c_Fun_Oinj__on(x,v_x,u,y)* -> equal(v,w).
% 299.79/300.46 44327[0:Res:13238.1,268.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(hAPP(c_in(t_a),v),u))* equal(hAPP(w,v_x),hAPP(w,v))* c_Fun_Oinj__on(w,u,t_a,x)* -> equal(v_x,v).
% 299.79/300.46 44298[0:Res:652.1,268.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v),u))* equal(hAPP(w,v_x),hAPP(w,v))* c_Fun_Oinj__on(w,u,tc_Com_Opname,x)* -> equal(v_x,v).
% 299.79/300.46 44389[0:SpR:90.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),x),c_Set_Oimage(y,w,z),tc_fun(w,tc_bool),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,w,z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,u,v,tc_fun(w,tc_bool))))**.
% 299.79/300.46 44407[0:Rew:586.0,44386.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oimage(x,y,z),hAPP(x1,v)),hAPP(c_Set_Oimage(x,y,z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x1,u,tc_fun(y,tc_bool))),tc_fun(z,tc_bool))*.
% 299.79/300.46 44443[0:SpR:30.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),x),c_Set_Ovimage(y,z,w),tc_fun(w,tc_bool),tc_fun(z,tc_bool)),hAPP(c_Set_Ovimage(y,z,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,u,v,tc_fun(w,tc_bool))))**.
% 299.79/300.46 44461[0:Rew:586.0,44440.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Ovimage(x,y,z),hAPP(x1,v)),hAPP(c_Set_Ovimage(x,y,z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x1,u,tc_fun(z,tc_bool))),tc_fun(y,tc_bool))*.
% 299.79/300.46 44773[0:SSi:44740.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v_x,t_a),x),tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v_x))*.
% 299.79/300.46 45256[0:SpR:55.1,37394.1] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)),v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),w),v)) hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(w,t_a),u),v,tc_fun(t_a,tc_bool)),tc_Com_Opname,tc_bool))*.
% 299.79/300.46 45350[0:Res:9258.0,487.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w),v_x),tc_bool))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,u,t_a)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,u,t_a)))*.
% 299.79/300.46 45458[0:Res:45357.1,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname),t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.46 45446[0:Res:45357.1,356.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,u),u,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname)),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.79/300.46 45417[0:SpR:181.1,45357.1] || hBOOL(hAPP(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Ovimage(c_COMBK(u,v,w),w,v),tc_Com_Opname)))* hBOOL(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.46 45504[0:Res:9258.0,237.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,t_a) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(u,v,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x),tc_bool))* equal(hAPP(u,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v_x,u,t_a,v)),v_x)**.
% 299.79/300.46 45620[0:SpL:323.0,325.0] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),z,tc_fun(y,tc_bool))* -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool)),z,tc_fun(y,tc_bool)).
% 299.79/300.46 45619[0:SpL:323.0,324.0] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),z,tc_fun(y,tc_bool))* -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),z,tc_fun(y,tc_bool)).
% 299.79/300.46 45618[0:SpL:323.0,345.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))** -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))).
% 299.79/300.46 45617[0:SpL:323.0,344.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))** -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))).
% 299.79/300.46 45637[0:SSi:45566.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool)),tc_fun(y,tc_bool)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),z),w,x,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.46 45638[0:SSi:45565.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool)),tc_fun(y,tc_bool)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),v),w,x,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.46 45751[0:SSi:45693.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) equal(v,v_Procs) -> hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w,hAPP(c_Set_Oinsert(v,tc_fun(tc_Com_Opname,tc_bool)),u),tc_fun(tc_Com_Opname,tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.79/300.46 45887[0:Res:526.1,482.2] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x))* hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,y,u)))* hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,y,u)))* -> hBOOL(hAPP(y,x))*.
% 299.79/300.46 45932[0:SpL:181.1,45899.0] || hBOOL(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) -> hBOOL(hAPP(hAPP(c_in(v),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Ovimage(c_COMBK(w,v,u),u,v),tc_Com_Opname)))* hBOOL(hAPP(c_Set_Ovimage(c_COMBK(w,v,u),u,v),v_x)).
% 299.79/300.46 46076[0:SpR:55.1,36802.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool))) -> hBOOL(hAPP(hAPP(c_in(w),x),v)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,w),u),v,tc_fun(w,tc_bool)),v_x))*.
% 299.79/300.46 46126[0:Res:8366.1,481.0] || equal(u,v_Procs) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),w),v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),w)))*.
% 299.79/300.46 46444[0:Res:8366.1,480.0] || equal(u,v_Procs) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),u),v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),u)))*.
% 299.79/300.46 46535[4:SpR:55.1,42029.1] || equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),x),v)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,w),u),v,tc_fun(w,tc_bool)),v_x))*.
% 299.79/300.46 46651[4:SpL:339.0,46565.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))* -> .
% 299.79/300.46 46639[4:SpL:465.1,46565.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(u,x,y),v_x))* -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)).
% 299.79/300.46 46708[0:Res:13.2,44639.0] || c_lessequals(u,v,tc_fun(tc_Com_Opname,tc_bool))* c_lessequals(w,x,tc_fun(tc_Com_Opname,tc_bool))* equal(c_HOL_Ominus__class_Ominus(u,x,tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(v,w,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.79/300.46 47169[0:SSi:47168.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),u),v))* c_Finite__Set_Ofinite(v,tc_bool) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w))* -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,hAPP(c_Set_Oinsert(x,tc_bool),v),tc_bool,tc_bool))*.
% 299.79/300.46 47401[0:Res:3284.1,485.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) hBOOL(hAPP(w,v_Procs)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,w,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,u)),v))*.
% 299.79/300.46 47632[0:Res:3284.1,484.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) hBOOL(hAPP(w,v_Procs)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,w,u)),v_x))*.
% 299.79/300.46 47970[0:Res:3284.1,490.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,w,u)))* -> hBOOL(hAPP(w,v_Procs)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,u)),v))*.
% 299.79/300.46 48082[0:Res:3284.1,489.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,u)))* -> hBOOL(hAPP(w,v_Procs)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,w,u)),v_x))*.
% 299.79/300.46 48137[4:SpR:523.1,39023.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))),z))*.
% 299.79/300.46 48136[4:SpR:460.1,39023.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),w))*.
% 299.79/300.46 48252[4:SpR:523.1,39064.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))),z,t_a)*.
% 299.79/300.46 48251[4:SpR:460.1,39064.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),w,t_a)*.
% 299.79/300.46 48678[7:SpL:197.1,27293.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) equal(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),v_x)** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),v_x)).
% 299.79/300.46 48677[0:SpL:197.1,4964.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) equal(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),v_x)).
% 299.79/300.46 48622[0:SpR:197.1,9567.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),z),hAPP(hAPP(c_Set_Oimage(u,v,w),x),z),tc_bool)*.
% 299.79/300.46 49003[0:MRR:49002.0,264.0] || -> hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)),x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),u,w)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))))*.
% 299.79/300.46 50497[0:SpL:223.1,214.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),x1,tc_fun(z,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(z),y),x1)).
% 299.79/300.46 50439[0:SpR:223.1,7253.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(x,y),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x2,v,x,u,y),u,y),w)))*.
% 299.79/300.46 51173[0:SpR:55.1,26873.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))**.
% 299.79/300.46 51138[0:SpR:26873.0,13.2] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(hAPP(c_Set_Oinsert(x,w),v),y,tc_fun(w,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.46 51349[0:SpR:523.1,51231.0] class_Lattices_Olattice(u) || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),hAPP(hAPP(c_Set_Oinsert(x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 51348[0:SpR:460.1,51231.0] || class_Lattices_Olattice(t_b) -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(hAPP(c_Set_Oinsert(u,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 51293[0:SpR:55.1,51231.0] || -> hBOOL(hAPP(hAPP(c_in(t_a),u),v)) equal(c_HOL_Ominus__class_Ominus(hAPP(c_HOL_Ominus__class_Ominus(w,v,tc_fun(t_a,tc_bool)),v_x),hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,t_a),w),v,tc_fun(t_a,tc_bool)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 51487[0:SpL:55.1,33513.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),w) equal(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,w),u),v,tc_fun(w,tc_bool)),w),c_HOL_Ozero__class_Ozero(tc_nat))** -> hBOOL(hAPP(hAPP(c_in(w),x),v)).
% 299.79/300.46 51854[4:Res:40792.1,449.0] || c_lessequals(v_x,hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,c_Set_Oinsert(v,w),x,y),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_Set_Oinsert(v,w),x,y)),tc_bool)* -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),x),c_Set_Oinsert(v,w)),t_a).
% 299.79/300.46 51816[4:SpR:55.1,40792.1] || c_lessequals(v_x,hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),tc_bool) -> hBOOL(hAPP(hAPP(c_in(w),y),v)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(y,w),u),v,tc_fun(w,tc_bool)),x))*.
% 299.79/300.46 52682[0:MRR:52681.2,96.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Fun_Ocomp(c_Fun_Othe__inv__into(w,x,u,y),x,y,u,u),u,u),v),v)**.
% 299.79/300.46 52826[0:SpR:24019.2,317.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(c_Set_Oimage(v_x,u,v),hAPP(c_Set_Oinsert(v_x,u),w)),hAPP(c_Set_Oinsert(v_x,v),hAPP(c_Set_Oimage(v_x,u,v),w)))*.
% 299.79/300.46 52825[0:SpR:24019.2,99.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Fun_Oinj__on(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x,u,v),v_x),v_x)**.
% 299.79/300.46 52824[0:SpR:24019.2,438.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Fun_Oinj__on(v_x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_x,u,v),v_x),v_x)**.
% 299.79/300.46 53008[0:Res:23739.1,479.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,w,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w)))*.
% 299.79/300.46 53007[0:Res:23739.1,478.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_x,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)))*.
% 299.79/300.46 53369[0:Res:31543.0,479.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w)))*.
% 299.79/300.46 53368[0:Res:31543.0,478.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.79/300.46 53807[0:SpR:53771.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Option_Othe(u),v,w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Option_Othe(u),x,z),v),x1)),hAPP(c_Set_Oinsert(y,w),hAPP(c_Set_Oimage(c_Option_Othe(u),v,w),x1)))*.
% 299.79/300.46 53838[0:SpR:53772.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Option_Othe(u),v,w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Option_Othe(u),y,x,z),v),x1)),hAPP(c_Set_Oinsert(y,w),hAPP(c_Set_Oimage(c_Option_Othe(u),v,w),x1)))*.
% 299.79/300.46 56004[0:SpL:339.0,55174.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x))) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)))* -> .
% 299.79/300.46 55991[0:SpL:465.1,55174.1] || equal(u,c_Set_Oimage(c_Fun_Ofun__upd(v,w,x,y,z),y,z))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(c_Set_Oimage(v,y,z),v_x))* -> hBOOL(hAPP(hAPP(c_in(y),w),v_x)).
% 299.79/300.46 55922[0:SpL:339.0,55174.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool),hAPP(x,v_x))* -> .
% 299.79/300.46 55909[0:SpL:465.1,55174.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),z)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,x,y),v_x),tc_bool),hAPP(z,v_x))* -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)).
% 299.79/300.46 57942[0:SpL:523.1,55910.1] class_Lattices_Olattice(u) || equal(c_COMBK(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),y),z))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(y,v_x)),hAPP(z,v_x)))* -> .
% 299.79/300.46 57941[0:SpL:460.1,55910.1] || class_Lattices_Olattice(t_b) equal(c_COMBK(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))* -> .
% 299.79/300.46 58099[0:SpL:523.1,55992.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_COMBK(x,y,z))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool),x)* -> .
% 299.79/300.46 58098[0:SpL:460.1,55992.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_COMBK(u,v,w))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool),u)* -> .
% 299.79/300.46 58480[0:SpL:537.1,58248.0] class_Lattices_Olattice(u) || equal(c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),x,y),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_fun(t_a,tc_bool)))** -> .
% 299.79/300.46 58479[0:SpL:534.1,58248.0] class_Lattices_Oupper__semilattice(u) || equal(c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),x,y),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_fun(t_a,tc_bool)))** -> .
% 299.79/300.46 58588[0:SpR:24914.0,10771.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(v,u),w),tc_Com_Opname,x),hAPP(hAPP(c_Set_Oinsert(v,u),w),v_x))),w))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),w),v_x)).
% 299.79/300.46 58815[0:SpL:28334.0,15629.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),w)))*.
% 299.79/300.46 58812[0:SpL:28031.0,15629.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),w)))*.
% 299.79/300.46 59323[0:SpL:28334.0,15857.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),x)))*.
% 299.79/300.46 59320[0:SpL:28031.0,15857.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),x)))*.
% 299.79/300.46 59799[0:Res:57755.3,251.1] class_Lattices_Oboolean__algebra(tc_fun(u,v)) class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(hAPP(c_Orderings_Obot__class_Obot(tc_fun(u,v)),w),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w),v)*.
% 299.79/300.46 60211[0:SpL:523.1,58170.1] class_Lattices_Olattice(u) || equal(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x)) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)),tc_bool),y,z),v)* -> .
% 299.79/300.46 60210[0:SpL:460.1,58170.1] || class_Lattices_Olattice(t_b) equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool),v,w),u)* -> .
% 299.79/300.46 61965[0:SpL:131.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.46 61964[0:SpL:158.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.46 61945[0:SpL:104.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.79/300.46 64042[0:SpR:55.1,63953.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),u)) c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),u,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))*.
% 299.79/300.46 64248[0:SpR:12944.0,646.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),v_Procs,tc_Com_Opname,y) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),tc_Com_Opname,y),c_Orderings_Otop__class_Otop(tc_bool)),v_x)**.
% 299.79/300.46 64241[0:SpR:11473.0,646.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_Com_Opname,w),c_Orderings_Otop__class_Otop(tc_bool)),v_x)**.
% 299.79/300.46 64231[0:SpR:329.1,646.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),v_x),v_x)**.
% 299.79/300.46 64230[0:SpR:328.1,646.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),u),v_x)**.
% 299.79/300.46 64226[0:SpR:538.0,646.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)),v_x)**.
% 299.79/300.46 64217[0:SpR:17045.0,646.1] || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),tc_Com_Opname,x),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.46 64163[0:SpR:646.1,545.1] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),x)) -> hBOOL(hAPP(hAPP(c_in(y),v_x),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,y),x)))*.
% 299.79/300.46 64159[0:SpR:646.1,362.1] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),x)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.46 64415[0:SpR:12944.0,645.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),v_Procs,tc_Com_Opname,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),tc_Com_Opname,y),c_Orderings_Otop__class_Otop(tc_bool)),v_x)**.
% 299.79/300.46 64408[0:SpR:11473.0,645.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),tc_Com_Opname,w),c_Orderings_Otop__class_Otop(tc_bool)),v_x)**.
% 299.79/300.46 64398[0:SpR:329.1,645.1] || c_lessequals(u,v_x,tc_fun(v,tc_bool)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),v_x),v_x)**.
% 299.79/300.46 64397[0:SpR:328.1,645.1] || c_lessequals(v_x,u,tc_fun(v,tc_bool)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),u),v_x)**.
% 299.79/300.46 64393[0:SpR:538.0,645.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v)),v_x)**.
% 299.79/300.46 64384[0:SpR:17045.0,645.1] || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),tc_Com_Opname,x),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.46 64330[0:SpR:645.1,545.1] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),x)) -> hBOOL(hAPP(hAPP(c_in(y),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,y),x)))*.
% 299.79/300.46 64326[0:SpR:645.1,362.1] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),x)) -> c_lessequals(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.46 64559[0:SpL:131.0,24257.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.46 64558[0:SpL:158.0,24257.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.46 64539[0:SpL:104.0,24257.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.46 64707[0:Res:27986.0,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))*.
% 299.79/300.46 64706[0:Res:27986.0,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs)))*.
% 299.79/300.46 64727[0:Res:27987.0,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))*.
% 299.79/300.46 64726[0:Res:27987.0,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs)))*.
% 299.79/300.46 64747[0:Res:28288.0,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))*.
% 299.79/300.46 64746[0:Res:28288.0,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs)))*.
% 299.79/300.46 64767[0:Res:28289.0,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))*.
% 299.79/300.46 64766[0:Res:28289.0,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs)))*.
% 299.79/300.46 66051[0:SpR:65404.1,118.0] class_Lattices_Olattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Fun_Ofun__upd(w,x,v,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,z,x1,y),x,v,y,x1))*.
% 299.79/300.46 66028[0:SpR:65404.1,71.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),w),w)**.
% 299.79/300.46 66027[0:SpR:65404.1,373.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),w),w)**.
% 299.79/300.46 66708[0:SpR:1188.2,545.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,x),w)))*.
% 299.79/300.46 66704[0:SpR:1188.2,362.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.46 67463[0:SpR:1189.2,545.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,x),w)))*.
% 299.79/300.46 67459[0:SpR:1189.2,362.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.46 68228[0:SpR:1250.3,365.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_HOL_Ozero__class_Ozero(tc_fun(t_a,u))) -> equal(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.46 69684[0:SpL:128.0,6239.0] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Ovimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))).
% 299.79/300.46 70076[0:SpL:21893.0,11883.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_Com_Opname,w)),u))* -> .
% 299.79/300.46 70075[0:SpL:21267.0,11883.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x),tc_Com_Opname,w)),u))* -> .
% 299.79/300.46 70370[0:SpL:223.1,12983.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(x),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(x,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,tc_Hoare__Mirabelle_Otriple(t_a)),u,tc_Hoare__Mirabelle_Otriple(t_a)),w)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,z,t_a).
% 299.79/300.46 71167[0:SSi:71133.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),w) -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),w,tc_fun(v,tc_bool))*.
% 299.79/300.46 71306[0:Res:7538.0,402.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),x,tc_fun(u,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),x).
% 299.79/300.46 71365[0:SSi:71343.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),x) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),x,tc_fun(u,tc_bool))*.
% 299.79/300.46 72181[0:SSi:72158.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),x) -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),x,tc_fun(v,tc_bool))*.
% 299.79/300.46 73088[7:Res:71608.1,477.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(t_a),v_x),u),v_x)** hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.46 73087[7:Res:71608.1,476.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(t_a),v_x),u),v_x)** hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.46 73045[7:Res:71608.1,481.0] || equal(u,v_x) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w),v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w)))*.
% 299.79/300.46 73044[7:Res:71608.1,480.0] || equal(u,v_x) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u),v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u)))*.
% 299.79/300.46 73953[7:SpL:71835.1,453.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(v_x,u)) c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.79/300.46 73915[7:SpR:71835.1,113.0] || equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,t_a)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(u,v,w),x),v_x,tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,v_x,tc_fun(w,tc_bool))))*.
% 299.79/300.46 73897[7:SpR:71835.1,89.0] || equal(c_COMBB(u,v,tc_fun(w,tc_bool),x),c_Set_Oinsert(v_x,t_a)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v_x,x,v),y),u,v,tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v_x,x,tc_fun(w,tc_bool)))**.
% 299.79/300.46 73692[7:SpR:71835.1,113.0] || equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,t_a)) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(v_x,x,tc_fun(w,tc_bool))))*.
% 299.79/300.46 73624[7:SpR:71835.1,410.0] || equal(c_Set_Oinsert(v_x,t_a),c_Set_Oinsert(u,v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(x,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,x,v,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,x,v,tc_fun(w,tc_bool)))**.
% 299.79/300.46 73289[7:SpR:71835.1,410.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,v),w),u,v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,u,v,tc_fun(x,tc_bool))))*.
% 299.79/300.46 73235[7:SpR:71835.1,89.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,hAPP(c_COMBB(x,w,tc_fun(y,tc_bool),v),u),v,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,x,w,tc_fun(y,tc_bool)))**.
% 299.79/300.46 74515[7:Rew:71835.1,74369.3] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(hAPP(c_in(v),w),x))* hBOOL(hAPP(v_x,hAPP(y,w)))* -> hBOOL(hAPP(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,tc_fun(u,tc_bool))))*.
% 299.79/300.46 74516[7:MRR:74263.2,6340.0] || equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,x,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),x)))*.
% 299.79/300.46 74517[7:MRR:74262.2,6340.0] || equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_x,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v_x)))*.
% 299.79/300.46 74518[7:Rew:71835.1,74220.2] || equal(c_Set_Oinsert(v_x,t_a),c_Hoare__Mirabelle_Otriple_Otriple(u)) c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(v_x,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x),u)* -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),hAPP(hAPP(v_x,hAPP(c_Com_Ocom_OBODY,w)),x),u).
% 299.79/300.46 74520[7:Rew:71835.1,73665.1] || equal(c_Set_Oinsert(v_x,t_a),c_Hoare__Mirabelle_Otriple_Otriple(u)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),hAPP(hAPP(v_x,hAPP(c_Com_Ocom_OBODY,w)),x),u) -> c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(v_x,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x),u)*.
% 299.79/300.46 75619[0:SSi:75381.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),u),v,w,tc_fun(x,tc_bool))),tc_fun(x,tc_bool))*.
% 299.79/300.46 75716[7:SpR:71883.1,475.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(v_x,u,w),v)),hAPP(c_Set_Oimage(v_x,u,w),v))**.
% 299.79/300.46 76087[0:SSi:75835.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),z),v,w,tc_fun(x,tc_bool))),tc_fun(x,tc_bool))*.
% 299.79/300.46 76151[0:SpR:9915.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(y,z,v),x1,x2,x3,x4),u,x),w)))*.
% 299.79/300.46 76147[0:SpR:9915.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Set_Ovimage(x,y,v),z,x1,x2,x3),u,tc_fun(x4,tc_bool)),tc_fun(x4,tc_bool))*.
% 299.79/300.46 76271[0:SpR:10469.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_Set_Oimage(y,v,z),x1,x2,x3,x4),u,x),w)))*.
% 299.79/300.46 76267[0:SpR:10469.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Set_Oimage(x,v,y),z,x1,x2,x3),u,tc_fun(x4,tc_bool)),tc_fun(x4,tc_bool))*.
% 299.79/300.46 76401[0:SpR:10470.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(y,z,v),x1,x2,x3,x4),u,x),w)))*.
% 299.79/300.46 76397[0:SpR:10470.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Set_Ovimage(x,y,v),z,x1,x2,x3),u,tc_fun(x4,tc_bool)),tc_fun(x4,tc_bool))*.
% 299.79/300.46 77453[7:SpR:71894.1,71.2] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v))* c_Fun_Oinj__on(v_x,v,u,w) -> equal(hAPP(c_Fun_Othe__inv__into(v,v_x,u,w),v_x),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 77452[7:SpR:71894.1,373.2] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v))* c_Fun_Oinj__on(v_x,v,u,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,v_x,u,w),v_x),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 78613[0:Res:1103.1,5986.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_COMBS(c_in(v),w,x,y,z),t_a) hBOOL(hAPP(hAPP(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_COMBS(c_in(v),w,x,y,z))),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_COMBS(c_in(v),w,x,y,z))))*.
% 299.79/300.46 78754[4:Res:78665.1,479.1] || equal(hAPP(hAPP(c_in(u),v),w),v_x)** hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,y,x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)))*.
% 299.79/300.46 78753[4:Res:78665.1,478.1] || equal(hAPP(hAPP(c_in(u),v),w),v_x)** hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,w,x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w)))*.
% 299.79/300.46 78743[4:Res:78665.1,199.0] || equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(u,w,v,x))),v_x)** c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(u,y))*.
% 299.79/300.46 78707[4:Res:78665.1,284.0] || equal(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(v,x,u),y)),v_x)** c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u)* -> hBOOL(hAPP(hAPP(c_in(x),w),y)).
% 299.79/300.46 78696[4:Res:78665.1,275.1] || equal(hAPP(hAPP(c_in(u),v),hAPP(w,x)),v_x)** hBOOL(hAPP(hAPP(c_in(y),x),z))* -> hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,w,y,tc_fun(u,tc_bool))))*.
% 299.79/300.46 79038[0:Res:15630.1,278.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(x,v)) -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,y),z),x1,hAPP(c_in(u),v),y),x2,x,u)))*.
% 299.79/300.46 79037[0:Res:15630.1,277.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(x,v)) -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,z),x1),x2,hAPP(c_in(u),v),z),x,u)))*.
% 299.79/300.46 78993[0:SpR:328.1,15630.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),v),z,tc_fun(y,tc_bool))* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),u)) -> hBOOL(z).
% 299.79/300.46 79258[0:Res:15858.1,278.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(x,v)) -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(w,z),x1),hAPP(c_in(u),v),z),x2,x,u)))*.
% 299.79/300.46 79257[0:Res:15858.1,277.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(x,v)) -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,hAPP(c_Set_Oinsert(w,x1),x2),hAPP(c_in(u),v),x1),x,u)))*.
% 299.79/300.46 79213[0:SpR:328.1,15858.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),w),z,tc_fun(y,tc_bool))* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),v)) -> hBOOL(z).
% 299.79/300.46 80188[0:SpL:21268.0,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),x),z,x1),hAPP(u,y)))*.
% 299.79/300.46 80156[0:SpL:21268.0,4126.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,y),v,u)*.
% 299.79/300.46 79880[0:SpR:540.1,21268.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v),w,y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v))**.
% 299.79/300.46 79879[0:SpR:539.1,21268.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v),w,y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v))**.
% 299.79/300.46 79854[0:SpR:25.1,21268.0] class_HOL_Ouminus(u) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),w,x)),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))**.
% 299.79/300.46 79640[0:SpR:21268.0,83.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),x),y,z),tc_fun(w,tc_bool))*.
% 299.79/300.46 79611[0:SpR:21268.0,229.0] || -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSKIP),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x,y)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.79/300.46 79556[0:SpR:21268.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(w,x),v,y)),z))* -> hBOOL(hAPP(hAPP(c_in(x1),hAPP(w,x)),hAPP(c_Set_Oimage(w,u,x1),z)))*.
% 299.79/300.46 79552[0:SpR:21268.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(w,x),v,y)),z))* -> c_lessequals(hAPP(w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,w,u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.46 79518[0:SpR:21268.0,299.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),v,y),w,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),w).
% 299.79/300.46 79438[0:SpR:21268.0,34.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Ovimage(v,w,x),hAPP(c_Set_Ovimage(v,w,x),y),u,z),hAPP(v,x1)))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,w,x),y),x1)).
% 299.79/300.46 81383[0:SpL:21894.0,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y)) -> hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x),c_Set_Ovimage(u,v,w),z,x1),hAPP(u,y)))*.
% 299.79/300.46 81351[0:SpL:21894.0,4126.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),v) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),v,u)*.
% 299.79/300.46 81074[0:SpR:540.1,21894.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v))**.
% 299.79/300.46 81073[0:SpR:539.1,21894.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v))**.
% 299.79/300.46 81048[0:SpR:25.1,21894.0] class_HOL_Ouminus(u) || -> equal(hAPP(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w,x)),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u))**.
% 299.79/300.46 80834[0:SpR:21894.0,83.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x),c_Set_Ovimage(u,v,w),y,z),tc_fun(w,tc_bool))*.
% 299.79/300.46 80805[0:SpR:21894.0,229.0] || -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSKIP),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Hoare__Mirabelle_Otriple_Otriple(v),x,y)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.79/300.46 80749[0:SpR:21894.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(w,x),w,v,y)),z))* -> hBOOL(hAPP(hAPP(c_in(x1),hAPP(w,x)),hAPP(c_Set_Oimage(w,u,x1),z)))*.
% 299.79/300.46 80745[0:SpR:21894.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(w,x),w,v,y)),z))* -> c_lessequals(hAPP(w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,w,u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.46 80711[0:SpR:21894.0,299.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),w,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),w).
% 299.79/300.46 80631[0:SpR:21894.0,34.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),y),c_Set_Ovimage(v,w,x),u,z),hAPP(v,x1)))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,w,x),y),x1)).
% 299.79/300.46 81859[0:SpR:600.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y,z,x1),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool))),u)*.
% 299.79/300.46 81795[0:SpR:196.1,5879.1] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_lessequals(y,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Ovimage(v,w,x),z,x1,x2),hAPP(c_Set_Oimage(v,w,x),y)),u)*.
% 299.79/300.46 82331[0:SpR:600.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y,z,x1),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool))),u)*.
% 299.79/300.46 82267[0:SpR:196.1,5880.1] class_Lattices_Olattice(u) || c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_lessequals(y,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Ovimage(v,w,x),z,x1,x2),hAPP(c_Set_Oimage(v,w,x),y)),u)*.
% 299.79/300.46 82563[7:Res:82148.0,481.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,v)),w),u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,v)),w)))*.
% 299.79/300.46 82562[7:Res:82148.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),c_Set_Oinsert(v_x,w)),u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),c_Set_Oinsert(v_x,w))))*.
% 299.79/300.46 83043[0:SpR:5924.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(hAPP(y,v),z)),hAPP(c_Set_Oimage(c_COMBS(y,c_COMBK(z,x1,x2),x3,x4,x5),u,x),w)))*.
% 299.79/300.46 83039[0:SpR:5924.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(hAPP(x,v),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(x,c_COMBK(y,z,x1),x2,x3,x4),u,tc_fun(x5,tc_bool)),tc_fun(x5,tc_bool))*.
% 299.79/300.46 83370[0:SpR:5961.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,hAPP(z,v))),hAPP(c_Set_Oimage(c_COMBS(c_COMBK(y,x1,x2),z,x3,x4,x5),u,x),w)))*.
% 299.79/300.46 83366[0:SpR:5961.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,hAPP(y,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_COMBK(x,z,x1),y,x2,x3,x4),u,tc_fun(x5,tc_bool)),tc_fun(x5,tc_bool))*.
% 299.79/300.46 83803[0:SpR:5899.0,15858.1] || hBOOL(hAPP(c_COMBS(u,v,w,x,y),z)) -> hBOOL(hAPP(c_COMBS(u,v,x1,x2,x3),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x4,hAPP(c_Set_Oinsert(z,x5),x6),c_COMBS(u,v,w,x,y),x5)))*.
% 299.79/300.46 83802[0:SpR:5899.0,15630.1] || hBOOL(hAPP(c_COMBS(u,v,w,x,y),z)) -> hBOOL(hAPP(c_COMBS(u,v,x1,x2,x3),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(z,x4),x5),x6,c_COMBS(u,v,w,x,y),x4)))*.
% 299.79/300.46 83752[0:SpR:5899.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_COMBS(y,z,x1,x2,x3),v)),hAPP(c_Set_Oimage(c_COMBS(y,z,x4,x5,x6),u,x),w)))*.
% 299.79/300.46 83748[0:SpR:5899.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_COMBS(x,y,z,x1,x2),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(x,y,x3,x4,x5),u,tc_fun(x6,tc_bool)),tc_fun(x6,tc_bool))*.
% 299.79/300.46 84080[0:Rew:584.0,83794.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(u,v_x),hAPP(v,v_x)),c_COMBS(u,v,z,x1,x2),tc_Com_Opname,x3)),hAPP(hAPP(u,v_x),hAPP(v,v_x)))**.
% 299.79/300.46 84081[0:Rew:584.0,83792.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(u,v,z,x1,x2),hAPP(hAPP(u,v_x),hAPP(v,v_x)),tc_Com_Opname,x3)),hAPP(hAPP(u,v_x),hAPP(v,v_x)))**.
% 299.79/300.46 84890[4:SpL:445.1,78744.0] || equal(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Fun_Ofun__upd(u,v,w,x,y),z)),v_x)** -> equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Fun_Ofun__upd(u,v,w,x,y),z),v) c_Hoare__Mirabelle_Ohoare__valids(c_Fun_Ofun__upd(u,v,w,x,y),z,t_a).
% 299.79/300.46 84976[0:SpR:338.0,84957.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v),x))))*.
% 299.79/300.46 85055[0:SpR:644.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> c_lessequals(hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_COMBK(x,y,tc_Com_Opname),tc_Com_Opname,y),v,u),u)*.
% 299.79/300.46 85039[0:SpR:644.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Ovimage(c_Set_Oimage(c_COMBK(v,w,tc_Com_Opname),tc_Com_Opname,w),u,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.46 85841[0:Res:9066.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x)),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,y)),u))* c_Hoare__Mirabelle_Otriple__valid(y,w,t_a)*.
% 299.79/300.46 85770[0:SpR:223.1,9066.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x1,v,y,u,x),u,x),w))))*.
% 299.79/300.46 86683[0:Res:86261.1,477.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(t_a),v_x),u),v_Procs)** hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.46 86682[0:Res:86261.1,476.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(t_a),v_x),u),v_Procs)** hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.46 86639[0:Res:86261.1,481.0] || equal(u,v_Procs) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w),v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w)))*.
% 299.79/300.46 86638[0:Res:86261.1,480.0] || equal(u,v_Procs) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u),v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u)))*.
% 299.79/300.46 87316[7:SpR:537.1,71492.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),x))*.
% 299.79/300.46 87315[7:SpR:534.1,71492.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),x))*.
% 299.79/300.46 87464[7:SpR:537.1,71493.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),x,t_a)*.
% 299.79/300.46 87463[7:SpR:534.1,71493.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),x,t_a)*.
% 299.79/300.46 87594[7:SpR:537.1,71679.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.46 87593[7:SpR:534.1,71679.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.46 88966[0:SpR:128.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),z),tc_fun(v,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),c_HOL_Ouminus__class_Ouminus(z,tc_fun(w,tc_bool))))*.
% 299.79/300.46 88897[0:SpR:544.1,14196.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)))*.
% 299.79/300.46 88896[0:SpR:543.1,14196.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)))*.
% 299.79/300.46 88885[0:SpR:181.1,14196.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))),w))*.
% 299.79/300.46 89061[0:Res:78099.0,479.1] || hBOOL(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),y)))*.
% 299.79/300.46 89060[0:Res:78099.0,478.1] || hBOOL(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.79/300.46 89163[0:SpL:532.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))),v)* -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y),v).
% 299.79/300.46 89482[7:SpR:78590.1,59525.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v),c_Set_Oinsert(v_x,t_a)) -> c_Hoare__Mirabelle_Ohoare__valids(w,c_Set_Oinsert(v_x,t_a),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v))*.
% 299.79/300.46 89481[7:SpR:78590.1,59017.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u),c_Set_Oinsert(v_x,t_a)) -> c_Hoare__Mirabelle_Ohoare__valids(w,c_Set_Oinsert(v_x,t_a),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u))*.
% 299.79/300.46 89379[7:SpR:78590.1,58968.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u),c_Set_Oinsert(v_x,t_a)) equal(c_Set_Oinsert(v_x,t_a),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u))*.
% 299.79/300.46 89378[7:SpR:78590.1,58969.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u),c_Set_Oinsert(v_x,t_a)) equal(c_Set_Oinsert(v_x,t_a),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u))*.
% 299.79/300.46 89377[7:SpR:78590.1,59476.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v),c_Set_Oinsert(v_x,t_a)) equal(c_Set_Oinsert(v_x,t_a),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v))*.
% 299.79/300.46 89376[7:SpR:78590.1,59477.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v),c_Set_Oinsert(v_x,t_a)) equal(c_Set_Oinsert(v_x,t_a),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v))*.
% 299.79/300.46 89729[7:Res:89344.1,237.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Set_Oinsert(v_x,t_a))** c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,t_a) -> equal(hAPP(u,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v_x,u,t_a,v)),v_x)**.
% 299.79/300.46 89728[7:Res:89344.1,487.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)))*.
% 299.79/300.46 89831[0:SpR:26183.0,532.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(x,u),v))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(x,u),v)))**.
% 299.79/300.46 89790[0:SpR:26183.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Set_Oinsert(w,x),y)),z)) -> c_lessequals(hAPP(c_Set_Oinsert(w,x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),v,u),u)*.
% 299.79/300.46 89769[0:SpR:26183.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),x),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.46 90273[4:SpR:78660.1,59525.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v),v_x),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(w,c_Set_Oinsert(v_x,t_a),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.46 90272[4:SpR:78660.1,59017.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u),v_x),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(w,c_Set_Oinsert(v_x,t_a),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u)).
% 299.79/300.46 90169[7:SpR:78660.1,58968.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u),v_x),v_x)** equal(c_Set_Oinsert(v_x,t_a),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u)).
% 299.79/300.46 90168[4:SpR:78660.1,58969.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u),v_x),v_x)** equal(c_Set_Oinsert(v_x,t_a),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u)).
% 299.79/300.46 90167[7:SpR:78660.1,59476.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v),v_x),v_x)** equal(c_Set_Oinsert(v_x,t_a),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.46 90166[4:SpR:78660.1,59477.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v),v_x),v_x)** equal(c_Set_Oinsert(v_x,t_a),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.46 90661[0:SpL:533.0,26231.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))),v)* -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v).
% 299.79/300.46 90804[0:SSi:90793.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)).
% 299.79/300.46 90805[0:SSi:90792.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)),x,tc_fun(v,tc_bool))* -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)).
% 299.79/300.46 90873[4:Res:90134.1,237.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x),v_x)** c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,t_a) -> equal(hAPP(u,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v_x,u,t_a,v)),v_x)**.
% 299.79/300.46 90872[4:Res:90134.1,487.1] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),v_x)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)))*.
% 299.79/300.46 91785[0:SpR:834.1,383.1] class_Lattices_Obounded__lattice(u) || -> equal(v,c_Orderings_Obot__class_Obot(u)) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x,y,z),c_Orderings_Obot__class_Obot(u),w,y,z),c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x,y,z))**.
% 299.79/300.46 92640[7:SpR:537.1,82151.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Set_Oinsert(v_x,x)))*.
% 299.79/300.46 92639[7:SpR:534.1,82151.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Set_Oinsert(v_x,x)))*.
% 299.79/300.46 92945[0:SpR:128.0,5876.0] || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Ovimage(u,v,w),z,x1,x2),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),tc_fun(y,tc_bool))*.
% 299.79/300.46 93239[0:SpL:5878.1,15629.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(v,c_Orderings_Obot__class_Obot(u))) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z)))*.
% 299.79/300.46 93238[0:SpL:5878.1,15857.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(v,c_Orderings_Obot__class_Obot(u))) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),x1)))*.
% 299.79/300.46 93212[0:SpR:5878.1,361.2] class_Lattices_Obounded__lattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Obot__class_Obot(u)),x)) -> c_lessequals(hAPP(y,c_Orderings_Obot__class_Obot(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),y,z,x1,x2),w,v),v)*.
% 299.79/300.46 93197[0:SpR:5878.1,176.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Ovimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),v,x1),hAPP(c_Set_Oinsert(hAPP(w,c_Orderings_Obot__class_Obot(u)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.79/300.46 93300[4:SpR:537.1,85556.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),x),tc_bool)*.
% 299.79/300.46 93299[4:SpR:534.1,85556.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),x),tc_bool)*.
% 299.79/300.46 93488[0:SpR:537.1,86147.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),x))*.
% 299.79/300.46 93487[0:SpR:534.1,86147.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),x))*.
% 299.79/300.46 93639[0:SpR:537.1,86148.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),x,t_a)*.
% 299.79/300.46 93638[0:SpR:534.1,86148.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),x,t_a)*.
% 299.79/300.46 93730[0:SpL:21894.0,7462.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,x),y),c_Set_Oinsert(w,x),v,z),tc_fun(x,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(w,x),y),x) -> c_Finite__Set_Ofinite(u,x).
% 299.79/300.46 93728[0:SpL:21268.0,7462.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),hAPP(c_Set_Oinsert(w,x),y),v,z),tc_fun(x,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(w,x),y),x) -> c_Finite__Set_Ofinite(u,x).
% 299.79/300.46 93705[0:SpL:338.0,7462.1] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool))* c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(y,v),x)),v)* -> c_Finite__Set_Ofinite(u,v).
% 299.79/300.46 93783[0:SpR:537.1,86342.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.46 93782[0:SpR:534.1,86342.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.46 94033[0:SpR:338.0,10791.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(y,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x))),tc_fun(u,tc_bool))*.
% 299.79/300.46 93991[0:SpR:21894.0,10791.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,v),y),c_Set_Oinsert(x,v),w,z)),hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(x,v),y)),tc_fun(v,tc_bool))*.
% 299.79/300.46 93989[0:SpR:21268.0,10791.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(x,v),y),w,z)),hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(x,v),y)),tc_fun(v,tc_bool))*.
% 299.79/300.46 93966[0:SpR:338.0,10791.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(y,v),x))),tc_fun(v,tc_bool))*.
% 299.79/300.46 94158[0:Res:14364.3,357.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Set_Oimage(w,x,u),y)))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_Finite__Set_Ofinite(y,x) -> c_Finite__Set_Ofinite(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),u)*.
% 299.79/300.46 7562[0:Res:49.2,363.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(hAPP(c_Set_Oinsert(v,u),w),c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.46 9553[0:Res:41.2,251.1] class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || c_lessequals(w,c_HOL_Ozero__class_Ozero(tc_fun(u,v)),tc_fun(u,v)) -> c_lessequals(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),x),hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),x),v)*.
% 299.79/300.46 9548[0:Res:53.2,251.1] class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w,tc_fun(u,v)) -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),x),hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),x),v)*.
% 299.79/300.46 9845[0:SpL:98.1,178.1] || c_Fun_Oinj__on(u,v,w,x) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,w,x),v),x)* equal(c_Finite__Set_Ocard(v,w),c_HOL_Ozero__class_Ozero(tc_nat)) -> equal(hAPP(c_Set_Oimage(u,w,x),v),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))).
% 299.79/300.46 13165[0:Res:108.1,402.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))).
% 299.79/300.46 14129[0:SpR:353.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Ovimage(c_Set_Oinsert(y,w),u,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(y,w),x)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.46 15118[0:SpR:181.1,687.1] || hBOOL(hAPP(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,c_Set_Ovimage(c_COMBK(u,v,w),w,v),tc_Com_Opname)))* hBOOL(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.46 15117[0:SpR:181.1,686.1] || hBOOL(hAPP(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,c_Set_Ovimage(c_COMBK(u,v,w),w,v),tc_Com_Opname)))* hBOOL(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.46 15085[0:SpR:181.1,9268.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Set_Ovimage(c_COMBK(v,u,w),w,u)),c_Set_Ovimage(c_COMBK(v,u,w),w,u))**.
% 299.79/300.46 15231[0:Res:446.1,402.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Oinsert(x,w),v),hAPP(c_Set_Oinsert(x,w),u),tc_fun(w,tc_bool))* -> equal(hAPP(c_Set_Oinsert(x,w),u),hAPP(c_Set_Oinsert(x,w),v)).
% 299.79/300.46 16514[0:SpR:353.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Set_Oinsert(w,x),y)),z)) -> c_lessequals(hAPP(c_Set_Oinsert(w,x),hAPP(c_Set_Oinsert(x1,x),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oinsert(x1,x),v,u),u)*.
% 299.79/300.46 18027[0:MRR:18021.2,418.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),w),u) -> hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(v,u),w),u)),w))* equal(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oinsert(v,u),w),u),v).
% 299.79/300.46 18028[0:MRR:18020.2,418.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),w),u) -> hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(v,u),w),u)),w))* equal(c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oinsert(v,u),w),u),v).
% 299.79/300.46 18420[0:Res:545.1,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(y,v,u),x),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(y,v,u),x),u),hAPP(y,w),u)*.
% 299.79/300.46 18419[0:Res:545.1,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(y,v,u),x),u) -> c_lessequals(hAPP(y,w),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(y,v,u),x),u),u)*.
% 299.79/300.46 18587[0:Res:153.1,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(w,x)),y)) c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(w,u,v),y),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Ovimage(w,u,v),y),u),x,u)*.
% 299.79/300.46 18586[0:Res:153.1,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(w,x)),y)) c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(w,u,v),y),u) -> c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Ovimage(w,u,v),y),u),u)*.
% 299.79/300.46 19353[0:SSi:19305.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* c_lessequals(w,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.46 19681[0:Res:171.2,496.0] class_Orderings_Olinorder(tc_Hoare__Mirabelle_Otriple(t_a)) || c_Finite__Set_Ofinite(u,tc_Hoare__Mirabelle_Otriple(t_a)) -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u)),u))* c_Hoare__Mirabelle_Otriple__valid(v,c_Finite__Set_Olinorder__class_OMin(u,tc_Hoare__Mirabelle_Otriple(t_a)),t_a).
% 299.79/300.46 19680[0:Res:172.2,496.0] class_Orderings_Olinorder(tc_Hoare__Mirabelle_Otriple(t_a)) || c_Finite__Set_Ofinite(u,tc_Hoare__Mirabelle_Otriple(t_a)) -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u)),u))* c_Hoare__Mirabelle_Otriple__valid(v,c_Finite__Set_Olinorder__class_OMax(u,tc_Hoare__Mirabelle_Otriple(t_a)),t_a).
% 299.79/300.46 19655[0:Res:254.1,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(t_a)),v))),hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(t_a)),v)))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.46 19706[0:SpL:329.1,19641.0] || c_lessequals(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),tc_fun(v,tc_bool))* hBOOL(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w,t_a).
% 299.79/300.46 19856[0:SpR:128.0,104.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)))),y),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(v,u,w),x),y,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))*.
% 299.79/300.46 19804[0:SpR:104.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(x,tc_bool))),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.79/300.46 19925[0:SSi:19812.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool)) c_lessequals(x,w,tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))*.
% 299.79/300.46 20021[0:SpL:64.0,62.0] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),w) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),w)*.
% 299.79/300.46 19975[0:SpR:64.0,63.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),x)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,x),v),tc_fun(x,tc_bool)),x).
% 299.79/300.46 19974[0:SpR:64.0,446.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(w,x),u),hAPP(c_Set_Oinsert(w,x),v),tc_fun(x,tc_bool))*.
% 299.79/300.46 19957[0:SpR:64.0,446.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,w),u),hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool))*.
% 299.79/300.46 20376[0:SpR:10063.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.79/300.46 20362[0:SpR:105.0,438.1] || c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.79/300.46 20358[0:SpR:38.0,438.1] || c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),x,y),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.79/300.46 20357[0:SpR:321.0,438.1] || c_Fun_Oinj__on(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(u,v,w),x,y),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.46 20335[0:SpR:87.1,438.1] class_Lattices_Oboolean__algebra(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),c_Orderings_Otop__class_Otop(u)),c_HOL_Ouminus__class_Ouminus(v,u))**.
% 299.79/300.46 20306[0:SpR:15476.0,438.1] || c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v,w),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)),v_x)**.
% 299.79/300.46 20274[0:SpR:438.1,415.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Fun_Ofun__upd(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(u,x),x,y,z),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w))**.
% 299.79/300.46 20396[0:Rew:20386.1,20301.1] || c_Fun_Oinj__on(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(y,v),z)),hAPP(c_Set_Oinsert(y,v),z))**.
% 299.79/300.46 20520[0:SpR:10063.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.79/300.46 20506[0:SpR:105.0,99.1] || c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.79/300.46 20502[0:SpR:38.0,99.1] || c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),x,y),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.79/300.46 20501[0:SpR:321.0,99.1] || c_Fun_Oinj__on(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(u,v,w),x,y),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.46 20479[0:SpR:87.1,99.1] class_Lattices_Oboolean__algebra(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),c_Orderings_Otop__class_Otop(u)),c_HOL_Ouminus__class_Ouminus(v,u))**.
% 299.79/300.46 20450[0:SpR:15476.0,99.1] || c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v,w),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)),v_x)**.
% 299.79/300.46 20416[0:SpR:99.1,415.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Fun_Ofun__upd(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(u,x),x,y,z),c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w))**.
% 299.79/300.46 20540[0:Rew:20386.1,20444.1] || c_Fun_Oinj__on(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(y,v),z)),hAPP(c_Set_Oinsert(y,v),z))**.
% 299.79/300.46 21010[0:SpR:10063.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,v),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u),w)),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,v),w)))*.
% 299.79/300.46 20996[0:SpR:105.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x),z)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),y),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),z)))*.
% 299.79/300.46 20992[0:SpR:38.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x),z)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),y),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),z)))*.
% 299.79/300.46 20991[0:SpR:321.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oimage(u,v,w),x,y),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),x),z)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),y),hAPP(c_Set_Oimage(c_Set_Oimage(u,v,w),x,y),z)))*.
% 299.79/300.46 20969[0:SpR:87.1,317.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(v,u),w),y)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),y)))*.
% 299.79/300.46 20953[0:SpR:302.1,317.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),y)))*.
% 299.79/300.46 20940[0:SpR:15476.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),w),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v,w),x)))*.
% 299.79/300.46 20931[0:SpR:369.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),y),w),z)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),y),x),hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),z)))*.
% 299.79/300.46 20930[0:SpR:2089.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),u),x)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),v),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,v),x)))*.
% 299.79/300.46 20877[0:SpR:317.0,446.1] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(hAPP(v,z),x),u),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(z,w),y)),tc_fun(x,tc_bool))*.
% 299.79/300.46 20860[0:SpR:317.0,446.1] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(z,v),x)),hAPP(c_Set_Oinsert(hAPP(u,z),w),y),tc_fun(w,tc_bool))*.
% 299.79/300.46 20856[0:SpR:317.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(y,v),z))),hAPP(c_Set_Oinsert(hAPP(u,x),w),hAPP(c_Set_Oinsert(hAPP(u,y),w),hAPP(c_Set_Oimage(u,v,w),z))))*.
% 299.79/300.46 20841[0:SpR:317.0,313.1] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(y,w,z),u),hAPP(c_Set_Oinsert(hAPP(y,v),z),hAPP(c_Set_Oimage(y,w,z),x)),tc_fun(z,tc_bool))*.
% 299.79/300.46 20831[0:SpR:317.0,313.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(hAPP(y,u),z),hAPP(c_Set_Oimage(y,v,z),w)),hAPP(c_Set_Oimage(y,v,z),x),tc_fun(z,tc_bool))*.
% 299.79/300.46 21256[0:SpL:317.0,469.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(hAPP(w,x),u),hAPP(c_Set_Oimage(w,y,u),z))))* -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(hAPP(c_Set_Oinsert(x,y),z),w,v,y,u)),v)**.
% 299.79/300.46 21687[0:SpL:21267.0,263.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),v_x))) -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(w,u),v_x),tc_Com_Opname,x)))* equal(v,w).
% 299.79/300.46 21680[0:SpL:21267.0,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),v_x)) -> hBOOL(hAPP(x,hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),x),hAPP(hAPP(c_Set_Ovimage(u,v,w),x),v_x),tc_Com_Opname,y))))*.
% 299.79/300.46 21483[0:SpR:21267.0,34.1] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Ovimage(v,w,x),u),hAPP(hAPP(c_Set_Ovimage(v,w,x),u),v_x),tc_Com_Opname,y))))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,w,x),u),v_x)).
% 299.79/300.46 21463[0:SpR:21267.0,518.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_Com_Opname,w),x))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),x)).
% 299.79/300.46 21880[0:SpL:317.0,464.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(hAPP(w,x),u),hAPP(c_Set_Oimage(w,y,u),z))))* -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(hAPP(c_Set_Oinsert(x,y),z),v,w,y,u)),v)**.
% 299.79/300.46 22316[0:SpL:21893.0,263.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),v_x))) -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(w,u),v_x),c_Set_Oinsert(w,u),tc_Com_Opname,x)))* equal(v,w).
% 299.79/300.46 22308[0:SpL:21893.0,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),v_x)) -> hBOOL(hAPP(x,hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Set_Ovimage(u,v,w),x),v_x),hAPP(c_Set_Ovimage(u,v,w),x),tc_Com_Opname,y))))*.
% 299.79/300.46 22109[0:SpR:21893.0,34.1] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Set_Ovimage(v,w,x),u),v_x),hAPP(c_Set_Ovimage(v,w,x),u),tc_Com_Opname,y))))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,w,x),u),v_x)).
% 299.79/300.46 22089[0:SpR:21893.0,518.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),x))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),x)).
% 299.79/300.46 22404[0:SpR:97.1,313.1] || c_Fun_Oinj__on(u,v,w,x) c_lessequals(y,hAPP(c_Set_Oimage(u,w,x),v),tc_fun(x,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y),v,tc_fun(w,tc_bool))*.
% 299.79/300.46 22395[0:SpR:97.1,415.0] || c_Fun_Oinj__on(u,v,w,x) -> equal(c_Fun_Ofun__upd(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),hAPP(c_Set_Oimage(u,w,x),v),v,y,z),c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w))**.
% 299.79/300.46 22393[0:SpR:97.1,313.1] || c_Fun_Oinj__on(u,v,w,x) c_lessequals(hAPP(c_Set_Oimage(u,w,x),v),y,tc_fun(x,tc_bool)) -> c_lessequals(v,hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y),tc_fun(w,tc_bool))*.
% 299.79/300.46 22669[0:SpL:158.0,469.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Fun_Ocomp(w,x,y,u,z),z,u),x1)))* -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(hAPP(c_Set_Oimage(x,z,y),x1),w,v,y,u)),v)**.
% 299.79/300.46 22668[0:SpL:158.0,464.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Fun_Ocomp(w,x,y,u,z),z,u),x1)))* -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(hAPP(c_Set_Oimage(x,z,y),x1),v,w,y,u)),v)**.
% 299.79/300.46 22666[0:SpL:158.0,447.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),x)* c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(v,y,w),z),w,x)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,y,w),z),w).
% 299.79/300.46 22632[0:SpR:97.1,158.0] || c_Fun_Oinj__on(u,v,w,x) -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(y,c_Fun_Othe__inv__into(v,u,w,x),w,z,x),x,z),hAPP(c_Set_Oimage(u,w,x),v)),hAPP(c_Set_Oimage(y,w,z),v))**.
% 299.79/300.46 22631[0:SpR:317.0,158.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Oinsert(z,y),x1)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(hAPP(v,z),w),hAPP(c_Set_Oimage(v,y,w),x1))))*.
% 299.79/300.46 22630[0:SpR:158.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oimage(y,z,v),x1))),hAPP(c_Set_Oinsert(hAPP(u,x),w),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,y,v,w,z),z,w),x1)))*.
% 299.79/300.46 22629[0:SpR:158.0,158.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(c_Fun_Ocomp(u,v,w,x,y),z,y,x,x1),x1,x),x2),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),hAPP(c_Set_Oimage(z,x1,y),x2))))*.
% 299.79/300.46 22628[0:SpR:158.0,158.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Oimage(z,x1,y),x2)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,z,y,w,x1),x1,w),x2)))*.
% 299.79/300.46 22612[0:SpR:158.0,313.1] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(z,x,x1),u),hAPP(c_Set_Oimage(c_Fun_Ocomp(z,v,x,x1,w),w,x1),y),tc_fun(x1,tc_bool))*.
% 299.79/300.46 22609[0:SpR:158.0,98.1] || c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(v,w,x),y),x,z)* -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,x,z,w),w,z),y),z),c_Finite__Set_Ocard(hAPP(c_Set_Oimage(v,w,x),y),x))*.
% 299.79/300.46 22600[0:SpR:158.0,313.1] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(z,u,w,x1,v),v,x1),x),hAPP(c_Set_Oimage(z,w,x1),y),tc_fun(x1,tc_bool))*.
% 299.79/300.46 22593[0:SpR:158.0,158.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,c_Fun_Ocomp(v,w,x,y,z),y,x1,z),z,x1),x2),hAPP(c_Set_Oimage(u,y,x1),hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),x2))))*.
% 299.79/300.46 22573[0:SpR:158.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,z,w),x1))),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(v,y,w,x,z),z,x),x2,u),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)))))*.
% 299.79/300.46 22570[0:SpR:158.0,313.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(x,y,z,x1,w),w,x1),u),hAPP(c_Set_Oimage(x,z,x1),hAPP(c_Set_Oimage(y,w,z),v)),tc_fun(x1,tc_bool))*.
% 299.79/300.46 22515[0:SpR:158.0,313.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(x,y,z),hAPP(c_Set_Oimage(x1,w,y),u)),hAPP(c_Set_Oimage(c_Fun_Ocomp(x,x1,y,z,w),w,z),v),tc_fun(z,tc_bool))*.
% 299.79/300.46 23008[0:SpR:131.0,131.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,c_Fun_Ocomp(v,w,x,y,z),y,x1,z),z,x1),x2),hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),hAPP(c_Set_Ovimage(u,y,x1),x2))))*.
% 299.79/300.46 23007[0:SpR:131.0,131.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Ovimage(z,x,x1),x2)),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(c_Fun_Ocomp(z,u,x,x1,w),w,x1),x2)))*.
% 299.79/300.46 22991[0:SpR:131.0,129.1] || c_lessequals(u,hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(z,x1,w),u),hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,z,w,x,x1),x1,x),y),tc_fun(x1,tc_bool))*.
% 299.79/300.46 22981[0:SpR:131.0,129.1] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),y,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,z,v,w,x1),x1,w),x),hAPP(c_Set_Ovimage(z,x1,v),y),tc_fun(x1,tc_bool))*.
% 299.79/300.46 22976[0:SpR:131.0,131.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(c_Fun_Ocomp(u,v,w,x,y),z,y,x,x1),x1,x),x2),hAPP(c_Set_Ovimage(z,x1,y),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x2))))*.
% 299.79/300.46 22957[0:SpR:131.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),hAPP(c_Set_Ovimage(y,x,z),x1))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(y,v,x,z,w),w,z),x2,u),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)))))*.
% 299.79/300.46 22956[0:SpR:131.0,129.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,y,z,w,x1),x1,w),u),hAPP(c_Set_Ovimage(y,x1,z),hAPP(c_Set_Ovimage(x,z,w),v)),tc_fun(x1,tc_bool))*.
% 299.79/300.46 22908[0:SpR:131.0,129.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(x,y,z),hAPP(c_Set_Ovimage(x1,z,w),u)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x1,x,z,w,y),y,w),v),tc_fun(y,tc_bool))*.
% 299.79/300.46 23129[0:SpR:23.0,23.0] || -> equal(c_Fun_Ocomp(u,c_Fun_Ocomp(v,c_Fun_Ocomp(w,x,y,z,x1),z,x2,x1),x2,x3,x1),c_Fun_Ocomp(c_Fun_Ocomp(c_Fun_Ocomp(u,v,x2,x3,z),w,z,x3,y),x,y,x3,x1))*.
% 299.79/300.46 23128[0:SpR:23.0,23.0] || -> equal(c_Fun_Ocomp(u,c_Fun_Ocomp(v,c_Fun_Ocomp(w,x,y,z,x1),z,x2,x1),x2,x3,x1),c_Fun_Ocomp(c_Fun_Ocomp(u,c_Fun_Ocomp(v,w,z,x2,y),x2,x3,y),x,y,x3,x1))*.
% 299.79/300.46 23126[0:SpR:23.0,23.0] || -> equal(c_Fun_Ocomp(c_Fun_Ocomp(u,v,w,x,y),c_Fun_Ocomp(z,x1,x2,y,x3),y,x,x3),c_Fun_Ocomp(c_Fun_Ocomp(u,c_Fun_Ocomp(v,z,y,w,x2),w,x,x2),x1,x2,x,x3))*.
% 299.79/300.46 23125[0:SpR:23.0,131.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,c_Fun_Ocomp(v,w,x,y,z),y,x1,z),z,x1),x2),hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,y,x1,x),x,x1),x2)))*.
% 299.79/300.46 23124[0:SpR:23.0,158.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,c_Fun_Ocomp(v,w,x,y,z),y,x1,z),z,x1),x2),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,y,x1,x),x,x1),hAPP(c_Set_Oimage(w,z,x),x2)))*.
% 299.79/300.46 23121[0:SpR:23.0,23.0] || -> equal(c_Fun_Ocomp(u,c_Fun_Ocomp(c_Fun_Ocomp(v,w,x,y,z),x1,z,y,x2),y,x3,x2),c_Fun_Ocomp(c_Fun_Ocomp(u,v,y,x3,x),c_Fun_Ocomp(w,x1,z,x,x2),x,x3,x2))*.
% 299.79/300.46 23119[0:SpR:23.0,23.0] || -> equal(c_Fun_Ocomp(u,c_Fun_Ocomp(c_Fun_Ocomp(v,w,x,y,z),x1,z,y,x2),y,x3,x2),c_Fun_Ocomp(c_Fun_Ocomp(c_Fun_Ocomp(u,v,y,x3,x),w,x,x3,z),x1,z,x3,x2))*.
% 299.79/300.46 23118[0:SpR:23.0,131.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(c_Fun_Ocomp(u,v,w,x,y),z,y,x,x1),x1,x),x2),hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,z,y,w,x1),x1,w),hAPP(c_Set_Ovimage(u,w,x),x2)))*.
% 299.79/300.46 23117[0:SpR:23.0,158.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(c_Fun_Ocomp(u,v,w,x,y),z,y,x,x1),x1,x),x2),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,z,y,w,x1),x1,w),x2)))*.
% 299.79/300.46 23402[0:SpL:460.1,3489.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.79/300.46 23401[0:SpL:460.1,3487.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.46 23363[0:SpR:460.1,3294.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_in(t_a)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 23580[0:SpL:523.1,3489.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.79/300.46 23579[0:SpL:523.1,3487.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.46 23494[0:SpR:523.1,3294.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_in(t_a)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 24349[0:SpR:393.1,584.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(c_COMBS(c_Set_Oimage(c_COMBK(w,x,v),v,x),y,z,x1,x2),u),hAPP(hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),hAPP(y,u)))**.
% 299.79/300.46 24348[0:SpR:393.1,584.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(c_COMBS(w,c_Set_Oimage(c_COMBK(x,y,v),v,y),z,x1,x2),u),hAPP(hAPP(w,u),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))))**.
% 299.79/300.46 24347[0:SpR:393.1,1103.1] || -> equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oimage(c_COMBK(v,w,x),x,w)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Oimage(c_COMBK(v,w,x),x,w),t_a)* hBOOL(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))).
% 299.79/300.46 24316[0:SpR:393.1,415.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(c_Fun_Ofun__upd(c_Set_Oimage(c_COMBK(w,x,v),v,x),u,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),y,z),c_Set_Oimage(c_COMBK(w,x,v),v,x))**.
% 299.79/300.46 25136[0:Res:252.1,348.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),hAPP(c_Com_Ocom_OBODY,w)),x),t_a) equal(c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(w,u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(v,x,hAPP(c_Com_Ocom_OBODY,w),u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,x,hAPP(c_Com_Ocom_OBODY,w),u))),u)**.
% 299.79/300.46 25432[0:SpL:512.0,3489.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_in(tc_Com_Opname))** hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.79/300.46 25431[0:SpL:512.0,3487.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.46 25419[0:SpL:512.0,193.1] || c_Finite__Set_Ofinite(u,v) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(w,x,y),hAPP(c_Set_Oimage(z,v,x),u)),y),c_Finite__Set_Ocard(u,v))** -> c_Fun_Oinj__on(hAPP(c_COMBB(w,x,y,v),z),u,v,y)*.
% 299.79/300.46 25388[0:SpR:512.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),z,x1,x2,x3),x4),hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),x4)),hAPP(z,x4)))*.
% 299.79/300.46 25387[0:SpR:512.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oimage(hAPP(c_COMBB(v,w,x,y),z),y,x),x1,x2,x3),x4),hAPP(hAPP(u,x4),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(z,y,w),x4))))*.
% 299.79/300.46 25345[0:SpR:512.0,3294.1] || equal(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_in(t_a))** -> equal(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),v_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 25733[0:Res:687.1,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname),t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.79/300.46 25732[0:Res:686.1,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname),t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.79/300.46 25708[0:Res:510.1,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),x),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,y),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.46 25707[0:Res:511.1,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),x),v),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,y),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.46 25684[0:SpL:8415.2,455.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(v_x,u)) c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.79/300.46 25809[0:SpL:8415.2,273.0] || equal(v_Procs,v_x) equal(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),v_x)** -> equal(v,v_x).
% 299.79/300.46 25977[0:SpL:339.0,3507.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),y)))* equal(hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v_x)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.79/300.46 25976[0:SpL:339.0,16327.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x)))* equal(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_Procs) -> .
% 299.79/300.46 25975[0:SpL:339.0,3499.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x))) hBOOL(hAPP(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.79/300.46 25969[0:SpL:339.0,13272.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.79/300.46 25968[0:SpL:339.0,3484.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Com_Ocom_OBODY) equal(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),hAPP(c_Com_Ocom_OBODY,x))* -> equal(v_x,x).
% 299.79/300.46 25946[0:SpR:8415.2,339.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Set_Oinsert(u,v)) -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w))**.
% 299.79/300.46 25900[0:SpR:339.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x,y),hAPP(c_Set_Oinsert(z,x),x1)),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z))))*.
% 299.79/300.46 25880[0:SpR:339.0,9569.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w))),x),tc_bool)*.
% 299.79/300.46 25879[0:SpR:339.0,9568.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w))),z),x),tc_bool)*.
% 299.79/300.46 25867[0:SpR:339.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),y))) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v_x))))*.
% 299.79/300.46 25866[0:SpR:339.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x)),tc_Com_Opname,y),u),hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x))))*.
% 299.79/300.46 25865[0:SpR:339.0,3317.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x))) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),hAPP(c_Set_Oinsert(v_x,u),y)))*.
% 299.79/300.46 25864[0:SpR:339.0,3305.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,y),v_Procs),hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x))))*.
% 299.79/300.46 25860[0:SpR:339.0,2771.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x))) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.79/300.46 25854[0:SpR:339.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),tc_Com_Opname,x),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.46 25853[0:SpR:339.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),t_a,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.46 25850[0:SpR:339.0,15262.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_in(t_a)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.79/300.46 25847[0:SpR:339.0,8376.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_in(tc_Com_Opname)) equal(x,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),x))*.
% 299.79/300.46 25846[0:SpR:339.0,8415.2] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),v_x)**.
% 299.79/300.46 25845[0:SpR:339.0,3291.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),v_Procs))*.
% 299.79/300.46 25844[0:SpR:339.0,3285.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)))*.
% 299.79/300.46 25840[0:SpR:339.0,3279.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),v_Procs),v_x))*.
% 299.79/300.46 26289[0:Rew:339.0,26206.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),y))),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y))))*.
% 299.79/300.46 26180[0:SpR:8415.2,338.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),v_x)),hAPP(c_Set_Oinsert(w,u),v_x))**.
% 299.79/300.46 26156[0:SpR:8415.2,338.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Set_Oinsert(u,v)) -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x))**.
% 299.79/300.46 26155[0:SpR:353.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(x,u),y))),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),y))))*.
% 299.79/300.46 26135[0:SpR:338.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z),w),x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),hAPP(c_Set_Oinsert(u,v),z))))*.
% 299.79/300.46 26124[0:SpR:338.0,254.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(y,u),x))))*.
% 299.79/300.46 26111[0:SpR:338.0,9569.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),c_Set_Oinsert(w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)),tc_bool)*.
% 299.79/300.46 26110[0:SpR:338.0,9568.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Oinsert(w,u)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)),tc_bool)*.
% 299.79/300.46 26095[0:SpR:338.0,2097.1] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(x,u),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w))**.
% 299.79/300.46 26080[0:SpR:338.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(x,u),y))),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y))))*.
% 299.79/300.46 26065[0:SpR:338.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(y,u),z),w),x1)),hAPP(c_Set_Oinsert(y,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z))))*.
% 299.79/300.46 26045[0:SpR:338.0,9569.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)),hAPP(c_Set_Oinsert(u,v),x)),tc_bool)*.
% 299.79/300.46 26044[0:SpR:338.0,9568.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)),z),hAPP(c_Set_Oinsert(u,v),x)),tc_bool)*.
% 299.79/300.46 26041[0:SpR:338.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)),y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v))**.
% 299.79/300.46 26359[0:SpL:339.0,85.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),tc_fun(w,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),y,tc_fun(w,tc_bool)).
% 299.79/300.46 26355[0:SpL:338.0,85.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),tc_fun(w,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),y),tc_fun(w,tc_bool)).
% 299.79/300.46 26327[0:SpL:8415.2,85.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(v,hAPP(v_x,w),tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))*.
% 299.79/300.46 26529[0:Res:84.1,2092.0] || c_lessequals(c_HOL_Ominus__class_Ominus(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)),v,tc_fun(tc_Com_Opname,tc_bool)) -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v))**.
% 299.79/300.46 26504[0:SpR:339.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),y,tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),tc_fun(w,tc_bool))*.
% 299.79/300.46 26500[0:SpR:338.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),y),tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y)),tc_fun(w,tc_bool))*.
% 299.79/300.46 26477[0:SpR:8415.2,84.1] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(c_HOL_Ominus__class_Ominus(w,v,tc_fun(u,tc_bool)),v_x,tc_fun(u,tc_bool))* -> c_lessequals(w,v_x,tc_fun(u,tc_bool)).
% 299.79/300.46 26472[0:SpR:8415.2,84.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))* -> c_lessequals(v,hAPP(v_x,w),tc_fun(u,tc_bool)).
% 299.79/300.46 26836[0:SpR:353.0,56.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,u),hAPP(c_Set_Oinsert(v,u),y)),w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,u),y),w,tc_fun(u,tc_bool)))**.
% 299.79/300.46 26952[0:Res:424.2,402.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(x,w,tc_fun(u,tc_bool)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool))* -> equal(hAPP(c_Set_Oinsert(v,u),x),w).
% 299.79/300.46 26931[0:SpR:353.0,424.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_Set_Oinsert(x,u),y),w,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(x,u),hAPP(c_Set_Oinsert(v,u),y)),w,tc_fun(u,tc_bool))*.
% 299.79/300.46 27002[0:SpL:584.0,175.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Ovimage(v,u,w),x,y,z),hAPP(c_Set_Oinsert(x1,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))))* -> equal(hAPP(v,hAPP(c_Set_Oinsert(x1,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),x1).
% 299.79/300.46 26997[0:SpL:8415.2,175.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))* -> equal(hAPP(v,v_x),x).
% 299.79/300.46 27053[0:SpL:8415.2,280.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(v,v_x),w)) hBOOL(hAPP(v_x,x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,u,tc_fun(y,tc_bool)),w))*.
% 299.79/300.46 27373[0:SpL:8415.2,470.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x))) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(x,v_x,v,w,u)),x))*.
% 299.79/300.46 27366[0:SpL:8415.2,470.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_x,x,u,v,w)),v_x))*.
% 299.79/300.46 27433[0:SpL:8415.2,466.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x))) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,v_x,w,u)),x))*.
% 299.79/300.46 27426[0:SpL:8415.2,466.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_x,u,x,v,w)),v_x))*.
% 299.79/300.46 27576[0:SpR:414.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Fun_Ofun__upd(x,v,y,z,x1),w,u,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Fun_Ofun__upd(x,v,y,z,x1),u,x2),y),v)**.
% 299.79/300.46 27567[0:SpR:524.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),w,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),u,y),v),v)**.
% 299.79/300.46 27563[0:SpR:8415.2,373.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(u,w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,u,v,x),v_x),v_x)**.
% 299.79/300.46 27559[0:SpR:365.1,373.2] class_Orderings_Obot(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,x),c_Orderings_Obot__class_Obot(u)),v_x)**.
% 299.79/300.46 27558[0:SpR:397.1,373.2] class_Orderings_Otop(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,x),c_Orderings_Otop__class_Otop(u)),v_x)**.
% 299.79/300.46 27544[0:SpR:3744.1,373.2] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,u),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oinsert(v_x,u),v,x),v_Procs),v_Procs)**.
% 299.79/300.46 27534[0:SpR:373.2,20881.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x1),hAPP(c_Set_Oinsert(hAPP(x,v),z),x2)),v))*.
% 299.79/300.46 27527[0:SpR:373.2,474.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> hBOOL(hAPP(hAPP(c_in(z),v),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(w,x,u,y),x1,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.79/300.46 27522[0:SpR:373.2,9569.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),c_Hilbert__Choice_Oinv__into(w,x,u,y)),hAPP(x,v)),tc_bool)*.
% 299.79/300.46 27521[0:SpR:373.2,9568.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Hilbert__Choice_Oinv__into(w,x,u,y)),x1),hAPP(x,v)),tc_bool)*.
% 299.79/300.46 27729[0:SpR:414.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Fun_Ofun__upd(x,v,y,z,x1),w,u,x2) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Fun_Ofun__upd(x,v,y,z,x1),u,x2),y),v)**.
% 299.79/300.46 27720[0:SpR:524.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),w,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),u,y),v),v)**.
% 299.79/300.46 27716[0:SpR:8415.2,71.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(u,w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,u,v,x),v_x),v_x)**.
% 299.79/300.46 27712[0:SpR:365.1,71.2] class_Orderings_Obot(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,x),c_Orderings_Obot__class_Obot(u)),v_x)**.
% 299.79/300.46 27711[0:SpR:397.1,71.2] class_Orderings_Otop(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,x),c_Orderings_Otop__class_Otop(u)),v_x)**.
% 299.79/300.46 27696[0:SpR:3744.1,71.2] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,u),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oinsert(v_x,u),v,x),v_Procs),v_Procs)**.
% 299.79/300.46 27686[0:SpR:71.2,20881.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(w,x,u,y),z,x1),hAPP(c_Set_Oinsert(hAPP(x,v),z),x2)),v))*.
% 299.79/300.46 27679[0:SpR:71.2,474.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> hBOOL(hAPP(hAPP(c_in(z),v),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(w,x,u,y),x1,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.79/300.46 27673[0:SpR:71.2,9569.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),c_Fun_Othe__inv__into(w,x,u,y)),hAPP(x,v)),tc_bool)*.
% 299.79/300.46 27672[0:SpR:71.2,9568.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> c_lessequals(v,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Fun_Othe__inv__into(w,x,u,y)),x1),hAPP(x,v)),tc_bool)*.
% 299.79/300.46 27946[0:Res:468.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,v),t_a)* -> equal(hAPP(c_Set_Oimage(w,tc_Hoare__Mirabelle_Otriple(t_a),x),v),hAPP(c_Set_Oimage(y,tc_Hoare__Mirabelle_Otriple(t_a),x),v)) c_Hoare__Mirabelle_Otriple__valid(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,w,y,tc_Hoare__Mirabelle_Otriple(t_a),x),t_a)*.
% 299.79/300.46 28243[0:SpL:465.1,390.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),z),y)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(y,c_Fun_Ofun__upd(v,z,x1,w,x),w,x),u,x,w)*.
% 299.79/300.46 28238[0:SpL:465.1,3507.1] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(c_Fun_Ofun__upd(w,x,y,z,x1),z,x1))* equal(hAPP(c_Set_Oimage(w,z,x1),v_x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(z),x),v_x)).
% 299.79/300.46 28237[0:SpL:465.1,16327.1] || equal(u,c_Set_Oimage(c_Fun_Ofun__upd(v,w,x,y,z),y,z))* equal(hAPP(c_Set_Oimage(v,y,z),v_x),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(y),w),v_x)).
% 299.79/300.46 28236[0:SpL:465.1,3499.1] || equal(c_in(u),c_Set_Oimage(c_Fun_Ofun__upd(v,w,x,y,z),y,z))* hBOOL(hAPP(hAPP(c_Set_Oimage(v,y,z),v_x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(y),w),v_x)).
% 299.79/300.46 28231[0:SpL:465.1,13272.0] || equal(hAPP(c_Set_Oimage(u,v,w),v_x),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),z)* -> hBOOL(hAPP(hAPP(c_in(v),x),v_x)) hBOOL(hAPP(z,v_x))*.
% 299.79/300.46 28230[0:SpL:465.1,3484.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Com_Ocom_OBODY)** equal(hAPP(c_Set_Oimage(u,x,y),v_x),hAPP(c_Com_Ocom_OBODY,z))* -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) equal(v_x,z).
% 299.79/300.46 28222[0:SpL:465.1,202.1] || c_Finite__Set_Ofinite(u,v) c_lessequals(u,hAPP(c_Set_Oimage(w,v,v),u),tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),x),u)) c_Fun_Oinj__on(c_Fun_Ofun__upd(w,x,y,v,v),u,v,v)*.
% 299.79/300.46 28195[0:SpR:465.1,20881.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1,x2),hAPP(c_Set_Oinsert(w,x1),x3)),hAPP(c_Set_Oimage(x,u,z),w)))*.
% 299.79/300.46 28176[0:SpR:465.1,9569.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_Set_Oimage(x,u,y),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),c_Set_Oimage(c_Fun_Ofun__upd(x,v,x2,u,y),u,y)),w),tc_bool)*.
% 299.79/300.46 28175[0:SpR:465.1,9568.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_Set_Oimage(x,u,y),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Set_Oimage(c_Fun_Ofun__upd(x,v,x1,u,y),u,y)),x2),w),tc_bool)*.
% 299.79/300.46 28171[0:SpR:465.1,3346.1] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(c_Fun_Ofun__upd(w,x,y,z,x1),z,x1))* -> hBOOL(hAPP(hAPP(c_in(z),x),v_x)) hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(w,z,x1),v_x)))*.
% 299.79/300.46 28170[0:SpR:465.1,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),w),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(x,w,y,v,z),v,z),tc_Com_Opname,x1),u),hAPP(c_Set_Oimage(x,v,z),v_x)))*.
% 299.79/300.46 28169[0:SpR:465.1,3317.1] || equal(c_in(u),c_Set_Oimage(c_Fun_Ofun__upd(v,w,x,y,z),y,z))* -> hBOOL(hAPP(hAPP(c_in(y),w),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(v,y,z),v_x),hAPP(c_Set_Oinsert(v_x,u),x1)))*.
% 299.79/300.46 28168[0:SpR:465.1,3305.1] || equal(u,c_Set_Oimage(c_Fun_Ofun__upd(v,w,x,y,z),y,z))* -> hBOOL(hAPP(hAPP(c_in(y),w),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x1),v_Procs),hAPP(c_Set_Oimage(v,y,z),v_x)))*.
% 299.79/300.46 28164[0:SpR:465.1,2771.1] || equal(u,c_Set_Oimage(c_Fun_Ofun__upd(v,w,x,y,z),y,z))* -> hBOOL(hAPP(hAPP(c_in(y),w),v_x)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(v,y,z),v_x),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.79/300.46 28156[0:SpR:465.1,21131.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),tc_Com_Opname,z),hAPP(c_Set_Oinsert(x1,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oimage(w,u,y),v_x)))*.
% 299.79/300.46 28155[0:SpR:465.1,21143.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),t_a,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Oimage(w,u,y),v_x)))*.
% 299.79/300.46 28152[0:SpR:465.1,15262.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(u,x,y),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.79/300.46 28149[0:SpR:465.1,8376.2] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_in(tc_Com_Opname))** equal(z,v_Procs) -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(u,x,y),v_x),z))*.
% 299.79/300.46 28148[0:SpR:465.1,8415.2] || equal(v_Procs,v_x) equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) equal(hAPP(c_Set_Oimage(u,x,y),v_x),v_x).
% 299.79/300.46 28147[0:SpR:465.1,3291.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(c_Set_Oimage(u,x,y),v_x)),v_Procs))*.
% 299.79/300.46 28146[0:SpR:465.1,3285.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oimage(u,x,y),v_x),hAPP(c_Set_Oinsert(z,tc_Com_Opname),v_Procs)))*.
% 299.79/300.46 28142[0:SpR:465.1,3279.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(hAPP(c_Set_Oimage(u,x,y),v_x),v_Procs),v_x))*.
% 299.79/300.46 28568[0:SpL:118.0,95.0] || c_Fun_Oinj__on(c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,w,x,y),z,hAPP(u,x1),y,x),x2,y,x)* -> c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(v,z,x1,y,w),y,w),x2),w,x)*.
% 299.79/300.46 28543[0:SpR:9987.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),c_Fun_Ofun__upd(u,v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),u,y,z,x),v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,z))*.
% 299.79/300.46 28541[0:SpR:2095.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(u,v),w,z,x1,y),x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),y,x1))*.
% 299.79/300.46 28537[0:SpR:23902.1,118.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(c_Fun_Ocomp(hAPP(u,v_x),c_Fun_Ofun__upd(v,w,c_Orderings_Obot__class_Obot(tc_bool),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(u,v_x),v,y,z,x),w,v_x,x,z))*.
% 299.79/300.46 28534[0:SpR:2935.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_in(t_a),v_x),c_Fun_Ofun__upd(u,v,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),w,x),x,y,w),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_in(t_a),v_x),u,x,y,w),v,c_Orderings_Obot__class_Obot(tc_bool),w,y))*.
% 299.79/300.46 28529[0:SpR:301.1,118.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Fun_Ofun__upd(w,x,c_Orderings_Obot__class_Obot(u),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,z,x1,y),x,v,y,x1))*.
% 299.79/300.46 28486[0:SpR:414.0,118.0] || -> equal(c_Fun_Ocomp(c_Fun_Ofun__upd(u,v,w,x,y),c_Fun_Ofun__upd(z,x1,v,x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Fun_Ofun__upd(u,v,w,x,y),z,x3,x4,x2),x1,w,x2,x4))*.
% 299.79/300.46 28477[0:SpR:524.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Fun_Ofun__upd(w,x,v,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,z,x1,y),x,v,y,x1))*.
% 299.79/300.46 28473[0:SpR:8415.2,118.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,w,v_x,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,y,z,x),w,v_x,x,z))*.
% 299.79/300.46 28469[0:SpR:365.1,118.0] class_Orderings_Obot(u) || -> equal(c_Fun_Ocomp(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Fun_Ofun__upd(v,w,v_x,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,y,z,x),w,c_Orderings_Obot__class_Obot(u),x,z))*.
% 299.79/300.46 28468[0:SpR:397.1,118.0] class_Orderings_Otop(u) || -> equal(c_Fun_Ocomp(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Fun_Ofun__upd(v,w,v_x,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,y,z,x),w,c_Orderings_Otop__class_Otop(u),x,z))*.
% 299.79/300.46 28454[0:SpR:2093.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_Procs,u),c_Fun_Ofun__upd(v,w,hAPP(c_in(tc_Com_Opname),v_x),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_Procs,u),v,y,z,x),w,hAPP(c_in(tc_Com_Opname),v_x),x,z))*.
% 299.79/300.46 28452[0:SpR:3744.1,118.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_x,u),c_Fun_Ofun__upd(v,w,v_Procs,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_x,u),v,y,z,x),w,v_Procs,x,z))*.
% 299.79/300.46 29173[0:SpL:537.1,3698.2] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* equal(c_Com_Ocom_OBODY,v) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.46 29167[0:SpL:537.1,3493.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(tc_Com_Opname)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> .
% 299.79/300.46 29051[0:SpR:537.1,7253.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z))))*.
% 299.79/300.46 29016[0:SpR:537.1,3339.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> equal(c_Fun_Ofun__upd(v,v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),y,z),v)**.
% 299.79/300.46 29015[0:SpR:537.1,3316.1] class_Lattices_Olattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.79/300.46 29012[0:SpR:537.1,648.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),tc_Com_Opname,v),v_Procs)))*.
% 299.79/300.46 29007[0:SpR:537.1,28031.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.46 29005[0:SpR:537.1,27381.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.46 29001[0:SpR:537.1,28334.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.46 28999[0:SpR:537.1,27441.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.46 28998[0:SpR:537.1,21141.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),t_a,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.46 28996[0:SpR:537.1,11030.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.79/300.46 28995[0:SpR:537.1,10090.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.46 28989[0:SpR:537.1,3284.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.46 28984[2:SpR:537.1,15483.1] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool))*.
% 299.79/300.46 28982[0:SpR:537.1,15482.1] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_fun(t_a,tc_bool)),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool))*.
% 299.79/300.46 28981[7:SpR:537.1,27219.1] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_fun(t_a,tc_bool)),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool))*.
% 299.79/300.46 28978[0:SpR:537.1,651.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.46 28974[0:SpR:537.1,21130.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_Procs))))*.
% 299.79/300.46 29289[0:SSi:29288.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))**.
% 299.79/300.46 29698[0:SpL:534.1,3698.2] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* equal(c_Com_Ocom_OBODY,v) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.46 29692[0:SpL:534.1,3493.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(tc_Com_Opname)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> .
% 299.79/300.46 29574[0:SpR:534.1,7253.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z))))*.
% 299.79/300.46 29538[0:SpR:534.1,3339.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> equal(c_Fun_Ofun__upd(v,v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),y,z),v)**.
% 299.79/300.46 29537[0:SpR:534.1,3316.1] class_Lattices_Oupper__semilattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))*.
% 299.79/300.46 29534[0:SpR:534.1,648.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),tc_Com_Opname,v),v_Procs)))*.
% 299.79/300.46 29529[0:SpR:534.1,28031.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.46 29527[0:SpR:534.1,27381.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.46 29523[0:SpR:534.1,28334.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.46 29521[0:SpR:534.1,27441.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.46 29520[0:SpR:534.1,21141.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),t_a,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.46 29518[0:SpR:534.1,11030.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.79/300.46 29517[0:SpR:534.1,10090.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.46 29511[0:SpR:534.1,3284.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.46 29506[2:SpR:534.1,15483.1] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool))*.
% 299.79/300.46 29504[0:SpR:534.1,15482.1] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_fun(t_a,tc_bool)),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool))*.
% 299.79/300.46 29503[7:SpR:534.1,27219.1] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_fun(t_a,tc_bool)),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool))*.
% 299.79/300.46 29500[0:SpR:534.1,651.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.46 29496[0:SpR:534.1,21130.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_Procs))))*.
% 299.79/300.46 29926[0:SpR:27043.1,317.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),x)))*.
% 299.79/300.46 29925[0:SpR:27043.1,99.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_Procs,u),v,w),v_x),v_x)**.
% 299.79/300.46 29924[0:SpR:27043.1,438.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_Procs,u),v,w),v_x),v_x)**.
% 299.79/300.46 30494[0:Rew:30493.2,29054.2] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)),z)**.
% 299.79/300.46 31041[0:Rew:31040.2,29577.2] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)),z)**.
% 299.79/300.46 31312[0:Res:687.1,356.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,u),u,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,v_Procs,hAPP(c_in(u),v),tc_Com_Opname)),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.79/300.46 31311[0:Res:686.1,356.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,u),u,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,y,hAPP(c_in(u),v),tc_Com_Opname)),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.79/300.46 31276[0:Res:153.1,356.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* -> equal(hAPP(c_Set_Oimage(c_COMBK(y,z,x1),x1,z),hAPP(c_Set_Ovimage(v,x1,u),x)),hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))**.
% 299.79/300.46 31268[0:Res:510.1,356.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(c_Set_Oimage(c_COMBK(x,y,u),u,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z)),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.46 31267[0:Res:511.1,356.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(c_Set_Oimage(c_COMBK(x,y,u),u,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),w)),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.46 31414[0:SpL:540.1,449.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,c_Lattices_Oupper__semilattice__class_Osup(u),w,x)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,c_Lattices_Oupper__semilattice__class_Osup(u),w,x)))* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),c_Lattices_Oupper__semilattice__class_Osup(u)),t_a).
% 299.79/300.46 31413[0:SpL:539.1,449.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,c_Lattices_Oupper__semilattice__class_Osup(u),w,x)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,c_Lattices_Oupper__semilattice__class_Osup(u),w,x)))* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),c_Lattices_Oupper__semilattice__class_Osup(u)),t_a).
% 299.79/300.46 31398[0:SpL:9936.1,449.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,x))) -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),t_a)*.
% 299.79/300.46 31488[0:SpL:339.0,24254.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.79/300.46 31476[0:SpL:465.1,24254.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(c_Set_Oimage(u,x,y),v_x),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)).
% 299.79/300.46 32068[0:Res:151.2,278.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_in(u),v),y))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool)),z,x,u)))*.
% 299.79/300.46 32067[0:Res:151.2,277.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_in(u),v),y))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool)),x,u)))*.
% 299.79/300.46 32374[0:Res:526.1,477.0] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(x),y),u),y))* hBOOL(hAPP(hAPP(c_in(u),z),v))* -> hBOOL(hAPP(hAPP(c_in(x),y),z))*.
% 299.79/300.46 32315[0:SpL:104.0,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),u,x)))* hBOOL(hAPP(hAPP(c_in(x),y),c_HOL_Ouminus__class_Ouminus(v,tc_fun(x,tc_bool))))* -> hBOOL(hAPP(u,y))*.
% 299.79/300.46 32408[0:MRR:32359.1,9408.1] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(hAPP(c_in(u),y),v))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),y))*.
% 299.79/300.46 32554[0:Res:526.1,476.0] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(x),y),u),y))* hBOOL(hAPP(hAPP(c_in(u),z),w))* -> hBOOL(hAPP(hAPP(c_in(x),y),z))*.
% 299.79/300.46 32586[0:MRR:32539.1,9408.1] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(hAPP(c_in(u),y),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),y))*.
% 299.79/300.46 32640[0:SpR:339.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),tc_Com_Opname,x),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))),v_Procs))*.
% 299.79/300.46 32628[0:SpR:465.1,31533.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),tc_Com_Opname,z),hAPP(c_Set_Oimage(w,u,y),v_x))),v_Procs))*.
% 299.79/300.46 33010[0:SpR:9925.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),v)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u,w),v)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u,w),v))**.
% 299.79/300.46 32986[0:SpR:23682.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(v,x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,x),w))**.
% 299.79/300.46 32906[0:SpR:8385.1,475.1] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> equal(hAPP(c_Set_Oinsert(u,x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,x),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,x),w))**.
% 299.79/300.46 32874[0:SpR:475.1,9567.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(hAPP(x,v),y),z,tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(x,u,y),w)),hAPP(c_Set_Oimage(x,u,y),w),tc_bool)*.
% 299.79/300.46 32847[0:SpR:475.1,5875.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oimage(x,u,y),w),z),c_Set_Oinsert(hAPP(x,v),y),x1,x2,x3),hAPP(c_Set_Oimage(x,u,y),w)))*.
% 299.79/300.46 33296[0:SpR:339.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),tc_Com_Opname,x),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.46 33284[0:SpR:465.1,32668.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),tc_Com_Opname,z),hAPP(c_Set_Oimage(w,u,y),v_x)),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.46 33439[0:Res:1103.1,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),w)),t_a)* -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),w),t_a) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,x)),u))* c_Hoare__Mirabelle_Otriple__valid(x,w,t_a)*.
% 299.79/300.46 33402[0:Res:254.1,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(t_a)),v),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,y)),w))* c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.46 33390[0:SpL:584.0,453.0] || hBOOL(hAPP(c_COMBS(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u,v,w,x),y))* c_Hoare__Mirabelle_Ohoare__valids(z,hAPP(u,y),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(z,x1)),z))* c_Hoare__Mirabelle_Otriple__valid(x1,y,t_a)*.
% 299.79/300.46 33443[4:MRR:33387.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_Set_Oinsert(v_x,tc_Com_Opname))** c_Hoare__Mirabelle_Ohoare__valids(v,v_x,t_a) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.46 33515[0:SpL:61.1,522.0] || c_Finite__Set_Ofinite(u,v) c_Hoare__Mirabelle_Otriple__valid(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,v),u),v),x,y) -> c_Hoare__Mirabelle_Otriple__valid(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),x,y)*.
% 299.79/300.46 33582[0:SpR:339.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),x)),tc_Com_Opname,y)))*.
% 299.79/300.46 33570[0:SpR:465.1,28704.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(x,u,y),v_x),c_Set_Oimage(c_Fun_Ofun__upd(x,v,z,u,y),u,y),tc_Com_Opname,x1)))*.
% 299.79/300.46 33673[0:SpR:339.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x)),hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),tc_Com_Opname,y)))*.
% 299.79/300.46 33661[0:SpR:465.1,28859.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),hAPP(c_Set_Oimage(x,u,z),v_x),tc_Com_Opname,x1)))*.
% 299.79/300.46 33764[7:SpL:339.0,31886.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x)))* equal(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_x) -> .
% 299.79/300.46 33752[7:SpL:465.1,31886.1] || equal(u,c_Set_Oimage(c_Fun_Ofun__upd(v,w,x,y,z),y,z))* equal(hAPP(c_Set_Oimage(v,y,z),v_x),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_x) -> hBOOL(hAPP(hAPP(c_in(y),w),v_x)).
% 299.79/300.46 33803[0:Res:248.4,17530.1] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* equal(c_Finite__Set_Olinorder__class_OMin(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) equal(c_Finite__Set_Olinorder__class_OMin(v,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.79/300.46 33856[0:SpR:23965.1,383.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)) -> equal(v,v_x) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(u,v_x,v_x,x,y),v,w,x,y),c_Fun_Ofun__upd(u,v,w,x,y))**.
% 299.79/300.46 33883[0:Res:247.4,17530.1] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* equal(c_Finite__Set_Olinorder__class_OMax(v,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) equal(c_Finite__Set_Olinorder__class_OMax(u,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.79/300.46 34356[0:SpL:24914.0,62.0] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),v_x),tc_fun(w,tc_bool)),w) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,x),hAPP(c_Set_Oinsert(v,w),v_x)),tc_fun(w,tc_bool)),w)*.
% 299.79/300.46 34277[0:SpL:24914.0,357.1] || c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v)* c_lessequals(y,hAPP(c_Set_Oimage(u,v,w),v_x),tc_fun(w,tc_bool))* -> c_Finite__Set_Ofinite(y,w).
% 299.79/300.46 34264[0:SpL:24914.0,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),u))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,w),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x)),t_a)*.
% 299.79/300.46 34133[0:SpR:24914.0,9569.0] || -> c_lessequals(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),x),tc_bool)*.
% 299.79/300.46 34103[0:SpR:24914.0,118.0] || -> equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,w,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,x),hAPP(u,v_x)),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,z,x1,y),w,hAPP(u,v_x),y,x1))*.
% 299.79/300.46 34024[0:SpR:24914.0,63.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,x),hAPP(c_Set_Oinsert(v,w),v_x)),tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),v_x),tc_fun(w,tc_bool)),w).
% 299.79/300.46 34023[0:SpR:24914.0,446.1] || c_lessequals(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,x),hAPP(c_Set_Oinsert(v,w),v_x)),tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,w),u),hAPP(c_Set_Oinsert(v,w),v_x),tc_fun(w,tc_bool)).
% 299.79/300.46 33915[0:SpR:24914.0,446.1] || c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),x,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(u,v),v_x),hAPP(c_Set_Oinsert(u,v),x),tc_fun(v,tc_bool)).
% 299.79/300.46 34505[0:Rew:584.0,34026.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),u)*.
% 299.79/300.46 34506[0:Rew:584.0,34025.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),u)*.
% 299.79/300.46 34510[0:Rew:56.1,34181.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,x),hAPP(c_Set_Oinsert(v,u),v_x)),w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v_x,w,tc_fun(u,tc_bool)))**.
% 299.79/300.46 34531[1:MRR:33906.0,31533.0] || -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Com_Ocom_OBODY,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_P,tc_Com_Opname,u),hAPP(v_P,v_x)))),hAPP(v_Q,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_P,tc_Com_Opname,u),hAPP(v_P,v_x)))),t_a)*.
% 299.79/300.46 34532[1:MRR:33904.0,31533.0] || -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Ocom_OBODY,tc_Com_Opname,u),hAPP(c_Com_Ocom_OBODY,v_x)))),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(v_Q,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Ocom_OBODY,tc_Com_Opname,u),hAPP(c_Com_Ocom_OBODY,v_x)))),t_a)*.
% 299.79/300.46 34533[1:MRR:33903.0,31533.0] || -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_Q,tc_Com_Opname,u),hAPP(v_Q,v_x)))),hAPP(c_Com_Ocom_OBODY,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v_Q,tc_Com_Opname,u),hAPP(v_Q,v_x)))),hAPP(v_Q,v_x)),t_a)*.
% 299.79/300.46 34655[0:SpL:55.1,371.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)),y))* -> hBOOL(hAPP(hAPP(c_in(v),u),x)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),y)) equal(u,y).
% 299.79/300.46 34611[0:SpR:55.1,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),z,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.46 34589[0:SpR:55.1,9566.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(y,z),c_Set_Oinsert(v,u)),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool))),tc_bool)*.
% 299.79/300.46 34587[0:SpR:55.1,415.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_Fun_Ofun__upd(c_Set_Oinsert(v,u),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),y,z),c_Set_Oinsert(v,u))**.
% 299.79/300.46 34891[0:SpR:339.0,28053.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),u,tc_Com_Opname,y)))*.
% 299.79/300.46 34879[0:SpR:465.1,28053.1] || equal(u,c_Set_Oimage(c_Fun_Ofun__upd(v,w,x,y,z),y,z))* -> hBOOL(hAPP(hAPP(c_in(y),w),v_x)) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(v,y,z),v_x),u,tc_Com_Opname,x1)))*.
% 299.79/300.46 34970[0:SpR:339.0,28356.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),tc_Com_Opname,y)))*.
% 299.79/300.46 34958[0:SpR:465.1,28356.1] || equal(u,c_Set_Oimage(c_Fun_Ofun__upd(v,w,x,y,z),y,z))* -> hBOOL(hAPP(hAPP(c_in(y),w),v_x)) hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(c_Set_Oimage(v,y,z),v_x),tc_Com_Opname,x1)))*.
% 299.79/300.46 35379[0:SpR:23840.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),u),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u,tc_fun(x,tc_bool))))*.
% 299.79/300.46 35326[0:SpR:10463.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),v,tc_fun(y,tc_bool))))*.
% 299.79/300.46 35325[0:SpR:9911.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),v,tc_fun(y,tc_bool))))*.
% 299.79/300.46 35195[0:SpR:410.0,9566.0] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,u))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool))),tc_bool)*.
% 299.79/300.46 35650[0:SSi:35621.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_COMBB(c_COMBK(y,tc_fun(z,tc_bool),w),w,tc_fun(z,tc_bool),v),u),v,tc_fun(z,tc_bool)),y)**.
% 299.79/300.46 36175[0:SpL:3229.1,516.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))* -> hBOOL(hAPP(hAPP(c_in(v),v_x),w)) hBOOL(hAPP(hAPP(c_in(v),v_x),x)).
% 299.79/300.46 36124[0:SpL:3229.1,516.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(hAPP(c_in(v),x),hAPP(u,v_x)))* -> hBOOL(hAPP(hAPP(c_in(v),x),w))* hBOOL(hAPP(hAPP(c_in(v),x),v_x)).
% 299.79/300.46 36118[0:SpL:3229.1,516.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_in(v),w),hAPP(hAPP(u,v_x),x)))* -> hBOOL(hAPP(hAPP(c_in(v),w),v_x)) hBOOL(hAPP(hAPP(c_in(v),w),x)).
% 299.79/300.46 36789[0:SSi:36788.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),hAPP(hAPP(c_Set_Oinsert(v,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x),tc_bool),hAPP(w,v_x),tc_bool),c_HOL_Ominus__class_Ominus(hAPP(u,v_x),hAPP(hAPP(c_Set_Oinsert(v,t_a),w),v_x),tc_bool))**.
% 299.79/300.46 36915[0:SSi:36914.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),hAPP(v,v_x),tc_bool),hAPP(hAPP(c_Set_Oinsert(w,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x),tc_bool),c_HOL_Ominus__class_Ominus(hAPP(u,v_x),hAPP(hAPP(c_Set_Oinsert(w,t_a),v),v_x),tc_bool))**.
% 299.79/300.46 36918[0:Rew:66.0,36879.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),hAPP(c_Set_Oinsert(y,u),w),tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,u),w),tc_fun(u,tc_bool)))**.
% 299.79/300.46 36996[0:Res:448.1,375.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> c_lessequals(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,z,v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* c_lessequals(hAPP(z,w),y,tc_fun(u,tc_bool))*.
% 299.79/300.46 36977[0:Res:364.1,375.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),y,tc_fun(x,tc_bool))* hBOOL(hAPP(hAPP(c_in(w),z),u))* -> c_lessequals(hAPP(v,z),hAPP(c_Set_Oinsert(x1,x),y),tc_fun(x,tc_bool))*.
% 299.79/300.46 37143[0:Res:364.1,471.1] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(v),z),x))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,z)),hAPP(c_Set_Oinsert(x1,w),y)))*.
% 299.79/300.46 37130[0:SpL:3229.1,471.1] || equal(u,c_Set_Oimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(w),y),v_x))* c_lessequals(hAPP(u,v_x),z,tc_fun(x,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(v,y)),z))*.
% 299.79/300.46 37299[0:SpL:3229.1,274.0] || equal(u,c_Set_Oinsert(v,w)) equal(hAPP(c_Set_Oinsert(v,w),x),hAPP(u,v_x))* -> hBOOL(hAPP(hAPP(c_in(w),v),x))* hBOOL(hAPP(hAPP(c_in(w),v),v_x))* equal(x,v_x).
% 299.79/300.46 37485[0:SpR:3229.1,205.1] || equal(u,c_Set_Oimage(v,w,x)) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,x),x,w),hAPP(u,v_x)),v_x)**.
% 299.79/300.46 38227[0:Res:13.2,436.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,y,tc_fun(w,tc_bool))* hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool)),z))* -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),z))*.
% 299.79/300.46 38508[0:MRR:38507.2,13435.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w,tc_fun(v,tc_bool))* c_Fun_Oinj__on(c_COMBK(u,v,v),w,v,v)* -> equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w).
% 299.79/300.46 39301[0:SpR:23902.1,533.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))**.
% 299.79/300.46 39785[0:SpR:23902.1,532.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Obot__class_Obot(tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x))**.
% 299.79/300.46 40168[4:Res:38631.1,477.0] || c_lessequals(v_x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u),tc_bool)* hBOOL(hAPP(hAPP(c_in(u),y),v))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),y))*.
% 299.79/300.46 40167[4:Res:38631.1,476.0] || c_lessequals(v_x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u),tc_bool)* hBOOL(hAPP(hAPP(c_in(u),y),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),y))*.
% 299.79/300.46 40937[0:Res:8376.2,479.1] || equal(c_in(tc_Com_Opname),c_in(u)) equal(v,v_Procs) hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,x,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))*.
% 299.79/300.46 40903[0:Res:3346.1,479.1] || equal(c_Set_Oinsert(u,v),w)* hBOOL(hAPP(x,u))* -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(w,v_x),y,x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(w,v_x)),y)))*.
% 299.79/300.46 40952[0:Rew:104.0,40897.2] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(w,v))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool)),y,u,x)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,y,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))))*.
% 299.79/300.46 41218[0:Res:8376.2,478.1] || equal(c_in(tc_Com_Opname),c_in(u)) equal(v,v_Procs) hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v)))*.
% 299.79/300.46 41184[0:Res:3346.1,478.1] || equal(c_Set_Oinsert(u,v),w)* hBOOL(hAPP(x,u))* -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(w,v_x),x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),hAPP(w,v_x))))*.
% 299.79/300.46 41230[0:Rew:19819.0,41178.2] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(w,v))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool)),u,x)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,y,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))))*.
% 299.79/300.46 41435[0:Res:8376.2,275.1] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(v,w),v_Procs)** hBOOL(hAPP(hAPP(c_in(x),w),y))* -> hBOOL(hAPP(hAPP(c_in(u),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v,x,tc_fun(u,tc_bool))))*.
% 299.79/300.46 41430[0:Res:168.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(x,hAPP(y,v),t_a) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,hAPP(y,v))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))))*.
% 299.79/300.46 41408[0:Res:176.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(hAPP(v,w),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),y))* -> hBOOL(hAPP(hAPP(c_in(z),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Ovimage(v,z,x),u,tc_fun(z,tc_bool))))*.
% 299.79/300.46 41353[0:SpL:23840.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) hBOOL(hAPP(hAPP(c_in(w),x),y)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),u,tc_fun(w,tc_bool))))*.
% 299.79/300.46 41337[0:SpL:23682.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),v))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(x,tc_bool))))*.
% 299.79/300.46 41296[0:SpL:10463.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)),u,tc_fun(x,tc_bool))))*.
% 299.79/300.46 41295[0:SpL:9911.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),u,tc_fun(x,tc_bool))))*.
% 299.79/300.46 41587[0:SpL:456.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Option_Othe(w),x,u),y)))* c_Fun_Oinj__on(c_Option_Othe(w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u)* -> hBOOL(hAPP(hAPP(c_in(x),c_Option_Ooption_OSome(v,w)),y)).
% 299.79/300.46 41685[0:Rew:20386.1,41543.2,20386.1,41543.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Set_Oinsert(w,x),y,u),z)))* c_Fun_Oinj__on(c_Set_Oinsert(w,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,u)* -> hBOOL(hAPP(hAPP(c_in(y),v),z)).
% 299.79/300.46 41742[1:Res:722.1,494.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs)) hBOOL(hAPP(hAPP(hAPP(v_P,u),v),w))* c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),w,v_na,x)* -> hBOOL(hAPP(hAPP(hAPP(v_Q,u),v),x))*.
% 299.79/300.46 41737[0:SpL:23902.1,494.1] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,v_x,t_a) c_Natural_Oevaln(v_x,w,x,y)* -> hBOOL(hAPP(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v),y))*.
% 299.79/300.46 41726[0:SpL:23902.1,494.1] || equal(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(v_x,u),v))* c_Hoare__Mirabelle_Otriple__valid(w,hAPP(v_x,x),t_a)* c_Natural_Oevaln(c_Orderings_Obot__class_Obot(tc_bool),v,w,y)* -> hBOOL(hAPP(hAPP(x,u),y))*.
% 299.79/300.46 41989[0:Res:82.0,18625.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),z),hAPP(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),z),tc_bool)*.
% 299.79/300.46 41946[0:SpR:10.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.46 42226[0:SSi:42122.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(w,x)) -> hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,hAPP(c_Set_Oinsert(w,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),x))*.
% 299.79/300.46 42227[0:SSi:42108.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.79/300.46 42493[0:SpL:9924.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),w,x)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Set_Oimage(u,w,x),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),w,x),v)).
% 299.79/300.46 42452[0:SpL:9924.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,w,x)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),w,x),v),hAPP(c_Set_Oimage(u,w,x),v)).
% 299.79/300.46 42654[0:SpR:161.0,335.2] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),w) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,v,tc_fun(w,tc_bool)),w) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v,tc_fun(w,tc_bool)),w)*.
% 299.79/300.46 42922[0:SpR:486.1,7253.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),z,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool))))*.
% 299.79/300.46 43472[0:SpR:507.0,335.2] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),y),w) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),w)*.
% 299.79/300.46 43694[0:SpR:162.0,335.2] || c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),x),v) c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),y),v) -> c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),v)*.
% 299.79/300.46 43809[0:Rew:331.0,43756.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)),hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y))**.
% 299.79/300.46 43810[0:Rew:330.0,43741.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w)),hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y))**.
% 299.79/300.46 44056[0:SpL:321.0,358.0] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> c_lessequals(x,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.79/300.46 44169[0:SpR:135.0,232.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool))),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.46 44338[0:Res:23946.1,268.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v),v_x))* equal(hAPP(w,v_Procs),hAPP(w,v))* c_Fun_Oinj__on(w,v_x,u,x)* -> equal(v_Procs,v).
% 299.79/300.46 44330[0:Res:15261.0,268.0] || hBOOL(hAPP(hAPP(c_in(t_a),u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* equal(hAPP(v,v_x),hAPP(v,u))* c_Fun_Oinj__on(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),t_a,w)* -> equal(v_x,u).
% 299.79/300.46 44303[0:Res:267.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* equal(hAPP(y,w),hAPP(y,v))* c_Fun_Oinj__on(y,hAPP(c_Set_Oinsert(w,u),x),u,z)* -> equal(w,v).
% 299.79/300.46 44294[0:Res:658.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))* equal(hAPP(w,v_x),hAPP(w,u))* c_Fun_Oinj__on(w,hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),tc_Com_Opname,x)* -> equal(v_x,u).
% 299.79/300.46 44784[0:Res:8375.1,593.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)),v_Procs) c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v))),hAPP(v_Q,v)),t_a)*.
% 299.79/300.46 45349[0:Res:13238.1,487.1] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)))*.
% 299.79/300.46 45348[0:Res:8375.1,487.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** hBOOL(hAPP(x,y))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)))*.
% 299.79/300.46 45342[0:Res:652.1,487.1] || c_lessequals(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,tc_Com_Opname)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,tc_Com_Opname)))*.
% 299.79/300.46 45461[0:Res:45357.1,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) -> c_Hoare__Mirabelle_Ohoare__valids(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname),v,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname),v),u,t_a)*.
% 299.79/300.46 45449[0:Res:45357.1,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),u),v,u)*.
% 299.79/300.46 45448[0:Res:45357.1,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),u),u)*.
% 299.79/300.46 45416[0:SpR:188.1,45357.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname)))* hBOOL(hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x)) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))).
% 299.79/300.46 45408[0:SpR:445.1,45357.1] || hBOOL(hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v_x)) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname),v) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname)))*.
% 299.79/300.46 45503[0:Res:13238.1,237.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),v_x),c_Orderings_Otop__class_Otop(tc_bool))** c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,t_a) -> equal(hAPP(u,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v_x,u,t_a,v)),v_x)**.
% 299.79/300.46 45502[0:Res:8375.1,237.0] || equal(hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(u,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(x,u,w,v)),x)**.
% 299.79/300.46 45498[0:Res:652.1,237.0] || c_lessequals(v_Procs,hAPP(c_Set_Oimage(u,v,tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),tc_fun(tc_Com_Opname,tc_bool))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,tc_Com_Opname) -> equal(hAPP(u,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v_x,u,tc_Com_Opname,v)),v_x)**.
% 299.79/300.46 45892[0:Res:9258.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,t_a)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,u,t_a)))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w),v_x),tc_bool))* hBOOL(hAPP(u,v_x)).
% 299.79/300.46 45931[0:SpL:188.1,45899.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname)))* hBOOL(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) -> hBOOL(hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x)).
% 299.79/300.46 45923[0:SpL:445.1,45899.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname)))* -> equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname),v) hBOOL(hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v_x)).
% 299.79/300.46 46142[0:Res:526.1,481.0] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(w,v))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),y),w,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),y)))*.
% 299.79/300.46 46460[0:Res:526.1,480.0] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(w,v))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u),w,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u)))*.
% 299.79/300.46 46646[4:SpL:537.1,46565.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))* -> .
% 299.79/300.46 46645[4:SpL:534.1,46565.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))* -> .
% 299.79/300.46 46705[0:Res:82.0,44639.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),hAPP(c_Set_Oimage(u,v,tc_Com_Opname),x),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool))),v_x)).
% 299.79/300.46 47260[0:MRR:47214.1,24483.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(v,c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* c_lessequals(w,hAPP(c_Set_Oinsert(x,u),v),tc_fun(u,tc_bool)).
% 299.79/300.46 47402[0:Res:3346.1,485.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,u))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,x,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,v)),w))*.
% 299.79/300.46 47396[0:Res:8366.1,485.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_Procs)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,tc_Com_Opname)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,tc_Com_Opname)),u))*.
% 299.79/300.46 47633[0:Res:3346.1,484.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,u))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,x,v)),v_x))*.
% 299.79/300.46 47627[0:Res:8366.1,484.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_Procs)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,tc_Com_Opname)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,tc_Com_Opname)),v))*.
% 299.79/300.46 47971[0:Res:3346.1,490.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,x,v)))* -> hBOOL(hAPP(x,u))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,v)),w))*.
% 299.79/300.46 47965[0:Res:8366.1,490.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_Procs)** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,tc_Com_Opname)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,tc_Com_Opname)),u))*.
% 299.79/300.46 48083[0:Res:3346.1,489.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,v)))* -> hBOOL(hAPP(x,u))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,x,v)),v_x))*.
% 299.79/300.46 48077[0:Res:8366.1,489.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_Procs)** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,tc_Com_Opname)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,tc_Com_Opname)),v))*.
% 299.79/300.46 48145[4:SpR:339.0,39023.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),z))*.
% 299.79/300.46 48133[4:SpR:465.1,39023.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(c_Set_Oimage(u,x,y),v_x)),x2))*.
% 299.79/300.46 48260[4:SpR:339.0,39064.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),z,t_a)*.
% 299.79/300.46 48248[4:SpR:465.1,39064.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(z,x1),hAPP(c_Set_Oimage(u,x,y),v_x)),x2,t_a)*.
% 299.79/300.46 48676[0:SpL:197.1,3863.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),z))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),z)).
% 299.79/300.46 49328[0:MRR:49327.1,264.0] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)),x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),u,w)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))))*.
% 299.79/300.46 51087[0:SSi:50986.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),u),v))* c_Finite__Set_Ofinite(v,tc_bool) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,v,tc_bool,tc_bool),c_Orderings_Obot__class_Obot(tc_bool))** hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w))* -> hBOOL(x)*.
% 299.79/300.46 51358[0:SpR:339.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),hAPP(hAPP(c_Set_Oinsert(x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 51345[0:SpR:465.1,51231.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(w,u,x),v_x),hAPP(hAPP(c_Set_Oinsert(y,t_a),c_Set_Oimage(c_Fun_Ofun__upd(w,v,z,u,x),u,x)),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 51988[0:Rew:337.0,51947.1,337.0,51947.1] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,w,x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** -> equal(c_List_Ofoldl(y,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),z,x,x1),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.79/300.46 52161[0:SSi:52095.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),u),v))* c_Finite__Set_Ofinite(v,tc_bool) c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,v,tc_bool,tc_bool),x,tc_bool)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w))* -> hBOOL(x).
% 299.79/300.46 53083[0:SpR:23955.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v,w,x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,y)),hAPP(v_x,hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,y))))**.
% 299.79/300.46 53082[0:SpR:23955.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,w,x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,y)),hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,y)),v_x))**.
% 299.79/300.46 53215[0:SpR:23958.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v,w,x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,y)),hAPP(v_x,hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,y))))**.
% 299.79/300.46 53214[0:SpR:23958.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,w,x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,y)),hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,y)),v_x))**.
% 299.79/300.46 53811[0:SpR:53771.0,584.0] || -> equal(hAPP(c_COMBS(c_Option_Othe(u),v,w,x,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Option_Othe(u),z,x2)),hAPP(x1,hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Option_Othe(u),z,x2))))*.
% 299.79/300.46 53810[0:SpR:53771.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Option_Othe(v),w,x,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Option_Othe(v),z,x2)),hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Option_Othe(v),z,x2)),x1))*.
% 299.79/300.46 53842[0:SpR:53772.0,584.0] || -> equal(hAPP(c_COMBS(c_Option_Othe(u),v,w,x,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Option_Othe(u),x1,z,x2)),hAPP(x1,hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Option_Othe(u),x1,z,x2))))*.
% 299.79/300.46 53841[0:SpR:53772.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Option_Othe(v),w,x,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Option_Othe(v),x1,z,x2)),hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Option_Othe(v),x1,z,x2)),x1))*.
% 299.79/300.46 54119[0:SpR:52997.1,410.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,v_Procs)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,v,w,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,v,w,tc_fun(u,tc_bool)))**.
% 299.79/300.46 54232[0:SpR:8667.0,13.2] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool)) c_lessequals(x,u,tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.79/300.46 55999[0:SpL:537.1,55174.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)))* -> .
% 299.79/300.46 55998[0:SpL:534.1,55174.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) equal(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)))* -> .
% 299.79/300.46 55917[0:SpL:537.1,55174.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),hAPP(x,v_x))* -> .
% 299.79/300.46 55916[0:SpL:534.1,55174.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),hAPP(x,v_x))* -> .
% 299.79/300.46 57951[0:SpL:339.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),z)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(c_Set_Oinsert(y,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),v_x)))* -> .
% 299.79/300.46 57938[0:SpL:465.1,55910.1] || equal(c_COMBK(u,v,w),c_Set_Oimage(c_Fun_Ofun__upd(x,y,z,x1,x2),x1,x2))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(c_Set_Oimage(x,x1,x2),v_x)) -> hBOOL(hAPP(hAPP(c_in(x1),y),v_x)).
% 299.79/300.46 58108[0:SpL:339.0,55992.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_COMBK(x,y,z))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool),x)* -> .
% 299.79/300.46 58095[0:SpL:465.1,55992.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_COMBK(z,x1,x2))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,x,y),v_x),tc_bool),z) -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)).
% 299.79/300.46 58598[0:Res:10771.1,449.0] || hBOOL(hAPP(hAPP(c_in(u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,c_Set_Oinsert(w,u),x,y)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,c_Set_Oinsert(w,u),x,y)))* -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),x),c_Set_Oinsert(w,u)),t_a).
% 299.79/300.46 58558[0:SpR:55.1,10771.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(u),y),x)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(y,u),w),x,tc_fun(u,tc_bool)),v))*.
% 299.79/300.46 59057[4:Res:42357.0,15629.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(x,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(x,tc_bool)),y)))*.
% 299.79/300.46 59053[0:Res:35466.0,15629.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(tc_Com_Opname),t_a,tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(tc_Com_Opname),t_a,tc_fun(u,tc_bool)),v)))*.
% 299.79/300.46 59052[0:Res:35453.0,15629.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(v,tc_bool)),w)))*.
% 299.79/300.46 59051[0:Res:35192.0,15629.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),c_in(tc_Com_Opname),u,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),c_in(tc_Com_Opname),u,tc_fun(w,tc_bool)),x)))*.
% 299.79/300.46 58967[4:Res:42414.0,15629.0] || -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x),y),z)))*.
% 299.79/300.46 58942[0:Res:36600.0,15629.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(v_x,t_a),w)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(v_x,t_a),w)),x)))*.
% 299.79/300.46 58939[0:Res:36599.0,15629.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v)),w),x)))*.
% 299.79/300.46 58906[0:Res:26119.0,15629.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),y)))*.
% 299.79/300.46 58743[0:SpL:614.2,15629.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),y)))*.
% 299.79/300.46 58739[0:SpL:536.1,15629.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)))*.
% 299.79/300.46 58738[0:SpL:535.1,15629.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)))*.
% 299.79/300.46 59127[0:AED:24.0,58669.1] || hBOOL(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))) -> hBOOL(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Set_Oimage(c_COMBK(u,v,w),w,v),x)))*.
% 299.79/300.46 59566[4:Res:42357.0,15857.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(x,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,tc_fun(x,tc_bool)),z)))*.
% 299.79/300.46 59562[0:Res:35466.0,15857.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(tc_Com_Opname),t_a,tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),c_in(tc_Com_Opname),t_a,tc_fun(u,tc_bool)),w)))*.
% 299.79/300.46 59561[0:Res:35453.0,15857.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_in(tc_Com_Opname),tc_Com_Opname,tc_fun(v,tc_bool)),x)))*.
% 299.79/300.46 59560[0:Res:35192.0,15857.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),c_in(tc_Com_Opname),u,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),c_in(tc_Com_Opname),u,tc_fun(w,tc_bool)),y)))*.
% 299.79/300.46 59475[4:Res:42414.0,15857.0] || -> hBOOL(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x),y),x1)))*.
% 299.79/300.46 59450[0:Res:36600.0,15857.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(v_x,t_a),w)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(v_x,t_a),w)),y)))*.
% 299.79/300.46 59447[0:Res:36599.0,15857.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v)),w),y)))*.
% 299.79/300.46 59414[0:Res:26119.0,15857.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),z)))*.
% 299.79/300.46 59251[0:SpL:614.2,15857.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),z)))*.
% 299.79/300.46 59247[0:SpL:536.1,15857.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)))*.
% 299.79/300.46 59246[0:SpL:535.1,15857.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)))*.
% 299.79/300.46 59637[0:AED:24.0,59177.1] || hBOOL(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))) -> hBOOL(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oimage(c_COMBK(u,v,w),w,v),y)))*.
% 299.79/300.46 60083[0:Res:4718.2,251.1] class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w,tc_fun(u,v)) -> c_lessequals(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),tc_fun(u,v)),x),hAPP(w,x),v)*.
% 299.79/300.46 60220[0:SpL:339.0,58170.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x))) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),tc_bool),y,z),u)* -> .
% 299.79/300.46 60207[0:SpL:465.1,58170.1] || equal(u,c_Set_Oimage(c_Fun_Ofun__upd(v,w,x,y,z),y,z))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(v,y,z),v_x),tc_bool),x1,x2),u)* -> hBOOL(hAPP(hAPP(c_in(y),w),v_x)).
% 299.79/300.46 60321[0:Res:4803.2,251.1] class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || c_lessequals(w,c_HOL_Ozero__class_Ozero(tc_fun(u,v)),tc_fun(u,v)) -> c_lessequals(hAPP(w,x),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),tc_fun(u,v)),x),v)*.
% 299.79/300.46 60377[7:SpR:9493.1,58968.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u),v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Set_Oinsert(v_x,t_a),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u)).
% 299.79/300.46 60375[7:SpR:8498.1,58968.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(w,x),u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))) equal(c_Set_Oinsert(w,x),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(w,x),u))*.
% 299.79/300.46 60490[0:SpR:9493.1,58969.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u),v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Set_Oinsert(v_x,t_a),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u)).
% 299.79/300.46 60488[0:SpR:8498.1,58969.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(w,x),u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))) equal(c_Set_Oinsert(w,x),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(w,x),u))*.
% 299.79/300.46 60563[7:SpR:9493.1,59476.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Set_Oinsert(v_x,t_a),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.46 60561[7:SpR:8498.1,59476.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))) equal(c_Set_Oinsert(w,x),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),v))*.
% 299.79/300.46 60636[0:SpR:9493.1,59477.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(c_Set_Oinsert(v_x,t_a),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.46 60634[0:SpR:8498.1,59477.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))) equal(c_Set_Oinsert(w,x),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),v))*.
% 299.79/300.46 60821[0:SpR:9493.1,59017.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(w,c_Set_Oinsert(v_x,t_a),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(v_x,t_a),u)).
% 299.79/300.46 60819[0:SpR:8498.1,59017.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(w,x),u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))) -> c_Hoare__Mirabelle_Ohoare__valids(y,c_Set_Oinsert(w,x),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oinsert(w,x),u))*.
% 299.79/300.46 60894[0:SpR:9493.1,59525.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(w,c_Set_Oinsert(v_x,t_a),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.46 60892[0:SpR:8498.1,59525.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))) -> c_Hoare__Mirabelle_Ohoare__valids(y,c_Set_Oinsert(w,x),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),v))*.
% 299.79/300.46 61937[0:SpL:523.1,15487.1] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.46 61936[0:SpL:460.1,15487.1] || class_Lattices_Olattice(t_b) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.46 62439[0:SSi:62228.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) equal(hAPP(c_Set_Oinsert(x,w),v),hAPP(c_Set_Oinsert(x,w),u)) -> c_lessequals(hAPP(c_Set_Oinsert(x,w),v),hAPP(c_Set_Oinsert(x,w),u),tc_fun(w,tc_bool))*.
% 299.79/300.46 62440[0:SSi:62224.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.46 62441[0:SSi:62215.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(x,w,tc_fun(u,tc_bool)) equal(w,hAPP(c_Set_Oinsert(v,u),x)) -> c_lessequals(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool))*.
% 299.79/300.46 63571[4:Res:62367.1,47318.0] || equal(c_HOL_Ominus__class_Ominus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool),u,tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool)) -> hBOOL(c_HOL_Ominus__class_Ominus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_bool),u,tc_bool))*.
% 299.79/300.46 63787[0:SSi:63634.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w))* -> c_lessequals(v,w,tc_fun(u,tc_bool))*.
% 299.79/300.46 64531[0:SpL:523.1,24257.1] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.46 64530[0:SpL:460.1,24257.1] || class_Lattices_Olattice(t_b) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.46 68383[7:SpL:1250.3,27217.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)))** equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x) -> hBOOL(c_Orderings_Obot__class_Obot(u)).
% 299.79/300.46 68382[2:SpL:1250.3,4255.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)))** equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_Orderings_Obot__class_Obot(u)).
% 299.79/300.46 68380[0:SpL:1250.3,3567.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)))** equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_Procs) -> hBOOL(c_Orderings_Obot__class_Obot(u)).
% 299.79/300.46 70074[0:SpL:24914.0,11883.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x)) hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),tc_Com_Opname,w),hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),v_x))),u))* -> .
% 299.79/300.46 71124[0:Res:7568.0,375.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,v),hAPP(c_Set_Oinsert(y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(z,tc_bool))),x1)),tc_fun(z,tc_bool))*.
% 299.79/300.46 71123[0:Res:7568.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,v)),hAPP(c_Set_Oinsert(z,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(y,u,x),w)),x1))))*.
% 299.79/300.46 71334[0:Res:7538.0,375.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Set_Oinsert(x1,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)))),tc_fun(y,tc_bool))*.
% 299.79/300.46 71333[0:Res:7538.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),hAPP(c_Set_Oinsert(x1,x),hAPP(c_Set_Oimage(y,u,x),w)))))*.
% 299.79/300.46 71601[7:SpR:71455.1,475.1] || equal(u,v_x) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> equal(hAPP(c_Set_Oinsert(u,x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,x),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,x),w))**.
% 299.79/300.46 72149[0:Res:7830.0,375.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,v),hAPP(c_Set_Oinsert(y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(z,tc_bool)))),tc_fun(z,tc_bool))*.
% 299.79/300.46 72148[0:Res:7830.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,v)),hAPP(c_Set_Oinsert(z,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),hAPP(c_Set_Oimage(y,u,x),w)))))*.
% 299.79/300.46 73077[7:Res:71608.1,485.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)),u))*.
% 299.79/300.46 73076[7:Res:71608.1,484.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)),v))*.
% 299.79/300.46 73069[7:Res:71608.1,489.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x)** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)),v))*.
% 299.79/300.46 73068[7:Res:71608.1,490.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x)** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)),u))*.
% 299.79/300.46 74223[7:SpL:71835.1,471.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(hAPP(c_in(v),x),v_x))* c_lessequals(v_x,y,tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,x)),y))*.
% 299.79/300.46 74215[7:SpL:71835.1,516.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(v_x,w)))* -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(u),v),w)).
% 299.79/300.46 73705[7:SpR:71835.1,205.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),v_x),v_x)**.
% 299.79/300.46 75088[0:Res:49.2,6845.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(v,c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),v) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))*.
% 299.79/300.46 75057[0:Res:47.2,6845.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)) equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),v) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.46 75634[7:SpR:71883.1,410.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),v_x,u,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_fun(w,tc_bool))))*.
% 299.79/300.46 77376[0:Res:2399.2,18768.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),tc_fun(u,tc_bool))* c_lessequals(v_Procs,hAPP(c_HOL_Ouminus__class_Ouminus(c_Set_Oinsert(v_x,tc_Com_Opname),tc_fun(u,tc_bool)),v_Procs),tc_bool)*.
% 299.79/300.46 77375[0:Res:2399.2,109.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* c_lessequals(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))*.
% 299.79/300.46 77372[4:Res:2399.2,43176.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(u,tc_bool))* c_Hoare__Mirabelle_Ohoare__valids(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_fun(u,tc_bool)),v,t_a)*.
% 299.79/300.46 77337[0:SpR:2267.1,2399.2] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || equal(v,w) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)).
% 299.79/300.46 77454[7:SpR:71894.1,475.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) -> equal(hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(v_x,u,w),v)),hAPP(c_Set_Oimage(v_x,u,w),v))**.
% 299.79/300.46 77899[0:Res:510.1,5892.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v))* -> hBOOL(hAPP(c_COMBS(c_in(x),c_in(u),y,z,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))*.
% 299.79/300.46 77898[0:Res:511.1,5892.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),w))* -> hBOOL(hAPP(c_COMBS(c_in(x),c_in(u),y,z,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))*.
% 299.79/300.46 77798[0:SpL:131.0,5892.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),z)),z))* -> hBOOL(hAPP(c_COMBS(c_in(x1),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x2,x3,x4),z))*.
% 299.79/300.46 77797[0:SpL:158.0,5892.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),z))* -> hBOOL(hAPP(c_COMBS(c_in(x1),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x2,x3,x4),z))*.
% 299.79/300.46 77740[0:SpL:104.0,5892.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v))* -> hBOOL(hAPP(c_COMBS(c_in(x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),y,z,x1),v))*.
% 299.79/300.46 77662[0:SpL:353.0,5892.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),hAPP(c_Set_Oinsert(u,v),x)))* -> hBOOL(hAPP(c_COMBS(c_in(y),c_Set_Oinsert(w,v),z,x1,x2),hAPP(c_Set_Oinsert(u,v),x)))*.
% 299.79/300.46 79031[0:Res:15630.1,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,x),y),z,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,u,t_a).
% 299.79/300.46 79015[0:Res:15630.1,255.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,hAPP(c_in(u),v),x),x1,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),x1)).
% 299.79/300.46 78969[7:SpR:71455.1,15630.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(v_x,t_a),v),v_x) hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),u)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(v_x,t_a),v))*.
% 299.79/300.46 78968[0:SpR:8385.1,15630.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(v_x,tc_Com_Opname),v),v_Procs) hBOOL(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(v_x,tc_Com_Opname),v))*.
% 299.79/300.46 79251[0:Res:15858.1,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(v,y),z),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),y)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,u,t_a).
% 299.79/300.46 79235[0:Res:15858.1,255.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(w,y),z),hAPP(c_in(u),v),y),x1,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),x1)).
% 299.79/300.46 79189[7:SpR:71455.1,15858.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v_x,t_a),w),v_x) hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),v)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v_x,t_a),w))*.
% 299.79/300.46 79188[0:SpR:8385.1,15858.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v_x,tc_Com_Opname),w),v_Procs) hBOOL(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v_x,tc_Com_Opname),w))*.
% 299.79/300.46 80285[0:SpL:21268.0,515.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),z),x1))* -> equal(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Hoare__Mirabelle_Otriple_Otriple(u),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),x2,x3))*.
% 299.79/300.46 80155[0:SpL:21268.0,296.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,u) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),y,z),x,u)*.
% 299.79/300.46 80153[0:SpL:21268.0,312.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_Orderings_Obot__class_Obot(u)) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,y),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.46 80097[0:SpL:21268.0,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_in(w),hAPP(c_in(w),x),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),z))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,x1,u,w)))*.
% 299.79/300.46 80096[0:SpL:21268.0,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_in(w),hAPP(c_in(w),x),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),z))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,z,u,w)))*.
% 299.79/300.46 80069[0:SpL:21268.0,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(w,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_in(u),hAPP(c_in(u),v),x,y),u)*.
% 299.79/300.46 80068[0:SpL:21268.0,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_in(u),hAPP(c_in(u),v),x,y),c_Finite__Set_Olinorder__class_OMax(w,u),u)*.
% 299.79/300.46 80012[0:SpL:21268.0,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) -> c_Hoare__Mirabelle_Ohoare__valids(v,w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x,y),t_a)*.
% 299.79/300.46 79990[0:SpR:32668.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),v_Procs,w,x)),v_Procs)**.
% 299.79/300.46 79989[0:SpR:28910.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),v_Procs,y,z)),v_Procs)**.
% 299.79/300.46 79988[0:SpR:28926.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v_Procs,v,w)),v_Procs)**.
% 299.79/300.46 79984[0:SpR:28755.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),v_Procs,y,z)),v_Procs)**.
% 299.79/300.46 79983[0:SpR:28771.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v_Procs,v,w)),v_Procs)**.
% 299.79/300.46 79948[0:SpR:26782.0,21268.0] || -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),w,x)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 79845[0:SpR:97.1,21268.0] || c_Fun_Oinj__on(u,v,w,x) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),v,y,z)),v)**.
% 299.79/300.46 79838[0:SpR:353.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(u,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(u,v),y)),w,z)),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(u,v),y)))**.
% 299.79/300.46 79760[0:SpR:21268.0,10930.1] || equal(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,u),v_x),hAPP(hAPP(c_Set_Oinsert(w,u),v_x),x),v,y)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,u),v_x),x)).
% 299.79/300.46 79759[7:SpR:21268.0,29397.1] || equal(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,u),v_x),hAPP(hAPP(c_Set_Oinsert(w,u),v_x),x),v,y)),v_x)** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,u),v_x),x)).
% 299.79/300.46 79684[0:SpR:21268.0,7820.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),v,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),u)*.
% 299.79/300.46 79683[0:SpR:21268.0,29199.1] class_Lattices_Olattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),v,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),u)*.
% 299.79/300.46 79682[0:SpR:21268.0,294.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y),w,z),u)* -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y),u).
% 299.79/300.46 79651[0:SpR:21268.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,hAPP(u,y),x,z),v),x1)),hAPP(c_Set_Oinsert(hAPP(u,y),w),hAPP(c_Set_Oimage(u,v,w),x1)))*.
% 299.79/300.46 79645[0:SpR:21268.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),y,z)),tc_bool)*.
% 299.79/300.46 79629[0:SpR:21268.0,353.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),y),x,z))),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(u,v),y)))**.
% 299.79/300.46 79574[0:SpR:21268.0,254.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(x,u),hAPP(c_Set_Oinsert(x,u),y),w,z)))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(x,u),y))).
% 299.79/300.46 79544[0:SpR:21268.0,8369.1] || -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),x),v,y)),w))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),x)).
% 299.79/300.46 79524[4:SpR:21268.0,40792.1] || c_lessequals(v_x,hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,x),u),hAPP(hAPP(c_Set_Oinsert(w,x),u),y),v,z)),tc_bool)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),u),y)).
% 299.79/300.46 79457[0:SpR:21268.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),hAPP(c_Set_Oinsert(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_in(u),hAPP(c_in(u),v),y,z)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.46 79384[0:SpR:21268.0,11064.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),u,z),w)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(v,w,x),y),x1,tc_fun(x,tc_bool)),x)*.
% 299.79/300.46 79352[0:SpR:21268.0,341.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool))*.
% 299.79/300.46 81480[0:SpL:21894.0,515.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),z),x1))* -> equal(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),c_Hoare__Mirabelle_Otriple_Otriple(u),x2,x3))*.
% 299.79/300.46 81350[0:SpL:21894.0,296.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x,u) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,z),x,u)*.
% 299.79/300.46 81348[0:SpL:21894.0,312.1] class_Lattices_Obounded__lattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_Orderings_Obot__class_Obot(u)) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.46 81292[0:SpL:21894.0,278.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(w),x),c_in(w),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),z))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,x1,u,w)))*.
% 299.79/300.46 81291[0:SpL:21894.0,277.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(w),x),c_in(w),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),z))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,z,u,w)))*.
% 299.79/300.46 81264[0:SpL:21894.0,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(w,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),c_in(u),x,y),u)*.
% 299.79/300.46 81263[0:SpL:21894.0,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),c_in(u),x,y),c_Finite__Set_Olinorder__class_OMax(w,u),u)*.
% 299.79/300.46 81207[0:SpL:21894.0,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) -> c_Hoare__Mirabelle_Ohoare__valids(v,w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x,y),t_a)*.
% 299.79/300.46 81184[0:SpR:32668.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_Procs,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),w,x)),v_Procs)**.
% 299.79/300.46 81183[0:SpR:28910.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),y,z)),v_Procs)**.
% 299.79/300.46 81182[0:SpR:28926.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v,w)),v_Procs)**.
% 299.79/300.46 81178[0:SpR:28755.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),y,z)),v_Procs)**.
% 299.79/300.46 81177[0:SpR:28771.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v,w)),v_Procs)**.
% 299.79/300.46 81142[0:SpR:26782.0,21894.0] || -> equal(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w,x)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 81039[0:SpR:97.1,21894.0] || c_Fun_Oinj__on(u,v,w,x) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),v,c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,z)),v)**.
% 299.79/300.46 81032[0:SpR:353.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(u,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(u,v),y)),c_Set_Oinsert(u,v),w,z)),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(u,v),y)))**.
% 299.79/300.46 80954[0:SpR:21894.0,10930.1] || equal(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Set_Oinsert(w,u),v_x),x),hAPP(c_Set_Oinsert(w,u),v_x),v,y)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,u),v_x),x)).
% 299.79/300.46 80953[7:SpR:21894.0,29397.1] || equal(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Set_Oinsert(w,u),v_x),x),hAPP(c_Set_Oinsert(w,u),v_x),v,y)),v_x)** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,u),v_x),x)).
% 299.79/300.46 80878[0:SpR:21894.0,7820.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),u)*.
% 299.79/300.46 80877[0:SpR:21894.0,29199.1] class_Lattices_Olattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),u)*.
% 299.79/300.46 80876[0:SpR:21894.0,294.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,z),u)* -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y),u).
% 299.79/300.46 80845[0:SpR:21894.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(u,y),u,x,z),v),x1)),hAPP(c_Set_Oinsert(hAPP(u,y),w),hAPP(c_Set_Oimage(u,v,w),x1)))*.
% 299.79/300.46 80839[0:SpR:21894.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),y,z)),tc_bool)*.
% 299.79/300.46 80823[0:SpR:21894.0,353.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),y),c_Set_Oinsert(u,v),x,z))),hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(u,v),y)))**.
% 299.79/300.46 80767[0:SpR:21894.0,254.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,u),y),c_Set_Oinsert(x,u),w,z)))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(x,u),y))).
% 299.79/300.46 80737[0:SpR:21894.0,8369.1] || -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),x),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),v,y)),w))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),x)).
% 299.79/300.46 80717[4:SpR:21894.0,40792.1] || c_lessequals(v_x,hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Set_Oinsert(w,x),u),y),hAPP(c_Set_Oinsert(w,x),u),v,z)),tc_bool)* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),u),y)).
% 299.79/300.46 80650[0:SpR:21894.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),hAPP(c_Set_Oinsert(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),c_in(u),y,z)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.79/300.46 80577[0:SpR:21894.0,11064.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),u,z),w)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(v,w,x),y),x1,tc_fun(x,tc_bool)),x)*.
% 299.79/300.46 80545[0:SpR:21894.0,341.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool))*.
% 299.79/300.46 81753[0:SpR:21894.0,5075.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),y),c_Set_Ovimage(v,w,x),u,z),x)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Ovimage(v,w,x),y)),x).
% 299.79/300.46 81751[0:SpR:21268.0,5075.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Ovimage(v,w,x),hAPP(c_Set_Ovimage(v,w,x),y),u,z),x)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Ovimage(v,w,x),y)),x).
% 299.79/300.46 81926[0:SpR:317.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(y,w),z)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oinsert(hAPP(v,y),x),x1,x2,x3),hAPP(c_Set_Oimage(v,w,x),z)),u)*.
% 299.79/300.46 81922[0:SpR:131.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),hAPP(c_Set_Ovimage(y,x,z),x1)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Ovimage(c_Fun_Ocomp(y,v,x,z,w),w,z),x2,x3,x4),x1),u)*.
% 299.79/300.46 81921[0:SpR:158.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,z,w),x1)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oimage(c_Fun_Ocomp(v,y,w,x,z),z,x),x2,x3,x4),x1),u)*.
% 299.79/300.46 81865[0:SpR:104.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(x,tc_bool))),y,z,x1),w),u)*.
% 299.79/300.46 81802[0:SpR:131.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Ovimage(w,z,x),x2,x3,x4),hAPP(c_Set_Ovimage(v,x,y),x1)),u)*.
% 299.79/300.46 81800[0:SpR:158.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oimage(v,x,y),x2,x3,x4),hAPP(c_Set_Oimage(w,z,x),x1)),u)*.
% 299.79/300.46 81797[0:SpR:99.1,5879.1] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_lessequals(y,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,x),z,x1,x2),hAPP(v,y)),u)*.
% 299.79/300.46 81796[0:SpR:438.1,5879.1] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_lessequals(y,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,x),z,x1,x2),hAPP(v,y)),u)*.
% 299.79/300.46 81792[0:SpR:317.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_Set_Oinsert(hAPP(v,w),x),hAPP(c_Set_Oimage(v,y,x),z)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oimage(v,y,x),x1,x2,x3),hAPP(c_Set_Oinsert(w,y),z)),u)*.
% 299.79/300.46 82141[7:SpR:78597.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Set_Oinsert(v_x,v)),w)) -> equal(hAPP(c_Set_Oinsert(c_Set_Oinsert(v_x,v),x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,x),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,x),w))**.
% 299.79/300.46 82140[7:SpR:78597.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Set_Oinsert(v_x,v)),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),w,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oinsert(v_x,t_a),u,x),c_Set_Oinsert(v_x,v)),c_Set_Oinsert(v_x,v))**.
% 299.79/300.46 82139[7:SpR:78597.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Set_Oinsert(v_x,v)),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),w,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oinsert(v_x,t_a),u,x),c_Set_Oinsert(v_x,v)),c_Set_Oinsert(v_x,v))**.
% 299.79/300.46 82398[0:SpR:317.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(y,w),z)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oinsert(hAPP(v,y),x),x1,x2,x3),hAPP(c_Set_Oimage(v,w,x),z)),u)*.
% 299.79/300.46 82394[0:SpR:131.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),hAPP(c_Set_Ovimage(y,x,z),x1)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Ovimage(c_Fun_Ocomp(y,v,x,z,w),w,z),x2,x3,x4),x1),u)*.
% 299.79/300.46 82393[0:SpR:158.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,z,w),x1)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oimage(c_Fun_Ocomp(v,y,w,x,z),z,x),x2,x3,x4),x1),u)*.
% 299.79/300.46 82337[0:SpR:104.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(x,tc_bool))),y,z,x1),w),u)*.
% 299.79/300.46 82274[0:SpR:131.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Ovimage(w,z,x),x2,x3,x4),hAPP(c_Set_Ovimage(v,x,y),x1)),u)*.
% 299.79/300.46 82272[0:SpR:158.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oimage(v,x,y),x2,x3,x4),hAPP(c_Set_Oimage(w,z,x),x1)),u)*.
% 299.79/300.46 82269[0:SpR:99.1,5880.1] class_Lattices_Olattice(u) || c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_lessequals(y,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,x),z,x1,x2),hAPP(v,y)),u)*.
% 299.79/300.46 82268[0:SpR:438.1,5880.1] class_Lattices_Olattice(u) || c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_lessequals(y,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,x),z,x1,x2),hAPP(v,y)),u)*.
% 299.79/300.46 82264[0:SpR:317.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Set_Oinsert(hAPP(v,w),x),hAPP(c_Set_Oimage(v,y,x),z)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oimage(v,y,x),x1,x2,x3),hAPP(c_Set_Oinsert(w,y),z)),u)*.
% 299.79/300.46 82836[7:Res:77991.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,x),v_x)))* equal(hAPP(y,v_x),hAPP(y,v))* c_Fun_Oinj__on(y,hAPP(c_Set_Oinsert(w,x),v_x),u,z)* -> equal(v_x,v).
% 299.79/300.46 82929[0:SpR:21894.0,22513.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),u,z),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x1,x,x2),hAPP(c_Set_Oimage(v,w,x),y)),x2)*.
% 299.79/300.46 82927[0:SpR:21268.0,22513.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),u,z),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x1,x,x2),hAPP(c_Set_Oimage(v,w,x),y)),x2)*.
% 299.79/300.46 83085[0:SpR:5924.0,59525.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2),t_a)* hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x3,c_Orderings_Otop__class_Otop(tc_fun(x4,tc_bool)),c_COMBS(v,c_COMBK(w,x,y),z,x1,x2),x4)),w))*.
% 299.79/300.46 83084[0:SpR:5924.0,59017.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2),t_a)* hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool)),x4,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2),x3)),w))*.
% 299.79/300.46 83067[7:SpR:5924.0,58968.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_x) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x3,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2)),v))*.
% 299.79/300.46 83066[0:SpR:5924.0,58969.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_Procs) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x3,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2)),v))*.
% 299.79/300.46 83065[7:SpR:5924.0,59476.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_x) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x2,c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool)),c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x3)),v))*.
% 299.79/300.46 83064[0:SpR:5924.0,59477.1] || equal(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_Procs) -> hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x2,c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool)),c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x3)),v))*.
% 299.79/300.46 83405[0:SpR:5961.0,59525.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2),t_a)* hBOOL(hAPP(v,hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x3,c_Orderings_Otop__class_Otop(tc_fun(x4,tc_bool)),c_COMBS(c_COMBK(v,w,x),y,z,x1,x2),x4))))*.
% 299.79/300.46 83404[0:SpR:5961.0,59017.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2),t_a)* hBOOL(hAPP(v,hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool)),x4,c_COMBS(c_COMBK(v,w,x),y,z,x1,x2),x3))))*.
% 299.79/300.46 83390[7:SpR:5961.0,58968.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_x) -> hBOOL(hAPP(u,hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x3,c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2))))*.
% 299.79/300.46 83389[0:SpR:5961.0,58969.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_Procs) -> hBOOL(hAPP(u,hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x3,c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2))))*.
% 299.79/300.46 83388[7:SpR:5961.0,59476.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_x) -> hBOOL(hAPP(u,hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x2,c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool)),c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x3))))*.
% 299.79/300.46 83387[0:SpR:5961.0,59477.1] || equal(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_Procs) -> hBOOL(hAPP(u,hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x2,c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool)),c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x3))))*.
% 299.79/300.46 84088[0:Rew:584.0,83780.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(u,v,z,x1,x2),tc_Com_Opname,x3),hAPP(hAPP(u,v_x),hAPP(v,v_x)))),hAPP(hAPP(u,v_x),hAPP(v,v_x)))**.
% 299.79/300.46 84900[4:SpL:188.1,78744.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Ovimage(c_COMBK(v,u,w),w,u),x)))* equal(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Ovimage(c_COMBK(v,u,w),w,u),x,t_a).
% 299.79/300.46 84992[0:Res:84957.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,x),w)))* equal(hAPP(y,w),hAPP(y,v))* c_Fun_Oinj__on(y,hAPP(c_Set_Oinsert(w,x),w),u,z)* -> equal(w,v).
% 299.79/300.46 85048[0:SpR:644.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(x,y,tc_Com_Opname),tc_Com_Opname,y),u,w),v)))*.
% 299.79/300.46 85044[0:SpR:644.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> c_lessequals(hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oimage(c_COMBK(w,x,tc_Com_Opname),tc_Com_Opname,x),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.46 85159[0:SpL:55.1,85001.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),w),u),v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(w),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool))),v)).
% 299.79/300.46 85219[0:SpR:66691.3,819.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || -> equal(c_Fun_Ofun__upd(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x,c_Orderings_Otop__class_Otop(u),v,w),c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)))**.
% 299.79/300.46 85218[0:SpR:66692.3,819.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || -> equal(c_Fun_Ofun__upd(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x,c_Orderings_Otop__class_Otop(u),v,w),c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)))**.
% 299.79/300.46 85217[0:SpR:67446.3,819.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || -> equal(c_Fun_Ofun__upd(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x,c_Orderings_Otop__class_Otop(u),v,w),c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)))**.
% 299.79/300.46 85216[0:SpR:67447.3,819.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Otop(u) || -> equal(c_Fun_Ofun__upd(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x,c_Orderings_Otop__class_Otop(u),v,w),c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)))**.
% 299.79/300.46 85270[0:SpR:67115.3,824.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || -> equal(c_Fun_Ofun__upd(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x,c_Orderings_Obot__class_Obot(u),v,w),c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)))**.
% 299.79/300.46 85269[0:SpR:67416.3,824.1] class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || -> equal(c_Fun_Ofun__upd(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x,c_Orderings_Obot__class_Obot(u),v,w),c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)))**.
% 299.79/300.46 85267[0:SpR:67573.3,824.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Oupper__semilattice(tc_fun(t_a,u)) class_Orderings_Obot(u) || -> equal(c_Fun_Ofun__upd(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x,c_Orderings_Obot__class_Obot(u),v,w),c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)))**.
% 299.79/300.46 85266[0:SpR:68745.3,824.1] class_OrderedGroup_Oordered__ab__group__add(tc_fun(t_a,u)) class_Lattices_Olattice(tc_fun(t_a,u)) class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_Orderings_Obot(u) || -> equal(c_Fun_Ofun__upd(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x,c_Orderings_Obot__class_Obot(u),v,w),c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)))**.
% 299.79/300.46 85472[4:SpR:78507.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_x,u),c_Fun_Ofun__upd(v,w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_x,u),v,y,z,x),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),x,z))*.
% 299.79/300.46 86397[0:SpR:86109.1,15858.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v_x,t_a),w),v_Procs) hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),v)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v_x,t_a),w))*.
% 299.79/300.46 86396[0:SpR:86109.1,15630.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(v_x,t_a),v),v_Procs) hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),u)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(v_x,t_a),v))*.
% 299.79/300.46 86254[0:SpR:86109.1,475.1] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> equal(hAPP(c_Set_Oinsert(u,x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,x),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,x),w))**.
% 299.79/300.46 86671[0:Res:86261.1,485.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_Procs)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)),u))*.
% 299.79/300.46 86670[0:Res:86261.1,484.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_Procs)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)),v))*.
% 299.79/300.46 86663[0:Res:86261.1,489.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_Procs)** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)),v))*.
% 299.79/300.46 86662[0:Res:86261.1,490.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_Procs)** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)),u))*.
% 299.79/300.46 86979[0:SpR:32817.1,113.0] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.79/300.46 86969[0:SpR:32817.1,55.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),x),v)) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,w),u),v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.79/300.46 87195[0:SpL:113.0,32820.0] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(y,x,tc_fun(w,tc_bool))),tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Ovimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.79/300.46 87226[0:MRR:87205.2,418.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool))))* c_lessequals(x,c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> .
% 299.79/300.46 88909[0:SpR:600.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),c_HOL_Ominus__class_Ominus(y,v,tc_fun(u,tc_bool))))*.
% 299.79/300.46 88884[0:SpR:188.1,14196.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))),w))*.
% 299.79/300.46 88845[0:SpR:196.1,14196.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Oinsert(z,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),hAPP(c_Set_Oimage(u,v,w),z)))*.
% 299.79/300.46 89367[7:SpR:78590.1,118.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),c_Fun_Ofun__upd(v,w,u,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),v,y,z,x),w,u,x,z))*.
% 299.79/300.46 89336[7:SpR:78590.1,71.2] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),u),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oinsert(v_x,t_a),v,x),u),u)**.
% 299.79/300.46 89335[7:SpR:78590.1,373.2] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),u),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oinsert(v_x,t_a),v,x),u),u)**.
% 299.79/300.46 89717[7:Res:89344.1,482.2] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)))* -> hBOOL(hAPP(w,v_x)).
% 299.79/300.46 89774[0:SpR:26183.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u,z),y)))*.
% 299.79/300.46 89770[0:SpR:26183.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> c_lessequals(hAPP(c_Set_Oinsert(v,w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.46 90157[4:SpR:78660.1,118.0] || equal(hAPP(u,v_x),v_x) -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),c_Fun_Ofun__upd(v,w,u,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),v,y,z,x),w,u,x,z))*.
% 299.79/300.46 90126[4:SpR:78660.1,71.2] || equal(hAPP(u,v_x),v_x) hBOOL(hAPP(hAPP(c_in(v),u),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oinsert(v_x,t_a),v,x),u),u)**.
% 299.79/300.46 90125[4:SpR:78660.1,373.2] || equal(hAPP(u,v_x),v_x) hBOOL(hAPP(hAPP(c_in(v),u),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oinsert(v_x,t_a),v,x),u),u)**.
% 299.79/300.46 90861[4:Res:90134.1,482.2] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),v_x)** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)))* -> hBOOL(hAPP(w,v_x)).
% 299.79/300.46 91360[0:Rew:91288.1,91104.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Fun_Ofun__upd(w,x,c_Orderings_Obot__class_Obot(u),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,z,x1,y),x,v,y,x1))*.
% 299.79/300.46 91950[0:SpR:79073.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_Procs,u),c_Fun_Ofun__upd(v,w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_Procs,u),v,z,x1,y),w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,x1))*.
% 299.79/300.46 92103[7:SpR:79101.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_x,u),c_Fun_Ofun__upd(v,w,hAPP(c_in(x),v_x),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_x,u),v,z,x1,y),w,hAPP(c_in(x),v_x),y,x1))*.
% 299.79/300.46 92584[0:SpL:5227.1,12979.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x) c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),hAPP(c_in(tc_Com_Opname),v_x)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),v_Procs,t_a).
% 299.79/300.46 92707[7:Res:82151.1,479.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Set_Oinsert(v_x,w),x,v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,w)),x)))*.
% 299.79/300.46 92706[7:Res:82151.1,478.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Set_Oinsert(v_x,x),v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_Set_Oinsert(v_x,x))))*.
% 299.79/300.46 92886[0:SpR:600.0,5876.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y,z,x1),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),tc_fun(x,tc_bool))*.
% 299.79/300.46 92822[0:SpR:196.1,5876.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Ovimage(u,v,w),z,x1,x2),hAPP(c_Set_Oimage(u,v,w),x)),tc_fun(y,tc_bool))*.
% 299.79/300.46 93205[0:SpR:5878.1,545.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,c_Orderings_Obot__class_Obot(u))),hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),y,z,x1,x2),v,x),w)))*.
% 299.79/300.46 93201[0:SpR:5878.1,362.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> c_lessequals(hAPP(x,c_Orderings_Obot__class_Obot(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.79/300.46 94004[0:SpR:2098.1,10791.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w),t_a) c_lessequals(hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w)),tc_Hoare__Mirabelle_Otriple(t_a)),w),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))*.
% 299.79/300.46 94145[0:Res:14364.3,430.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,x,tc_fun(u,tc_bool))* -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))*.
% 299.79/300.46 94255[0:Res:14491.3,325.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> c_lessequals(w,c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.46 94254[0:Res:14491.3,324.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.46 94250[0:Res:14491.3,430.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))* -> c_lessequals(w,x,tc_fun(u,tc_bool))*.
% 299.79/300.46 629[0:Res:589.0,223.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oimage(w,tc_Com_Opname,v),c_HOL_Ominus__class_Ominus(v_Procs,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),tc_fun(tc_Com_Opname,tc_bool)))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v_x,u,tc_Com_Opname,v),tc_Com_Opname,v),v_Procs))**.
% 299.79/300.46 9095[0:Res:49.2,214.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(hAPP(c_Set_Oinsert(v,u),w),c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool))))*.
% 299.79/300.46 10844[0:SpR:353.0,2098.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w),t_a) equal(hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w)),tc_Hoare__Mirabelle_Otriple(t_a)),w)),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w))**.
% 299.79/300.46 14133[0:SpR:130.1,176.0] class_HOL_Ominus(u) || -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Ovimage(c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u)),v,y),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.46 14698[0:SpR:128.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_HOL_Ouminus__class_Ouminus(x2,tc_fun(w,tc_bool))),hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x2),tc_fun(v,tc_bool)),hAPP(x,c_HOL_Ouminus__class_Ouminus(x2,tc_fun(w,tc_bool)))))*.
% 299.79/300.46 14697[0:SpR:128.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Ovimage(v,w,x),y,z,x1),c_HOL_Ouminus__class_Ouminus(x2,tc_fun(x,tc_bool))),hAPP(hAPP(u,c_HOL_Ouminus__class_Ouminus(x2,tc_fun(x,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,w,x),x2),tc_fun(w,tc_bool))))*.
% 299.79/300.46 16597[0:Res:361.2,405.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Orderings_Oorder(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,u),hAPP(y,w),u)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,u),hAPP(y,w)).
% 299.79/300.46 16519[0:SpR:130.1,361.2] class_HOL_Ominus(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(y,v_x),hAPP(z,v_x),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_HOL_Ominus__class_Ominus(y,z,tc_fun(t_a,u)),w,v),v)*.
% 299.79/300.46 16610[0:SSi:16586.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),hAPP(x,v),tc_fun(y,tc_bool))* -> equal(hAPP(x,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))).
% 299.79/300.46 17881[0:SpR:188.1,687.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,c_Set_Ovimage(c_COMBK(v,u,x),x,u),tc_Com_Opname)))* hBOOL(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),v_x)) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))).
% 299.79/300.46 17880[0:SpR:188.1,686.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,c_Set_Ovimage(c_COMBK(v,u,x),x,u),tc_Com_Opname)))* hBOOL(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),v_x)) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))).
% 299.79/300.46 17844[0:SpR:188.1,9268.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Set_Ovimage(c_COMBK(v,u,w),w,u)),c_Set_Ovimage(c_COMBK(v,u,w),w,u))**.
% 299.79/300.46 18019[0:Res:168.0,263.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w),t_a) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w))),w))* equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w)),v).
% 299.79/300.46 18141[0:SpR:353.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> c_lessequals(hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(z,w),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(z,w),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.46 18341[0:SpR:353.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x1,w),x))),hAPP(c_Set_Oimage(c_Set_Oinsert(x1,w),u,z),y)))*.
% 299.79/300.46 18902[0:Res:463.1,121.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x) c_Natural_Oevaln(y,x,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,w,v,x),z)* -> c_Natural_Oevaln(c_Com_Ocom_OSemi(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u)),y),v,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,w,v,x),z)*.
% 299.79/300.46 19356[0:SSi:19306.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,v,tc_fun(w,tc_bool))* c_lessequals(v,y,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),y,tc_fun(w,tc_bool))*.
% 299.79/300.46 19685[0:Res:1103.1,496.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v),t_a) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v)))),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v))))* c_Hoare__Mirabelle_Otriple__valid(w,v,t_a).
% 299.79/300.46 19668[0:Res:9067.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x)))),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x))))* c_Hoare__Mirabelle_Otriple__valid(u,w,t_a).
% 299.79/300.46 19662[0:Res:9071.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))))* c_Hoare__Mirabelle_Otriple__valid(u,v,t_a).
% 299.79/300.46 19652[0:Res:474.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))),hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(v,x),t_a)*.
% 299.79/300.46 20023[0:SpL:64.0,263.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x))) -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))* equal(v,w).
% 299.79/300.46 20350[0:SpR:584.0,438.1] || c_Fun_Oinj__on(hAPP(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(u,v),w,x),hAPP(c_COMBS(u,y,z,x1,x2),v)),hAPP(y,v))**.
% 299.79/300.46 20288[0:SpR:438.1,584.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_COMBS(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y,z,x1),hAPP(u,x2)),hAPP(x2,hAPP(x,hAPP(u,x2))))*.
% 299.79/300.46 20287[0:SpR:438.1,584.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_COMBS(x,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),y,z,x1),hAPP(u,x2)),hAPP(hAPP(x,hAPP(u,x2)),x2))*.
% 299.79/300.46 20494[0:SpR:584.0,99.1] || c_Fun_Oinj__on(hAPP(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(u,v),w,x),hAPP(c_COMBS(u,y,z,x1,x2),v)),hAPP(y,v))**.
% 299.79/300.46 20431[0:SpR:99.1,584.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_COMBS(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y,z,x1),hAPP(u,x2)),hAPP(x2,hAPP(x,hAPP(u,x2))))*.
% 299.79/300.46 20430[0:SpR:99.1,584.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_COMBS(x,c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),y,z,x1),hAPP(u,x2)),hAPP(hAPP(x,hAPP(u,x2)),x2))*.
% 299.79/300.46 21029[0:SpL:317.0,263.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oinsert(y,x),z))))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),z))) equal(v,hAPP(w,y)).
% 299.79/300.46 20995[0:SpR:1196.1,317.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),v),x)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w),x)))*.
% 299.79/300.46 20990[0:SpR:330.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),w),y)),hAPP(c_Set_Oinsert(v,x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),y)))*.
% 299.79/300.46 20989[0:SpR:1195.1,317.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),v),x)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),x)))*.
% 299.79/300.46 20984[0:SpR:584.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(u,v),w,x),hAPP(c_Set_Oinsert(hAPP(y,v),w),z)),hAPP(c_Set_Oinsert(hAPP(c_COMBS(u,y,x1,x2,x3),v),x),hAPP(c_Set_Oimage(hAPP(u,v),w,x),z)))*.
% 299.79/300.46 20982[0:SpR:9936.1,317.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w),y)))*.
% 299.79/300.46 20980[0:SpR:9935.1,317.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),hAPP(c_Set_Oinsert(u,w),y)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),y)))*.
% 299.79/300.46 20840[0:SpR:317.0,96.1] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),x),w,y) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(hAPP(c_Set_Oinsert(v,w),x),u,w,y),hAPP(c_Set_Oinsert(hAPP(u,v),y),hAPP(c_Set_Oimage(u,w,y),x)),y,w)*.
% 299.79/300.46 21684[0:SpL:21267.0,390.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),v_x),tc_fun(x,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),v_x),tc_Com_Opname,y),v,w,x),u,x,w)*.
% 299.79/300.46 21678[0:SpL:21267.0,514.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),v_x),z))* -> equal(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),v_x),tc_Com_Opname,x1))*.
% 299.79/300.46 21649[0:SpL:21267.0,278.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(w),v),hAPP(hAPP(c_in(w),v),v_x),tc_Com_Opname,x),y,u,w)))*.
% 299.79/300.46 21648[0:SpL:21267.0,277.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(w),v),hAPP(hAPP(c_in(w),v),v_x),tc_Com_Opname,y),u,w)))*.
% 299.79/300.46 21559[0:SpL:21267.0,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),u)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u)),u))* c_Hoare__Mirabelle_Otriple__valid(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),tc_Com_Opname,w),t_a)*.
% 299.79/300.46 21541[0:SpR:538.0,21267.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),tc_Com_Opname,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))**.
% 299.79/300.46 21498[0:SpR:21267.0,317.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,x),hAPP(c_Set_Oinsert(v,x),v_x),tc_Com_Opname,y))),hAPP(c_Set_Oimage(u,x,w),hAPP(c_Set_Oinsert(v,x),v_x)))**.
% 299.79/300.46 21481[0:SpR:21267.0,10746.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),v_x),tc_Com_Opname,x),hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),v_x),tc_bool)*.
% 299.79/300.46 21465[0:SpR:21267.0,328.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_Com_Opname,w),v,tc_fun(u,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),v).
% 299.79/300.46 21434[0:SpR:21267.0,128.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x),tc_Com_Opname,x),tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),v_x),tc_fun(v,tc_bool)))**.
% 299.79/300.46 21292[0:SpR:21267.0,2097.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),u))* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)).
% 299.79/300.46 22312[0:SpL:21893.0,390.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),v_x),tc_fun(x,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(v,w,x),v_x),c_Set_Oimage(v,w,x),tc_Com_Opname,y),v,w,x),u,x,w)*.
% 299.79/300.46 22306[0:SpL:21893.0,514.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),v_x),z))* -> equal(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),v_x),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),tc_Com_Opname,x1))*.
% 299.79/300.46 22277[0:SpL:21893.0,278.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(w),v),v_x),hAPP(c_in(w),v),tc_Com_Opname,x),y,u,w)))*.
% 299.79/300.46 22276[0:SpL:21893.0,277.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(w),v),v_x),hAPP(c_in(w),v),tc_Com_Opname,y),u,w)))*.
% 299.79/300.46 22186[0:SpL:21893.0,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),u)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u)),u))* c_Hoare__Mirabelle_Otriple__valid(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,w),t_a)*.
% 299.79/300.46 22168[0:SpR:538.0,21893.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))**.
% 299.79/300.46 22124[0:SpR:21893.0,317.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,x),v_x),c_Set_Oinsert(v,x),tc_Com_Opname,y))),hAPP(c_Set_Oimage(u,x,w),hAPP(c_Set_Oinsert(v,x),v_x)))**.
% 299.79/300.46 22107[0:SpR:21893.0,10746.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),v_x),hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),tc_Com_Opname,x),hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),v_x),tc_bool)*.
% 299.79/300.46 22091[0:SpR:21893.0,328.1] || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),v,tc_fun(u,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),v).
% 299.79/300.46 22060[0:SpR:21893.0,128.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),v_x),c_Set_Ovimage(u,v,w),tc_Com_Opname,x),tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),v_x),tc_fun(v,tc_bool)))**.
% 299.79/300.46 21918[0:SpR:21893.0,2097.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),u))* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)).
% 299.79/300.46 22590[0:SpR:158.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y),t_a) hBOOL(hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y)))))*.
% 299.79/300.46 22561[0:SpR:158.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),z)),x1,x2),c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x))**.
% 299.79/300.46 22749[0:SpR:3294.1,317.0] || equal(c_in(t_a),u) -> equal(hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v),x)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),hAPP(c_Set_Oimage(hAPP(u,v_x),v,w),x)))*.
% 299.79/300.46 22748[0:SpR:3294.1,99.1] || equal(c_in(t_a),u) c_Fun_Oinj__on(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(u,v_x),v,w),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))**.
% 299.79/300.46 22747[0:SpR:3294.1,438.1] || equal(c_in(t_a),u) c_Fun_Oinj__on(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(u,v_x),v,w),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))**.
% 299.79/300.46 22972[0:SpR:131.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y),t_a) hBOOL(hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y)))))*.
% 299.79/300.46 22948[0:SpR:131.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),z)),x1,x2),c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x))**.
% 299.79/300.46 23382[0:SpR:460.1,474.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))))*.
% 299.79/300.46 23374[0:SpR:460.1,415.0] || class_Lattices_Olattice(t_b) -> equal(c_Fun_Ofun__upd(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g))**.
% 299.79/300.46 23513[0:SpR:523.1,474.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x),y,v),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.79/300.46 23505[0:SpR:523.1,415.0] class_Lattices_Olattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w))**.
% 299.79/300.46 24377[0:SpL:393.1,19641.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))) -> equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oimage(c_COMBK(u,v,w),w,v),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oimage(c_COMBK(u,v,w),w,v),x,t_a)*.
% 299.79/300.46 24350[0:SpR:393.1,158.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(w,c_COMBK(x,y,v),y,z,v),v,z),u),hAPP(c_Set_Oimage(w,y,z),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))))*.
% 299.79/300.46 24325[0:SpR:393.1,313.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) c_lessequals(hAPP(c_Set_Oimage(c_COMBK(x,y,w),w,y),u),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool))*.
% 299.79/300.46 24279[0:SpR:393.1,158.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(c_COMBK(y,z,w),u,w,z,v),v,z),x),hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))**.
% 299.79/300.46 24266[0:SpR:393.1,313.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) c_lessequals(hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),hAPP(c_Set_Oimage(c_COMBK(x,y,w),w,y),v),tc_fun(y,tc_bool))*.
% 299.79/300.46 24898[0:SpL:158.0,467.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Fun_Ocomp(w,x,y,u,z),z,u),x1)))* -> equal(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,z,y),x1),w,y,u),v)),v)**.
% 299.79/300.46 24896[0:SpL:317.0,467.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(hAPP(w,x),u),hAPP(c_Set_Oimage(w,y,u),z))))* -> equal(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oinsert(x,y),z),w,y,u),v)),v)**.
% 299.79/300.46 25389[0:SpR:512.0,158.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,hAPP(c_COMBB(v,w,x,y),z),x,x1,y),y,x1),x2),hAPP(c_Set_Oimage(u,x,x1),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(z,y,w),x2))))*.
% 299.79/300.46 25369[0:SpR:512.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,z,w),x1))),hAPP(c_Set_Oimage(c_Set_Oimage(hAPP(c_COMBB(v,w,x,z),y),z,x),x2,u),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)))))*.
% 299.79/300.46 25318[0:SpR:512.0,158.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(hAPP(c_COMBB(u,v,w,x),y),z,x,w,x1),x1,w),x2),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),hAPP(c_Set_Oimage(z,x1,x),x2))))*.
% 299.79/300.46 25972[0:SpL:339.0,3489.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.79/300.46 25971[0:SpL:339.0,3487.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.46 25932[0:SpR:339.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x,y,z,x1),x2),hAPP(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x2)),hAPP(x,x2)))*.
% 299.79/300.46 25931[0:SpR:339.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x)),y,z,x1),x2),hAPP(hAPP(u,x2),hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),x2))))*.
% 299.79/300.46 25923[0:SpR:339.0,584.0] || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),hAPP(c_Set_Oinsert(z,u),x1)),hAPP(c_Set_Oinsert(z,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x1),hAPP(v,hAPP(c_Set_Oinsert(z,u),x1)))))*.
% 299.79/300.46 25909[0:SpR:339.0,600.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(u,v),w),tc_fun(v,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(u,v),w)))**.
% 299.79/300.46 25856[0:SpR:339.0,3294.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_in(t_a)) -> equal(hAPP(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 27001[0:SpL:21893.0,175.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))* -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y)),x)*.
% 299.79/300.46 27000[0:SpL:21267.0,175.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))* -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y)),x)*.
% 299.79/300.46 27057[0:SpL:21893.0,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(v),v_x),c_in(v),tc_Com_Opname,w)),x))* hBOOL(hAPP(hAPP(c_in(v),v_x),y)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,u,v,tc_fun(z,tc_bool)),x))*.
% 299.79/300.46 27056[0:SpL:21267.0,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(v),hAPP(c_in(v),v_x),tc_Com_Opname,w)),x))* hBOOL(hAPP(hAPP(c_in(v),v_x),y)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,u,v,tc_fun(z,tc_bool)),x))*.
% 299.79/300.46 27193[0:Res:450.0,33.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Set_Ovimage(v,w,x)),y),z),t_a) hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Ovimage(v,w,x),z,y,u),hAPP(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Set_Ovimage(v,w,x),z,y,u))))*.
% 299.79/300.46 27188[0:Res:450.0,279.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(v)),w),x),t_a) equal(hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(v),x,w,u),v),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),x,w,u)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),x,w,u))**.
% 299.79/300.46 27160[0:SpR:14216.0,450.0] || -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,y,z))) c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))),y),x),t_a)*.
% 299.79/300.46 27203[0:MRR:27202.1,826.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Ovimage(c_COMBK(v,u,w),w,u),x,y,z)))* c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Set_Ovimage(c_COMBK(v,u,w),w,u)),y),x),t_a)*.
% 299.79/300.46 27377[0:SpL:21893.0,470.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y),v,w,u)),x))*.
% 299.79/300.46 27376[0:SpL:21267.0,470.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y),v,w,u)),x))*.
% 299.79/300.46 27437[0:SpL:21893.0,466.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y),w,u)),x))*.
% 299.79/300.46 27436[0:SpL:21267.0,466.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y),w,u)),x))*.
% 299.79/300.46 27626[0:SpR:23902.1,373.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_bool)),w)) c_Fun_Oinj__on(hAPP(u,v_x),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(u,v_x),v,x),v_x),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 27618[0:SpR:301.1,373.2] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),x),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.46 27612[0:SpR:11176.1,373.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),w),x))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,y),u),w)*.
% 299.79/300.46 27608[0:SpR:11177.1,373.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),u),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),w,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v,y),u),u)**.
% 299.79/300.46 27570[0:SpR:300.1,373.2] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,y),w),w)**.
% 299.79/300.46 27566[0:SpR:3586.1,373.2] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) c_Fun_Oinj__on(c_Set_Oinsert(v,u),x,w,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,c_Set_Oinsert(v,u),w,y),v_x),v_x)**.
% 299.79/300.46 27540[0:SpR:9493.1,373.2] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(hAPP(c_in(v),u),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oinsert(v_x,t_a),v,x),u),u)**.
% 299.79/300.46 27538[0:SpR:8498.1,373.2] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),u),x)) c_Fun_Oinj__on(c_Set_Oinsert(y,v),x,w,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,c_Set_Oinsert(y,v),w,z),u),u)**.
% 299.79/300.46 27779[0:SpR:23902.1,71.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_bool)),w)) c_Fun_Oinj__on(hAPP(u,v_x),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(u,v_x),v,x),v_x),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 27771[0:SpR:301.1,71.2] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),x),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.46 27765[0:SpR:11176.1,71.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),w),x))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,y),u),w)*.
% 299.79/300.46 27761[0:SpR:11177.1,71.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),u),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),w,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v,y),u),u)**.
% 299.79/300.46 27723[0:SpR:300.1,71.2] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,y),w),w)**.
% 299.79/300.46 27719[0:SpR:3586.1,71.2] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) c_Fun_Oinj__on(c_Set_Oinsert(v,u),x,w,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,c_Set_Oinsert(v,u),w,y),v_x),v_x)**.
% 299.79/300.46 27692[0:SpR:9493.1,71.2] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(hAPP(c_in(v),u),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oinsert(v_x,t_a),v,x),u),u)**.
% 299.79/300.46 27690[0:SpR:8498.1,71.2] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),u),x)) c_Fun_Oinj__on(c_Set_Oinsert(y,v),x,w,z) -> equal(hAPP(c_Fun_Othe__inv__into(x,c_Set_Oinsert(y,v),w,z),u),u)**.
% 299.79/300.46 28234[0:SpL:465.1,3489.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_in(tc_Com_Opname))** hBOOL(hAPP(hAPP(c_Set_Oimage(u,x,y),v_x),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)).
% 299.79/300.46 28233[0:SpL:465.1,3487.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,x,y),v_x),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)).
% 299.79/300.46 28221[0:SpL:465.1,193.1] || c_Finite__Set_Ofinite(u,v) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(w,v,x),u),x),c_Finite__Set_Ocard(u,v)) -> hBOOL(hAPP(hAPP(c_in(v),y),u)) c_Fun_Oinj__on(c_Fun_Ofun__upd(w,y,z,v,x),u,v,x)*.
% 299.79/300.46 28207[0:SpR:465.1,584.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_COMBS(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1,x2,x3,x4),w),hAPP(hAPP(c_Set_Oimage(x,u,z),w),hAPP(x1,w)))*.
% 299.79/300.46 28206[0:SpR:465.1,584.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_COMBS(x,c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),x2,x3,x4),w),hAPP(hAPP(x,w),hAPP(c_Set_Oimage(y,u,x1),w)))*.
% 299.79/300.46 28188[0:SpR:465.1,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),x),w)) hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Fun_Ofun__upd(z,x,x1,u,y),v)),hAPP(c_Set_Oimage(z,u,y),w)))*.
% 299.79/300.46 28160[0:SpR:465.1,3294.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_in(t_a))** -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) equal(hAPP(hAPP(c_Set_Oimage(u,x,y),v_x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.46 28545[0:SpR:10090.1,118.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(c_Fun_Ocomp(hAPP(u,v_x),c_Fun_Ofun__upd(v,w,c_Orderings_Otop__class_Otop(tc_bool),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(u,v_x),v,y,z,x),w,c_Orderings_Otop__class_Otop(tc_bool),x,z))*.
% 299.79/300.46 28538[0:SpR:303.1,118.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Fun_Ofun__upd(w,x,c_Orderings_Otop__class_Otop(u),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,z,x1,y),x,c_Orderings_Otop__class_Otop(u),y,x1))*.
% 299.79/300.46 28523[0:SpR:11176.1,118.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Fun_Ofun__upd(v,w,x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,z,x1,y),w,u,y,x1))*.
% 299.79/300.46 28519[0:SpR:11177.1,118.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Fun_Ofun__upd(w,x,u,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,z,x1,y),x,u,y,x1))*.
% 299.79/300.46 28480[0:SpR:300.1,118.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Fun_Ofun__upd(v,w,x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,z,x1,y),w,x,y,x1))*.
% 299.79/300.46 28476[0:SpR:3586.1,118.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(c_Fun_Ocomp(c_Set_Oinsert(v,u),c_Fun_Ofun__upd(w,x,v_x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v,u),w,z,x1,y),x,v_x,y,x1))*.
% 299.79/300.46 28448[0:SpR:9493.1,118.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),c_Fun_Ofun__upd(v,w,u,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),v,y,z,x),w,u,x,z))*.
% 299.79/300.46 28446[0:SpR:8498.1,118.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(c_Fun_Ocomp(c_Set_Oinsert(w,v),c_Fun_Ofun__upd(x,y,u,z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(w,v),x,x1,x2,z),y,u,z,x2))*.
% 299.79/300.46 29176[0:SpL:537.1,3507.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v_x)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.79/300.46 29175[0:SpL:537.1,16327.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(v,v_Procs) -> .
% 299.79/300.46 29174[0:SpL:537.1,3499.1] class_Lattices_Olattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.79/300.46 29169[0:SpL:537.1,13272.0] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.79/300.46 29168[0:SpL:537.1,3484.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(c_Com_Ocom_OBODY,x))* -> equal(v_x,x).
% 299.79/300.46 29108[0:SpR:8415.2,537.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w))**.
% 299.79/300.46 29056[0:SpR:537.1,20881.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y),hAPP(c_Set_Oinsert(z,x),x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z))))*.
% 299.79/300.46 29033[0:SpR:537.1,9569.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))),x),tc_bool)*.
% 299.79/300.46 29032[0:SpR:537.1,9568.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))),z),x),tc_bool)*.
% 299.79/300.46 29020[0:SpR:537.1,3346.1] class_Lattices_Olattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y))) -> hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v_x))))*.
% 299.79/300.46 29019[0:SpR:537.1,21126.1] class_Lattices_Olattice(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),tc_Com_Opname,y),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x))))*.
% 299.79/300.46 29018[0:SpR:537.1,3317.1] class_Lattices_Olattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),hAPP(c_Set_Oinsert(v_x,v),y)))*.
% 299.79/300.46 29017[0:SpR:537.1,3305.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,y),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x))))*.
% 299.79/300.46 29013[0:SpR:537.1,2771.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))*.
% 299.79/300.46 29004[0:SpR:537.1,21131.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.46 29003[0:SpR:537.1,21143.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),t_a,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.46 28997[0:SpR:537.1,15262.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.79/300.46 28994[0:SpR:537.1,8376.2] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(tc_Com_Opname)) equal(x,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),x))*.
% 299.79/300.46 28993[0:SpR:537.1,8415.2] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),v_x)**.
% 299.79/300.46 28992[0:SpR:537.1,3291.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),v_Procs))*.
% 299.79/300.46 28991[0:SpR:537.1,3285.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)))*.
% 299.79/300.46 28987[0:SpR:537.1,3279.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),v_Procs),v_x))*.
% 299.79/300.46 29270[0:SSi:29190.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),y))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),y)) hBOOL(hAPP(x,y)).
% 299.79/300.46 29271[0:SSi:29189.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),y,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),y,tc_fun(u,tc_bool)).
% 299.79/300.46 29272[0:SSi:29187.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.79/300.46 29405[7:SpR:27278.1,118.0] || equal(hAPP(c_in(u),v),v_x) -> equal(c_Fun_Ocomp(c_Set_Oinsert(v,u),c_Fun_Ofun__upd(w,x,v_x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v,u),w,z,x1,y),x,v_x,y,x1))*.
% 299.79/300.46 29383[7:SpR:27278.1,71.2] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) c_Fun_Oinj__on(c_Set_Oinsert(v,u),x,w,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,c_Set_Oinsert(v,u),w,y),v_x),v_x)**.
% 299.79/300.46 29382[7:SpR:27278.1,373.2] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) c_Fun_Oinj__on(c_Set_Oinsert(v,u),x,w,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,c_Set_Oinsert(v,u),w,y),v_x),v_x)**.
% 299.79/300.46 29701[0:SpL:534.1,3507.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v_x)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.79/300.46 29700[0:SpL:534.1,16327.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(v,v_Procs) -> .
% 299.79/300.46 29699[0:SpL:534.1,3499.1] class_Lattices_Oupper__semilattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))* -> .
% 299.79/300.46 29694[0:SpL:534.1,13272.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.79/300.46 29693[0:SpL:534.1,3484.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(c_Com_Ocom_OBODY,x))* -> equal(v_x,x).
% 299.79/300.46 29632[0:SpR:8415.2,534.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),w))**.
% 299.79/300.46 29579[0:SpR:534.1,20881.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y),hAPP(c_Set_Oinsert(z,x),x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z))))*.
% 299.79/300.46 29555[0:SpR:534.1,9569.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))),x),tc_bool)*.
% 299.79/300.46 29554[0:SpR:534.1,9568.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))),z),x),tc_bool)*.
% 299.79/300.47 29542[0:SpR:534.1,3346.1] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y))) -> hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v_x))))*.
% 299.79/300.47 29541[0:SpR:534.1,21126.1] class_Lattices_Oupper__semilattice(u) || equal(v,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),tc_Com_Opname,y),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x))))*.
% 299.79/300.47 29540[0:SpR:534.1,3317.1] class_Lattices_Oupper__semilattice(u) || equal(c_in(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),hAPP(c_Set_Oinsert(v_x,v),y)))*.
% 299.79/300.47 29539[0:SpR:534.1,3305.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(v,tc_Com_Opname,y),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x))))*.
% 299.79/300.47 29535[0:SpR:534.1,2771.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool))*.
% 299.79/300.47 29526[0:SpR:534.1,21131.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.47 29525[0:SpR:534.1,21143.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),t_a,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))*.
% 299.79/300.47 29519[0:SpR:534.1,15262.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.79/300.47 29516[0:SpR:534.1,8376.2] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(tc_Com_Opname)) equal(x,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),x))*.
% 299.79/300.47 29515[0:SpR:534.1,8415.2] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),v_x)**.
% 299.79/300.47 29514[0:SpR:534.1,3291.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),v_Procs))*.
% 299.79/300.47 29513[0:SpR:534.1,3285.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)))*.
% 299.79/300.47 29509[0:SpR:534.1,3279.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),v_Procs),v_x))*.
% 299.79/300.47 30216[0:SpR:8415.2,536.1] class_Lattices_Olattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))**.
% 299.79/300.47 30103[0:SpR:536.1,20881.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z),w),x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z))))*.
% 299.79/300.47 30079[0:SpR:536.1,9569.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)),tc_bool)*.
% 299.79/300.47 30078[0:SpR:536.1,9568.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)),tc_bool)*.
% 299.79/300.47 30445[0:SSi:30312.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),y))* -> hBOOL(hAPP(w,y)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),y)).
% 299.79/300.47 30446[0:SSi:30310.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),y,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),y,tc_fun(u,tc_bool)).
% 299.79/300.47 30447[0:SSi:30308.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.79/300.47 30778[0:SpR:8415.2,535.1] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))**.
% 299.79/300.47 30659[0:SpR:535.1,20881.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z),w),x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z))))*.
% 299.79/300.47 30635[0:SpR:535.1,9569.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)),tc_bool)*.
% 299.79/300.47 30634[0:SpR:535.1,9568.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)),tc_bool)*.
% 299.79/300.47 31237[0:SpL:8415.2,356.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,v)) -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,u),u,x),v),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.79/300.47 31483[0:SpL:537.1,24254.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.79/300.47 31482[0:SpL:534.1,24254.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.79/300.47 31525[0:SpL:8415.2,473.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x))) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),v_x)),x))*.
% 299.79/300.47 31517[0:SpL:8415.2,473.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(v_x,u,v,w),x)),v_x))*.
% 299.79/300.47 31745[0:SpL:8415.2,389.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(hAPP(c_Set_Oimage(u,v,w),x),v_x)** c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(x,v_x).
% 299.79/300.47 32054[0:Res:151.2,255.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),x))* hBOOL(hAPP(hAPP(c_in(u),v),y))*.
% 299.79/300.47 32166[0:SSi:32156.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,v,tc_fun(w,tc_bool))* c_lessequals(y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),tc_fun(w,tc_bool))* -> c_lessequals(y,v,tc_fun(w,tc_bool))*.
% 299.79/300.47 32385[0:Res:12687.1,477.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y),c_HOL_Ouminus__class_Ouminus(x,tc_fun(z,tc_bool)),u)))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(x,tc_fun(z,tc_bool)),v))*.
% 299.79/300.47 32378[0:Res:9258.0,477.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),hAPP(c_in(t_a),v_x),u),v_x),tc_bool))* hBOOL(hAPP(hAPP(c_in(t_a),v_x),v))*.
% 299.79/300.47 32399[0:MRR:32358.1,820.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u),tc_bool)* hBOOL(hAPP(hAPP(c_in(u),y),v))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),y))*.
% 299.79/300.47 32401[0:SSi:32305.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),u,v)))* hBOOL(hAPP(hAPP(c_in(v),z),x))* -> hBOOL(hAPP(u,z))*.
% 299.79/300.47 32565[0:Res:12687.1,476.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(z,tc_bool)),u)))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(x,tc_fun(z,tc_bool)),v))*.
% 299.79/300.47 32558[0:Res:9258.0,476.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w),hAPP(c_in(t_a),v_x),u),v_x),tc_bool))* hBOOL(hAPP(hAPP(c_in(t_a),v_x),v))*.
% 299.79/300.47 32579[0:MRR:32538.1,820.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u),tc_bool)* hBOOL(hAPP(hAPP(c_in(u),y),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),y))*.
% 299.79/300.47 32581[0:SSi:32487.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),u,v)))* hBOOL(hAPP(hAPP(c_in(v),z),y))* -> hBOOL(hAPP(u,z))*.
% 299.79/300.47 32635[0:SpR:537.1,31533.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))),v_Procs))*.
% 299.79/300.47 32634[0:SpR:534.1,31533.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))),v_Procs))*.
% 299.79/300.47 33042[0:SpL:475.1,215.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oimage(y,u,tc_Hoare__Mirabelle_Otriple(z)),w),z)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(y,v),tc_Hoare__Mirabelle_Otriple(z)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(z),tc_bool))),z)*.
% 299.79/300.47 33035[0:SpR:21893.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)),x))* -> equal(hAPP(c_Set_Oinsert(hAPP(v,v_x),y),hAPP(c_Set_Oimage(v,u,y),x)),hAPP(c_Set_Oimage(v,u,y),x))**.
% 299.79/300.47 33034[0:SpR:21267.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)),x))* -> equal(hAPP(c_Set_Oinsert(hAPP(v,v_x),y),hAPP(c_Set_Oimage(v,u,y),x)),hAPP(c_Set_Oimage(v,u,y),x))**.
% 299.79/300.47 32991[0:SpR:24020.1,475.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(c_Set_Oinsert(v_x,x),hAPP(c_Set_Oimage(hAPP(u,v_x),v,x),w)),hAPP(c_Set_Oimage(hAPP(u,v_x),v,x),w))**.
% 299.79/300.47 32983[0:SpR:9924.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,x),w))**.
% 299.79/300.47 32939[0:SpR:525.1,475.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(c_Set_Oinsert(w,y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),x))**.
% 299.79/300.47 32904[0:SpR:2097.1,475.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),u),x)) -> equal(hAPP(c_Set_Oinsert(u,y),hAPP(c_Set_Oimage(c_Set_Oinsert(v,z),w,y),x)),hAPP(c_Set_Oimage(c_Set_Oinsert(v,z),w,y),x))**.
% 299.79/300.47 32846[0:SpR:475.1,415.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(hAPP(x,v),y),hAPP(c_Set_Oimage(x,u,y),w),hAPP(c_Set_Oimage(x,u,y),w),z,x1),c_Set_Oinsert(hAPP(x,v),y))**.
% 299.79/300.47 33291[0:SpR:537.1,32668.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.47 33290[0:SpR:534.1,32668.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.47 33404[0:Res:176.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),w),hAPP(c_Set_Oinsert(hAPP(v,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,y)),u))* c_Hoare__Mirabelle_Otriple__valid(y,x,t_a)*.
% 299.79/300.47 33577[0:SpR:537.1,28704.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),tc_Com_Opname,y)))*.
% 299.79/300.47 33576[0:SpR:534.1,28704.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),tc_Com_Opname,y)))*.
% 299.79/300.47 33668[0:SpR:537.1,28859.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),tc_Com_Opname,y)))*.
% 299.79/300.47 33667[0:SpR:534.1,28859.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),tc_Com_Opname,y)))*.
% 299.79/300.47 33759[7:SpL:537.1,31886.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(v,v_x) -> .
% 299.79/300.47 33758[7:SpL:534.1,31886.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(v,v_x) -> .
% 299.79/300.47 33805[0:Res:248.4,24120.1] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* equal(c_Finite__Set_Olinorder__class_OMin(v,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) equal(c_Finite__Set_Olinorder__class_OMin(u,tc_bool),c_Finite__Set_Olinorder__class_OMin(v,tc_bool)).
% 299.79/300.47 33885[0:Res:247.4,24120.1] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* equal(c_Finite__Set_Olinorder__class_OMax(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) equal(c_Finite__Set_Olinorder__class_OMax(v,tc_bool),c_Finite__Set_Olinorder__class_OMax(u,tc_bool)).
% 299.79/300.47 34425[0:SpL:24914.0,263.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),v_x))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(w,u),tc_Com_Opname,x),hAPP(c_Set_Oinsert(w,u),v_x))))* equal(v,w).
% 299.79/300.47 34411[0:SpL:24914.0,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),v_x)) -> hBOOL(hAPP(x,hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Ovimage(u,v,w),x),tc_Com_Opname,y),hAPP(hAPP(c_Set_Ovimage(u,v,w),x),v_x)))))*.
% 299.79/300.47 34158[0:SpR:24914.0,34.1] || hBOOL(hAPP(u,hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Ovimage(v,w,x),u),tc_Com_Opname,y),hAPP(hAPP(c_Set_Ovimage(v,w,x),u),v_x)))))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,w,x),u),v_x)).
% 299.79/300.47 34132[0:SpR:24914.0,518.1] || hBOOL(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),x))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),x)).
% 299.79/300.47 34564[0:SpR:34427.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v,w),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v),x)),hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v,w),x)))*.
% 299.79/300.47 34563[0:SpR:34427.0,99.1] || c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v,w),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))**.
% 299.79/300.47 34562[0:SpR:34427.0,438.1] || c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v,w),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))**.
% 299.79/300.47 34660[0:SpL:55.1,442.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),x),y,tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),w)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(w)),v),y)) c_Hoare__Mirabelle_Ohoare__derivs(u,c_HOL_Ominus__class_Ominus(x,y,tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),w).
% 299.79/300.47 34658[0:SpL:55.1,363.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)),y,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),u),x)) c_lessequals(c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),y,tc_fun(v,tc_bool)).
% 299.79/300.47 34617[0:SpR:55.1,9567.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(v,u),x,tc_fun(y,tc_bool)),c_HOL_Ominus__class_Ominus(z,w,tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),z),w,tc_fun(u,tc_bool)),tc_bool)*.
% 299.79/300.47 34594[0:SpR:55.1,364.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(x),y),w)) c_lessequals(u,c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(y,x),v),w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.47 34588[0:SpR:55.1,5875.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(c_COMBS(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),y),c_Set_Oinsert(v,u),z,x1,x2),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool))))*.
% 299.79/300.47 34886[0:SpR:537.1,28053.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),v,tc_Com_Opname,y)))*.
% 299.79/300.47 34885[0:SpR:534.1,28053.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),v,tc_Com_Opname,y)))*.
% 299.79/300.47 34965[0:SpR:537.1,28356.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),tc_Com_Opname,y)))*.
% 299.79/300.47 34964[0:SpR:534.1,28356.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),tc_Com_Opname,y)))*.
% 299.79/300.47 35427[0:SpL:410.0,327.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool)))** -> c_lessequals(hAPP(x,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.47 35388[0:SpR:9925.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),u),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),u,tc_fun(x,tc_bool))))*.
% 299.79/300.47 35363[0:SpR:23682.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 35281[0:SpR:8385.1,410.0] || equal(u,v_Procs) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(v_x,tc_Com_Opname),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,tc_Com_Opname),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 35246[0:SpR:410.0,329.1] || c_lessequals(hAPP(u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,u,x,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,x),w),u,x,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,u,x,tc_fun(y,tc_bool)))**.
% 299.79/300.47 35238[0:SpR:410.0,339.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(x,y),v,tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(x,y),v,tc_fun(y,tc_bool)))))*.
% 299.79/300.47 35218[0:SpR:410.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),x,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,v,x1,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x1),z),v,x1,tc_fun(u,tc_bool)),tc_bool)*.
% 299.79/300.47 35194[0:SpR:410.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,u)),x1,x2,x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool))))*.
% 299.79/300.47 36164[0:SpL:3294.1,516.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) hBOOL(hAPP(hAPP(c_in(u),v),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(u),v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))))*.
% 299.79/300.47 36159[0:SpL:584.0,516.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w,x,y,z),x1)))* -> hBOOL(hAPP(hAPP(c_in(u),v),x1)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(w,x1))).
% 299.79/300.47 36149[0:SpL:600.0,516.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(hAPP(c_in(u),v),x)) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)))).
% 299.79/300.47 37151[0:Res:362.1,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),v))* -> hBOOL(hAPP(hAPP(c_in(z),hAPP(x1,y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(x1,x,z),u,tc_fun(z,tc_bool))))*.
% 299.79/300.47 37461[0:SpR:205.1,474.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),z,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.47 37448[0:SpR:205.1,9566.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(hAPP(c_Set_Oinsert(y,z),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v)),hAPP(c_Set_Oimage(u,v,w),x)),tc_bool)*.
% 299.79/300.47 38032[0:Res:448.1,441.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),w,tc_fun(u,tc_bool))* equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))).
% 299.79/300.47 38248[0:SpR:3229.1,201.3] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))* hBOOL(hAPP(hAPP(c_in(u),w),x))* c_Finite__Set_Ofinite(x,u) -> c_lessequals(hAPP(v,v_x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),v_x,x,u,u),u)*.
% 299.79/300.47 38242[0:SpR:3229.1,201.3] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) hBOOL(hAPP(hAPP(c_in(u),v_x),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(hAPP(hAPP(v,v_x),x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,w,u,u),u)*.
% 299.79/300.47 38415[0:SpL:10090.1,493.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(c_Set_Oimage(v,u,w),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(v,u,w),v_x))** c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_bool),u,w) -> equal(c_Orderings_Otop__class_Otop(tc_bool),v_x).
% 299.79/300.47 38369[0:SpL:3229.1,493.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* equal(hAPP(c_Set_Oimage(x,v,y),w),hAPP(c_Set_Oimage(x,v,y),v_x))* c_Fun_Oinj__on(x,hAPP(u,v_x),v,y)* -> equal(w,v_x).
% 299.79/300.47 38363[0:SpL:3229.1,493.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) equal(hAPP(c_Set_Oimage(w,v,x),v_x),hAPP(c_Set_Oimage(w,v,x),y)) c_Fun_Oinj__on(w,hAPP(hAPP(u,v_x),y),v,x)* -> equal(v_x,y).
% 299.79/300.47 38500[0:Res:448.1,385.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,u) c_Fun_Oinj__on(w,v,u,u) -> c_lessequals(v,hAPP(c_Set_Oimage(w,u,u),v),tc_fun(u,tc_bool))* equal(hAPP(c_Set_Oimage(w,u,u),v),v).
% 299.79/300.47 38479[0:SpL:3229.1,385.1] || equal(u,c_Set_Oimage(v,w,w))* c_Finite__Set_Ofinite(v_x,w) c_lessequals(hAPP(u,v_x),v_x,tc_fun(w,tc_bool))* c_Fun_Oinj__on(v,v_x,w,w) -> equal(hAPP(c_Set_Oimage(v,w,w),v_x),v_x)**.
% 299.79/300.47 38649[0:SpL:3229.1,184.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(w,x,v),y)))* c_Fun_Oinj__on(w,y,x,v) -> equal(hAPP(w,hAPP(c_Fun_Othe__inv__into(y,w,x,v),v_x)),v_x)**.
% 299.79/300.47 38640[0:SpL:3229.1,184.0] || equal(u,c_Set_Oimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(u,v_x)))* c_Fun_Oinj__on(v,v_x,w,x) -> equal(hAPP(v,hAPP(c_Fun_Othe__inv__into(v_x,v,w,x),y)),y)**.
% 299.79/300.47 38989[0:SpR:3229.1,354.2] || equal(u,c_Set_Oimage(v,w,x)) c_lessequals(v_x,y,tc_fun(w,tc_bool)) c_Fun_Oinj__on(v,y,w,x) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(y,v,w,x),x,w),hAPP(u,v_x)),v_x)**.
% 299.79/300.47 39315[0:SpL:533.0,3483.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.47 39306[0:SpR:10090.1,533.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),v))**.
% 299.79/300.47 39252[0:SpR:8415.2,533.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v_x,v)),w),hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))**.
% 299.79/300.47 39793[0:SpR:8415.2,532.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(v_x,w)),hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))**.
% 299.79/300.47 39790[0:SpR:10090.1,532.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.79/300.47 39611[0:SpR:532.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z,u),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.47 40450[0:SpL:584.0,529.0] || c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(v),c_Option_Othe(tc_Com_Ocom),w,x,y),hAPP(c_Com_Obody,z)),x1),v)* -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(c_Com_Obody,z)),hAPP(c_Com_Ocom_OBODY,z)),x1),v)*.
% 299.79/300.47 40699[0:SpR:584.0,530.1] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(c_Com_Obody,w)),hAPP(c_Com_Ocom_OBODY,w)),x),v)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(v),c_Option_Othe(tc_Com_Ocom),y,z,x1),hAPP(c_Com_Obody,w)),x),v)*.
% 299.79/300.47 41415[0:Res:153.1,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* hBOOL(hAPP(hAPP(c_in(y),x),z))* -> hBOOL(hAPP(hAPP(c_in(x1),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Ovimage(v,x1,u),y,tc_fun(x1,tc_bool))))*.
% 299.79/300.47 41410[0:Res:510.1,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),y),z))* -> hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x,tc_fun(u,tc_bool))))*.
% 299.79/300.47 41409[0:Res:511.1,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),w),y))* -> hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),x,tc_fun(u,tc_bool))))*.
% 299.79/300.47 41362[0:SpL:9925.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),v)) hBOOL(hAPP(hAPP(c_in(w),x),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),u,tc_fun(w,tc_bool))))*.
% 299.79/300.47 41334[0:SpL:9924.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,tc_fun(x,tc_bool))))*.
% 299.79/300.47 41293[0:SpL:414.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),y),z)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ofun__upd(x1,v,z,x2,x3),u,tc_fun(x,tc_bool))))*.
% 299.79/300.47 41284[0:SpL:524.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),y),v)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),v),u,tc_fun(x,tc_bool))))*.
% 299.79/300.47 41674[0:SpL:584.0,284.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(v,w,u),x,y,z),hAPP(v,x1)))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u)* -> hBOOL(hAPP(hAPP(c_in(w),x1),hAPP(v,x1)))*.
% 299.79/300.47 41739[0:SpL:10090.1,494.1] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,c_Orderings_Otop__class_Otop(tc_bool),t_a)* c_Natural_Oevaln(v_x,w,x,y)* -> hBOOL(hAPP(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v),y))*.
% 299.79/300.47 41728[0:SpL:10090.1,494.1] || equal(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(v_x,u),v))* c_Hoare__Mirabelle_Otriple__valid(w,hAPP(c_Orderings_Otop__class_Otop(tc_bool),x),t_a)* c_Natural_Oevaln(c_Orderings_Otop__class_Otop(tc_bool),v,w,y)* -> hBOOL(hAPP(hAPP(x,u),y))*.
% 299.79/300.47 41863[0:Rew:300.1,41796.3] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,v,x)))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(y)*.
% 299.79/300.47 41993[0:Res:82.0,436.1] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),z))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),z)).
% 299.79/300.47 42222[0:SSi:42131.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Finite__Set_Ofinite(u,tc_bool) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,u,tc_bool,tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,hAPP(c_Set_Oinsert(w,tc_bool),u),tc_bool,tc_bool),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,u,tc_bool,tc_bool))**.
% 299.79/300.47 42657[0:SpR:161.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z),w,tc_fun(u,tc_bool))))*.
% 299.79/300.47 43026[0:SpR:456.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(v,w)),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Option_Othe(w),u,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Option_Othe(w),u,tc_fun(y,tc_bool)))**.
% 299.79/300.47 42976[0:SpR:659.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(w,tc_bool)))**.
% 299.79/300.47 43475[0:SpR:507.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),y,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x1))))*.
% 299.79/300.47 43697[0:SpR:162.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),y,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x1))))*.
% 299.79/300.47 43963[0:Res:20152.0,231.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))),y,tc_fun(v,tc_bool))*.
% 299.79/300.47 44183[0:Res:232.1,437.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool))),w)*.
% 299.79/300.47 44314[0:Res:3284.1,268.0] || equal(c_in(tc_Com_Opname),u) hBOOL(hAPP(hAPP(c_in(v),w),hAPP(u,v_x)))* equal(hAPP(x,v_Procs),hAPP(x,w))* c_Fun_Oinj__on(x,hAPP(u,v_x),v,y)* -> equal(v_Procs,w).
% 299.79/300.47 45092[0:SpR:538.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,y,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),tc_fun(w,tc_bool))*.
% 299.79/300.47 45036[0:SpR:329.1,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,u,tc_fun(w,tc_bool))* c_lessequals(y,v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),v,tc_fun(w,tc_bool))*.
% 299.79/300.47 45035[0:SpR:328.1,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,v,tc_fun(w,tc_bool)) c_lessequals(y,u,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),v,tc_fun(w,tc_bool))*.
% 299.79/300.47 45133[0:SSi:45075.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),tc_fun(w,tc_bool))*.
% 299.79/300.47 45134[0:SSi:45074.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool))* c_lessequals(u,x,tc_fun(v,tc_bool))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool))*.
% 299.79/300.47 45574[0:SpR:323.0,510.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,y,tc_fun(u,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),w),z),x,y,tc_fun(u,tc_bool))))*.
% 299.79/300.47 45573[0:SpR:323.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,y,tc_fun(u,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),w),x,y,tc_fun(u,tc_bool))))*.
% 299.79/300.47 45891[0:Res:13238.1,482.2] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)))* -> hBOOL(hAPP(w,v_x)).
% 299.79/300.47 45890[0:Res:8375.1,482.2] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)))* -> hBOOL(hAPP(x,y))*.
% 299.79/300.47 45884[0:Res:652.1,482.2] || c_lessequals(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,tc_Com_Opname)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,tc_Com_Opname)))* -> hBOOL(hAPP(w,v_x)).
% 299.79/300.47 46158[0:Res:11029.0,481.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w),u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)))*.
% 299.79/300.47 46157[0:Res:9258.0,481.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w),v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w)))*.
% 299.79/300.47 46150[0:Res:3283.1,481.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_Procs),w),v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_Procs),w)))*.
% 299.79/300.47 46128[0:Res:678.0,481.0] || -> hBOOL(hAPP(u,v_Procs)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),w),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),w)))*.
% 299.79/300.47 46476[0:Res:11029.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))*.
% 299.79/300.47 46475[0:Res:9258.0,480.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u),v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u)))*.
% 299.79/300.47 46468[0:Res:3283.1,480.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_Procs),v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_Procs)))*.
% 299.79/300.47 46446[0:Res:678.0,480.0] || -> hBOOL(hAPP(u,v_Procs)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_in(tc_Com_Opname),v_x)),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_in(tc_Com_Opname),v_x))))*.
% 299.79/300.47 46592[7:MRR:46583.1,27297.0] || equal(u,c_Set_Oimage(v,w,tc_fun(x,tc_bool))) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(u,v_x),c_Set_Oinsert(y,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,v,w,tc_fun(x,tc_bool))))*.
% 299.79/300.47 47092[0:Res:247.4,38189.0] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* hBOOL(c_Finite__Set_Olinorder__class_OMax(v,tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),c_Finite__Set_Olinorder__class_OMax(u,tc_bool)))*.
% 299.79/300.47 47091[0:Res:248.4,38189.0] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* hBOOL(c_Finite__Set_Olinorder__class_OMin(u,tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),c_Finite__Set_Olinorder__class_OMin(v,tc_bool)))*.
% 299.79/300.47 47400[0:Res:526.1,485.1] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x))* hBOOL(hAPP(y,x))* -> hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,y,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,y,u)),v))*.
% 299.79/300.47 47631[0:Res:526.1,484.1] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x))* hBOOL(hAPP(y,x))* -> hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,y,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,y,u)),w))*.
% 299.79/300.47 47812[0:Res:247.4,38190.0] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* hBOOL(c_Finite__Set_Olinorder__class_OMax(v,tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Finite__Set_Olinorder__class_OMax(u,tc_bool)),w))*.
% 299.79/300.47 47811[0:Res:248.4,38190.0] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* hBOOL(c_Finite__Set_Olinorder__class_OMin(u,tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Finite__Set_Olinorder__class_OMin(v,tc_bool)),w))*.
% 299.79/300.47 47969[0:Res:526.1,490.1] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x))* hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,y,u)))* -> hBOOL(hAPP(y,x))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,y,u)),v))*.
% 299.79/300.47 48081[0:Res:526.1,489.1] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x))* hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,y,u)))* -> hBOOL(hAPP(y,x))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,y,u)),w))*.
% 299.79/300.47 48140[4:SpR:537.1,39023.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),z))*.
% 299.79/300.47 48139[4:SpR:534.1,39023.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),z))*.
% 299.79/300.47 48255[4:SpR:537.1,39064.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),z,t_a)*.
% 299.79/300.47 48254[4:SpR:534.1,39064.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),z,t_a)*.
% 299.79/300.47 48465[0:Res:8375.1,224.0] || equal(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,v),x),v,w) -> .
% 299.79/300.47 48463[0:Res:526.1,224.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),hAPP(u,y)))* c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,v),x),v,w) -> .
% 299.79/300.47 48633[0:SpR:197.1,19747.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(y,x,tc_fun(v,tc_bool))),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.47 48624[0:SpR:197.1,20186.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.47 48777[0:Res:8366.1,619.0] || equal(u,v_Procs) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,tc_Com_Opname,tc_fun(w,tc_bool)),u),c_Set_Oinsert(x,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,tc_Com_Opname,tc_fun(w,tc_bool))))**.
% 299.79/300.47 48978[0:Res:3284.1,483.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) -> hBOOL(hAPP(w,v_Procs)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,w,u)),v_x))*.
% 299.79/300.47 49182[0:Res:3284.1,239.0] || equal(c_Set_Oimage(u,v,w),c_in(tc_Com_Opname)) c_lessequals(v_x,x,tc_fun(v,tc_bool)) c_Fun_Oinj__on(u,v_x,v,w) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Fun_Othe__inv__into(v_x,u,v,w),v_Procs)),x))*.
% 299.79/300.47 50176[0:Rew:35438.0,50175.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_COMBK(y,tc_fun(w,tc_bool),v),v,tc_fun(w,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y))**.
% 299.79/300.47 50998[0:Res:247.4,50575.0] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* equal(c_Finite__Set_Olinorder__class_OMax(u,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) hBOOL(c_Finite__Set_Olinorder__class_OMax(v,tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) hBOOL(w)*.
% 299.79/300.47 50997[0:Res:248.4,50575.0] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* equal(c_Finite__Set_Olinorder__class_OMin(v,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) hBOOL(c_Finite__Set_Olinorder__class_OMin(u,tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) hBOOL(w)*.
% 299.79/300.47 51110[0:MRR:51105.1,23754.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs)))* equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v),v_x) -> equal(v,v_x).
% 299.79/300.47 51128[0:SpR:26873.0,55.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x))) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),hAPP(c_Set_Oinsert(w,u),x),tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))**.
% 299.79/300.47 51353[0:SpR:537.1,51231.0] class_Lattices_Olattice(u) || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(hAPP(c_Set_Oinsert(x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.47 51352[0:SpR:534.1,51231.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(hAPP(c_Set_Oinsert(x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.47 52107[0:Res:247.4,50366.0] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* c_lessequals(c_Finite__Set_Olinorder__class_OMax(u,tc_bool),w,tc_bool)* hBOOL(c_Finite__Set_Olinorder__class_OMax(v,tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) hBOOL(w).
% 299.79/300.47 52106[0:Res:248.4,50366.0] class_Orderings_Olinorder(tc_bool) || c_Finite__Set_Ofinite(u,tc_bool) c_lessequals(v,u,tc_fun(tc_bool,tc_bool))* c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,tc_bool),w,tc_bool)* hBOOL(c_Finite__Set_Olinorder__class_OMin(u,tc_bool)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_bool,tc_bool))) hBOOL(w).
% 299.79/300.47 52828[0:SpR:24019.2,118.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_Fun_Ocomp(v_x,c_Fun_Ofun__upd(u,v,v_x,w,x),x,y,w),c_Fun_Ofun__upd(c_Fun_Ocomp(v_x,u,x,y,w),v,v_x,w,y))*.
% 299.79/300.47 52816[0:SpR:24019.2,71.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(v_x,v,u,w) -> equal(hAPP(c_Fun_Othe__inv__into(v,v_x,u,w),v_x),v_x)**.
% 299.79/300.47 52815[0:SpR:24019.2,373.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(v_x,v,u,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,v_x,u,w),v_x),v_x)**.
% 299.79/300.47 52992[0:Res:23739.1,268.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v),v_x))* equal(hAPP(w,v_Procs),hAPP(w,v))* c_Fun_Oinj__on(w,v_x,u,x)* -> equal(v_Procs,v).
% 299.79/300.47 53809[0:SpR:53771.0,118.0] || -> equal(c_Fun_Ocomp(c_Option_Othe(u),c_Fun_Ofun__upd(v,w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Option_Othe(u),x,z),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Option_Othe(u),v,x2,x3,x1),w,y,x1,x3))*.
% 299.79/300.47 53840[0:SpR:53772.0,118.0] || -> equal(c_Fun_Ocomp(c_Option_Othe(u),c_Fun_Ofun__upd(v,w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Option_Othe(u),y,x,z),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Option_Othe(u),v,x2,x3,x1),w,y,x1,x3))*.
% 299.79/300.47 54134[0:SpR:52997.1,317.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),v,w),x)))*.
% 299.79/300.47 54133[0:SpR:52997.1,99.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_Procs,u),v,w),v_x),v_x)**.
% 299.79/300.47 54132[0:SpR:52997.1,438.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(v_Procs,u),v,w),v_x),v_x)**.
% 299.79/300.47 56312[0:SpR:30368.2,450.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w,x)))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),w),v),t_a)*.
% 299.79/300.47 56754[0:SpR:30928.2,450.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w,x)))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),w),v),t_a)*.
% 299.79/300.47 57946[0:SpL:537.1,55910.1] class_Lattices_Olattice(u) || equal(c_COMBK(v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v_x)))* -> .
% 299.79/300.47 57945[0:SpL:534.1,55910.1] class_Lattices_Oupper__semilattice(u) || equal(c_COMBK(v,w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)))* equal(c_HOL_Ouminus__class_Ouminus(v,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v_x)))* -> .
% 299.79/300.47 58103[0:SpL:537.1,55992.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_COMBK(x,y,z))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),x)* -> .
% 299.79/300.47 58102[0:SpL:534.1,55992.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_COMBK(x,y,z))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),x)* -> .
% 299.79/300.47 58905[0:Res:450.0,15629.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),x),t_a) hBOOL(hAPP(hAPP(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,x,w,u)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,x,w,u)),y)))*.
% 299.79/300.47 58818[0:SpL:32668.0,15629.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),w)))*.
% 299.79/300.47 58817[0:SpL:28910.0,15629.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),y)))*.
% 299.79/300.47 58816[0:SpL:28926.0,15629.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v)))*.
% 299.79/300.47 58814[0:SpL:28755.0,15629.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),y)))*.
% 299.79/300.47 58813[0:SpL:28771.0,15629.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v)))*.
% 299.79/300.47 58805[0:SpL:55.1,15629.0] || hBOOL(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(v),u),x)) hBOOL(hAPP(c_Set_Oinsert(u,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_Set_Oinsert(u,v),y)))*.
% 299.79/300.47 58695[0:SpL:130.1,15629.0] class_HOL_Ominus(u) || hBOOL(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x)))*.
% 299.79/300.47 58684[0:SpL:97.1,15629.0] || c_Fun_Oinj__on(u,v,w,x) hBOOL(v) -> hBOOL(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y)))*.
% 299.79/300.47 59413[0:Res:450.0,15857.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),x),t_a) hBOOL(hAPP(hAPP(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,x,w,u)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,x,w,u)),z)))*.
% 299.79/300.47 59326[0:SpL:32668.0,15857.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),x)))*.
% 299.79/300.47 59325[0:SpL:28910.0,15857.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),z)))*.
% 299.79/300.47 59324[0:SpL:28926.0,15857.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),w)))*.
% 299.79/300.47 59322[0:SpL:28755.0,15857.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),z)))*.
% 299.79/300.47 59321[0:SpL:28771.0,15857.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),w)))*.
% 299.79/300.47 59313[0:SpL:55.1,15857.0] || hBOOL(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(v),u),x)) hBOOL(hAPP(c_Set_Oinsert(u,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oinsert(u,v),z)))*.
% 299.79/300.47 59203[0:SpL:130.1,15857.0] class_HOL_Ominus(u) || hBOOL(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)) -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),y)))*.
% 299.79/300.47 59192[0:SpL:97.1,15857.0] || c_Fun_Oinj__on(u,v,w,x) hBOOL(v) -> hBOOL(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),z)))*.
% 299.79/300.47 59933[0:SSi:59869.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),hAPP(x,v)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),hAPP(x,v),tc_fun(y,tc_bool))*.
% 299.79/300.47 60215[0:SpL:537.1,58170.1] class_Lattices_Olattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),tc_bool),y,z),v)* -> .
% 299.79/300.47 60214[0:SpL:534.1,58170.1] class_Lattices_Oupper__semilattice(u) || equal(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_x)),tc_bool),y,z),v)* -> .
% 299.79/300.47 60428[7:Res:58968.1,280.1] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(hAPP(w,v),x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y),w,u,tc_fun(x1,tc_bool)),x))*.
% 299.79/300.47 60426[7:Res:58968.1,279.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w))**.
% 299.79/300.47 60541[0:Res:58969.1,280.1] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(hAPP(w,v),x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y),w,u,tc_fun(x1,tc_bool)),x))*.
% 299.79/300.47 60539[0:Res:58969.1,279.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w))**.
% 299.79/300.47 60614[7:Res:59476.1,280.1] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(hAPP(w,v),x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z),w,u,tc_fun(x1,tc_bool)),x))*.
% 299.79/300.47 60612[7:Res:59476.1,279.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x))**.
% 299.79/300.47 60687[0:Res:59477.1,280.1] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(hAPP(w,v),x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z),w,u,tc_fun(x1,tc_bool)),x))*.
% 299.79/300.47 60685[0:Res:59477.1,279.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x))**.
% 299.79/300.47 60724[0:SpL:197.1,59706.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) equal(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),y),w)*.
% 299.79/300.47 60872[0:Res:59017.1,280.1] || hBOOL(hAPP(hAPP(u,v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(x,hAPP(c_in(y),v),t_a)* hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_in(y),v),z),u,y,tc_fun(x2,tc_bool)),w))*.
% 299.79/300.47 60870[0:Res:59017.1,279.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a)* equal(hAPP(c_Set_Oinsert(w,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(v),w),x)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(v),w),x))**.
% 299.79/300.47 60945[0:Res:59525.1,280.1] || hBOOL(hAPP(hAPP(u,v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(x,hAPP(c_in(y),v),t_a)* hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_in(y),v),x1),u,y,tc_fun(x2,tc_bool)),w))*.
% 299.79/300.47 60943[0:Res:59525.1,279.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a)* equal(hAPP(c_Set_Oinsert(w,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(v),w),y)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(v),w),y))**.
% 299.79/300.47 61946[0:SpL:339.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.47 61933[0:SpL:465.1,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,x,y),v_x),tc_bool),c_Com_Ocom_OSKIP) -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)).
% 299.79/300.47 62183[0:Res:23754.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs)))* c_Hoare__Mirabelle_Otriple__valid(u,v_x,t_a).
% 299.79/300.47 62307[0:Res:361.2,4246.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,u),hAPP(y,w)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,u),hAPP(y,w),u)*.
% 299.79/300.47 62642[0:Res:361.2,4340.1] class_Complete__Lattice_Ocomplete__lattice(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,u),hAPP(y,w),u)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,u),hAPP(y,w)).
% 299.79/300.47 63788[0:SSi:63662.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(hAPP(c_Set_Oimage(v,w,u),x),hAPP(c_Set_Oimage(v,w,u),y))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u)* -> c_lessequals(x,y,tc_fun(w,tc_bool))*.
% 299.79/300.47 63789[0:SSi:63626.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(v,hAPP(c_Set_Oimage(w,x,u),y)) c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u) -> c_lessequals(hAPP(c_Set_Ovimage(w,x,u),v),y,tc_fun(x,tc_bool))*.
% 299.79/300.47 63990[0:SpR:55.1,647.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),u)) equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs,tc_fun(tc_Com_Opname,tc_bool)))**.
% 299.79/300.47 63971[0:SpR:647.0,13.2] || c_lessequals(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v,tc_fun(tc_Com_Opname,tc_bool)) c_lessequals(w,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))*.
% 299.79/300.47 63970[0:SpR:647.0,13.2] || c_lessequals(u,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),tc_fun(tc_Com_Opname,tc_bool)) c_lessequals(v_Procs,w,tc_fun(tc_Com_Opname,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,w,tc_fun(tc_Com_Opname,tc_bool)),c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))*.
% 299.79/300.47 64099[0:SpR:55.1,679.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(tc_Com_Opname,tc_bool)),v_Procs,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),v)) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v,tc_fun(tc_Com_Opname,tc_bool)),v_Procs,tc_fun(tc_Com_Opname,tc_bool))*.
% 299.79/300.47 64249[0:SpR:15172.0,646.1] || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),v_Procs,tc_Com_Opname,y) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),tc_Com_Opname,y),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.47 64225[0:SpR:337.0,646.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x)**.
% 299.79/300.47 64263[7:MRR:64180.1,27297.0] || c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_Com_Opname,x),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),v_x)**.
% 299.79/300.47 64416[0:SpR:15172.0,645.1] || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),v_Procs,tc_Com_Opname,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),tc_Com_Opname,y),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.47 64392[0:SpR:337.0,645.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v_x)**.
% 299.79/300.47 64429[7:MRR:64347.1,27297.0] || c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(u,v,w),w,v),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_Com_Opname,x),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),v_x)**.
% 299.79/300.47 64430[0:MRR:64425.2,648.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs)))* equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w),v_x) -> equal(w,hAPP(u,v_x)).
% 299.79/300.47 64540[0:SpL:339.0,24257.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.47 64527[0:SpL:465.1,24257.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(c_Set_Oimage(u,x,y),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.47 66029[0:SpR:65404.1,475.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(c_Set_Oinsert(w,y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),x))**.
% 299.79/300.47 70928[0:SpL:21893.0,6582.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),v) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),v,tc_fun(u,tc_bool))*.
% 299.79/300.47 70927[0:SpL:21267.0,6582.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),v) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_Com_Opname,w),v,tc_fun(u,tc_bool))*.
% 299.79/300.47 71169[0:SSi:71168.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> c_lessequals(w,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(y,v),w),tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.79/300.47 71245[0:SpR:55.1,7538.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool))),tc_fun(u,tc_bool))*.
% 299.79/300.47 71496[7:SpR:71455.1,410.0] || equal(u,v_x) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 72109[0:SpR:21893.0,7830.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),tc_fun(u,tc_bool))*.
% 299.79/300.47 72108[0:SpR:21267.0,7830.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),tc_fun(u,tc_bool))*.
% 299.79/300.47 72483[0:SpL:21893.0,12554.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x)),u))*.
% 299.79/300.47 72482[0:SpL:21267.0,12554.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x),tc_Com_Opname,x)),u))*.
% 299.79/300.47 72697[0:Res:252.1,18903.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),hAPP(c_Com_Ocom_OBODY,w)),x),t_a) c_Natural_Oevalc(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(v,x,hAPP(c_Com_Ocom_OBODY,w),u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,x,hAPP(c_Com_Ocom_OBODY,w),u))*.
% 299.79/300.47 73043[7:Res:71608.1,619.0] || equal(u,v_x) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,t_a,tc_fun(w,tc_bool)),u),c_Set_Oinsert(x,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,t_a,tc_fun(w,tc_bool))))**.
% 299.79/300.47 74373[7:SpL:71835.1,493.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) equal(hAPP(c_Set_Oimage(v,u,w),v_x),hAPP(c_Set_Oimage(v,u,w),x)) c_Fun_Oinj__on(v,hAPP(v_x,x),u,w)* -> equal(v_x,x).
% 299.79/300.47 74350[7:SpL:71835.1,184.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) c_Fun_Oinj__on(u,v_x,v,w) -> equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(v_x,u,v,w),x)),x)**.
% 299.79/300.47 74331[7:SpL:71835.1,493.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a)) equal(hAPP(c_Set_Oimage(w,u,x),v),hAPP(c_Set_Oimage(w,u,x),v_x))* c_Fun_Oinj__on(w,v_x,u,x) -> equal(v,v_x).
% 299.79/300.47 74135[7:SpL:71835.1,184.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x))) c_Fun_Oinj__on(v,x,w,u) -> equal(hAPP(v,hAPP(c_Fun_Othe__inv__into(x,v,w,u),v_x)),v_x)**.
% 299.79/300.47 73549[7:SpR:71835.1,201.3] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Finite__Set_Ofinite(v,u) -> c_lessequals(hAPP(v_x,w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u),u)*.
% 299.79/300.47 73233[7:SpR:71835.1,354.2] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_lessequals(v_x,x,tc_fun(v,tc_bool)) c_Fun_Oinj__on(u,x,v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(x,u,v,w),w,v),v_x),v_x)**.
% 299.79/300.47 74523[7:MRR:74255.1,6340.0] || equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(hAPP(c_in(u),w),v_x))* equal(hAPP(x,v),hAPP(x,w))* c_Fun_Oinj__on(x,v_x,u,y)* -> equal(v,w).
% 299.79/300.47 74526[7:MRR:73228.1,27297.0] || equal(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,c_Set_Oinsert(x,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,u,v,tc_fun(w,tc_bool))))*.
% 299.79/300.47 76639[0:Res:29199.1,405.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),x,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),x).
% 299.79/300.47 76994[0:Res:30321.1,405.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),w,u)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),w).
% 299.79/300.47 77384[0:Res:2399.2,251.1] class_Orderings_Olinorder(tc_fun(u,v)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w,tc_fun(u,v))* c_lessequals(hAPP(w,x),hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),x),v)*.
% 299.79/300.47 77349[0:Res:2399.2,431.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_Fun_Oinj__on(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),u,x)* -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool)) c_Fun_Oinj__on(v,w,u,x).
% 299.79/300.47 77444[7:SpR:71894.1,410.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),u),v),v_x,u,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_fun(w,tc_bool))))*.
% 299.79/300.47 77576[0:Res:2429.2,251.1] class_Orderings_Olinorder(tc_fun(u,v)) class_OrderedGroup_Oordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w,tc_fun(u,v))* c_lessequals(hAPP(w,x),hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),x),v)*.
% 299.79/300.47 77829[0:SpL:53771.0,5892.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,c_Option_Othe(w),v,x)))* -> hBOOL(hAPP(c_COMBS(c_in(y),c_Option_Othe(w),z,x1,x2),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,c_Option_Othe(w),v,x)))*.
% 299.79/300.47 77826[0:SpL:53772.0,5892.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(w),u,v,x)))* -> hBOOL(hAPP(c_COMBS(c_in(y),c_Option_Othe(w),z,x1,x2),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(w),u,v,x)))*.
% 299.79/300.47 78332[7:SpR:78167.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,x),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,x),u,tc_fun(w,tc_bool)))**.
% 299.79/300.47 78501[4:Res:77988.0,481.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),w)))*.
% 299.79/300.47 78500[4:Res:77988.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))))*.
% 299.79/300.47 78616[0:Rew:584.0,78612.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(v,v_x))) -> hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_COMBS(c_in(u),v,w,x,y),tc_Com_Opname)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_COMBS(c_in(u),v,w,x,y),tc_Com_Opname)))*.
% 299.79/300.47 78666[7:MRR:71790.1,78665.1] || equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oinsert(v_x,t_a),v,u,w)),v_x)** c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),x))*.
% 299.79/300.47 78685[4:Res:78665.1,268.0] || equal(hAPP(hAPP(c_in(u),v),w),v_x)** hBOOL(hAPP(hAPP(c_in(u),x),w))* equal(hAPP(y,v),hAPP(y,x))* c_Fun_Oinj__on(y,w,u,z)* -> equal(v,x).
% 299.79/300.47 78966[0:SpR:2097.1,15630.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(y,z),v),y))* hBOOL(hAPP(c_Set_Oinsert(y,z),u)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(y,z),v)).
% 299.79/300.47 79067[0:Res:78077.0,481.0] || -> hBOOL(hAPP(u,v_Procs)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)))*.
% 299.79/300.47 79066[0:Res:78077.0,480.0] || -> hBOOL(hAPP(u,v_Procs)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.79/300.47 79095[7:Res:78199.0,481.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_in(w),v_x)),x),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_in(w),v_x)),x)))*.
% 299.79/300.47 79094[7:Res:78199.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_in(x),v_x)),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_in(x),v_x))))*.
% 299.79/300.47 79186[0:SpR:2097.1,15858.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(y,z),w),y))* hBOOL(hAPP(c_Set_Oinsert(y,z),v)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(y,z),w)).
% 299.79/300.47 80229[0:SpL:21268.0,332.0] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,y),u)*.
% 299.79/300.47 80193[0:SpL:21268.0,319.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),x),y,z),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.47 80192[0:SpL:21268.0,3863.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),y,z)))*.
% 299.79/300.47 80080[0:SpL:21268.0,156.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y))) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1))),y))*.
% 299.79/300.47 79761[0:SpR:21268.0,10771.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,u),x),hAPP(hAPP(c_Set_Oinsert(w,u),x),y),v,z)),x))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,u),x),y)).
% 299.79/300.47 79609[0:SpR:21268.0,153.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(x),hAPP(c_in(x),y),w,z))),x1))* -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Ovimage(v,x,u),x1))).
% 299.79/300.47 80436[0:Rew:21268.0,80079.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* -> hBOOL(hAPP(hAPP(c_in(u),v),x)) equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_in(u),hAPP(c_in(u),v),y,z),w)*.
% 299.79/300.47 81424[0:SpL:21894.0,332.0] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,y),u)*.
% 299.79/300.47 81388[0:SpL:21894.0,319.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x),c_Set_Oimage(u,v,w),y,z),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.47 81387[0:SpL:21894.0,3863.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),y,z)))*.
% 299.79/300.47 81275[0:SpL:21894.0,156.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y))) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1))),y))*.
% 299.79/300.47 80955[0:SpR:21894.0,10771.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Set_Oinsert(w,u),x),y),hAPP(c_Set_Oinsert(w,u),x),v,z)),x))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,u),x),y)).
% 299.79/300.47 80802[0:SpR:21894.0,153.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(x),y),c_in(x),w,z))),x1))* -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Ovimage(v,x,u),x1))).
% 299.79/300.47 81631[0:Rew:21894.0,81274.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* -> hBOOL(hAPP(hAPP(c_in(u),v),x)) equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),c_in(u),y,z),w)*.
% 299.79/300.47 82085[0:Rew:584.0,81774.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),tc_Com_Opname,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),u)*.
% 299.79/300.47 82086[0:Rew:584.0,81772.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),tc_Com_Opname,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),u)*.
% 299.79/300.47 82125[7:SpR:78597.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Set_Oinsert(v_x,u),v),w),c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Set_Oinsert(v_x,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 82456[0:Res:5880.1,405.1] class_Lattices_Olattice(u) class_Orderings_Oorder(u) || c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),hAPP(v,z),u)* -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z),hAPP(v,z)).
% 299.79/300.47 82552[0:Rew:584.0,82246.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),tc_Com_Opname,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),u)*.
% 299.79/300.47 82553[0:Rew:584.0,82244.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),tc_Com_Opname,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),u)*.
% 299.79/300.47 82555[0:SSi:82434.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),hAPP(v,z),tc_fun(u,tc_bool))* -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),hAPP(v,z)).
% 299.79/300.47 82556[0:SSi:82429.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),hAPP(v,z)) -> c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),hAPP(v,z),tc_fun(u,tc_bool))*.
% 299.79/300.47 82561[7:Res:82148.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,t_a,tc_fun(v,tc_bool)),c_Set_Oinsert(v_x,w)),c_Set_Oinsert(x,v),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(x,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(v_x,w),u,t_a,tc_fun(v,tc_bool))))**.
% 299.79/300.47 84400[0:SpR:2936.0,383.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(hAPP(c_in(t_a),v_x),u,v,w,x),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),w,x),c_Fun_Ofun__upd(hAPP(c_in(t_a),v_x),u,v,w,x))**.
% 299.79/300.47 84912[4:SpL:329.1,78744.0] || c_lessequals(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),tc_fun(v,tc_bool))* equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w,t_a).
% 299.79/300.47 86151[0:SpR:86109.1,410.0] || equal(u,v_Procs) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 86594[0:Res:19823.1,15629.0] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),y)))*.
% 299.79/300.47 86593[0:Res:19823.1,15857.0] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),z)))*.
% 299.79/300.47 86637[0:Res:86261.1,619.0] || equal(u,v_Procs) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,t_a,tc_fun(w,tc_bool)),u),c_Set_Oinsert(x,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,t_a,tc_fun(w,tc_bool))))**.
% 299.79/300.47 86996[0:SpR:32817.1,66.0] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(x,w),v),tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.47 88330[0:Res:7227.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oimage(c_COMBK(u,v,w),x,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),y,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oimage(c_COMBK(u,v,w),x,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),y),u,t_a)*.
% 299.79/300.47 88434[0:Res:8176.1,208.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),v),c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool))))* c_lessequals(c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))*.
% 299.79/300.47 88977[0:SpR:317.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(hAPP(u,v),w),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,z,w),hAPP(c_Set_Oinsert(v,z),x1)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),hAPP(c_Set_Oimage(u,z,w),x1)))*.
% 299.79/300.47 88973[0:SpR:131.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x2)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),x2))*.
% 299.79/300.47 88972[0:SpR:158.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x2)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),x2))*.
% 299.79/300.47 88915[0:SpR:104.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w,x),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,y,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),y))*.
% 299.79/300.47 88852[0:SpR:131.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(c_Fun_Ocomp(z,u,w,x1,v),v,x1),x2),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),hAPP(c_Set_Ovimage(z,w,x1),x2)))*.
% 299.79/300.47 88850[0:SpR:158.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oimage(u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,z,v,w,x1),x1,w),x2),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),hAPP(c_Set_Oimage(z,x1,v),x2)))*.
% 299.79/300.47 88848[0:SpR:97.1,14196.0] || c_Fun_Oinj__on(u,v,w,x) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,z),hAPP(c_Set_Oinsert(v,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))),hAPP(c_Set_Oimage(u,w,x),v)))*.
% 299.79/300.47 88847[0:SpR:99.1,14196.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y),hAPP(c_Set_Oinsert(z,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),hAPP(u,z)))*.
% 299.79/300.47 88846[0:SpR:438.1,14196.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y),hAPP(c_Set_Oinsert(z,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),hAPP(u,z)))*.
% 299.79/300.47 88842[0:SpR:317.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oimage(u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(hAPP(u,z),w),hAPP(c_Set_Oimage(u,v,w),x1)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),hAPP(c_Set_Oinsert(z,v),x1)))*.
% 299.79/300.47 89739[7:Res:89344.1,477.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(t_a),v_x),u),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.47 89738[7:Res:89344.1,476.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(t_a),v_x),u),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.47 89695[7:Res:89344.1,481.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w),v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w)))*.
% 299.79/300.47 89694[7:Res:89344.1,480.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u),v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u)))*.
% 299.79/300.47 90883[4:Res:90134.1,477.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(t_a),v_x),u),v_x),v_x)** hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.47 90882[4:Res:90134.1,476.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(t_a),v_x),u),v_x),v_x)** hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.47 90839[4:Res:90134.1,481.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w),v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w)))*.
% 299.79/300.47 90838[4:Res:90134.1,480.0] || equal(hAPP(u,v_x),v_x) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u),v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u)))*.
% 299.79/300.47 91368[0:Rew:91288.1,91076.3,91288.1,91076.1] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),x),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.47 91369[0:Rew:91288.1,91075.3,91288.1,91075.1] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),x),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.47 91829[4:SpL:188.1,78747.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname)))* equal(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_x) -> hBOOL(hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x)).
% 299.79/300.47 91819[4:SpL:445.1,78747.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname)),v_x)** -> equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname),v) hBOOL(hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v_x)).
% 299.79/300.47 92345[0:SpL:353.0,5022.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),hAPP(c_Set_Oinsert(u,v),x),tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(u,v),x)),hAPP(c_Set_Oinsert(u,v),x)).
% 299.79/300.47 92585[0:SpL:5227.1,12982.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x) c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),y,t_a)*.
% 299.79/300.47 92956[0:SpR:317.0,5876.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Set_Oinsert(hAPP(u,x),w),x1,x2,x3),hAPP(c_Set_Oimage(u,v,w),y)),tc_fun(z,tc_bool))*.
% 299.79/300.47 92952[0:SpR:131.0,5876.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),z)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x2,x3,x4),z),tc_fun(x1,tc_bool))*.
% 299.79/300.47 92951[0:SpR:158.0,5876.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x2,x3,x4),z),tc_fun(x1,tc_bool))*.
% 299.79/300.47 92892[0:SpR:104.0,5876.0] || -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),y,z,x1),v),tc_fun(x,tc_bool))*.
% 299.79/300.47 92829[0:SpR:131.0,5876.0] || -> c_lessequals(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Set_Ovimage(v,y,w),x2,x3,x4),hAPP(c_Set_Ovimage(u,w,x),z)),tc_fun(x1,tc_bool))*.
% 299.79/300.47 92827[0:SpR:158.0,5876.0] || -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Set_Oimage(u,w,x),x2,x3,x4),hAPP(c_Set_Oimage(v,y,w),z)),tc_fun(x1,tc_bool))*.
% 299.79/300.47 92824[0:SpR:99.1,5876.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x1,x2),hAPP(u,x)),tc_fun(y,tc_bool))*.
% 299.79/300.47 92823[0:SpR:438.1,5876.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x1,x2),hAPP(u,x)),tc_fun(y,tc_bool))*.
% 299.79/300.47 92819[0:SpR:317.0,5876.0] || -> c_lessequals(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Set_Oimage(u,x,w),x1,x2,x3),hAPP(c_Set_Oinsert(v,x),y)),tc_fun(z,tc_bool))*.
% 299.79/300.47 93211[0:SpR:5878.1,21894.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(v,c_Orderings_Obot__class_Obot(u)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1)),hAPP(v,c_Orderings_Obot__class_Obot(u)))**.
% 299.79/300.47 93210[0:SpR:5878.1,21268.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),hAPP(v,c_Orderings_Obot__class_Obot(u)),z,x1)),hAPP(v,c_Orderings_Obot__class_Obot(u)))**.
% 299.79/300.47 94064[0:Res:10791.0,402.0] || c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),hAPP(c_Set_Oinsert(u,v),x),tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),hAPP(c_Set_Oinsert(u,v),x)).
% 299.79/300.47 94059[0:Res:10791.0,6845.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),hAPP(c_Set_Oinsert(u,v),x)) -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),hAPP(c_Set_Oinsert(u,v),x),tc_fun(v,tc_bool))*.
% 299.79/300.47 94152[0:Res:14364.3,70.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,c_HOL_Ouminus__class_Ouminus(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> equal(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.79/300.47 94150[0:Res:14364.3,390.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Set_Oimage(w,x,u),y))) c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(y,w,x,u),c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),u,x)*.
% 299.79/300.47 94147[0:Res:14364.3,402.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,w)) c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> equal(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),w).
% 299.79/300.47 94276[0:Res:14491.3,6239.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,c_HOL_Ouminus__class_Ouminus(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> equal(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))).
% 299.79/300.47 94252[0:Res:14491.3,402.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,w)) c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))* -> equal(w,c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool))).
% 299.79/300.47 2602[0:SpR:445.1,687.1] || hBOOL(hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v_x)) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,v_Procs,c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname),v) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,v_Procs,c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname)))*.
% 299.79/300.47 2601[0:SpR:445.1,686.1] || hBOOL(hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v_x)) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,z,c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname),v) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,z,c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname)))*.
% 299.79/300.47 10513[0:Res:687.1,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) -> c_Hoare__Mirabelle_Ohoare__valids(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname),w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname),w),u,t_a)*.
% 299.79/300.47 10512[0:Res:686.1,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) -> c_Hoare__Mirabelle_Ohoare__valids(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,v,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname),w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,v,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname),w),u,t_a)*.
% 299.79/300.47 13730[0:SpR:544.1,584.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x1)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x1),hAPP(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x1))))*.
% 299.79/300.47 13729[0:SpR:544.1,584.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1)),hAPP(hAPP(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1)))*.
% 299.79/300.47 14024[0:SpR:543.1,584.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x1)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x1),hAPP(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x1))))*.
% 299.79/300.47 14023[0:SpR:543.1,584.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1)),hAPP(hAPP(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1)))*.
% 299.79/300.47 14195[0:Res:176.0,279.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Ovimage(w,v,x),hAPP(c_Set_Oinsert(hAPP(w,u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))),hAPP(c_Set_Ovimage(w,v,x),hAPP(c_Set_Oinsert(hAPP(w,u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))))**.
% 299.79/300.47 14158[0:SpR:544.1,176.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.47 14157[0:SpR:543.1,176.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.47 14382[0:Res:687.1,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_in(u),v),tc_Com_Opname),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_in(u),v),tc_Com_Opname),u),v,u)*.
% 299.79/300.47 14381[0:Res:686.1,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_in(u),v),tc_Com_Opname),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_in(u),v),tc_Com_Opname),u),v,u)*.
% 299.79/300.47 14509[0:Res:687.1,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_in(u),v),tc_Com_Opname),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_in(u),v),tc_Com_Opname),u),u)*.
% 299.79/300.47 14508[0:Res:686.1,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_in(u),v),tc_Com_Opname),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_in(u),v),tc_Com_Opname),u),u)*.
% 299.79/300.47 14690[0:SpR:128.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(c_Set_Ovimage(x,y,w),u,z),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(x,y,w),v),tc_fun(y,tc_bool)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.47 15109[0:SpR:181.1,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),w),hAPP(c_Set_Ovimage(c_Set_Ovimage(c_COMBK(v,u,y),y,u),x,z),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.47 16576[0:SpR:128.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(x,tc_bool))),y)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(z,x1,x),w),tc_fun(x1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Ovimage(z,x1,x),v,u),u)*.
% 299.79/300.47 16546[0:SpR:544.1,361.2] class_Lattices_Olattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),z)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,v),v)*.
% 299.79/300.47 16545[0:SpR:543.1,361.2] class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),z)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,v),v)*.
% 299.79/300.47 16540[0:SpR:181.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> hBOOL(hAPP(hAPP(c_in(y),z),w))* c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Ovimage(c_COMBK(z,y,x1),x1,y),v,u),u)*.
% 299.79/300.47 17103[0:Res:511.1,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),v),x,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),v),x),u,t_a)*.
% 299.79/300.47 17099[0:Res:511.1,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w),u),v,u)*.
% 299.79/300.47 17098[0:Res:511.1,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w),u),u)*.
% 299.79/300.47 17260[0:Res:510.1,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w),x,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w),x),u,t_a)*.
% 299.79/300.47 17256[0:Res:510.1,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),u),v,u)*.
% 299.79/300.47 17255[0:Res:510.1,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),u),u)*.
% 299.79/300.47 17360[0:Res:172.2,150.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u) hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMax(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u)),v))* -> equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.79/300.47 17478[0:Res:171.2,150.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u) hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMin(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u)),v))* -> equal(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.79/300.47 18146[0:SpR:130.1,362.1] class_HOL_Ominus(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(x,v_x),hAPP(y,v_x),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(x,y,tc_fun(t_a,u)),v,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.47 18346[0:SpR:130.1,545.1] class_HOL_Ominus(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_HOL_Ominus__class_Ominus(hAPP(y,v_x),hAPP(z,v_x),u)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(y,z,tc_fun(t_a,u)),v,x),w)))*.
% 299.79/300.47 19836[0:SpR:104.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))),t_a) hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool)))),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))*.
% 299.79/300.47 19787[0:SpR:104.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))))**.
% 299.79/300.47 19962[0:SpR:64.0,8385.1] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),tc_fun(tc_Com_Opname,tc_bool)),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u)).
% 299.79/300.47 20370[0:SpR:9.0,438.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Fun_Ocomp(u,v,w,x,y),z,x1),hAPP(u,hAPP(v,x2))),x2)**.
% 299.79/300.47 20353[0:SpR:11695.0,438.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),x,y),c_Orderings_Otop__class_Otop(tc_bool)),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),w))**.
% 299.79/300.47 20322[0:SpR:2098.1,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,x),v),v)**.
% 299.79/300.47 20514[0:SpR:9.0,99.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Fun_Ocomp(u,v,w,x,y),z,x1),hAPP(u,hAPP(v,x2))),x2)**.
% 299.79/300.47 20497[0:SpR:11695.0,99.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),x,y),c_Orderings_Otop__class_Otop(tc_bool)),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),w))**.
% 299.79/300.47 20469[0:SpR:297.2,99.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),w),w)**.
% 299.79/300.47 20466[0:SpR:2098.1,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,x),v),v)**.
% 299.79/300.47 21004[0:SpR:9.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(c_Set_Oinsert(hAPP(u,hAPP(v,x2)),x1),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),z,x1),x3)))*.
% 299.79/300.47 20987[0:SpR:11695.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),x,y),hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),w),x),z)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),y),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),x,y),z)))*.
% 299.79/300.47 20968[0:SpR:88.1,317.0] class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),w,x),hAPP(c_Set_Oinsert(v,w),y)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),w,x),y)))*.
% 299.79/300.47 20961[0:SpR:540.1,317.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(y,w),z)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),z)))*.
% 299.79/300.47 20960[0:SpR:539.1,317.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(y,w),z)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),z)))*.
% 299.79/300.47 20959[0:SpR:297.2,317.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),hAPP(c_Set_Oinsert(w,x),z)),hAPP(c_Set_Oinsert(w,y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),z)))*.
% 299.79/300.47 20956[0:SpR:2098.1,317.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,x),hAPP(c_Set_Oinsert(v,w),y)),hAPP(c_Set_Oinsert(v,x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,x),y)))*.
% 299.79/300.47 20950[0:SpR:299.2,317.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y),hAPP(c_Set_Oinsert(v,x),z)),hAPP(c_Set_Oinsert(w,y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y),z)))*.
% 299.79/300.47 20916[0:SpR:64.0,317.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))),hAPP(c_Set_Oimage(u,x,w),hAPP(c_Set_Oinsert(v,x),y)))**.
% 299.79/300.47 20898[0:SpR:317.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),hAPP(c_Set_Oinsert(z,y),x1))),hAPP(c_Set_Oinsert(hAPP(u,hAPP(x,z)),w),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),x1))))*.
% 299.79/300.47 21686[0:SpL:21267.0,156.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),v_x))) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,v)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(w,u,x),hAPP(c_Set_Ovimage(w,u,x),v_x),tc_Com_Opname,y)))*.
% 299.79/300.47 21670[0:SpL:21267.0,346.0] || c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),v,x) -> c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),tc_Com_Opname,y),v,x)*.
% 299.79/300.47 21643[0:SpL:21267.0,255.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,w),x,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),x)).
% 299.79/300.47 21535[0:SpR:181.1,21267.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.79/300.47 21455[0:SpR:21267.0,304.3] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,x),w,u)* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),w,u).
% 299.79/300.47 21435[0:SpR:21267.0,153.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(v,x,u),hAPP(c_Set_Ovimage(v,x,u),v_x),tc_Com_Opname,y)))* -> hBOOL(hAPP(hAPP(c_in(x),w),hAPP(c_Set_Ovimage(v,x,u),v_x))).
% 299.79/300.47 21423[0:SpR:21267.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,u,x),hAPP(c_Set_Oimage(w,u,x),v_x),tc_Com_Opname,y)))* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,v)),hAPP(c_Set_Oimage(w,u,x),v_x))).
% 299.79/300.47 21405[0:SpR:21267.0,335.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x),tc_Com_Opname,w),v)* -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x),v).
% 299.79/300.47 22315[0:SpL:21893.0,156.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),v_x))) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,v)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(w,u,x),v_x),c_Set_Ovimage(w,u,x),tc_Com_Opname,y)))*.
% 299.79/300.47 22298[0:SpL:21893.0,346.0] || c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),v,x) -> c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname,y),v,x)*.
% 299.79/300.47 22271[0:SpL:21893.0,255.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,w),x,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),x)).
% 299.79/300.47 22162[0:SpR:181.1,21893.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.79/300.47 22081[0:SpR:21893.0,304.3] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,x),w,u)* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),w,u).
% 299.79/300.47 22061[0:SpR:21893.0,153.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(v,x,u),v_x),c_Set_Ovimage(v,x,u),tc_Com_Opname,y)))* -> hBOOL(hAPP(hAPP(c_in(x),w),hAPP(c_Set_Ovimage(v,x,u),v_x))).
% 299.79/300.47 22049[0:SpR:21893.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,u,x),v_x),c_Set_Oimage(w,u,x),tc_Com_Opname,y)))* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,v)),hAPP(c_Set_Oimage(w,u,x),v_x))).
% 299.79/300.47 22031[0:SpR:21893.0,335.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),v)* -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x),v).
% 299.79/300.47 22659[0:SpL:158.0,19641.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z))))* -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z,t_a).
% 299.79/300.47 22610[0:SpR:158.0,96.1] || c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(v,w,x),y),x,z) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(v,w,x),y),u,x,z),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,x,z,w),w,z),y),z,x)*.
% 299.79/300.47 22568[0:SpR:158.0,96.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),z,y,x) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(z,c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),z)),x,y)*.
% 299.79/300.47 22683[0:Rew:9.0,22662.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1))))* -> equal(hAPP(w,hAPP(y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x1,c_Fun_Ocomp(w,y,x,u,z),v,z,u))),v)**.
% 299.79/300.47 22684[0:Rew:9.0,22661.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1))))* -> equal(hAPP(w,hAPP(y,c_ATP__Linkup_Osko__Set__XimageE__1__1(x1,v,c_Fun_Ocomp(w,y,x,u,z),z,u))),v)**.
% 299.79/300.47 22685[0:Rew:9.0,22595.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Oinsert(z,y),x1)),hAPP(c_Set_Oinsert(hAPP(u,hAPP(v,z)),x),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x1))))*.
% 299.79/300.47 23036[0:SpL:131.0,19641.0] || hBOOL(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z))))* -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z,t_a).
% 299.79/300.47 24058[0:SpL:98.1,75.1] || c_Fun_Oinj__on(u,v,w,x) c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x) equal(c_Finite__Set_Ocard(v,w),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x))* -> equal(hAPP(c_Set_Oimage(u,w,x),v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))**.
% 299.79/300.47 24448[0:SpL:21893.0,208.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),v_x),tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),v),u)) c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,w),v_x),c_Set_Oinsert(v,w),tc_Com_Opname,x),tc_fun(w,tc_bool))*.
% 299.79/300.47 24447[0:SpL:21267.0,208.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),v_x),tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),v),u)) c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),v_x),tc_Com_Opname,x),tc_fun(w,tc_bool))*.
% 299.79/300.47 25730[0:Res:171.2,455.0] class_Orderings_Olinorder(tc_Hoare__Mirabelle_Otriple(t_a)) || c_Finite__Set_Ofinite(u,tc_Hoare__Mirabelle_Otriple(t_a)) c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))) c_Hoare__Mirabelle_Otriple__valid(w,c_Finite__Set_Olinorder__class_OMin(u,tc_Hoare__Mirabelle_Otriple(t_a)),t_a)*.
% 299.79/300.47 25729[0:Res:172.2,455.0] class_Orderings_Olinorder(tc_Hoare__Mirabelle_Otriple(t_a)) || c_Finite__Set_Ofinite(u,tc_Hoare__Mirabelle_Otriple(t_a)) c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))) c_Hoare__Mirabelle_Otriple__valid(w,c_Finite__Set_Olinorder__class_OMax(u,tc_Hoare__Mirabelle_Otriple(t_a)),t_a)*.
% 299.79/300.47 25893[0:SpR:339.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),x)),z,u),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.47 26016[0:SSi:25904.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)) c_lessequals(y,x,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)),x,tc_fun(v,tc_bool))*.
% 299.79/300.47 26249[0:SpL:338.0,62.0] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),y)),tc_fun(v,tc_bool)),v)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y),tc_fun(v,tc_bool)),v).
% 299.79/300.47 26116[0:SpR:338.0,63.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)),v) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(y,v),x)),tc_fun(v,tc_bool)),v)*.
% 299.79/300.47 26115[0:SpR:338.0,446.1] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(y,v),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(y,v),x)),tc_fun(v,tc_bool))*.
% 299.79/300.47 26099[0:SpR:338.0,8498.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(x,u),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w))**.
% 299.79/300.47 26097[0:SpR:338.0,446.1] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(y,u),w)),hAPP(c_Set_Oinsert(y,u),x),tc_fun(u,tc_bool))*.
% 299.79/300.47 26294[0:SSi:26067.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Oinsert(x,w),y),v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y)),v,tc_fun(w,tc_bool))*.
% 299.79/300.47 27199[0:Res:450.0,278.1] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(v),w,x,y))) -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(v)),x),w),t_a) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),w,x,y),z,u,v)))*.
% 299.79/300.47 27198[0:Res:450.0,277.1] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(v),w,x,y))) -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(v)),x),w),t_a) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),w,x,y),u,v)))*.
% 299.79/300.47 27157[0:SpR:23682.0,450.0] || -> hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v,w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v,w)))* c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))),v),u),t_a).
% 299.79/300.47 27370[0:SpL:158.0,470.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1))))* -> hBOOL(hAPP(hAPP(c_in(z),c_ATP__Linkup_Osko__Set__XimageE__1__1(x1,v,c_Fun_Ocomp(w,y,x,u,z),z,u)),x1))*.
% 299.79/300.47 27430[0:SpL:158.0,466.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1))))* -> hBOOL(hAPP(hAPP(c_in(z),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x1,c_Fun_Ocomp(w,y,x,u,z),v,z,u)),x1))*.
% 299.79/300.47 27634[0:SpR:10090.1,373.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),w)) c_Fun_Oinj__on(hAPP(u,v_x),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(u,v_x),v,x),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.47 27627[0:SpR:303.1,373.2] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.47 27574[0:SpR:302.1,373.2] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y),c_Orderings_Otop__class_Otop(u)),w)*.
% 299.79/300.47 27561[0:SpR:15476.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,tc_bool)),v,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,tc_bool)),u,x),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool)),v_x)**.
% 299.79/300.47 27787[0:SpR:10090.1,71.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),w)) c_Fun_Oinj__on(hAPP(u,v_x),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(u,v_x),v,x),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.47 27780[0:SpR:303.1,71.2] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.47 27727[0:SpR:302.1,71.2] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y),c_Orderings_Otop__class_Otop(u)),w)*.
% 299.79/300.47 27714[0:SpR:15476.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,tc_bool)),v,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,tc_bool)),u,x),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool)),v_x)**.
% 299.79/300.47 27945[0:Res:468.0,496.0] || -> equal(hAPP(c_Set_Oimage(u,tc_Hoare__Mirabelle_Otriple(t_a),v),w),hAPP(c_Set_Oimage(x,tc_Hoare__Mirabelle_Otriple(t_a),v),w)) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(y,w)),w))* c_Hoare__Mirabelle_Otriple__valid(y,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,u,x,tc_Hoare__Mirabelle_Otriple(t_a),v),t_a)*.
% 299.79/300.47 27941[0:Res:468.0,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,w,x,y,z)),x1))* -> equal(hAPP(c_Set_Oimage(w,y,z),v),hAPP(c_Set_Oimage(x,y,z),v)) hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,u,y,tc_fun(x2,tc_bool)),x1))*.
% 299.79/300.47 28208[0:SpR:465.1,158.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(x,c_Fun_Ofun__upd(y,v,z,u,x1),x1,x2,u),u,x2),w),hAPP(c_Set_Oimage(x,x1,x2),hAPP(c_Set_Oimage(y,u,x1),w)))**.
% 299.79/300.47 28186[0:SpR:465.1,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),w)),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(y,v,x1,u,z),u,z),x2,x),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)))))*.
% 299.79/300.47 28181[0:SpR:465.1,313.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),x),v)) c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,x,z,w,x1),w,x1),u),hAPP(c_Set_Oimage(y,w,x1),v),tc_fun(x1,tc_bool))*.
% 299.79/300.47 28118[0:SpR:465.1,313.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),x),u)) c_lessequals(hAPP(c_Set_Oimage(y,w,z),u),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,x,x1,w,z),w,z),v),tc_fun(z,tc_bool))*.
% 299.79/300.47 28565[0:SpR:23.0,118.0] || -> equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(c_Fun_Ocomp(v,w,x,y,z),x1,x2,z,y),y,x3,z),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Fun_Ocomp(u,v,y,x3,x),w,x,x3,z),x1,hAPP(u,x2),z,x3))*.
% 299.79/300.47 28557[0:SpR:10063.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),c_Fun_Ofun__upd(u,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),w,x),x,y,w),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_x,t_a),u,x,y,w),v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),w,y))*.
% 299.79/300.47 28540[0:SpR:105.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Ovimage(u,v,w),c_Fun_Ofun__upd(x,y,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Ovimage(u,v,w),x,x1,x2,z),y,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),z,x2))*.
% 299.79/300.47 28533[0:SpR:38.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Ovimage(u,v,w),c_Fun_Ofun__upd(x,y,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Ovimage(u,v,w),x,x1,x2,z),y,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),z,x2))*.
% 299.79/300.47 28532[0:SpR:321.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oimage(u,v,w),c_Fun_Ofun__upd(x,y,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oimage(u,v,w),x,x1,x2,z),y,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),z,x2))*.
% 299.79/300.47 28503[0:SpR:87.1,118.0] class_Lattices_Oboolean__algebra(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Fun_Ofun__upd(w,x,c_HOL_Ouminus__class_Ouminus(v,u),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,z,x1,y),x,c_Orderings_Otop__class_Otop(u),y,x1))*.
% 299.79/300.47 28484[0:SpR:302.1,118.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Fun_Ofun__upd(v,w,x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,z,x1,y),w,c_Orderings_Otop__class_Otop(u),y,x1))*.
% 299.79/300.47 28471[0:SpR:15476.0,118.0] || -> equal(c_Fun_Ocomp(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),c_Fun_Ofun__upd(v,w,v_x,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v,y,z,x),w,c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),x,z))*.
% 299.79/300.47 28456[0:SpR:369.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,hAPP(c_Set_Oinsert(u,v),y),z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(u,v),w,x1,x2,z),x,hAPP(c_Set_Oinsert(u,v),y),z,x2))*.
% 299.79/300.47 28455[0:SpR:2089.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_x,tc_Com_Opname),c_Fun_Ofun__upd(u,v,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_x,tc_Com_Opname),u,y,z,x),v,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),x,z))*.
% 299.79/300.47 28425[0:SpR:118.0,23.0] || -> equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(c_Fun_Ocomp(v,w,x,y,z),x1,hAPP(v,x2),z,y),y,x3,z),c_Fun_Ocomp(c_Fun_Ocomp(u,v,y,x3,x),c_Fun_Ofun__upd(w,x1,x2,z,x),x,x3,z))*.
% 299.79/300.47 28423[0:SpR:118.0,23.0] || -> equal(c_Fun_Ocomp(u,c_Fun_Ocomp(c_Fun_Ofun__upd(v,w,x,y,z),x1,y,z,x2),z,x3,x2),c_Fun_Ocomp(c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,z,x3,y),w,hAPP(u,x),y,x3),x1,y,x3,x2))*.
% 299.79/300.47 28422[0:SpR:118.0,131.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,w,x,y),z,hAPP(u,x1),y,x),y,x),x2),hAPP(c_Set_Ovimage(c_Fun_Ofun__upd(v,z,x1,y,w),y,w),hAPP(c_Set_Ovimage(u,w,x),x2)))*.
% 299.79/300.47 28421[0:SpR:118.0,158.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,w,x,y),z,hAPP(u,x1),y,x),y,x),x2),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(v,z,x1,y,w),y,w),x2)))*.
% 299.79/300.47 29172[0:SpL:537.1,3489.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.79/300.47 29171[0:SpL:537.1,3487.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.47 29100[0:SpR:537.1,584.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y,z,x1),x2),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x2)),hAPP(x,x2)))*.
% 299.79/300.47 29099[0:SpR:537.1,584.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y,z,x1),x2),hAPP(hAPP(v,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),x2))))*.
% 299.79/300.47 29009[0:SpR:537.1,3294.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(t_a)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.47 29697[0:SpL:534.1,3489.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.79/300.47 29696[0:SpL:534.1,3487.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.47 29624[0:SpR:534.1,584.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y,z,x1),x2),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x2)),hAPP(x,x2)))*.
% 299.79/300.47 29623[0:SpR:534.1,584.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y,z,x1),x2),hAPP(hAPP(v,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),x2))))*.
% 299.79/300.47 29531[0:SpR:534.1,3294.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_in(t_a)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.47 29928[0:SpR:27043.1,118.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_Procs,u),c_Fun_Ofun__upd(v,w,v_x,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_Procs,u),v,y,z,x),w,v_x,x,z))*.
% 299.79/300.47 29907[0:SpR:27043.1,71.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,w),v,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(v_Procs,w),u,x),v_x),v_x)**.
% 299.79/300.47 29906[0:SpR:27043.1,373.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,w),v,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(v_Procs,w),u,x),v_x),v_x)**.
% 299.79/300.47 31295[0:Res:450.0,356.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(v)),w),x),t_a) equal(hAPP(c_Set_Oimage(c_COMBK(y,z,v),v,z),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),x,w,u)),hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))**.
% 299.79/300.47 31427[0:Res:34.1,449.0] || hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,c_Set_Ovimage(v,w,x),y,z),hAPP(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_Set_Ovimage(v,w,x),y,z))))* -> c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),c_Set_Ovimage(v,w,x)),t_a).
% 299.79/300.47 31400[0:SpL:14216.0,449.0] || hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),y,z))) -> c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))),t_a)*.
% 299.79/300.47 31437[0:MRR:31436.1,820.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z)))* -> c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),w),y),c_Set_Ovimage(c_COMBK(v,u,x),x,u)),t_a)*.
% 299.79/300.47 31529[0:SpL:21893.0,473.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y))),x))*.
% 299.79/300.47 31528[0:SpL:21267.0,473.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y))),x))*.
% 299.79/300.47 32065[0:Res:151.2,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,c_HOL_Ominus__class_Ominus(v,x,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.47 32085[0:SpR:8415.2,340.2] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(v_x,v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(v_x,w),v,tc_fun(u,tc_bool))*.
% 299.79/300.47 32382[0:Res:8376.2,477.0] || equal(c_in(tc_Com_Opname),u) equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(u,v_x),v),v_Procs)** hBOOL(hAPP(hAPP(c_in(v),y),w))* -> hBOOL(hAPP(hAPP(u,v_x),y))*.
% 299.79/300.47 32379[0:Res:212.1,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Set_Oinsert(y,z),u),v)))* hBOOL(hAPP(hAPP(c_in(v),x1),w))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,z),u),x1))*.
% 299.79/300.47 32377[0:Res:13238.1,477.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(t_a),v_x),u),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.47 32375[0:Res:8375.1,477.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(x),y),u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))** hBOOL(hAPP(hAPP(c_in(u),z),v))* -> hBOOL(hAPP(hAPP(c_in(x),y),z))*.
% 299.79/300.47 32373[0:Res:652.1,477.0] || c_lessequals(v_Procs,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(tc_Com_Opname),v_x),u),tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),x))*.
% 299.79/300.47 32316[0:SpL:339.0,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),z),hAPP(c_Set_Oinsert(v,w),x)))* -> hBOOL(hAPP(u,z))*.
% 299.79/300.47 32283[0:SpL:8415.2,477.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,w,u)))* hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(hAPP(w,x))*.
% 299.79/300.47 32278[0:SpL:8415.2,477.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(v_x,w),v,u)))* hBOOL(hAPP(hAPP(c_in(u),x),v_x))* -> hBOOL(hAPP(v,x))*.
% 299.79/300.47 32562[0:Res:8376.2,476.0] || equal(c_in(tc_Com_Opname),u) equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(u,v_x),v),v_Procs)** hBOOL(hAPP(hAPP(c_in(v),y),x))* -> hBOOL(hAPP(hAPP(u,v_x),y))*.
% 299.79/300.47 32559[0:Res:212.1,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Set_Oinsert(y,z),u),v)))* hBOOL(hAPP(hAPP(c_in(v),x1),x))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,z),u),x1))*.
% 299.79/300.47 32557[0:Res:13238.1,476.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(t_a),v_x),u),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.47 32555[0:Res:8375.1,476.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(x),y),u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))** hBOOL(hAPP(hAPP(c_in(u),z),w))* -> hBOOL(hAPP(hAPP(c_in(x),y),z))*.
% 299.79/300.47 32553[0:Res:652.1,476.0] || c_lessequals(v_Procs,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_in(tc_Com_Opname),v_x),u),tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),x))*.
% 299.79/300.47 32492[0:SpL:338.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),z),hAPP(c_Set_Oinsert(v,w),y)))* -> hBOOL(hAPP(u,z))*.
% 299.79/300.47 32458[0:SpL:8415.2,476.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(v_x,w),v,u)))* hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(hAPP(v,x))*.
% 299.79/300.47 32770[0:SpR:35.2,15367.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool))),tc_fun(w,tc_bool))* c_lessequals(hAPP(c_Set_Oinsert(v,w),c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool))),x,tc_fun(w,tc_bool))* -> c_Finite__Set_Ofinite(u,w).
% 299.79/300.47 33009[0:SpR:9987.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,x),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,x),w))**.
% 299.79/300.47 33007[0:SpR:2095.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oimage(c_Set_Oinsert(y,v),u,x),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(y,v),u,x),w))**.
% 299.79/300.47 33003[0:SpR:23902.1,475.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_bool)),w)) -> equal(hAPP(c_Set_Oinsert(v_x,x),hAPP(c_Set_Oimage(hAPP(u,v_x),v,x),w)),hAPP(c_Set_Oimage(hAPP(u,v_x),v,x),w))**.
% 299.79/300.47 33000[0:SpR:2935.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),hAPP(c_Set_Oimage(hAPP(c_in(t_a),v_x),u,w),v)),hAPP(c_Set_Oimage(hAPP(c_in(t_a),v_x),u,w),v))**.
% 299.79/300.47 32995[0:SpR:301.1,475.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> equal(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),w))**.
% 299.79/300.47 32946[0:SpR:414.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,x,x1,x2),u,y),w)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,x,x1,x2),u,y),w))**.
% 299.79/300.47 32937[0:SpR:524.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(v,x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),u,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),u,x),w))**.
% 299.79/300.47 32932[0:SpR:8415.2,475.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(c_Set_Oinsert(v_x,x),hAPP(c_Set_Oimage(u,v,x),w)),hAPP(c_Set_Oimage(u,v,x),w))**.
% 299.79/300.47 32928[0:SpR:365.1,475.1] class_Orderings_Obot(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),x),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,x),w)),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,x),w))**.
% 299.79/300.47 32927[0:SpR:397.1,475.1] class_Orderings_Otop(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,x),w)),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,x),w))**.
% 299.79/300.47 32913[0:SpR:2093.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(tc_Com_Opname),v_x)),v)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_in(tc_Com_Opname),v_x),w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,x),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,x),u,w),v))**.
% 299.79/300.47 32911[0:SpR:3744.1,475.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> equal(hAPP(c_Set_Oinsert(v_Procs,x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,x),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),v,x),w))**.
% 299.79/300.47 32878[0:SpR:475.1,20881.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(x,v),y),z,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,u,y),w),z),x2)),hAPP(c_Set_Oimage(x,u,y),w)))*.
% 299.79/300.47 32872[0:SpR:475.1,353.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(x,v),y),hAPP(c_Set_Oinsert(z,y),hAPP(c_Set_Oimage(x,u,y),w))),hAPP(c_Set_Oinsert(z,y),hAPP(c_Set_Oimage(x,u,y),w)))**.
% 299.79/300.47 32850[0:SpR:475.1,9569.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oimage(x,u,y),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),c_Set_Oinsert(hAPP(x,v),y)),hAPP(c_Set_Oimage(x,u,y),w)),tc_bool)*.
% 299.79/300.47 32849[0:SpR:475.1,9568.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oimage(x,u,y),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Set_Oinsert(hAPP(x,v),y)),x1),hAPP(c_Set_Oimage(x,u,y),w)),tc_bool)*.
% 299.79/300.47 33076[0:SpL:8415.2,94.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Fun_Oinj__on(u,v_x,v,w) c_Fun_Oinj__on(x,v_x,w,y) -> c_Fun_Oinj__on(c_Fun_Ocomp(x,u,w,y,v),v_x,v,y)*.
% 299.79/300.47 33415[0:Res:153.1,453.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),u),x),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(y,z)),y))* c_Hoare__Mirabelle_Otriple__valid(z,w,t_a)*.
% 299.79/300.47 33414[0:Res:545.1,453.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Hoare__Mirabelle_Ohoare__valids(x,hAPP(c_Set_Oimage(y,u,tc_Hoare__Mirabelle_Otriple(t_a)),w),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(x,z)),x))* c_Hoare__Mirabelle_Otriple__valid(z,hAPP(y,v),t_a)*.
% 299.79/300.47 33494[0:SpR:61.1,288.1] || c_Finite__Set_Ofinite(u,v) c_Natural_Oevaln(w,x,c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(y,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),z)* -> c_Natural_Oevaln(w,x,c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(y,v),u),v),z).
% 299.79/300.47 34426[0:SpL:24914.0,280.1] || hBOOL(hAPP(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(v),tc_Com_Opname,w),hAPP(c_in(v),v_x))),x))* hBOOL(hAPP(hAPP(c_in(v),v_x),y)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,u,v,tc_fun(z,tc_bool)),x))*.
% 299.79/300.47 34416[0:SpL:24914.0,390.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),v_x),tc_fun(x,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(v,w,x),tc_Com_Opname,y),hAPP(c_Set_Oimage(v,w,x),v_x)),v,w,x),u,x,w)*.
% 299.79/300.47 34409[0:SpL:24914.0,514.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),v_x),z))* -> equal(w,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),tc_Com_Opname,x1),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),v_x)))*.
% 299.79/300.47 34372[0:SpL:24914.0,278.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(w),v),tc_Com_Opname,x),hAPP(hAPP(c_in(w),v),v_x)),y,u,w)))*.
% 299.79/300.47 34371[0:SpL:24914.0,277.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),v_x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(w),v),tc_Com_Opname,y),hAPP(hAPP(c_in(w),v),v_x)),u,w)))*.
% 299.79/300.47 34307[0:SpL:24914.0,175.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))* -> equal(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x))),x)*.
% 299.79/300.47 34303[0:SpL:24914.0,470.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x)),v,w,u)),x))*.
% 299.79/300.47 34302[0:SpL:24914.0,466.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x)),w,u)),x))*.
% 299.79/300.47 34263[0:SpL:24914.0,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),u)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,u)),u))* c_Hoare__Mirabelle_Otriple__valid(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,w),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x)),t_a)*.
% 299.79/300.47 34234[0:SpR:538.0,24914.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v))**.
% 299.79/300.47 34178[0:SpR:24914.0,317.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,x),tc_Com_Opname,y),hAPP(c_Set_Oinsert(v,x),v_x)))),hAPP(c_Set_Oimage(u,x,w),hAPP(c_Set_Oinsert(v,x),v_x)))**.
% 299.79/300.47 34155[0:SpR:24914.0,10746.0] || -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),tc_Com_Opname,x),hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),v_x)),hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),v_x),tc_bool)*.
% 299.79/300.47 34134[0:SpR:24914.0,328.1] || c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),v,tc_fun(u,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),v).
% 299.79/300.47 34093[0:SpR:24914.0,128.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Ovimage(u,v,w),v_x)),tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),v_x),tc_fun(v,tc_bool)))**.
% 299.79/300.47 34038[0:SpR:24914.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))),x))* -> equal(hAPP(c_Set_Oinsert(hAPP(v,v_x),y),hAPP(c_Set_Oimage(v,u,y),x)),hAPP(c_Set_Oimage(v,u,y),x))**.
% 299.79/300.47 35418[0:SpR:21893.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),w),x),u,w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(u,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,u,w,tc_fun(y,tc_bool))))*.
% 299.79/300.47 35417[0:SpR:21267.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),w),x),u,w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(u,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,u,w,tc_fun(y,tc_bool))))*.
% 299.79/300.47 35368[0:SpR:24020.1,410.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,v),w),hAPP(u,v_x),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 35360[0:SpR:9924.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 35316[0:SpR:525.1,410.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(y,tc_bool))))*.
% 299.79/300.47 35279[0:SpR:2097.1,410.0] || hBOOL(hAPP(u,v)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,w),x),c_Set_Oinsert(v,y),w,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v,y),w,tc_fun(z,tc_bool))))*.
% 299.79/300.47 35180[0:SpR:410.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* -> c_lessequals(hAPP(y,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,u,tc_fun(z,tc_bool))),tc_fun(z,tc_bool))*.
% 299.79/300.47 35617[0:SpR:89.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* -> c_lessequals(hAPP(z,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_COMBB(z,u,tc_fun(x1,tc_bool),x),w),x,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.47 36154[0:SpL:104.0,516.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)))) hBOOL(hAPP(hAPP(c_in(u),v),x)).
% 299.79/300.47 36854[0:SpR:66.0,61.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),w) -> equal(c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(x,w),v),tc_fun(w,tc_bool)),w)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(x,w),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool))),w))**.
% 299.79/300.47 37466[0:SpR:205.1,9567.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(u,v,w),z)),z,tc_bool)*.
% 299.79/300.47 37447[0:SpR:205.1,5875.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(x,y),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),z,x1,x2),hAPP(c_Set_Oimage(u,v,w),x)))*.
% 299.79/300.47 38225[0:Res:13.2,431.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,y,tc_fun(w,tc_bool))* c_Fun_Oinj__on(z,c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),w,x1)* -> c_Fun_Oinj__on(z,c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool)),w,x1)*.
% 299.79/300.47 38221[0:SpR:117.0,13.2] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)) c_lessequals(y,v,tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.47 38295[0:SpR:3294.1,201.3] class_Lattices_Oupper__semilattice(u) || equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(t_a)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v,u,u),u)*.
% 299.79/300.47 38290[0:SpR:584.0,201.3] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(x,v),w,u,u),u)*.
% 299.79/300.47 38512[0:MRR:38511.3,96.1] || c_Fun_Oinj__on(u,v,w,w) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,w,w),v),w) c_lessequals(v,hAPP(c_Set_Oimage(u,w,w),v),tc_fun(w,tc_bool))* -> equal(hAPP(c_Set_Oimage(u,w,w),v),v).
% 299.79/300.47 38964[0:SpR:354.2,474.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> hBOOL(hAPP(hAPP(c_in(z),u),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),x1,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.79/300.47 38951[0:SpR:354.2,9566.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> c_lessequals(u,hAPP(hAPP(c_Set_Oinsert(z,x1),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w)),hAPP(c_Set_Oimage(x,w,y),u)),tc_bool)*.
% 299.79/300.47 39321[0:SpL:533.0,16286.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_Procs) -> .
% 299.79/300.47 39320[7:SpL:533.0,31868.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_x) -> .
% 299.79/300.47 39260[0:SpR:3229.1,533.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(u,v_x)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),x)))*.
% 299.79/300.47 39144[0:SpR:533.0,3229.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) -> equal(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)))*.
% 299.79/300.47 39140[4:SpR:533.0,38042.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),x,t_a)*.
% 299.79/300.47 39130[0:SpR:533.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname,x)))*.
% 299.79/300.47 39124[0:SpR:533.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_Com_Opname,x)))*.
% 299.79/300.47 39117[4:SpR:533.0,37987.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),x))*.
% 299.79/300.47 39109[0:SpR:533.0,3283.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),v_Procs))*.
% 299.79/300.47 39102[0:SpR:533.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname,x),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.47 39743[0:SpR:3229.1,532.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(u,v_x)))*.
% 299.79/300.47 39668[0:SpR:532.0,8376.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(tc_Com_Opname)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),w)))*.
% 299.79/300.47 39937[0:Rew:39935.1,35219.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,z),x1),v,z,tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,v,z,tc_fun(u,tc_bool)))**.
% 299.79/300.47 40184[0:SpR:3229.1,399.1] || equal(u,c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool)) c_lessequals(v_x,w,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(u,v_x),hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),w),tc_fun(v,tc_bool))*.
% 299.79/300.47 40178[0:SpR:3229.1,399.1] || equal(u,c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool)) c_lessequals(w,v_x,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),w),hAPP(u,v_x),tc_fun(v,tc_bool))*.
% 299.79/300.47 40294[0:Res:448.1,398.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || -> c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w),tc_fun(u,tc_bool))* c_lessequals(w,v,tc_fun(u,tc_bool)).
% 299.79/300.47 40279[0:SpL:3229.1,398.0] || equal(u,c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool)) c_lessequals(hAPP(u,v_x),hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),w),tc_fun(v,tc_bool))* -> c_lessequals(v_x,w,tc_fun(v,tc_bool)).
% 299.79/300.47 40273[0:SpL:3229.1,398.0] || equal(u,c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool)) c_lessequals(hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),w),hAPP(u,v_x),tc_fun(v,tc_bool))* -> c_lessequals(w,v_x,tc_fun(v,tc_bool)).
% 299.79/300.47 40453[0:SpL:3229.1,529.0] || equal(u,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))))* c_Hoare__Mirabelle_Otriple__valid(y,hAPP(u,v_x),v)* -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(y),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),v_x),v)*.
% 299.79/300.47 40446[0:SpL:3229.1,529.0] || equal(u,c_Hoare__Mirabelle_Otriple_Otriple(v)) c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(u,v_x),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),v)* -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),v_x),hAPP(c_Com_Ocom_OBODY,x)),y),v)*.
% 299.79/300.47 40440[0:SpL:3229.1,529.0] || equal(u,c_Com_Obody) c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),x),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(u,v_x))),y),w)* -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),x),hAPP(c_Com_Ocom_OBODY,v_x)),y),w).
% 299.79/300.47 40702[0:SpR:3229.1,530.1] || equal(u,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(y),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),v_x),v)* -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(u,v_x),v)*.
% 299.79/300.47 40695[0:SpR:3229.1,530.1] || equal(u,c_Hoare__Mirabelle_Otriple_Otriple(v)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),v_x),hAPP(c_Com_Ocom_OBODY,x)),y),v)* -> c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(u,v_x),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),v)*.
% 299.79/300.47 40689[0:SpR:3229.1,530.1] || equal(u,c_Com_Obody) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),x),hAPP(c_Com_Ocom_OBODY,v_x)),y),w) -> c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),x),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(u,v_x))),y),w)*.
% 299.79/300.47 40951[0:Rew:339.0,40922.2] || equal(u,v_Procs) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,tc_Com_Opname),u),x,v,tc_Com_Opname)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),x))))*.
% 299.79/300.47 40914[0:Res:11030.1,479.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)))*.
% 299.79/300.47 40910[0:Res:3316.1,479.1] || equal(c_in(u),c_in(v)) hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),x,w,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),x)))*.
% 299.79/300.47 40888[0:Res:648.0,479.1] || hBOOL(hAPP(u,hAPP(v,v_x))) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),x,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs)),x)))*.
% 299.79/300.47 40871[0:SpL:3229.1,479.1] || equal(u,hAPP(c_in(v),w))* hBOOL(hAPP(x,w))* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,y,x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),y)))*.
% 299.79/300.47 40865[0:SpL:3229.1,479.1] || equal(u,c_in(v))* hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(u,v_x),x))* -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,y,w,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))*.
% 299.79/300.47 41203[0:Res:19436.1,478.1] || equal(u,v_Procs) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oinsert(x,tc_Com_Opname),u),v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),u))))*.
% 299.79/300.47 41195[0:Res:11030.1,478.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.79/300.47 41191[0:Res:3316.1,478.1] || equal(c_in(u),c_in(v)) hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))))*.
% 299.79/300.47 41169[0:Res:648.0,478.1] || hBOOL(hAPP(u,hAPP(v,v_x))) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs))))*.
% 299.79/300.47 41152[0:SpL:3229.1,478.1] || equal(u,hAPP(c_in(v),w))* hBOOL(hAPP(x,w))* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,v_x,x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),v_x)))*.
% 299.79/300.47 41146[0:SpL:3229.1,478.1] || equal(u,c_in(v))* hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(u,v_x),x))* -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,x,w,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x)))*.
% 299.79/300.47 41391[0:SpL:3229.1,275.1] || equal(u,c_in(v))* hBOOL(hAPP(hAPP(c_in(w),x),y))* hBOOL(hAPP(hAPP(u,v_x),hAPP(z,x)))* -> hBOOL(hAPP(hAPP(c_in(v),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,z,w,tc_fun(v,tc_bool))))*.
% 299.79/300.47 41286[0:SpL:525.1,275.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) hBOOL(hAPP(hAPP(c_in(y),z),w)) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(y,tc_bool))))*.
% 299.79/300.47 41280[0:SpL:3229.1,275.1] || equal(u,v)* hBOOL(hAPP(hAPP(c_in(w),v_x),x)) hBOOL(hAPP(hAPP(c_in(y),z),hAPP(u,v_x)))* -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,w,tc_fun(y,tc_bool))))*.
% 299.79/300.47 41249[0:SpL:8385.1,275.1] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(x),y),u))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,tc_Com_Opname),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 41622[0:SpL:23912.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,u),x)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u)* -> hBOOL(hAPP(hAPP(c_in(w),v),x)).
% 299.79/300.47 41564[0:SpL:3229.1,284.0] || equal(u,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),hAPP(c_Set_Oimage(v,x,w),y)))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w)* -> hBOOL(hAPP(hAPP(c_in(x),v_x),y)).
% 299.79/300.47 41524[0:SpL:3229.1,284.0] || equal(u,c_Set_Oimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(x),hAPP(v,y)),hAPP(u,v_x)))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> hBOOL(hAPP(hAPP(c_in(w),y),v_x))*.
% 299.79/300.47 41733[0:SpL:3229.1,494.1] || equal(u,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w))* hBOOL(hAPP(hAPP(v,x),y))* c_Hoare__Mirabelle_Otriple__valid(z,hAPP(u,v_x),t_a)* c_Natural_Oevaln(w,y,z,x1)* -> hBOOL(hAPP(hAPP(v_x,x),x1))*.
% 299.79/300.47 41722[0:SpL:3229.1,494.1] || equal(u,hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v))* hBOOL(hAPP(hAPP(v,w),x))* c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(u,v_x),z),t_a)* c_Natural_Oevaln(v_x,x,y,x1)* -> hBOOL(hAPP(hAPP(z,w),x1))*.
% 299.79/300.47 41716[0:SpL:3229.1,494.1] || equal(u,c_Hoare__Mirabelle_Otriple_Otriple(t_a)) hBOOL(hAPP(hAPP(v_x,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(u,v_x),y),z),t_a)* c_Natural_Oevaln(y,w,x,x1)* -> hBOOL(hAPP(hAPP(z,v),x1))*.
% 299.79/300.47 41836[0:Res:37799.1,199.0] || hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v,u,w)))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),y))*.
% 299.79/300.47 41868[0:Rew:331.0,41799.2] || hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),v,u,w)))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(y)*.
% 299.79/300.47 41978[0:SpR:3229.1,82.0] || equal(u,c_Set_Oimage(v,w,x)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),c_HOL_Ominus__class_Ominus(v_x,y,tc_fun(w,tc_bool))),tc_fun(x,tc_bool))*.
% 299.79/300.47 41963[0:SpR:3229.1,82.0] || equal(u,c_Set_Oimage(v,w,x)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(v,w,x),y),hAPP(u,v_x),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),c_HOL_Ominus__class_Ominus(y,v_x,tc_fun(w,tc_bool))),tc_fun(x,tc_bool))*.
% 299.79/300.47 42161[0:SpL:180.2,312.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Obounded__lattice(u) || c_Finite__Set_Ofinite(v,u) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u),c_Orderings_Obot__class_Obot(u))** -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u),c_Orderings_Obot__class_Obot(u)).
% 299.79/300.47 42151[0:SpR:3229.1,180.2] class_Lattices_Oupper__semilattice(u) || equal(v,c_Lattices_Oupper__semilattice__class_Osup(u)) c_Finite__Set_Ofinite(w,u) -> equal(hAPP(hAPP(v,v_x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,w,u,u)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(v_x,u),w),u,u))*.
% 299.79/300.47 42144[0:SpR:180.2,8376.2] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) equal(c_Lattices_Oupper__semilattice__class_Osup(u),c_in(tc_Com_Opname)) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u),v_Procs) -> hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(v_x,u),v),u,u))*.
% 299.79/300.47 42084[0:SpR:180.2,474.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> hBOOL(hAPP(hAPP(c_in(w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(y,u),v),u,u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.47 42229[0:SSi:42175.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) c_Fun_Oinj__on(w,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,hAPP(c_Set_Oinsert(y,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v,z)* -> c_Fun_Oinj__on(w,y,v,z).
% 299.79/300.47 42312[0:SpR:3229.1,221.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(v,c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w)) -> equal(c_List_Ofoldl(c_COMBC(hAPP(v,v_x),w,u,u),c_Orderings_Obot__class_Obot(u),x,u,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(x,w),v_x,w,u))**.
% 299.79/300.47 42498[0:SpL:11176.1,315.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x,y)),u)** -> equal(hAPP(c_Set_Oimage(v,x,y),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x,y),w)).
% 299.79/300.47 42457[0:SpL:11176.1,315.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,x,y)),u)** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x,y),w),hAPP(c_Set_Oimage(v,x,y),w)).
% 299.79/300.47 42737[0:SpL:161.0,519.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),y))* -> hBOOL(hAPP(c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool)),y)) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),y)).
% 299.79/300.47 43556[0:SpL:507.0,519.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),z))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),z)) hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),y),z)).
% 299.79/300.47 43778[0:SpL:162.0,519.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),z))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),z)) hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),y),z)).
% 299.79/300.47 43961[0:Res:83.0,231.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oimage(x,y,w),hAPP(c_Set_Ovimage(x,y,w),hAPP(c_Set_Oimage(u,v,w),z)))),z,tc_fun(v,tc_bool))*.
% 299.79/300.47 44178[0:Res:232.1,18625.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool))),y),hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),y),tc_bool)*.
% 299.79/300.47 44349[0:Res:8376.2,268.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(v,v_Procs) hBOOL(hAPP(hAPP(c_in(u),w),v))* equal(hAPP(x,v_x),hAPP(x,w))* c_Fun_Oinj__on(x,v,u,y)* -> equal(v_x,w).
% 299.79/300.47 44344[0:Res:168.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* equal(hAPP(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,v)),hAPP(w,u))* c_Fun_Oinj__on(w,v,tc_Hoare__Mirabelle_Otriple(t_a),y)* -> c_Hoare__Mirabelle_Ohoare__valids(x,v,t_a) equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,v),u).
% 299.79/300.47 44315[0:Res:3346.1,268.0] || equal(c_Set_Oinsert(u,v),w)* hBOOL(hAPP(hAPP(c_in(v),x),hAPP(w,v_x)))* equal(hAPP(y,u),hAPP(y,x))* c_Fun_Oinj__on(y,hAPP(w,v_x),v,z)* -> equal(u,x).
% 299.79/300.47 45125[0:Res:326.2,437.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,y,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),w)* -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),w)*.
% 299.79/300.47 45338[0:SpL:584.0,487.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(c_COMBS(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y,z,x1),v))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,u,w)))*.
% 299.79/300.47 45457[0:Res:45357.1,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.47 45428[0:SpR:329.1,45357.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname),tc_fun(v,tc_bool))* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname)).
% 299.79/300.47 45482[0:Rew:104.0,45424.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),tc_Com_Opname),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))*.
% 299.79/300.47 45943[0:SpL:329.1,45899.0] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname),tc_fun(v,tc_bool))* hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)).
% 299.79/300.47 46005[0:Rew:104.0,45939.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),tc_Com_Opname),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))).
% 299.79/300.47 46182[0:Res:27441.0,481.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))*.
% 299.79/300.47 46179[0:Res:27381.0,481.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))*.
% 299.79/300.47 46172[0:Res:3282.1,481.0] || equal(hAPP(c_in(u),v),v_Procs)** -> hBOOL(hAPP(w,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),x),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),x)))*.
% 299.79/300.47 46171[7:Res:27207.1,481.0] || equal(hAPP(c_in(u),v),v_x)** -> hBOOL(hAPP(w,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),x),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),x)))*.
% 299.79/300.47 46156[0:Res:13238.1,481.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w),v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w)))*.
% 299.79/300.47 46149[0:Res:8375.1,481.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> hBOOL(hAPP(w,x))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),y),w,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),y)))*.
% 299.79/300.47 46127[0:Res:652.1,481.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),w),v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),w)))*.
% 299.79/300.47 46500[0:Res:27441.0,480.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs)))*.
% 299.79/300.47 46497[0:Res:27381.0,480.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs)))*.
% 299.79/300.47 46490[0:Res:3282.1,480.0] || equal(hAPP(c_in(u),v),v_Procs)** -> hBOOL(hAPP(w,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v_x),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v_x)))*.
% 299.79/300.47 46489[7:Res:27207.1,480.0] || equal(hAPP(c_in(u),v),v_x)** -> hBOOL(hAPP(w,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v_x),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v_x)))*.
% 299.79/300.47 46474[0:Res:13238.1,480.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u),v,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),u)))*.
% 299.79/300.47 46445[0:Res:652.1,480.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),u),v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),u)))*.
% 299.79/300.47 46700[0:Res:232.1,44639.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,tc_Com_Opname) equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))),v_Procs)** -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.79/300.47 47405[0:Res:9258.0,485.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w),v_x),tc_bool))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,u,t_a)))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,u,t_a)),v))*.
% 299.79/300.47 47636[0:Res:9258.0,484.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w),v_x),tc_bool))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,u,t_a)))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,u,t_a)),w))*.
% 299.79/300.47 47974[0:Res:9258.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,t_a)))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),v),v_x),tc_bool))* hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,u,t_a)),w))*.
% 299.79/300.47 48086[0:Res:9258.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,t_a)))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w),v_x),tc_bool))* hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,u,t_a)),w))*.
% 299.79/300.47 48468[0:Rew:2095.0,48307.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(v,x,u),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u) -> .
% 299.79/300.47 48632[0:SpR:197.1,114.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(x,hAPP(c_Set_Oimage(u,v,w),y),w,z) -> c_Fun_Oinj__on(x,hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(y,x1,tc_fun(v,tc_bool))),w,z)*.
% 299.79/300.47 48793[0:Res:526.1,619.0] || hBOOL(hAPP(u,v))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,x,tc_fun(y,tc_bool)),u),c_Set_Oinsert(z,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(z,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,w,x,tc_fun(y,tc_bool))))**.
% 299.79/300.47 48979[0:Res:3346.1,483.0] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* -> hBOOL(hAPP(x,u))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,v)),w))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,x,v)),v_x))*.
% 299.79/300.47 48973[0:Res:8366.1,483.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_Procs)** -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,tc_Com_Opname)),u))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,tc_Com_Opname)),v))*.
% 299.79/300.47 49012[0:Res:48989.1,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))* equal(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,w,tc_Com_Opname)),hAPP(v,u))* c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,x)* -> hBOOL(hAPP(w,v_x)) equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,w,tc_Com_Opname),u).
% 299.79/300.47 49011[0:Res:48989.1,481.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w),v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w)))*.
% 299.79/300.47 49010[0:Res:48989.1,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs),v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.79/300.47 49085[0:SpR:49017.1,317.0] || -> hBOOL(hAPP(u,v_x)) equal(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,v),x)),hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),x)))*.
% 299.79/300.47 49084[0:SpR:49017.1,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(u,v_x)) equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),v_Procs),v_Procs)**.
% 299.79/300.47 49083[0:SpR:49017.1,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(u,v_x)) equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),v_Procs),v_Procs)**.
% 299.79/300.47 49183[0:Res:3346.1,239.0] || equal(c_Set_Oinsert(u,v),c_Set_Oimage(w,x,v)) c_lessequals(v_x,y,tc_fun(x,tc_bool)) c_Fun_Oinj__on(w,v_x,x,v) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Fun_Othe__inv__into(v_x,w,x,v),u)),y))*.
% 299.79/300.47 49176[0:Res:8366.1,239.0] || equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),v_Procs) c_lessequals(w,x,tc_fun(v,tc_bool)) c_Fun_Oinj__on(u,w,v,tc_Com_Opname) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Fun_Othe__inv__into(w,u,v,tc_Com_Opname),v_x)),x))*.
% 299.79/300.47 49303[0:Res:3284.1,488.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_in(tc_Com_Opname)) hBOOL(hAPP(w,v_Procs)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,w,u)),v_x))*.
% 299.79/300.47 50434[0:SpR:223.1,474.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(z,x1),x2,x),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)))))*.
% 299.79/300.47 53056[0:SpR:23955.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w),u),x)),hAPP(c_Set_Oinsert(v_x,v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v),x)))*.
% 299.79/300.47 53188[0:SpR:23958.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),u),x)),hAPP(c_Set_Oinsert(v_x,v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v),x)))*.
% 299.79/300.47 54326[0:SpR:54251.0,161.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_HOL_Ominus__class_Ominus(w,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))**.
% 299.79/300.47 54746[0:SpR:13749.2,317.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),y)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),y)))*.
% 299.79/300.47 55220[0:SpR:14043.2,317.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),y)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),y)))*.
% 299.79/300.47 56390[0:SpL:30368.2,449.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,x)))* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),t_a)*.
% 299.79/300.47 56832[0:SpL:30928.2,449.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(c_Orderings_Otop__class_Otop(u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,x)))* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u))),t_a)*.
% 299.79/300.47 58211[0:SpL:533.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool),x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))** -> .
% 299.79/300.47 58993[0:Res:1588.0,15629.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_in(tc_Com_Opname),v_x),u,v),tc_Com_Opname,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_in(tc_Com_Opname),v_x),u,v),tc_Com_Opname,tc_fun(w,tc_bool)),x)))*.
% 299.79/300.47 58807[0:SpL:475.1,15629.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(c_Set_Oimage(x,u,y),w))* -> hBOOL(hAPP(c_Set_Oinsert(hAPP(x,v),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Set_Oinsert(hAPP(x,v),y),z)))*.
% 299.79/300.47 58747[0:SpL:338.0,15629.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)))*.
% 299.79/300.47 59501[0:Res:1588.0,15857.0] || -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_in(tc_Com_Opname),v_x),u,v),tc_Com_Opname,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_in(tc_Com_Opname),v_x),u,v),tc_Com_Opname,tc_fun(w,tc_bool)),y)))*.
% 299.79/300.47 59315[0:SpL:475.1,15857.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(c_Set_Oimage(x,u,y),w))* -> hBOOL(hAPP(c_Set_Oinsert(hAPP(x,v),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Set_Oinsert(hAPP(x,v),y),x1)))*.
% 299.79/300.47 59255[0:SpL:338.0,15857.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),z)))*.
% 299.79/300.47 59687[0:SpL:197.1,19883.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),tc_fun(w,tc_bool)),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),y),w).
% 299.79/300.47 60436[7:Res:58968.1,455.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,y),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.47 60422[7:Res:58968.1,356.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,u),u,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y)),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.79/300.47 60390[7:SpR:181.1,58968.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_x) -> hBOOL(hAPP(hAPP(c_in(v),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Set_Ovimage(c_COMBK(u,v,w),w,v),x)))* hBOOL(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.47 60549[0:Res:58969.1,455.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Procs) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,y),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.47 60535[0:Res:58969.1,356.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,u),u,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y)),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.79/300.47 60503[0:SpR:181.1,58969.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Set_Ovimage(c_COMBK(u,v,w),w,v),x)))* hBOOL(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.47 60622[7:Res:59476.1,455.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,y),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.47 60608[7:Res:59476.1,356.0] || equal(hAPP(c_in(u),v),v_x) -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,u),u,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z)),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.79/300.47 60576[7:SpR:181.1,59476.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_x) -> hBOOL(hAPP(hAPP(c_in(v),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Ovimage(c_COMBK(u,v,w),w,v),y)))* hBOOL(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.47 60695[0:Res:59477.1,455.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Procs) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,y),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.47 60681[0:Res:59477.1,356.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,u),u,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z)),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.79/300.47 60649[0:SpR:181.1,59477.1] || equal(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_Procs) -> hBOOL(hAPP(hAPP(c_in(v),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Ovimage(c_COMBK(u,v,w),w,v),y)))* hBOOL(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.47 60880[0:Res:59017.1,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x),v),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,y),t_a)* -> c_Hoare__Mirabelle_Ohoare__valids(z,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,x,t_a)*.
% 299.79/300.47 60866[0:Res:59017.1,356.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a)* equal(hAPP(c_Set_Oimage(c_COMBK(x,y,v),v,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_in(v),w),z)),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.47 60834[0:SpR:181.1,59017.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Ovimage(c_COMBK(v,u,y),y,u),w)))* c_Hoare__Mirabelle_Ohoare__valids(z,c_Set_Ovimage(c_COMBK(v,u,y),y,u),t_a)* hBOOL(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))).
% 299.79/300.47 60953[0:Res:59525.1,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x),w),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,y),t_a)* -> c_Hoare__Mirabelle_Ohoare__valids(z,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,x,t_a)*.
% 299.79/300.47 60939[0:Res:59525.1,356.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a)* equal(hAPP(c_Set_Oimage(c_COMBK(x,y,v),v,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_in(v),w),x1)),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.47 60907[0:SpR:181.1,59525.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,y),y,u),x)))* c_Hoare__Mirabelle_Ohoare__valids(z,c_Set_Ovimage(c_COMBK(v,u,y),y,u),t_a)* hBOOL(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))).
% 299.79/300.47 61941[0:SpL:537.1,15487.1] class_Lattices_Olattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.47 61940[0:SpL:534.1,15487.1] class_Lattices_Oupper__semilattice(u) || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.47 63967[0:SpR:647.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),w)),hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(u,tc_Com_Opname,v),c_HOL_Ominus__class_Ominus(w,v_Procs,tc_fun(tc_Com_Opname,tc_bool))),tc_fun(v,tc_bool))*.
% 299.79/300.47 64186[0:SpR:130.1,646.1] class_HOL_Ominus(u) || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_Com_Opname,x),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)),v_x)**.
% 299.79/300.47 64353[0:SpR:130.1,645.1] class_HOL_Ominus(u) || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_Com_Opname,x),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)),v_x)**.
% 299.79/300.47 64535[0:SpL:537.1,24257.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.47 64534[0:SpL:534.1,24257.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.47 66212[0:SpL:65404.1,275.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) hBOOL(hAPP(hAPP(c_in(y),z),w)) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(y,tc_bool))))*.
% 299.79/300.47 65939[0:SpR:65404.1,410.0] class_Lattices_Olattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(y,tc_bool))))*.
% 299.79/300.47 68381[0:SpL:1250.3,3695.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)))** equal(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),c_Com_Ocom_OBODY) equal(c_Orderings_Obot__class_Obot(u),c_Com_Ocom_OSKIP) -> .
% 299.79/300.47 70920[0:SpL:24914.0,6582.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),v) -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),v,tc_fun(u,tc_bool))*.
% 299.79/300.47 71419[7:SpL:533.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_x) -> .
% 299.79/300.47 71764[7:SpL:71455.1,275.1] || equal(u,v_x) hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(x),y),u))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 72101[0:SpR:24914.0,7830.0] || -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),tc_fun(u,tc_bool))*.
% 299.79/300.47 72480[0:SpL:24914.0,12554.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x))),u))*.
% 299.79/300.47 73058[7:Res:71608.1,239.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_x) c_lessequals(w,x,tc_fun(v,tc_bool)) c_Fun_Oinj__on(u,w,v,t_a) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Fun_Othe__inv__into(w,u,v,t_a),v_x)),x))*.
% 299.79/300.47 73041[7:Res:71608.1,483.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x)** -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)),u))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)),v))*.
% 299.79/300.47 74357[7:SpL:71835.1,284.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,x)),v_x))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> hBOOL(hAPP(hAPP(c_in(v),x),v_x))*.
% 299.79/300.47 74340[7:SpL:71835.1,494.1] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(v_x,y),t_a)* c_Natural_Oevaln(v_x,w,x,z)* -> hBOOL(hAPP(hAPP(y,v),z))*.
% 299.79/300.47 74338[7:SpL:71835.1,529.0] || equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),c_Set_Oinsert(v_x,t_a)) c_Hoare__Mirabelle_Otriple__valid(x,v_x,u) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),u)*.
% 299.79/300.47 74327[7:SpL:71835.1,494.1] || equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(hAPP(u,w),x))* c_Hoare__Mirabelle_Otriple__valid(y,v_x,t_a) c_Natural_Oevaln(v,x,y,z)* -> hBOOL(hAPP(hAPP(v_x,w),z))*.
% 299.79/300.47 74249[7:SpL:71835.1,529.0] || equal(c_Set_Oinsert(v_x,t_a),c_Com_Obody) c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),v_x)),x),v) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,v_x)),x),v)*.
% 299.79/300.47 74225[7:SpL:71835.1,398.0] || equal(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),c_Set_Oinsert(v_x,t_a)) c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),v_x,tc_fun(u,tc_bool))* -> c_lessequals(v,v_x,tc_fun(u,tc_bool)).
% 299.79/300.47 74217[7:SpL:71835.1,284.0] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(u,w,v),x)))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v)* -> hBOOL(hAPP(hAPP(c_in(w),v_x),x)).
% 299.79/300.47 74191[7:SpL:71835.1,275.1] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) hBOOL(hAPP(hAPP(c_in(x),y),v_x)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,u,v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 74190[7:SpL:71835.1,398.0] || equal(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),c_Set_Oinsert(v_x,t_a)) c_lessequals(v_x,hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),tc_fun(u,tc_bool))* -> c_lessequals(v_x,v,tc_fun(u,tc_bool)).
% 299.79/300.47 74148[7:SpL:71835.1,479.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,w)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,x,v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))*.
% 299.79/300.47 74147[7:SpL:71835.1,478.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,w)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,w,v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w)))*.
% 299.79/300.47 74006[7:SpL:71835.1,494.1] || equal(c_Set_Oinsert(v_x,t_a),c_Hoare__Mirabelle_Otriple_Otriple(t_a)) hBOOL(hAPP(hAPP(v_x,u),v))* c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(v_x,x),y),t_a)* c_Natural_Oevaln(x,v,w,z)* -> hBOOL(hAPP(hAPP(y,u),z))*.
% 299.79/300.47 73911[7:SpR:71835.1,82.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),v_x,tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,v_x,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.47 73905[7:SpR:71835.1,530.1] || equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),c_Set_Oinsert(v_x,t_a)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),u)* -> c_Hoare__Mirabelle_Otriple__valid(x,v_x,u).
% 299.79/300.47 73778[7:SpR:71835.1,532.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))**.
% 299.79/300.47 73776[7:SpR:71835.1,533.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),v_x)**.
% 299.79/300.47 73762[7:SpR:71835.1,533.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),w))**.
% 299.79/300.47 73711[7:SpR:71835.1,530.1] || equal(c_Set_Oinsert(v_x,t_a),c_Com_Obody) c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,v_x)),x),v)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),v_x)),x),v).
% 299.79/300.47 73706[7:SpR:71835.1,82.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) -> c_lessequals(c_HOL_Ominus__class_Ominus(v_x,hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(v_x,x,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.47 73677[7:SpR:71835.1,221.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),v),c_Set_Oinsert(v_x,t_a)) -> equal(c_List_Ofoldl(c_COMBC(v_x,v,u,u),c_Orderings_Obot__class_Obot(u),w,u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(w,v),v_x,v,u))**.
% 299.79/300.47 73651[7:SpR:71835.1,180.2] class_Lattices_Oupper__semilattice(u) || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(u)) c_Finite__Set_Ofinite(v,u) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(v_x,u),v),u,u),hAPP(v_x,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u)))**.
% 299.79/300.47 73615[7:SpR:71835.1,399.1] || equal(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),c_Set_Oinsert(v_x,t_a)) c_lessequals(v,v_x,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),v_x,tc_fun(u,tc_bool))*.
% 299.79/300.47 73294[7:SpR:71835.1,399.1] || equal(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),c_Set_Oinsert(v_x,t_a)) c_lessequals(v_x,v,tc_fun(u,tc_bool)) -> c_lessequals(v_x,hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),tc_fun(u,tc_bool))*.
% 299.79/300.47 75620[0:SSi:75477.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)))**.
% 299.79/300.47 76088[0:SSi:75931.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)))**.
% 299.79/300.47 77792[0:SpL:128.0,5892.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))))* -> hBOOL(hAPP(c_COMBS(c_in(y),c_Set_Ovimage(u,v,w),z,x1,x2),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))))*.
% 299.79/300.47 77741[0:SpL:339.0,5892.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),x))* -> hBOOL(hAPP(c_COMBS(c_in(y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),z,x1,x2),x))*.
% 299.79/300.47 77711[0:SpL:465.1,5892.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),x))* -> hBOOL(hAPP(hAPP(c_in(v),y),x)) hBOOL(hAPP(c_COMBS(c_in(z),c_Set_Oimage(c_Fun_Ofun__upd(u,y,x1,v,w),v,w),x2,x3,x4),x))*.
% 299.79/300.47 77668[0:SpL:99.1,5892.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(x,hAPP(u,x)))* -> hBOOL(hAPP(c_COMBS(c_in(y),c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x1,x2),hAPP(u,x)))*.
% 299.79/300.47 77667[0:SpL:438.1,5892.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(x,hAPP(u,x)))* -> hBOOL(hAPP(c_COMBS(c_in(y),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x1,x2),hAPP(u,x)))*.
% 299.79/300.47 78725[4:Res:78665.1,237.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))),v_x)** c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u) -> equal(hAPP(w,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v,w,u,x)),v)**.
% 299.79/300.47 78724[4:Res:78665.1,487.1] || equal(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),v_x)** hBOOL(hAPP(y,v))* -> hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,y,u)))* hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,y,u)))*.
% 299.79/300.47 78673[4:Res:78665.1,593.0] || equal(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs),v_x) c_Hoare__Mirabelle_Otriple__valid(v,v_n(v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,u)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u))),hAPP(v_Q,u)),t_a)*.
% 299.79/300.47 80180[0:SpL:21268.0,62.0] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),w) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),y,z),tc_fun(w,tc_bool)),w)*.
% 299.79/300.47 80176[0:SpL:21268.0,11883.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w),x,y)),u))* -> .
% 299.79/300.47 80034[0:SpL:21268.0,357.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),u,z),w)* c_lessequals(x1,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool))* -> c_Finite__Set_Ofinite(x1,x).
% 299.79/300.47 80011[0:SpL:21268.0,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x,y),t_a)*.
% 299.79/300.47 79991[0:SpR:33303.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v_Procs,v,w)),v_Procs)**.
% 299.79/300.47 79987[0:SpR:28903.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),v_Procs,w,x)),v_Procs)**.
% 299.79/300.47 79986[0:SpR:28902.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),v_Procs,w,x)),v_Procs)**.
% 299.79/300.47 79982[0:SpR:28748.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),v_Procs,w,x)),v_Procs)**.
% 299.79/300.47 79981[0:SpR:28747.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),v_Procs,w,x)),v_Procs)**.
% 299.79/300.47 79967[0:SpR:584.0,21268.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_COMBS(u,v,w,x,y),hAPP(hAPP(u,x1),hAPP(v,x1)),z,x2)),hAPP(hAPP(u,x1),hAPP(v,x1)))**.
% 299.79/300.47 79851[0:SpR:71.2,21268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,x,u,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Fun_Othe__inv__into(w,x,u,y),v,z,x1)),v)**.
% 299.79/300.47 79850[0:SpR:373.2,21268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,x,u,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Hilbert__Choice_Oinv__into(w,x,u,y),v,z,x1)),v)**.
% 299.79/300.47 79718[0:SpR:21268.0,35656.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),w),u,x),v_Procs)** -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),w),v_x)).
% 299.79/300.47 79708[0:SpR:21268.0,9569.0] || -> c_lessequals(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,y),z),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),z),tc_bool)*.
% 299.79/300.47 79653[0:SpR:21268.0,118.0] || -> equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,hAPP(u,y),x,z),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,x2,x3,x1),w,hAPP(u,y),x1,x3))*.
% 299.79/300.47 79540[0:SpR:21268.0,63.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),hAPP(c_Set_Oinsert(w,x),y),v,z),tc_fun(x,tc_bool)),x)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,x),y),tc_fun(x,tc_bool)),x).
% 299.79/300.47 79539[0:SpR:21268.0,446.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,x),hAPP(c_Set_Oinsert(w,x),y),v,z),tc_fun(x,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(w,x),u),hAPP(c_Set_Oinsert(w,x),y),tc_fun(x,tc_bool)).
% 299.79/300.47 79443[0:SpR:21268.0,37962.1] || hBOOL(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),z),u,x1))* -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),z)).
% 299.79/300.47 79364[0:SpR:21268.0,446.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),z,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Set_Oinsert(v,w),z),tc_fun(w,tc_bool)).
% 299.79/300.47 80408[0:Rew:56.1,79799.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v,u),y),x,z),w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool)))**.
% 299.79/300.47 81375[0:SpL:21894.0,62.0] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),w) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),y,z),tc_fun(w,tc_bool)),w)*.
% 299.79/300.47 81371[0:SpL:21894.0,11883.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),x,y)),u))* -> .
% 299.79/300.47 81229[0:SpL:21894.0,357.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),u,z),w)* c_lessequals(x1,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool))* -> c_Finite__Set_Ofinite(x1,x).
% 299.79/300.47 81206[0:SpL:21894.0,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x,y),t_a)*.
% 299.79/300.47 81185[0:SpR:33303.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v_Procs,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v,w)),v_Procs)**.
% 299.79/300.47 81181[0:SpR:28903.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x)),v_Procs)**.
% 299.79/300.47 81180[0:SpR:28902.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x)),v_Procs)**.
% 299.79/300.47 81176[0:SpR:28748.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x)),v_Procs)**.
% 299.79/300.47 81175[0:SpR:28747.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v_Procs,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x)),v_Procs)**.
% 299.79/300.47 81161[0:SpR:584.0,21894.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(u,x1),hAPP(v,x1)),c_COMBS(u,v,w,x,y),z,x2)),hAPP(hAPP(u,x1),hAPP(v,x1)))**.
% 299.79/300.47 81045[0:SpR:71.2,21894.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,x,u,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),v,c_Fun_Othe__inv__into(w,x,u,y),z,x1)),v)**.
% 299.79/300.47 81044[0:SpR:373.2,21894.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,x,u,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),v,c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x1)),v)**.
% 299.79/300.47 80912[0:SpR:21894.0,35656.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),u,x),v_Procs)** -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),w),v_x)).
% 299.79/300.47 80902[0:SpR:21894.0,9569.0] || -> c_lessequals(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,y),z),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),z),tc_bool)*.
% 299.79/300.47 80847[0:SpR:21894.0,118.0] || -> equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(v,w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(u,y),u,x,z),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,x2,x3,x1),w,hAPP(u,y),x1,x3))*.
% 299.79/300.47 80733[0:SpR:21894.0,63.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,x),y),c_Set_Oinsert(w,x),v,z),tc_fun(x,tc_bool)),x)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,x),y),tc_fun(x,tc_bool)),x).
% 299.79/300.47 80732[0:SpR:21894.0,446.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,x),y),c_Set_Oinsert(w,x),v,z),tc_fun(x,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(w,x),u),hAPP(c_Set_Oinsert(w,x),y),tc_fun(x,tc_bool)).
% 299.79/300.47 80636[0:SpR:21894.0,37962.1] || hBOOL(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),z),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),u,x1))* -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),z)).
% 299.79/300.47 80557[0:SpR:21894.0,446.1] || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),z,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Set_Oinsert(v,w),z),tc_fun(w,tc_bool)).
% 299.79/300.47 81603[0:Rew:56.1,80993.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(v,u),y),c_Set_Oinsert(v,u),x,z),w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool)))**.
% 299.79/300.47 81929[0:SpR:338.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oinsert(x,v),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)),u)*.
% 299.79/300.47 81866[0:SpR:339.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),x)),z,x1,x2),y),u)*.
% 299.79/300.47 81861[0:SpR:338.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z,x1,x2),hAPP(c_Set_Oinsert(v,w),y)),u)*.
% 299.79/300.47 81836[0:SpR:465.1,5879.1] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),x)) c_lessequals(hAPP(c_Set_Oimage(y,v,z),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oimage(c_Fun_Ofun__upd(y,w,x1,v,z),v,z),x2,x3,x4),x),u)*.
% 299.79/300.47 81804[0:SpR:71.2,5879.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(y,x,v,z) -> c_lessequals(w,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Fun_Othe__inv__into(x,y,v,z),x1,x2,x3),hAPP(y,w)),u)*.
% 299.79/300.47 81803[0:SpR:373.2,5879.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(y,x,v,z) -> c_lessequals(w,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Hilbert__Choice_Oinv__into(x,y,v,z),x1,x2,x3),hAPP(y,w)),u)*.
% 299.79/300.47 82087[0:Rew:584.0,81769.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),u)*.
% 299.79/300.47 82205[7:SpL:78597.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Set_Oinsert(v_x,v)),w))* hBOOL(hAPP(hAPP(c_in(x),y),c_Set_Oinsert(v_x,v)))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),u,tc_fun(x,tc_bool))))*.
% 299.79/300.47 82402[0:SpR:338.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oinsert(x,v),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)),u)*.
% 299.79/300.47 82338[0:SpR:339.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),x)),z,x1,x2),y),u)*.
% 299.79/300.47 82333[0:SpR:338.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z,x1,x2),hAPP(c_Set_Oinsert(v,w),y)),u)*.
% 299.79/300.47 82308[0:SpR:465.1,5880.1] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),x)) c_lessequals(hAPP(c_Set_Oimage(y,v,z),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oimage(c_Fun_Ofun__upd(y,w,x1,v,z),v,z),x2,x3,x4),x),u)*.
% 299.79/300.47 82276[0:SpR:71.2,5880.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(y,x,v,z) -> c_lessequals(w,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Fun_Othe__inv__into(x,y,v,z),x1,x2,x3),hAPP(y,w)),u)*.
% 299.79/300.47 82275[0:SpR:373.2,5880.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(y,x,v,z) -> c_lessequals(w,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Hilbert__Choice_Oinv__into(x,y,v,z),x1,x2,x3),hAPP(y,w)),u)*.
% 299.79/300.47 82554[0:Rew:584.0,82241.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),hAPP(v,v_x)),u)*.
% 299.79/300.47 82816[0:Obv:82733.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Finite__Set_Ofinite(w,u) c_lessequals(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),u)* -> c_lessequals(x,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),y,w,u,u),u)*.
% 299.79/300.47 83014[0:SpR:5924.0,646.1] || c_Fun_Oinj__on(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_Procs,tc_Com_Opname,x2) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname,x2),hAPP(hAPP(u,v_x),v)),v_x)**.
% 299.79/300.47 83008[0:SpR:5924.0,645.1] || c_Fun_Oinj__on(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),v_Procs,tc_Com_Opname,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(u,c_COMBK(v,w,x),y,z,x1),tc_Com_Opname,x2),hAPP(hAPP(u,v_x),v)),v_x)**.
% 299.79/300.47 83250[7:SpR:533.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,y),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.47 83344[0:SpR:5961.0,646.1] || c_Fun_Oinj__on(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_Procs,tc_Com_Opname,x2) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_COMBS(c_COMBK(u,v,w),x,y,z,x1),tc_Com_Opname,x2),hAPP(u,hAPP(x,v_x))),v_x)**.
% 299.79/300.47 83338[0:SpR:5961.0,645.1] || c_Fun_Oinj__on(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),v_Procs,tc_Com_Opname,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(c_COMBK(u,v,w),x,y,z,x1),tc_Com_Opname,x2),hAPP(u,hAPP(x,v_x))),v_x)**.
% 299.79/300.47 84889[4:SpL:393.1,78744.0] || equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x) -> equal(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oimage(c_COMBK(u,v,w),w,v),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oimage(c_COMBK(u,v,w),w,v),x,t_a)*.
% 299.79/300.47 84985[0:SpR:21894.0,84957.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(u),v),c_in(u),w,x),y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(u),v),c_in(u),w,x))))*.
% 299.79/300.47 84983[0:SpR:21268.0,84957.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(u),hAPP(c_in(u),v),w,x),y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(u),hAPP(c_in(u),v),w,x))))*.
% 299.79/300.47 85133[0:Rew:20920.0,85023.2] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) c_Fun_Oinj__on(c_COMBK(v,w,tc_Com_Opname),u,tc_Com_Opname,w) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(u,c_COMBK(v,w,tc_Com_Opname),tc_Com_Opname,w),v),tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v_Procs)**.
% 299.79/300.47 85442[4:SpR:78507.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,x),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,x),u,w),v))**.
% 299.79/300.47 85825[0:Res:9066.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),u),w,u)*.
% 299.79/300.47 85824[0:Res:9066.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),u) -> c_lessequals(w,c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),u),u)*.
% 299.79/300.47 85941[0:SpL:21893.0,13582.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x)),v))* -> .
% 299.79/300.47 85939[0:SpL:21267.0,13582.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x),tc_Com_Opname,x)),v))* -> .
% 299.79/300.47 86067[0:SpL:533.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_Procs) -> .
% 299.79/300.47 86449[0:SpL:86109.1,275.1] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(x),y),u))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 86652[0:Res:86261.1,239.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),v_Procs) c_lessequals(w,x,tc_fun(v,tc_bool)) c_Fun_Oinj__on(u,w,v,t_a) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Fun_Othe__inv__into(w,u,v,t_a),v_x)),x))*.
% 299.79/300.47 86635[0:Res:86261.1,483.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_Procs)** -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)),u))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)),v))*.
% 299.79/300.47 86985[0:SpR:32817.1,13.2] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,u,tc_fun(w,tc_bool))* c_lessequals(v,y,tc_fun(w,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.47 87165[7:Rew:339.0,87161.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,t_a),c_Set_Oinsert(v_x,w)),x,u,t_a)),hAPP(c_Set_Oinsert(v,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,w)),x))))*.
% 299.79/300.47 87160[7:Res:82177.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(w,t_a),c_Set_Oinsert(v_x,x)),u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),hAPP(c_Set_Oinsert(w,t_a),c_Set_Oinsert(v_x,x)))))*.
% 299.79/300.47 88308[0:Res:7227.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_COMBK(v,w,x),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(c_COMBK(v,w,x),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u),v,u)*.
% 299.79/300.47 88307[0:Res:7227.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_COMBK(v,w,x),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(c_COMBK(v,w,x),y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u),u)*.
% 299.79/300.47 88576[0:Res:47.2,8306.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool))*.
% 299.79/300.47 88552[0:Res:424.2,8306.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))))* c_lessequals(y,c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool))*.
% 299.79/300.47 88910[0:SpR:542.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)))*.
% 299.79/300.47 88905[0:SpR:614.2,14196.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,y),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u)))*.
% 299.79/300.47 88892[0:SpR:523.1,14196.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),v_x))*.
% 299.79/300.47 88891[0:SpR:460.1,14196.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,v),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),v_x))*.
% 299.79/300.47 88830[0:SpR:393.1,14196.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oimage(c_COMBK(w,x,v),v,x),y,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))),u))*.
% 299.79/300.47 89188[0:SpL:21893.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),v)* -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname,x),v)*.
% 299.79/300.47 89186[0:SpL:21267.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),v)* -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),tc_Com_Opname,x),v)*.
% 299.79/300.47 89484[7:SpR:78590.1,15858.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v_x,t_a),w),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),v)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v_x,t_a),w))*.
% 299.79/300.47 89483[7:SpR:78590.1,15630.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(v_x,t_a),v),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),u)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(v_x,t_a),v))*.
% 299.79/300.47 89337[7:SpR:78590.1,475.1] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> equal(hAPP(c_Set_Oinsert(u,x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,x),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,x),w))**.
% 299.79/300.47 89727[7:Res:89344.1,485.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)),u))*.
% 299.79/300.47 89726[7:Res:89344.1,484.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)),v))*.
% 299.79/300.47 89719[7:Res:89344.1,489.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)),v))*.
% 299.79/300.47 89718[7:Res:89344.1,490.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)),u))*.
% 299.79/300.47 89951[0:SpL:26183.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oimage(u,v,w),y))** c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(x,v),y),v,w) -> equal(hAPP(c_Set_Oinsert(x,v),y),y).
% 299.79/300.47 89857[0:SpR:26183.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,hAPP(c_Set_Oinsert(y,w),v),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(c_Set_Oinsert(y,w),v),tc_fun(w,tc_bool))*.
% 299.79/300.47 90275[4:SpR:78660.1,15858.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v_x,t_a),w),v_x),v_x)** hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),v)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v_x,t_a),w)).
% 299.79/300.47 90274[4:SpR:78660.1,15630.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(v_x,t_a),v),v_x),v_x)** hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),u)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.47 90127[4:SpR:78660.1,475.1] || equal(hAPP(u,v_x),v_x) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> equal(hAPP(c_Set_Oinsert(u,x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,x),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,x),w))**.
% 299.79/300.47 90715[0:SSi:90714.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) c_Finite__Set_Ofinite(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(x,v),y),tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v)* -> c_Finite__Set_Ofinite(y,v).
% 299.79/300.47 90871[4:Res:90134.1,485.1] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),v_x)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)),u))*.
% 299.79/300.47 90870[4:Res:90134.1,484.1] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),v_x)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)),v))*.
% 299.79/300.47 90863[4:Res:90134.1,489.1] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),v_x)** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)),v))*.
% 299.79/300.47 90862[4:Res:90134.1,490.1] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),v_x)** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)),u))*.
% 299.79/300.47 91362[0:Rew:91288.1,91077.1] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> equal(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),w))**.
% 299.79/300.47 91920[0:SpR:79073.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,y),u,x),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,y),u,x),w))**.
% 299.79/300.47 92072[7:SpR:79101.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(v),v_x)),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_in(v),v_x),x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,y),u,x),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,y),u,x),w))**.
% 299.79/300.47 92590[0:SpL:5227.1,12988.1] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x) hBOOL(hAPP(y,z))* c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),y),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),z,t_a)*.
% 299.79/300.47 92586[0:SpL:5227.1,12983.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x) c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),hAPP(c_Set_Oinsert(y,tc_Hoare__Mirabelle_Otriple(t_a)),z)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),y,t_a).
% 299.79/300.47 92687[7:Res:82151.1,268.0] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(hAPP(c_in(u),v),c_Set_Oinsert(v_x,w)))* equal(hAPP(x,v_x),hAPP(x,v))* c_Fun_Oinj__on(x,c_Set_Oinsert(v_x,w),u,y)* -> equal(v_x,v).
% 299.79/300.47 93700[0:SpL:55.1,7462.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(y,x),v),w,tc_fun(x,tc_bool)),x)* -> hBOOL(hAPP(hAPP(c_in(x),y),w)) c_Finite__Set_Ofinite(u,x).
% 299.79/300.47 94028[0:SpR:55.1,10791.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(y,u),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)))),tc_fun(u,tc_bool))*.
% 299.79/300.47 93961[0:SpR:55.1,10791.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_Set_Oinsert(x,u),c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(x,u),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool))),tc_fun(u,tc_bool))*.
% 299.79/300.47 94157[0:Res:14364.3,32820.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,c_HOL_Ominus__class_Ominus(w,c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> equal(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.79/300.47 94278[0:Res:14491.3,26480.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,c_HOL_Ominus__class_Ominus(w,c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> c_lessequals(w,c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)).
% 299.79/300.47 11080[0:Res:47.2,357.1] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x),tc_fun(u,tc_bool))* c_Finite__Set_Ofinite(x,w) -> c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(v,w,u),x),tc_fun(u,tc_bool)),u).
% 299.79/300.47 16948[0:SpR:600.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y,z),c_HOL_Ominus__class_Ominus(x1,v,tc_fun(u,tc_bool))),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x1),v),hAPP(w,c_HOL_Ominus__class_Ominus(x1,v,tc_fun(u,tc_bool)))))*.
% 299.79/300.47 16947[0:SpR:600.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y,z),c_HOL_Ominus__class_Ominus(x1,w,tc_fun(v,tc_bool))),hAPP(hAPP(u,c_HOL_Ominus__class_Ominus(x1,w,tc_fun(v,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),w)))*.
% 299.79/300.47 16935[0:SpR:600.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(y,tc_bool))),z)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),x),v,u),u)*.
% 299.79/300.47 16926[0:SpR:600.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),u,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),w),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.47 17874[0:SpR:188.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* hBOOL(hAPP(hAPP(c_in(y),x),z))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Ovimage(c_COMBK(w,v,x1),x1,v),y,u),u)*.
% 299.79/300.47 17870[0:SpR:188.1,176.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),w),hAPP(c_Set_Ovimage(c_Set_Ovimage(c_COMBK(v,u,y),y,u),x,z),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.47 18208[0:SpR:128.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),x)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(y,z,w),v),tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Ovimage(y,z,w),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.47 18176[0:SpR:544.1,362.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.47 18175[0:SpR:543.1,362.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.47 18168[0:SpR:181.1,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),y),v))* c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(c_COMBK(y,x,z),z,x),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.47 18408[0:SpR:128.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),x)) -> hBOOL(hAPP(hAPP(c_in(y),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(z,x1,w),v),tc_fun(x1,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(z,x1,w),u,y),x)))*.
% 299.79/300.47 18376[0:SpR:544.1,545.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,z),y)))*.
% 299.79/300.47 18375[0:SpR:543.1,545.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,z),y)))*.
% 299.79/300.47 18368[0:SpR:181.1,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),y),v))* hBOOL(hAPP(hAPP(c_in(z),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(y,x,x1),x1,x),u,z),w)))*.
% 299.79/300.47 19114[0:SpR:196.1,584.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),hAPP(c_Set_Oimage(u,v,w),x2)),hAPP(x2,hAPP(x,hAPP(c_Set_Oimage(u,v,w),x2))))*.
% 299.79/300.47 19113[0:SpR:196.1,584.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_COMBS(x,c_Set_Ovimage(u,v,w),y,z,x1),hAPP(c_Set_Oimage(u,v,w),x2)),hAPP(hAPP(x,hAPP(c_Set_Oimage(u,v,w),x2)),x2))*.
% 299.79/300.47 19107[0:SpR:196.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oimage(v,w,x),z)),x1))* -> c_lessequals(z,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Ovimage(v,w,x),y,u),u)*.
% 299.79/300.47 19101[0:SpR:196.1,176.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),hAPP(c_Set_Ovimage(c_Set_Ovimage(u,v,w),x,z),hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.47 19667[0:Res:153.1,496.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(y,hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),u),x))),hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),u),x)))* c_Hoare__Mirabelle_Otriple__valid(y,w,t_a)*.
% 299.79/300.47 19666[0:Res:545.1,496.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(x,hAPP(c_Set_Oimage(y,u,tc_Hoare__Mirabelle_Otriple(t_a)),w))),hAPP(c_Set_Oimage(y,u,tc_Hoare__Mirabelle_Otriple(t_a)),w)))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(y,v),t_a)*.
% 299.79/300.47 19893[0:SpL:104.0,19641.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),w),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),w,t_a).
% 299.79/300.47 19923[0:Rew:104.0,19833.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),tc_Com_Opname),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))*.
% 299.79/300.47 19924[0:Rew:104.0,19832.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),tc_Com_Opname),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))*.
% 299.79/300.47 19955[0:SpR:64.0,2097.1] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),v))* -> equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),u)).
% 299.79/300.47 20305[0:SpR:25.1,438.1] class_HOL_Ouminus(u) || c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w,x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)),v_x)**.
% 299.79/300.47 20293[0:SpR:445.1,438.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(x2,v) equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Fun_Ofun__upd(u,v,w,x,y),z,x1),hAPP(u,x2)),x2)**.
% 299.79/300.47 20449[0:SpR:25.1,99.1] class_HOL_Ouminus(u) || c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w,x),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)),v_x)**.
% 299.79/300.47 20436[0:SpR:445.1,99.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(x2,v) equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Fun_Ofun__upd(u,v,w,x,y),z,x1),hAPP(u,x2)),x2)**.
% 299.79/300.47 20985[0:SpR:14216.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,y),hAPP(c_Set_Oinsert(z,x),x1)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),y),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,y),x1)))*.
% 299.79/300.47 20939[0:SpR:25.1,317.0] class_HOL_Ouminus(u) || -> equal(hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w,x),hAPP(c_Set_Oinsert(v_x,w),y)),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),x),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w,x),y)))*.
% 299.79/300.47 20928[0:SpR:653.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,v),x)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),v,w),x)))*.
% 299.79/300.47 20925[0:SpR:445.1,317.0] || -> equal(u,v) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,y,z),x1,x2),hAPP(c_Set_Oinsert(u,x1),x3)),hAPP(c_Set_Oinsert(hAPP(w,u),x2),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,y,z),x1,x2),x3)))*.
% 299.79/300.47 20855[0:SpR:317.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),hAPP(c_Set_Oinsert(x2,v),x3)),hAPP(hAPP(c_Set_Oinsert(hAPP(u,x2),w),hAPP(c_Set_Oimage(u,v,w),x3)),hAPP(x,hAPP(c_Set_Oinsert(x2,v),x3))))*.
% 299.79/300.47 20854[0:SpR:317.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oimage(v,w,x),y,z,x1),hAPP(c_Set_Oinsert(x2,w),x3)),hAPP(hAPP(u,hAPP(c_Set_Oinsert(x2,w),x3)),hAPP(c_Set_Oinsert(hAPP(v,x2),x),hAPP(c_Set_Oimage(v,w,x),x3))))*.
% 299.79/300.47 21685[0:SpL:21267.0,469.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),v_x),tc_Com_Opname,y),w,v,x,u)),v)**.
% 299.79/300.47 21673[0:SpL:21267.0,8513.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x)) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x),tc_Com_Opname,w),u)**.
% 299.79/300.47 21652[0:SpL:21267.0,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x),tc_Com_Opname,w)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.47 21534[0:SpR:188.1,21267.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.79/300.47 21496[0:SpR:21267.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,y))),hAPP(c_Set_Oinsert(hAPP(u,x),w),hAPP(c_Set_Oimage(u,v,w),v_x)))**.
% 299.79/300.47 21454[0:SpR:21267.0,9568.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x),tc_Com_Opname,x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x),tc_bool)*.
% 299.79/300.47 21452[0:SpR:21267.0,9569.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x),tc_Com_Opname,x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x),tc_bool)*.
% 299.79/300.47 21391[0:SpR:21267.0,129.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(v,w,x),hAPP(c_Set_Ovimage(v,w,x),v_x),tc_Com_Opname,y),tc_fun(x,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),u),hAPP(c_Set_Ovimage(v,w,x),v_x),tc_fun(w,tc_bool))*.
% 299.79/300.47 21386[0:SpR:21267.0,313.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),v_x),tc_Com_Opname,y),tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),u),hAPP(c_Set_Oimage(v,w,x),v_x),tc_fun(x,tc_bool))*.
% 299.79/300.47 21324[0:SpR:21267.0,129.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x),tc_Com_Opname,x),y,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),v_x),hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool))*.
% 299.79/300.47 21307[0:SpR:21267.0,313.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),y,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),v_x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))*.
% 299.79/300.47 21296[0:SpR:21267.0,8498.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)).
% 299.79/300.47 21290[0:SpR:21267.0,463.1] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Obody,hAPP(c_Com_Obody,v_x),tc_Com_Opname,u)),v,w,x) -> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x)),v,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Obody,hAPP(c_Com_Obody,v_x),tc_Com_Opname,u),w,v,x),x)*.
% 299.79/300.47 21885[0:SpL:21267.0,464.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),v_x),tc_Com_Opname,y),v,w,x,u)),v)**.
% 299.79/300.47 22314[0:SpL:21893.0,469.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,x,u),v_x),c_Set_Oimage(w,x,u),tc_Com_Opname,y),w,v,x,u)),v)**.
% 299.79/300.47 22313[0:SpL:21893.0,464.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,x,u),v_x),c_Set_Oimage(w,x,u),tc_Com_Opname,y),v,w,x,u)),v)**.
% 299.79/300.47 22301[0:SpL:21893.0,8513.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x)) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_Com_Opname,w),u)**.
% 299.79/300.47 22280[0:SpL:21893.0,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname,w)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.47 22161[0:SpR:188.1,21893.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.79/300.47 22122[0:SpR:21893.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,y))),hAPP(c_Set_Oinsert(hAPP(u,x),w),hAPP(c_Set_Oimage(u,v,w),v_x)))**.
% 299.79/300.47 22080[0:SpR:21893.0,9568.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),tc_Com_Opname,x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x),tc_bool)*.
% 299.79/300.47 22078[0:SpR:21893.0,9569.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),tc_Com_Opname,x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x),tc_bool)*.
% 299.79/300.47 22017[0:SpR:21893.0,129.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(v,w,x),v_x),c_Set_Ovimage(v,w,x),tc_Com_Opname,y),tc_fun(x,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),u),hAPP(c_Set_Ovimage(v,w,x),v_x),tc_fun(w,tc_bool))*.
% 299.79/300.47 22012[0:SpR:21893.0,313.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(v,w,x),v_x),c_Set_Oimage(v,w,x),tc_Com_Opname,y),tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),u),hAPP(c_Set_Oimage(v,w,x),v_x),tc_fun(x,tc_bool))*.
% 299.79/300.47 21950[0:SpR:21893.0,129.1] || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),v_x),c_Set_Ovimage(u,v,w),tc_Com_Opname,x),y,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),v_x),hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool))*.
% 299.79/300.47 21933[0:SpR:21893.0,313.1] || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),y,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),v_x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))*.
% 299.79/300.47 21922[0:SpR:21893.0,8498.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)).
% 299.79/300.47 21916[0:SpR:21893.0,463.1] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Obody,v_x),c_Com_Obody,tc_Com_Opname,u)),v,w,x) -> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x)),v,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Obody,v_x),c_Com_Obody,tc_Com_Opname,u),w,v,x),x)*.
% 299.79/300.47 22416[0:SpR:97.1,196.1] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(c_Fun_Othe__inv__into(v,u,w,x),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w)* -> equal(hAPP(c_Set_Ovimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),v),hAPP(c_Set_Oimage(u,w,x),v))**.
% 299.79/300.47 22638[0:SpR:21893.0,158.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(v,y,w),v_x),c_Set_Oimage(v,y,w),tc_Com_Opname,z)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))**.
% 299.79/300.47 22637[0:SpR:21267.0,158.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(v,y,w),hAPP(c_Set_Oimage(v,y,w),v_x),tc_Com_Opname,z)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))**.
% 299.79/300.47 23020[0:SpR:21893.0,131.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,w,x),v_x),c_Set_Ovimage(u,w,x),tc_Com_Opname,z)),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)))**.
% 299.79/300.47 23019[0:SpR:21267.0,131.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(u,w,x),hAPP(c_Set_Ovimage(u,w,x),v_x),tc_Com_Opname,z)),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)))**.
% 299.79/300.47 24061[0:MRR:24057.0,1273.1] || c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u) equal(c_Suc(c_Finite__Set_Ocard(v,u)),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u))* -> hBOOL(hAPP(hAPP(c_in(u),w),v))* equal(hAPP(c_Set_Oinsert(w,u),v),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))).
% 299.79/300.47 24446[0:SpL:64.0,208.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),v),u)) c_lessequals(u,c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.47 24443[0:SpL:317.0,208.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(y,w),z)),tc_fun(x,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(v,y)),u)) c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),z),tc_fun(x,tc_bool)).
% 299.79/300.47 24929[0:Rew:9.0,24903.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1))))* -> equal(hAPP(w,hAPP(y,hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Fun_Ocomp(w,y,x,u,z),z,u),v))),v)**.
% 299.79/300.47 25386[0:SpR:512.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Oimage(hAPP(c_COMBB(v,w,x,y),z),y,x),t_a) hBOOL(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(z,y,w),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_Set_Oimage(hAPP(c_COMBB(v,w,x,y),z),y,x)))))*.
% 299.79/300.47 25357[0:SpR:512.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),z,hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),z)),x1,x2),c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w))**.
% 299.79/300.47 25516[0:Rew:586.0,25445.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1))))* -> equal(hAPP(w,hAPP(y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x1,hAPP(c_COMBB(w,x,u,z),y),v,z,u))),v)**.
% 299.79/300.47 25517[0:Rew:586.0,25444.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1))))* -> equal(hAPP(w,hAPP(y,c_ATP__Linkup_Osko__Set__XimageE__1__1(x1,v,hAPP(c_COMBB(w,x,u,z),y),z,u))),v)**.
% 299.79/300.47 25688[0:SpL:21893.0,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),u))* c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,x),t_a)*.
% 299.79/300.47 25687[0:SpL:21267.0,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),u))* c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),tc_Com_Opname,x),t_a)*.
% 299.79/300.47 26009[0:Rew:339.0,25959.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w)),x)),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),x)))**.
% 299.79/300.47 26010[0:Rew:339.0,25958.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w)),x)),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),x)))**.
% 299.79/300.47 26252[0:SpL:338.0,263.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(x,u),y))))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y))) equal(v,x).
% 299.79/300.47 26169[0:SpR:21893.0,338.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(u,v),v_x)))**.
% 299.79/300.47 26168[0:SpR:21267.0,338.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(u,v),v_x)))**.
% 299.79/300.47 26523[0:Res:84.1,402.0] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)) c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),u,tc_fun(w,tc_bool))* -> equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x)).
% 299.79/300.47 26962[0:Res:424.2,357.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* c_lessequals(z,hAPP(c_Set_Oimage(w,x,u),y),tc_fun(u,tc_bool))* c_Finite__Set_Ofinite(y,x) -> c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),z),u)*.
% 299.79/300.47 26946[0:SpR:21893.0,424.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,u),v_x),c_Set_Oinsert(v,u),tc_Com_Opname,x),w,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,u),v_x),w,tc_fun(u,tc_bool)).
% 299.79/300.47 26945[0:SpR:21267.0,424.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v,u),v_x),tc_Com_Opname,x),w,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,u),v_x),w,tc_fun(u,tc_bool)).
% 299.79/300.47 27185[0:Res:450.0,255.0] || c_lessequals(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(u),v,w,x),y,tc_fun(u,tc_bool)) -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(u)),w),v),t_a)* hBOOL(hAPP(hAPP(c_in(u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(u),v,w,x)),y))*.
% 299.79/300.47 27167[0:SpR:12944.0,450.0] || -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y,z,x1))) c_Hoare__Mirabelle_Otriple__valid(x1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x))),z),y),t_a)*.
% 299.79/300.47 27161[0:SpR:11473.0,450.0] || -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,x,y))) c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))),x),w),t_a)*.
% 299.79/300.47 27148[0:SpR:17045.0,450.0] || -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x,y,z))) c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool))),y),x),t_a)*.
% 299.79/300.47 27343[7:MRR:24304.0,27297.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_Com_Opname,x)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.79/300.47 27344[7:MRR:24301.0,27297.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_Com_Opname,x)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.79/300.47 27362[0:SpL:393.1,470.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> equal(x,c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))) hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__XimageE__1__1(x,v,c_COMBK(w,u,y),y,u)),x))*.
% 299.79/300.47 27422[0:SpL:393.1,466.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> equal(x,c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))) hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,c_COMBK(w,u,y),v,y,u)),x))*.
% 299.79/300.47 27632[0:SpR:9987.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),w,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oinsert(v_x,t_a),u,x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.79/300.47 27630[0:SpR:2095.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_Set_Oinsert(x,v),w,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oinsert(x,v),u,y),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.79/300.47 27623[0:SpR:2935.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v)) c_Fun_Oinj__on(hAPP(c_in(t_a),v_x),v,u,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,hAPP(c_in(t_a),v_x),u,w),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))**.
% 299.79/300.47 27611[0:SpR:9936.1,373.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),w),x))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,y),c_Orderings_Otop__class_Otop(tc_bool)),w)*.
% 299.79/300.47 27607[0:SpR:9935.1,373.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),u),w))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),w,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v,y),c_Orderings_Otop__class_Otop(tc_bool)),u)*.
% 299.79/300.47 27546[0:SpR:2093.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(tc_Com_Opname),v_x)),v)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,w),v,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(v_Procs,w),u,x),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_in(tc_Com_Opname),v_x))**.
% 299.79/300.47 27536[0:SpR:373.2,584.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(hAPP(c_COMBS(c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x1,x2,x3),hAPP(x,v)),hAPP(v,hAPP(z,hAPP(x,v))))*.
% 299.79/300.47 27535[0:SpR:373.2,584.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(hAPP(c_COMBS(z,c_Hilbert__Choice_Oinv__into(w,x,u,y),x1,x2,x3),hAPP(x,v)),hAPP(hAPP(z,hAPP(x,v)),v))*.
% 299.79/300.47 27785[0:SpR:9987.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),w,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oinsert(v_x,t_a),u,x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.79/300.47 27783[0:SpR:2095.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_Set_Oinsert(x,v),w,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oinsert(x,v),u,y),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.79/300.47 27776[0:SpR:2935.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v)) c_Fun_Oinj__on(hAPP(c_in(t_a),v_x),v,u,w) -> equal(hAPP(c_Fun_Othe__inv__into(v,hAPP(c_in(t_a),v_x),u,w),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))**.
% 299.79/300.47 27764[0:SpR:9936.1,71.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),w),x))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,y),c_Orderings_Otop__class_Otop(tc_bool)),w)*.
% 299.79/300.47 27760[0:SpR:9935.1,71.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),u),w))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),w,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v,y),c_Orderings_Otop__class_Otop(tc_bool)),u)*.
% 299.79/300.47 27698[0:SpR:2093.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(tc_Com_Opname),v_x)),v)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,w),v,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(v_Procs,w),u,x),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_in(tc_Com_Opname),v_x))**.
% 299.79/300.47 27688[0:SpR:71.2,584.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(hAPP(c_COMBS(c_Fun_Othe__inv__into(w,x,u,y),z,x1,x2,x3),hAPP(x,v)),hAPP(v,hAPP(z,hAPP(x,v))))*.
% 299.79/300.47 27687[0:SpR:71.2,584.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(hAPP(c_COMBS(z,c_Fun_Othe__inv__into(w,x,u,y),x1,x2,x3),hAPP(x,v)),hAPP(hAPP(z,hAPP(x,v)),v))*.
% 299.79/300.47 28172[0:SpR:465.1,415.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_Fun_Ofun__upd(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w,hAPP(c_Set_Oimage(x,u,z),w),x1,x2),c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z))**.
% 299.79/300.47 28539[0:SpR:1196.1,118.0] class_Lattices_Oboolean__algebra(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Fun_Ofun__upd(v,w,c_Orderings_Otop__class_Otop(u),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,y,z,x),w,c_Orderings_Otop__class_Otop(u),x,z))*.
% 299.79/300.47 28535[0:SpR:3294.1,118.0] || equal(c_in(t_a),u) -> equal(c_Fun_Ocomp(hAPP(u,v_x),c_Fun_Ofun__upd(v,w,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(u,v_x),v,y,z,x),w,c_Orderings_Obot__class_Obot(tc_bool),x,z))*.
% 299.79/300.47 28531[0:SpR:330.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Fun_Ofun__upd(w,x,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,z,x1,y),x,v,y,x1))*.
% 299.79/300.47 28530[0:SpR:1195.1,118.0] class_Lattices_Oboolean__algebra(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Fun_Ofun__upd(v,w,c_Orderings_Obot__class_Obot(u),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y,z,x),w,c_Orderings_Otop__class_Otop(u),x,z))*.
% 299.79/300.47 28524[0:SpR:584.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(u,v),c_Fun_Ofun__upd(w,x,hAPP(y,v),z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(u,v),w,x1,x2,z),x,hAPP(c_COMBS(u,y,x3,x4,x5),v),z,x2))*.
% 299.79/300.47 28522[0:SpR:9936.1,118.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),c_Fun_Ofun__upd(v,w,x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,z,x1,y),w,c_Orderings_Otop__class_Otop(tc_bool),y,x1))*.
% 299.79/300.47 28518[0:SpR:9935.1,118.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Fun_Ofun__upd(w,x,u,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,z,x1,y),x,c_Orderings_Otop__class_Otop(tc_bool),y,x1))*.
% 299.79/300.47 29088[0:SpR:537.1,584.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),hAPP(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1)))))*.
% 299.79/300.47 29049[0:SpR:537.1,474.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),z,v),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.47 29286[0:SSi:29285.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(w,v,tc_fun(u,tc_bool))),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))**.
% 299.79/300.47 29287[0:SSi:29073.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y))))*.
% 299.79/300.47 29612[0:SpR:534.1,584.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),hAPP(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1)))))*.
% 299.79/300.47 29572[0:SpR:534.1,474.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),z,v),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.47 30449[0:Rew:537.1,30448.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y))))*.
% 299.79/300.47 30470[0:SSi:30239.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_HOL_Ominus__class_Ominus(x,v,tc_fun(u,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v)))**.
% 299.79/300.47 30471[0:SSi:30123.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),x))))*.
% 299.79/300.47 31006[0:Rew:534.1,31005.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y))))*.
% 299.79/300.47 31397[0:SpL:23682.0,449.0] || hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,w)))* -> c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool))),t_a).
% 299.79/300.47 31522[0:SpL:158.0,473.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1))))* -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Fun_Ocomp(w,y,x,u,z),z,u),v)),x1))*.
% 299.79/300.47 31744[0:SpL:158.0,389.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,y,v,w,z),z,w),x1))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(x,hAPP(c_Set_Oimage(y,z,v),x1)).
% 299.79/300.47 31742[0:SpL:317.0,389.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oinsert(hAPP(u,y),w),hAPP(c_Set_Oimage(u,v,w),z)))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> equal(x,hAPP(c_Set_Oinsert(y,v),z)).
% 299.79/300.47 32185[0:SpR:21893.0,31323.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v_x),hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v_x),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),tc_Com_Opname,u)),tc_bool)*.
% 299.79/300.47 32184[0:SpR:21267.0,31323.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v_x),hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v_x),tc_Com_Opname,u)),tc_bool)*.
% 299.79/300.47 32400[0:Rew:9.0,32365.2] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),c_Fun_Ocomp(u,v,z,x1,x2),w))))* hBOOL(hAPP(hAPP(c_in(w),x3),x))* -> hBOOL(hAPP(u,hAPP(v,x3)))*.
% 299.79/300.47 32580[0:Rew:9.0,32545.2] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),c_Fun_Ocomp(u,v,z,x1,x2),w))))* hBOOL(hAPP(hAPP(c_in(w),x3),y))* -> hBOOL(hAPP(u,hAPP(v,x3)))*.
% 299.79/300.47 32826[0:Rew:600.0,32766.2,538.0,32766.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(v,x,tc_fun(w,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u))**.
% 299.79/300.47 33011[0:SpR:10090.1,475.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),hAPP(c_Set_Oimage(hAPP(u,v_x),v,x),w)),hAPP(c_Set_Oimage(hAPP(u,v_x),v,x),w))**.
% 299.79/300.47 33004[0:SpR:303.1,475.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,x),w))**.
% 299.79/300.47 32989[0:SpR:11176.1,475.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),w),x))* -> equal(hAPP(c_Set_Oinsert(u,y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,y),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,y),x))**.
% 299.79/300.47 32985[0:SpR:11177.1,475.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> equal(hAPP(c_Set_Oinsert(u,x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v,x),w))**.
% 299.79/300.47 32940[0:SpR:300.1,475.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(c_Set_Oinsert(w,y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,y),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,y),x))**.
% 299.79/300.47 32936[0:SpR:3586.1,475.1] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> equal(hAPP(c_Set_Oinsert(v_x,y),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,y),x)),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,y),x))**.
% 299.79/300.47 32935[7:SpR:27278.1,475.1] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> equal(hAPP(c_Set_Oinsert(v_x,y),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,y),x)),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),w,y),x))**.
% 299.79/300.47 32907[0:SpR:9493.1,475.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> equal(hAPP(c_Set_Oinsert(u,x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,x),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,x),w))**.
% 299.79/300.47 32905[0:SpR:8498.1,475.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),u),x)) -> equal(hAPP(c_Set_Oinsert(u,y),hAPP(c_Set_Oimage(c_Set_Oinsert(z,v),w,y),x)),hAPP(c_Set_Oimage(c_Set_Oinsert(z,v),w,y),x))**.
% 299.79/300.47 33438[0:Res:687.1,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,x)),v))* c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.79/300.47 33437[0:Res:686.1,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,x)),v))* c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.79/300.47 33406[0:Res:510.1,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),x),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,y)),w))* c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.47 33405[0:Res:511.1,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),x),v),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,y)),w))* c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.47 33382[0:SpL:8415.2,453.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(tc_Hoare__Mirabelle_Otriple(t_a))) hBOOL(hAPP(v_x,u)) c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,v_x,t_a).
% 299.79/300.47 33801[0:Res:248.4,427.1] class_Orderings_Olinorder(u) class_Orderings_Opreorder(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,v,tc_fun(u,tc_bool))* c_lessequals(c_Finite__Set_Olinorder__class_OMin(w,u),x,u)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,u),x,u)*.
% 299.79/300.47 33800[0:Res:248.4,426.1] class_Orderings_Olinorder(u) class_Orderings_Oorder(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,v,tc_fun(u,tc_bool))* c_lessequals(x,c_Finite__Set_Olinorder__class_OMin(v,u),u)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) c_lessequals(x,c_Finite__Set_Olinorder__class_OMin(w,u),u)*.
% 299.79/300.47 33881[0:Res:247.4,427.1] class_Orderings_Olinorder(u) class_Orderings_Opreorder(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,v,tc_fun(u,tc_bool))* c_lessequals(c_Finite__Set_Olinorder__class_OMax(v,u),x,u)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) c_lessequals(c_Finite__Set_Olinorder__class_OMax(w,u),x,u)*.
% 299.79/300.47 33880[0:Res:247.4,426.1] class_Orderings_Olinorder(u) class_Orderings_Oorder(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,v,tc_fun(u,tc_bool))* c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(w,u),u)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.79/300.47 34424[0:SpL:24914.0,156.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),v_x))) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,v)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(w,u,x),tc_Com_Opname,y),hAPP(c_Set_Ovimage(w,u,x),v_x))))*.
% 299.79/300.47 34395[0:SpL:24914.0,346.0] || c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),v,x) -> c_Fun_Oinj__on(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),v,x)*.
% 299.79/300.47 34366[0:SpL:24914.0,255.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,w),hAPP(hAPP(c_in(u),v),v_x)),x,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),x)).
% 299.79/300.47 34357[0:SpL:24914.0,208.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),v_x),tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),v),u)) c_lessequals(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,x),hAPP(c_Set_Oinsert(v,w),v_x)),tc_fun(w,tc_bool))*.
% 299.79/300.47 34301[0:SpL:24914.0,473.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x)))),x))*.
% 299.79/300.47 34223[0:SpR:181.1,24914.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.79/300.47 34115[0:SpR:24914.0,304.3] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),w,u)* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),w,u).
% 299.79/300.47 34094[0:SpR:24914.0,153.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(v,x,u),tc_Com_Opname,y),hAPP(c_Set_Ovimage(v,x,u),v_x))))* -> hBOOL(hAPP(hAPP(c_in(x),w),hAPP(c_Set_Ovimage(v,x,u),v_x))).
% 299.79/300.47 34079[0:SpR:24914.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,u,x),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,u,x),v_x))))* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,v)),hAPP(c_Set_Oimage(w,u,x),v_x))).
% 299.79/300.47 34059[0:SpR:24914.0,335.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)),v)* -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x),v).
% 299.79/300.47 33913[0:SpR:24914.0,2097.1] || hBOOL(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),u))* -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),hAPP(c_Set_Oinsert(u,v),v_x)).
% 299.79/300.47 34566[0:SpR:34427.0,118.0] || -> equal(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),c_Fun_Ofun__upd(v,w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v,y,z,x),w,v_x,x,z))*.
% 299.79/300.47 34621[0:SpR:55.1,20881.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),x,y),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(z,w,tc_fun(u,tc_bool)),x),x1)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),z),w,tc_fun(u,tc_bool))))*.
% 299.79/300.47 34615[0:SpR:55.1,353.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(x,u),c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool)))),hAPP(c_Set_Oinsert(x,u),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool))))*.
% 299.79/300.47 34610[0:SpR:55.1,254.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(u),y),x)) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(y,u),w),x,tc_fun(u,tc_bool))))*.
% 299.79/300.47 34591[0:SpR:55.1,9569.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),c_Set_Oinsert(v,u)),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool))),tc_bool)*.
% 299.79/300.47 34590[0:SpR:55.1,9568.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Oinsert(v,u)),z),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool))),tc_bool)*.
% 299.79/300.47 35436[0:SpL:410.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),y,w,tc_fun(z,tc_bool)),u,z)))* hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,w,tc_fun(z,tc_bool))))* -> hBOOL(hAPP(u,x1))*.
% 299.79/300.47 35435[0:SpL:410.0,85.0] || c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),y,w,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(y,v),tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,w,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.47 35387[0:SpR:9987.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 35385[0:SpR:2095.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(x,u),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(x,u),v,tc_fun(y,tc_bool))))*.
% 299.79/300.47 35381[0:SpR:24914.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),w),x),u,w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(u,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,u,w,tc_fun(y,tc_bool))))*.
% 299.79/300.47 35380[0:SpR:23902.1,410.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),v),w),hAPP(u,v_x),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 35377[0:SpR:2935.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),u),v),hAPP(c_in(t_a),v_x),u,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_in(t_a),v_x),u,tc_fun(w,tc_bool))))*.
% 299.79/300.47 35372[0:SpR:301.1,410.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,tc_fun(y,tc_bool))))*.
% 299.79/300.47 35323[0:SpR:414.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Fun_Ofun__upd(x,u,y,z,x1),v,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ofun__upd(x,u,y,z,x1),v,tc_fun(x2,tc_bool))))*.
% 299.79/300.47 35314[0:SpR:524.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),v,tc_fun(y,tc_bool))))*.
% 299.79/300.47 35308[0:SpR:8415.2,410.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,v),w),u,v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,u,v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 35304[0:SpR:365.1,410.0] class_Orderings_Obot(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,v),w),c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 35303[0:SpR:397.1,410.0] class_Orderings_Otop(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,v),w),c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 35288[0:SpR:2093.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_in(tc_Com_Opname),v_x),u),v),c_Set_Oinsert(v_Procs,w),u,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_Procs,w),u,tc_fun(x,tc_bool))))*.
% 299.79/300.47 35286[0:SpR:3744.1,410.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,v),w),c_Set_Oinsert(v_x,u),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,u),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 35259[0:SpR:8415.2,410.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Set_Oinsert(u,v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(x,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,x,v,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,x,v,tc_fun(w,tc_bool)))**.
% 299.79/300.47 35258[0:SpR:353.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),y,v,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),x),y,v,tc_fun(z,tc_bool))))*.
% 299.79/300.47 35247[0:SpR:410.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(v,w),tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v,z,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,z),y),v,z,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.47 35239[0:SpR:410.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),hAPP(c_Set_Oinsert(x,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v,z,tc_fun(u,tc_bool)))),hAPP(c_Set_Oinsert(x,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,z),y),v,z,tc_fun(u,tc_bool))))*.
% 299.79/300.47 35222[0:SpR:410.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),x,y),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,v,x1,tc_fun(u,tc_bool)),x),x2)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x1),z),v,x1,tc_fun(u,tc_bool))))*.
% 299.79/300.47 35197[0:SpR:410.0,9569.0] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,u))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool))),tc_bool)*.
% 299.79/300.47 35196[0:SpR:410.0,9568.0] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,u))),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool))),tc_bool)*.
% 299.79/300.47 35519[0:SpR:128.0,113.0] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),y,tc_fun(w,tc_bool))))*.
% 299.79/300.47 35511[0:SpR:8415.2,113.0] || equal(v_Procs,v_x) equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(v_x,x,tc_fun(w,tc_bool))))*.
% 299.79/300.47 35504[0:SpR:128.0,113.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(u,v,w),x),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,c_HOL_Ouminus__class_Ouminus(y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))))*.
% 299.79/300.47 35496[0:SpR:8415.2,113.0] || equal(v_Procs,v_x) equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(u,v,w),x),v_x,tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,v_x,tc_fun(w,tc_bool))))*.
% 299.79/300.47 35546[0:Rew:10.0,35514.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y),tc_fun(x,tc_bool)),hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool))))*.
% 299.79/300.47 35548[0:Rew:113.0,35522.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),v_x),c_Set_Ovimage(u,v,w),tc_Com_Opname,x),y,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(v_x,y,tc_fun(w,tc_bool))))**.
% 299.79/300.47 35549[0:Rew:113.0,35521.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x),tc_Com_Opname,x),y,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(v_x,y,tc_fun(w,tc_bool))))**.
% 299.79/300.47 35550[0:Rew:113.0,35507.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),v_x),c_Set_Ovimage(u,v,w),tc_Com_Opname,y),tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,v_x,tc_fun(w,tc_bool))))**.
% 299.79/300.47 35551[0:Rew:113.0,35506.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x),tc_Com_Opname,y),tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,v_x,tc_fun(w,tc_bool))))**.
% 299.79/300.47 35634[0:SpR:8415.2,89.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,hAPP(c_COMBB(x,w,tc_fun(y,tc_bool),v),u),v,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,x,w,tc_fun(y,tc_bool)))**.
% 299.79/300.47 35624[0:SpR:8415.2,89.0] || equal(v_Procs,v_x) equal(c_COMBB(u,v,tc_fun(w,tc_bool),x),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v_x,x,v),y),u,v,tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v_x,x,tc_fun(w,tc_bool)))**.
% 299.79/300.47 36524[0:Rew:586.0,36520.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,u,y),w),z,y,tc_fun(x1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))** -> equal(hAPP(z,hAPP(x,v)),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))*.
% 299.79/300.47 36774[0:SpL:67.0,148.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,u),y),tc_fun(u,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))*.
% 299.79/300.47 37016[0:SSi:37002.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),y,tc_fun(x,tc_bool))* hBOOL(hAPP(hAPP(c_in(w),z),u))* -> c_lessequals(hAPP(v,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),x1),tc_fun(x,tc_bool))*.
% 299.79/300.47 37017[0:SSi:36999.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),y,tc_fun(x,tc_bool))* hBOOL(hAPP(hAPP(c_in(w),z),u))* -> c_lessequals(hAPP(v,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),y),tc_fun(x,tc_bool))*.
% 299.79/300.47 37018[0:Rew:586.0,36969.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,u,y),w),z,y,tc_fun(x1,tc_bool)),x2,tc_fun(x1,tc_bool))* -> c_lessequals(hAPP(z,hAPP(x,v)),x2,tc_fun(x1,tc_bool))*.
% 299.79/300.47 37189[0:Rew:9.0,37134.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(hAPP(c_Set_Oimage(x,y,z),hAPP(c_Set_Oimage(x1,u,y),w)),x2,tc_fun(z,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(z),hAPP(x,hAPP(x1,v))),x2))*.
% 299.79/300.47 37195[0:SSi:37172.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(v),z),x))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),x1)))*.
% 299.79/300.47 37196[0:SSi:37169.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(v),z),x))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),y)))*.
% 299.79/300.47 38969[0:SpR:354.2,9567.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(x,w,y),u)),u,tc_bool)*.
% 299.79/300.47 38950[0:SpR:354.2,5875.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(u,z),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),x1,x2,x3),hAPP(c_Set_Oimage(x,w,y),u)))*.
% 299.79/300.47 39316[0:SpL:533.0,3506.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Com_Ocom_OBODY) equal(c_Com_Ocom_OSemi(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))* -> .
% 299.79/300.47 39300[0:SpR:3294.1,533.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),v))**.
% 299.79/300.47 39295[0:SpR:584.0,533.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z)),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,z)),x1)))*.
% 299.79/300.47 39165[0:SpR:533.0,9566.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),hAPP(hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w))),x),tc_bool)*.
% 299.79/300.47 39136[0:SpR:533.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))))*.
% 299.79/300.47 39113[0:SpR:533.0,24020.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),v_x),v_x)**.
% 299.79/300.47 39784[0:SpR:3294.1,532.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Obot__class_Obot(tc_bool)))**.
% 299.79/300.47 39779[0:SpR:584.0,532.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(x,v))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x,y,z,x1),v)))*.
% 299.79/300.47 39591[0:SpR:532.0,9566.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),hAPP(hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)),tc_bool)*.
% 299.79/300.47 40190[0:Res:399.1,431.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),v),w,y)* -> c_Fun_Oinj__on(x,hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),u),w,y)*.
% 299.79/300.47 40461[0:Rew:8415.2,40444.3] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(u)) c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(v_x,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x),u)* -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),hAPP(hAPP(v_x,hAPP(c_Com_Ocom_OBODY,w)),x),u).
% 299.79/300.47 40709[0:Rew:8415.2,40693.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(u)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),hAPP(hAPP(v_x,hAPP(c_Com_Ocom_OBODY,w)),x),u) -> c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(v_x,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x),u)*.
% 299.79/300.47 40957[0:Rew:104.0,40898.2] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(hAPP(c_in(w),v),x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),y,u,w)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))))*.
% 299.79/300.47 40962[4:MRR:40869.3,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_x,x,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),x)))*.
% 299.79/300.47 41231[0:Rew:19819.0,41179.2] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(hAPP(c_in(w),v),x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),u,w)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))))*.
% 299.79/300.47 41232[4:MRR:41150.3,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(w,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_x,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v_x)))*.
% 299.79/300.47 41351[0:SpL:2935.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v)) hBOOL(hAPP(hAPP(c_in(w),x),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_in(t_a),v_x),u,tc_fun(w,tc_bool))))*.
% 299.79/300.47 41346[0:SpL:301.1,275.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) hBOOL(hAPP(hAPP(c_in(x),y),z)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 41342[0:SpL:24020.1,275.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) hBOOL(hAPP(hAPP(c_in(x),y),v_x)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 41287[0:SpL:300.1,275.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* hBOOL(hAPP(hAPP(c_in(y),z),w))* -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,tc_fun(y,tc_bool))))*.
% 299.79/300.47 41274[0:SpL:365.1,275.1] class_Orderings_Obot(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Obot__class_Obot(u))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 41273[0:SpL:397.1,275.1] class_Orderings_Otop(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(u))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 41247[0:SpL:2097.1,275.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),u),x))* hBOOL(hAPP(hAPP(c_in(y),z),u))* -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v,x1),w,tc_fun(y,tc_bool))))*.
% 299.79/300.47 41436[0:Rew:8415.2,41389.4] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(c_in(v),w),x))* hBOOL(hAPP(v_x,hAPP(y,w)))* -> hBOOL(hAPP(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,tc_fun(u,tc_bool))))*.
% 299.79/300.47 41637[0:SpL:23840.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,u),x)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u)* -> hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Obot__class_Obot(tc_bool)),x)).
% 299.79/300.47 41734[0:SpL:584.0,494.1] || hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(c_COMBS(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y,z,x1,x2),x3),t_a)* c_Natural_Oevaln(x3,w,x,x4)* -> hBOOL(hAPP(hAPP(hAPP(y,x3),v),x4))*.
% 299.79/300.47 41725[0:SpL:3294.1,494.1] || equal(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(t_a)) hBOOL(hAPP(hAPP(v_x,u),v))* c_Hoare__Mirabelle_Otriple__valid(w,hAPP(c_Orderings_Obot__class_Obot(tc_bool),x),t_a)* c_Natural_Oevaln(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v,w,y)* -> hBOOL(hAPP(hAPP(x,u),y))*.
% 299.79/300.47 41723[0:SpL:584.0,494.1] || hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(t_a),y,z,x1,x2),u),x3),t_a)* c_Natural_Oevaln(hAPP(y,u),w,x,x4)* -> hBOOL(hAPP(hAPP(x3,v),x4))*.
% 299.79/300.47 41831[0:Res:8366.1,199.0] || equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_in(tc_Com_Opname),v_x),v,u,w)),v_Procs)** c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),x))*.
% 299.79/300.47 41991[0:Res:82.0,431.0] || c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(v,w,x),c_HOL_Ominus__class_Ominus(y,z,tc_fun(w,tc_bool))),x,x1) -> c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(v,w,x),y),hAPP(c_Set_Oimage(v,w,x),z),tc_fun(x,tc_bool)),x,x1)*.
% 299.79/300.47 42064[0:SpR:180.2,9566.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u),hAPP(hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u)),tc_bool)*.
% 299.79/300.47 42475[0:SpL:302.1,315.0] class_Lattices_Obounded__lattice(u) || equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,y)),c_Orderings_Otop__class_Otop(u))** -> equal(hAPP(c_Set_Oimage(v,x,y),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,y),w)).
% 299.79/300.47 42434[0:SpL:302.1,315.0] class_Lattices_Obounded__lattice(u) || equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,x,y)),c_Orderings_Otop__class_Otop(u))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,y),w),hAPP(c_Set_Oimage(v,x,y),w)).
% 299.79/300.47 42770[0:SSi:42690.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(t_a,tc_bool)),v_x)),hAPP(c_HOL_Ominus__class_Ominus(w,v,tc_fun(t_a,tc_bool)),v_x)),hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w),v,tc_fun(t_a,tc_bool)),v_x))**.
% 299.79/300.47 43135[0:SpL:486.1,477.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)),x,z)))* hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(y,v)))* -> hBOOL(hAPP(x,x1))*.
% 299.79/300.47 43063[0:SpR:23912.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,tc_fun(x,tc_bool)))**.
% 299.79/300.47 43028[0:SpR:351.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBK(y,z,x1),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBK(y,z,x1),u,tc_fun(x,tc_bool)))**.
% 299.79/300.47 43003[0:SpR:3229.1,486.1] || equal(u,v) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(u,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,w,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,w,tc_fun(y,tc_bool)))**.
% 299.79/300.47 42920[0:SpR:486.1,474.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x1,x),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.79/300.47 43140[0:SSi:42962.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(x,v),v_x)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(t_a,tc_bool)),v_x)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(t_a,tc_bool)),v_x))**.
% 299.79/300.47 43535[0:SpR:3229.1,507.0] || equal(u,c_Set_Oimage(v,w,x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(u,v_x)),hAPP(c_Set_Oimage(v,w,x),y)),hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),y)))*.
% 299.79/300.47 43520[0:SpR:3229.1,507.0] || equal(u,c_Set_Oimage(v,w,x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y)),hAPP(u,v_x)),hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v_x)))*.
% 299.79/300.47 43577[0:SSi:43508.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x)),hAPP(hAPP(c_Set_Oimage(u,v,t_a),x),v_x)),hAPP(hAPP(c_Set_Oimage(u,v,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),v_x))**.
% 299.79/300.47 43589[0:Rew:331.0,43527.1,339.0,43527.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(c_Set_Oinsert(w,x),hAPP(c_Set_Oimage(c_COMBK(w,x,v),v,x),y)),hAPP(c_Set_Oimage(c_COMBK(w,x,v),v,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),y)))*.
% 299.79/300.47 43592[0:Rew:331.0,43512.1,339.0,43512.1,538.0,43512.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(c_Set_Oinsert(w,x),hAPP(c_Set_Oimage(c_COMBK(w,x,v),v,x),y)),hAPP(c_Set_Oimage(c_COMBK(w,x,v),v,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),u)))*.
% 299.79/300.47 43754[0:SpR:3229.1,162.0] || equal(u,c_Set_Ovimage(v,w,x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(u,v_x)),hAPP(c_Set_Ovimage(v,w,x),y)),hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),y)))*.
% 299.79/300.47 43739[0:SpR:3229.1,162.0] || equal(u,c_Set_Ovimage(v,w,x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),y)),hAPP(u,v_x)),hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),v_x)))*.
% 299.79/300.47 43803[0:SSi:43730.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Set_Ovimage(u,t_a,v),w),v_x)),hAPP(hAPP(c_Set_Ovimage(u,t_a,v),x),v_x)),hAPP(hAPP(c_Set_Ovimage(u,t_a,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),v_x))**.
% 299.79/300.47 43987[0:Res:448.1,231.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u) -> c_lessequals(hAPP(c_Set_Oimage(v,w,u),x),y,tc_fun(u,tc_bool))* c_lessequals(hAPP(c_Set_Ovimage(v,w,u),y),x,tc_fun(w,tc_bool))*.
% 299.79/300.47 43948[0:SpL:3229.1,231.0] || equal(u,c_Set_Oimage(v,w,x))* c_lessequals(y,hAPP(u,v_x),tc_fun(x,tc_bool))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),y),v_x,tc_fun(w,tc_bool))*.
% 299.79/300.47 44088[0:Res:448.1,358.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u) -> c_lessequals(hAPP(c_Set_Oimage(v,w,u),x),hAPP(c_Set_Oimage(v,w,u),y),tc_fun(u,tc_bool))* c_lessequals(y,x,tc_fun(w,tc_bool)).
% 299.79/300.47 44069[0:SpL:3229.1,358.0] || equal(u,c_Set_Oimage(v,w,x)) c_lessequals(hAPP(u,v_x),hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> c_lessequals(v_x,y,tc_fun(w,tc_bool)).
% 299.79/300.47 44054[0:SpL:3229.1,358.0] || equal(u,c_Set_Oimage(v,w,x)) c_lessequals(hAPP(c_Set_Oimage(v,w,x),y),hAPP(u,v_x),tc_fun(x,tc_bool))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x)* -> c_lessequals(y,v_x,tc_fun(w,tc_bool)).
% 299.79/300.47 44182[0:Res:232.1,436.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool))),y))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),y))*.
% 299.79/300.47 44362[0:MRR:44346.5,11894.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(hAPP(c_in(u),w),v))* equal(hAPP(x,c_Finite__Set_Olinorder__class_OMin(v,u)),hAPP(x,w))* c_Fun_Oinj__on(x,v,u,y)* -> equal(c_Finite__Set_Olinorder__class_OMin(v,u),w).
% 299.79/300.47 44363[0:MRR:44345.5,11894.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(hAPP(c_in(u),w),v))* equal(hAPP(x,c_Finite__Set_Olinorder__class_OMax(v,u)),hAPP(x,w))* c_Fun_Oinj__on(x,v,u,y)* -> equal(c_Finite__Set_Olinorder__class_OMax(v,u),w).
% 299.79/300.47 45118[0:Res:326.2,18625.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,y,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),z),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),z),tc_bool)*.
% 299.79/300.47 45045[0:SpR:23902.1,326.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(v,v_x,tc_fun(u,tc_bool)) c_lessequals(w,c_Orderings_Obot__class_Obot(tc_bool),tc_fun(u,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x,tc_fun(u,tc_bool))*.
% 299.79/300.47 45356[0:Res:8376.2,487.1] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_Procs)** hBOOL(hAPP(x,v_x)) -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)))*.
% 299.79/300.47 45441[0:SpR:131.0,45357.1] || hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)) -> hBOOL(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname))))*.
% 299.79/300.47 45440[0:SpR:158.0,45357.1] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)) -> hBOOL(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname))))*.
% 299.79/300.47 45510[0:Res:8376.2,237.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_Procs)** c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u) -> equal(hAPP(v,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v_x,v,u,w)),v_x)**.
% 299.79/300.47 45554[0:SpR:323.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),y,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),x1),w,x,tc_fun(u,tc_bool))))*.
% 299.79/300.47 45551[0:SpR:323.0,335.2] || c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),x) c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v,w,tc_fun(x,tc_bool)),x) -> c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),v,w,tc_fun(x,tc_bool)),x)*.
% 299.79/300.47 45880[0:SpL:584.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)))* hBOOL(hAPP(c_COMBS(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y,z,x1),x))* -> hBOOL(hAPP(u,x)).
% 299.79/300.47 45956[0:SpL:131.0,45899.0] || hBOOL(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),tc_Com_Opname))))* -> hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_x)).
% 299.79/300.47 45955[0:SpL:158.0,45899.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),tc_Com_Opname))))* -> hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x)).
% 299.79/300.47 46185[0:Res:31533.0,481.0] || -> hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))*.
% 299.79/300.47 46184[0:Res:27443.0,481.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),z),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),z)))*.
% 299.79/300.47 46183[0:Res:28312.0,481.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w)))*.
% 299.79/300.47 46181[0:Res:27383.0,481.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),z),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),z)))*.
% 299.79/300.47 46180[0:Res:28009.0,481.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w)))*.
% 299.79/300.47 46167[0:Res:23946.1,481.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(u,v_Procs)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w)))*.
% 299.79/300.47 46159[0:Res:15261.0,481.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v),u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v)))*.
% 299.79/300.47 46192[0:Rew:339.0,46123.1] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w)),u,tc_Com_Opname)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w))))*.
% 299.79/300.47 46194[0:Rew:104.0,46138.2] || -> hBOOL(hAPP(u,v))* hBOOL(hAPP(w,v))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,y,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),w,x)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,y,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))))*.
% 299.79/300.47 46503[0:Res:31533.0,480.0] || -> hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs)))*.
% 299.79/300.47 46502[0:Res:27443.0,480.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),z),v_Procs),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),z),v_Procs)))*.
% 299.79/300.47 46501[0:Res:28312.0,480.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.79/300.47 46499[0:Res:27383.0,480.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),z),v_Procs),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),z),v_Procs)))*.
% 299.79/300.47 46498[0:Res:28009.0,480.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.79/300.47 46485[0:Res:23946.1,480.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> hBOOL(hAPP(u,v_Procs)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)))*.
% 299.79/300.47 46477[0:Res:15261.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))))*.
% 299.79/300.47 46450[0:Res:267.0,480.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(v,w),y)),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(v,w),y))))*.
% 299.79/300.47 46441[0:Res:658.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))))*.
% 299.79/300.47 46704[0:Res:326.2,44639.0] || c_lessequals(u,v,tc_fun(tc_Com_Opname,tc_bool))* c_lessequals(w,x,tc_fun(tc_Com_Opname,tc_bool))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),w),v_Procs)** -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),x),v_x))*.
% 299.79/300.47 47404[0:Res:13238.1,485.1] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)),u))*.
% 299.79/300.47 47403[0:Res:8375.1,485.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** hBOOL(hAPP(x,y))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)),v))*.
% 299.79/300.47 47397[0:Res:652.1,485.1] || c_lessequals(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,tc_Com_Opname)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,tc_Com_Opname)),u))*.
% 299.79/300.47 47635[0:Res:13238.1,484.1] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)),v))*.
% 299.79/300.47 47634[0:Res:8375.1,484.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** hBOOL(hAPP(x,y))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)),w))*.
% 299.79/300.47 47628[0:Res:652.1,484.1] || c_lessequals(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,tc_Com_Opname)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,tc_Com_Opname)),v))*.
% 299.79/300.47 47973[0:Res:13238.1,490.1] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)),u))*.
% 299.79/300.47 47972[0:Res:8375.1,490.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)))* -> hBOOL(hAPP(x,y))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)),v))*.
% 299.79/300.47 47966[0:Res:652.1,490.1] || c_lessequals(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,tc_Com_Opname)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,tc_Com_Opname)),u))*.
% 299.79/300.47 48085[0:Res:13238.1,489.1] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)),v))*.
% 299.79/300.47 48084[0:Res:8375.1,489.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)))* -> hBOOL(hAPP(x,y))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.79/300.47 48078[0:Res:652.1,489.1] || c_lessequals(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,tc_Com_Opname)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,tc_Com_Opname)),v))*.
% 299.79/300.47 48824[0:Res:168.0,619.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a)* equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,tc_Hoare__Mirabelle_Otriple(t_a),tc_fun(x,tc_bool)),v),c_Set_Oinsert(y,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,tc_Hoare__Mirabelle_Otriple(t_a),tc_fun(x,tc_bool))))**.
% 299.79/300.47 48808[0:Res:9258.0,619.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,t_a,tc_fun(w,tc_bool)),u),c_Set_Oinsert(x,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,t_a,tc_fun(w,tc_bool))))**.
% 299.79/300.47 48801[0:Res:3283.1,619.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(w,tc_bool)),v_Procs),c_Set_Oinsert(x,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,u,tc_fun(w,tc_bool))))**.
% 299.79/300.47 48977[0:Res:526.1,483.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x))* -> hBOOL(hAPP(y,x))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,y,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,y,u)),w))*.
% 299.79/300.47 49181[0:Res:526.1,239.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),y)) c_lessequals(x,z,tc_fun(v,tc_bool)) c_Fun_Oinj__on(u,x,v,w) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Fun_Othe__inv__into(x,u,v,w),y)),z))*.
% 299.79/300.47 49304[0:Res:3346.1,488.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,u))* -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,v)),w))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,x,v)),v_x))*.
% 299.79/300.47 49298[0:Res:8366.1,488.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),v_Procs)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,tc_Com_Opname)),u))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,tc_Com_Opname)),v))*.
% 299.79/300.47 49337[0:Res:49314.1,268.0] || hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v),v_Procs))* equal(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)),hAPP(w,v))* c_Fun_Oinj__on(w,v_Procs,tc_Com_Opname,x)* -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),v).
% 299.79/300.47 49336[0:Res:49314.1,481.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w),v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w)))*.
% 299.79/300.47 49335[0:Res:49314.1,480.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs),v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.79/300.47 49408[0:SpR:49342.1,317.0] || hBOOL(hAPP(u,v_x)) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,v),x)),hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),x)))*.
% 299.79/300.47 49407[0:SpR:49342.1,99.1] || hBOOL(hAPP(u,v_x)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),v_Procs),v_Procs)**.
% 299.79/300.47 49406[0:SpR:49342.1,438.1] || hBOOL(hAPP(u,v_x)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w),v_Procs),v_Procs)**.
% 299.79/300.47 50512[0:MRR:50478.0,264.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oimage(w,x,v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(y,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,y,u,x,v),x,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))**.
% 299.79/300.47 51626[0:Rew:11.0,51625.3] || equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) c_lessequals(w,x,tc_fun(v,tc_bool))* c_Fun_Oinj__on(y,x,v,z)* -> equal(hAPP(c_Set_Oimage(y,v,z),c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))**.
% 299.79/300.47 52817[0:SpR:24019.2,475.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(v_x,u,w),v)),hAPP(c_Set_Oimage(v_x,u,w),v))**.
% 299.79/300.47 53798[0:SpR:53771.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Option_Othe(x),v,y)),z))* -> equal(hAPP(c_Set_Oinsert(w,x1),hAPP(c_Set_Oimage(c_Option_Othe(x),u,x1),z)),hAPP(c_Set_Oimage(c_Option_Othe(x),u,x1),z))**.
% 299.79/300.47 53829[0:SpR:53772.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(w),x,v,y)),z))* -> equal(hAPP(c_Set_Oinsert(x,x1),hAPP(c_Set_Oimage(c_Option_Othe(w),u,x1),z)),hAPP(c_Set_Oimage(c_Option_Othe(w),u,x1),z))**.
% 299.79/300.47 54136[0:SpR:52997.1,118.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(c_Fun_Ocomp(c_Set_Oinsert(v_Procs,u),c_Fun_Ofun__upd(v,w,v_x,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_Procs,u),v,y,z,x),w,v_x,x,z))*.
% 299.79/300.47 54112[0:SpR:52997.1,71.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,w),v,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(v_Procs,w),u,x),v_x),v_x)**.
% 299.79/300.47 54111[0:SpR:52997.1,373.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,w),v,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(v_Procs,w),u,x),v_x),v_x)**.
% 299.79/300.47 54327[0:SpR:54251.0,56.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool))))* -> equal(c_HOL_Ominus__class_Ominus(w,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w))**.
% 299.79/300.47 56224[0:SpR:30368.2,317.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),y)))*.
% 299.79/300.47 56666[0:SpR:30928.2,317.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w),y)))*.
% 299.79/300.47 58822[0:SpL:223.1,15629.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w))* -> hBOOL(hAPP(c_Set_Oinsert(y,z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_Set_Oinsert(y,z),x1)))*.
% 299.79/300.47 58819[0:SpL:33303.0,15629.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v)))*.
% 299.79/300.47 58690[0:SpL:71.2,15629.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(x,w,u,y) hBOOL(v) -> hBOOL(hAPP(c_Fun_Othe__inv__into(w,x,u,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Fun_Othe__inv__into(w,x,u,y),z)))*.
% 299.79/300.47 58689[0:SpL:373.2,15629.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(x,w,u,y) hBOOL(v) -> hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(w,x,u,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Hilbert__Choice_Oinv__into(w,x,u,y),z)))*.
% 299.79/300.47 59330[0:SpL:223.1,15857.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w))* -> hBOOL(hAPP(c_Set_Oinsert(y,z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Set_Oinsert(y,z),x2)))*.
% 299.79/300.47 59327[0:SpL:33303.0,15857.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),w)))*.
% 299.79/300.47 59198[0:SpL:71.2,15857.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(x,w,u,y) hBOOL(v) -> hBOOL(hAPP(c_Fun_Othe__inv__into(w,x,u,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Fun_Othe__inv__into(w,x,u,y),x1)))*.
% 299.79/300.47 59197[0:SpL:373.2,15857.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(x,w,u,y) hBOOL(v) -> hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(w,x,u,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Hilbert__Choice_Oinv__into(w,x,u,y),x1)))*.
% 299.79/300.47 60389[7:SpR:188.1,58968.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Ovimage(c_COMBK(v,u,y),y,u),w)))* equal(c_Set_Ovimage(c_COMBK(v,u,y),y,u),v_x) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))).
% 299.79/300.47 60502[0:SpR:188.1,58969.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Ovimage(c_COMBK(v,u,y),y,u),w)))* equal(c_Set_Ovimage(c_COMBK(v,u,y),y,u),v_Procs) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))).
% 299.79/300.47 60575[7:SpR:188.1,59476.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,y),y,u),x)))* equal(c_Set_Ovimage(c_COMBK(v,u,y),y,u),v_x) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))).
% 299.79/300.47 60648[0:SpR:188.1,59477.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,y),y,u),x)))* equal(c_Set_Ovimage(c_COMBK(v,u,y),y,u),v_Procs) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))).
% 299.79/300.47 60833[0:SpR:188.1,59017.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Ovimage(c_COMBK(v,u,y),y,u),w)))* -> c_Hoare__Mirabelle_Ohoare__valids(z,c_Set_Ovimage(c_COMBK(v,u,y),y,u),t_a)* hBOOL(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))).
% 299.79/300.47 60906[0:SpR:188.1,59525.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,y),y,u),x)))* -> c_Hoare__Mirabelle_Ohoare__valids(z,c_Set_Ovimage(c_COMBK(v,u,y),y,u),t_a)* hBOOL(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))).
% 299.79/300.47 62442[0:SSi:62229.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),u) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),u,tc_fun(w,tc_bool))*.
% 299.79/300.47 63572[4:Res:62367.1,47549.0] || equal(c_HOL_Ominus__class_Ominus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool),u,tc_bool),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool)) -> hBOOL(c_HOL_Ominus__class_Ominus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_bool),u,tc_bool))*.
% 299.79/300.47 64475[0:SpR:21893.0,662.1] || hBOOL(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),tc_Com_Opname,w)))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),v_x)).
% 299.79/300.47 64474[0:SpR:21267.0,662.1] || hBOOL(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),v_x),tc_Com_Opname,w)))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),v_x)).
% 299.79/300.47 64862[0:SpL:28747.0,15629.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w)))*.
% 299.79/300.47 64861[0:SpL:28747.0,15857.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),x)))*.
% 299.79/300.47 64982[0:SpL:28748.0,15629.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w)))*.
% 299.79/300.47 64981[0:SpL:28748.0,15857.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),x)))*.
% 299.79/300.47 65102[0:SpL:28902.0,15629.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w)))*.
% 299.79/300.47 65101[0:SpL:28902.0,15857.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),x)))*.
% 299.79/300.47 65222[0:SpL:28903.0,15629.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w)))*.
% 299.79/300.47 65221[0:SpL:28903.0,15857.0] || hBOOL(v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),x)))*.
% 299.79/300.47 68244[0:SpR:1250.3,614.2] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Ogroup__add(u) class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) c_Finite__Set_Ofinite(v,w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u))**.
% 299.79/300.47 69694[0:Res:84.1,6239.0] || c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))).
% 299.79/300.47 72471[0:SpL:197.1,12554.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),z))* -> hBOOL(hAPP(hAPP(c_in(w),z),hAPP(c_Set_Oimage(u,v,w),x)))*.
% 299.79/300.47 72972[7:Rew:339.0,72951.1] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v_x),w)),u,t_a)),hAPP(c_Set_Oinsert(v,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v_x),w))))*.
% 299.79/300.47 73085[7:Res:71608.1,199.0] || equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_in(t_a),v_x),v,u,w)),v_x)** c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.47 73075[7:Res:71608.1,488.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)),u))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)),v))*.
% 299.79/300.47 74348[7:SpL:71835.1,358.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),v_x,tc_fun(w,tc_bool))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> c_lessequals(x,v_x,tc_fun(v,tc_bool)).
% 299.79/300.47 74345[7:SpL:71835.1,231.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_lessequals(x,v_x,tc_fun(w,tc_bool)) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),v_x,tc_fun(v,tc_bool))*.
% 299.79/300.47 74248[7:SpL:71835.1,358.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_lessequals(v_x,hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> c_lessequals(v_x,x,tc_fun(v,tc_bool)).
% 299.79/300.47 74521[7:Rew:538.0,73916.1] || equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),hAPP(c_Set_Ovimage(u,v,w),x)),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))*.
% 299.79/300.47 74522[7:Rew:538.0,73913.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),hAPP(c_Set_Oimage(u,v,w),x)),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)))*.
% 299.79/300.47 73710[7:SpR:71835.1,507.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),hAPP(c_Set_Oimage(u,v,w),x)),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),x)))*.
% 299.79/300.47 73694[7:SpR:71835.1,162.0] || equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),hAPP(c_Set_Ovimage(u,v,w),x)),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),x)))*.
% 299.79/300.47 73612[7:SpR:71835.1,486.1] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,u,v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,u,v,tc_fun(x,tc_bool)))**.
% 299.79/300.47 75621[0:SSi:75496.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)))),tc_fun(y,tc_bool))*.
% 299.79/300.47 75622[0:SSi:75495.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),hAPP(c_Set_Oimage(y,u,x),w)))))*.
% 299.79/300.47 75761[7:SpL:71883.1,275.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_fun(w,tc_bool))))*.
% 299.79/300.47 76089[0:SSi:75950.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(x,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))),x1)),tc_fun(y,tc_bool))*.
% 299.79/300.47 76090[0:SSi:75949.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(y,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(y,u,x),w)),x1))))*.
% 299.79/300.47 77187[7:SpL:533.0,74788.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),x)* -> hBOOL(x)*.
% 299.79/300.47 77348[0:Res:2399.2,430.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))* -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)) c_lessequals(v,w,tc_fun(u,tc_bool)).
% 299.79/300.47 77729[0:SpL:537.1,5892.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),x))* -> hBOOL(hAPP(c_COMBS(c_in(y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),z,x1,x2),x))*.
% 299.79/300.47 77728[0:SpL:534.1,5892.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),x))* -> hBOOL(hAPP(c_COMBS(c_in(y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),z,x1,x2),x))*.
% 299.79/300.47 77722[0:SpL:544.1,5892.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))* -> hBOOL(hAPP(c_COMBS(c_in(x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,z,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))*.
% 299.79/300.47 77721[0:SpL:543.1,5892.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))* -> hBOOL(hAPP(c_COMBS(c_in(x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,z,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))*.
% 299.79/300.47 78499[4:Res:77988.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),c_Set_Oinsert(x,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,v,tc_fun(w,tc_bool))))**.
% 299.79/300.47 78617[0:Rew:584.0,78607.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(v,v_x))) -> hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,c_COMBS(c_in(u),v,x,y,z),tc_Com_Opname)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,c_COMBS(c_in(u),v,x,y,z),tc_Com_Opname)))*.
% 299.79/300.47 78618[0:Rew:584.0,78606.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(v,v_x))) -> hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,c_COMBS(c_in(u),v,x,y,z),tc_Com_Opname)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,c_COMBS(c_in(u),v,x,y,z),tc_Com_Opname)))*.
% 299.79/300.47 78709[4:Res:78665.1,482.2] || equal(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),v_x)** hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,y,u)))* hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,y,u)))* -> hBOOL(hAPP(y,v))*.
% 299.79/300.47 79020[0:Res:15630.1,280.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(x,v),y)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,z),x1),x2,hAPP(c_in(u),v),z),x,u,tc_fun(x3,tc_bool)),y))*.
% 299.79/300.47 78970[0:SpR:9493.1,15630.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(v_x,t_a),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),u)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.47 78967[0:SpR:8498.1,15630.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(y,z),v),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))) hBOOL(hAPP(c_Set_Oinsert(y,z),u)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(u,v),w),x,c_Set_Oinsert(y,z),v))*.
% 299.79/300.47 79065[0:Res:78077.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Set_Oinsert(y,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(y,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),u,v,tc_fun(w,tc_bool))))**.
% 299.79/300.47 79093[7:Res:78199.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),hAPP(c_in(x),v_x)),c_Set_Oinsert(y,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(y,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_in(x),v_x),u,v,tc_fun(w,tc_bool))))**.
% 299.79/300.47 79240[0:Res:15858.1,280.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(x,v),y)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,hAPP(c_Set_Oinsert(w,x1),x2),hAPP(c_in(u),v),x1),x,u,tc_fun(x3,tc_bool)),y))*.
% 299.79/300.47 79190[0:SpR:9493.1,15858.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v_x,t_a),w),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),v)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v_x,t_a),w)).
% 299.79/300.47 79187[0:SpR:8498.1,15858.1] || equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(y,z),w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))) hBOOL(hAPP(c_Set_Oinsert(y,z),v)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(y,z),w))*.
% 299.79/300.47 80305[0:SpL:21268.0,263.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x))) -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(w,u),x),y,z)))* equal(v,w).
% 299.79/300.47 80271[0:SpL:21268.0,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y)) -> hBOOL(hAPP(x,hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x),hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y),z,x1))))*.
% 299.79/300.47 79902[0:SpR:614.2,21268.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u),x,z)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u))**.
% 299.79/300.47 79844[0:SpR:99.1,21268.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),y,x,z)),y)**.
% 299.79/300.47 79843[0:SpR:438.1,21268.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),y,x,z)),y)**.
% 299.79/300.47 79766[0:SpR:21268.0,584.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),u,hAPP(u,x1),z,x2)),hAPP(hAPP(u,x1),hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),u,hAPP(u,x1),z,x2))))*.
% 299.79/300.47 79764[0:SpR:21268.0,584.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),v,hAPP(v,x1),z,x2)),hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),v,hAPP(v,x1),z,x2)),hAPP(v,x1)))*.
% 299.79/300.47 79763[0:SpR:21268.0,34.1] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,x,y),u),hAPP(hAPP(c_Set_Ovimage(v,x,y),u),z),w,x1))))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,x,y),u),z)).
% 299.79/300.47 79707[0:SpR:21268.0,518.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,y),z))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),z)).
% 299.79/300.47 81500[0:SpL:21894.0,263.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x))) -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(w,u),x),c_Set_Oinsert(w,u),y,z)))* equal(v,w).
% 299.79/300.47 81466[0:SpL:21894.0,33.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y)) -> hBOOL(hAPP(x,hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Set_Ovimage(u,v,w),x),y),hAPP(c_Set_Ovimage(u,v,w),x),z,x1))))*.
% 299.79/300.47 81096[0:SpR:614.2,21894.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,z)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u))**.
% 299.79/300.47 81038[0:SpR:99.1,21894.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,z)),y)**.
% 299.79/300.47 81037[0:SpR:438.1,21894.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,z)),y)**.
% 299.79/300.47 80960[0:SpR:21894.0,584.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(u,x1),u,z,x2)),hAPP(hAPP(u,x1),hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(u,x1),u,z,x2))))*.
% 299.79/300.47 80958[0:SpR:21894.0,584.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(v,x1),v,z,x2)),hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(v,x1),v,z,x2)),hAPP(v,x1)))*.
% 299.79/300.47 80957[0:SpR:21894.0,34.1] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Set_Ovimage(v,x,y),u),z),hAPP(c_Set_Ovimage(v,x,y),u),w,x1))))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,x,y),u),z)).
% 299.79/300.47 80901[0:SpR:21894.0,518.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,y),z))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),z)).
% 299.79/300.47 81854[0:SpR:537.1,5879.1] class_Lattices_Olattice(u) class_Lattices_Oupper__semilattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),z,x1,x2),y),v)*.
% 299.79/300.47 81853[0:SpR:534.1,5879.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Oupper__semilattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),z,x1,x2),y),v)*.
% 299.79/300.47 81851[0:SpR:536.1,5879.1] class_Lattices_Olattice(u) class_Lattices_Oupper__semilattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),v)*.
% 299.79/300.47 81850[0:SpR:535.1,5879.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Oupper__semilattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),v)*.
% 299.79/300.47 82326[0:SpR:537.1,5880.1] class_Lattices_Olattice(u) class_Lattices_Olattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),z,x1,x2),y),v)*.
% 299.79/300.47 82325[0:SpR:534.1,5880.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Olattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),z,x1,x2),y),v)*.
% 299.79/300.47 82323[0:SpR:536.1,5880.1] class_Lattices_Olattice(u) class_Lattices_Olattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),v)*.
% 299.79/300.47 82322[0:SpR:535.1,5880.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Olattice(v) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),v)*.
% 299.79/300.47 82743[0:Res:247.4,7671.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,v,tc_fun(u,tc_bool))* c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(w,u),u)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(v,u),u)*.
% 299.79/300.47 82742[0:Res:248.4,7671.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,v,tc_fun(u,tc_bool))* c_lessequals(x,c_Finite__Set_Olinorder__class_OMin(v,u),u)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) c_lessequals(x,c_Finite__Set_Olinorder__class_OMin(w,u),u)*.
% 299.79/300.47 82835[7:Res:77991.0,481.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,x),v_x)),y),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,x),v_x)),y)))*.
% 299.79/300.47 82834[7:Res:77991.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,y),v_x)),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,y),v_x))))*.
% 299.79/300.47 84201[7:SpL:533.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_x) -> .
% 299.79/300.47 84926[4:SpL:131.0,78744.0] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z))),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z,t_a).
% 299.79/300.47 84925[4:SpL:158.0,78744.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z))),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z,t_a).
% 299.79/300.47 84991[0:Res:84957.0,481.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,x),v)),y),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,x),v)),y)))*.
% 299.79/300.47 84990[0:Res:84957.0,480.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(v,y),v)),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(v,y),v))))*.
% 299.79/300.47 85441[4:SpR:78507.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,w),v,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(v_x,w),u,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))**.
% 299.79/300.47 85440[4:SpR:78507.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,w),v,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(v_x,w),u,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))**.
% 299.79/300.47 85418[4:SpR:78507.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),v),c_Set_Oinsert(v_x,w),u,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,w),u,tc_fun(x,tc_bool))))*.
% 299.79/300.47 85845[0:Res:9066.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),u),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w)),x,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),u),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),w)),x),v,t_a)*.
% 299.79/300.47 85937[0:SpL:24914.0,13582.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x)) hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),v_x))),v))* -> .
% 299.79/300.47 86680[0:Res:86261.1,199.0] || equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_in(t_a),v_x),v,u,w)),v_Procs)** c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.47 86669[0:Res:86261.1,488.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_Procs)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)),u))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)),v))*.
% 299.79/300.47 86746[4:SpL:533.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool),v_x)** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_Procs) -> .
% 299.79/300.47 88432[0:Res:8176.1,202.1] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,w),c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool))),tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),w) -> c_Fun_Oinj__on(v,c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),w,w).
% 299.79/300.47 88653[7:SpL:533.0,88086.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_x) hBOOL(c_HOL_Ominus__class_Ominus(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool))* -> .
% 299.79/300.47 88981[0:SpR:338.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),hAPP(c_Set_Oinsert(u,v),z)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z)))*.
% 299.79/300.47 88916[0:SpR:339.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),z))*.
% 299.79/300.47 88911[0:SpR:338.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(y,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),hAPP(c_Set_Oinsert(y,u),z)))*.
% 299.79/300.47 88886[0:SpR:465.1,14196.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1,x2),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,u,z),w),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool)))),w))*.
% 299.79/300.47 88854[0:SpR:71.2,14196.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Fun_Othe__inv__into(w,x,u,y),z,x1),hAPP(c_Set_Oinsert(v,x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),hAPP(x,v)))*.
% 299.79/300.47 88853[0:SpR:373.2,14196.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x1),hAPP(c_Set_Oinsert(v,x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),hAPP(x,v)))*.
% 299.79/300.47 89179[0:SpL:24914.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),v)* -> c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),v)*.
% 299.79/300.47 89231[7:SpR:78590.1,410.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 89693[7:Res:89344.1,619.0] || equal(c_Set_Oinsert(v_x,t_a),u) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,t_a,tc_fun(w,tc_bool)),u),c_Set_Oinsert(x,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,t_a,tc_fun(w,tc_bool))))**.
% 299.79/300.47 90021[4:SpR:78660.1,410.0] || equal(hAPP(u,v_x),v_x) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 90837[4:Res:90134.1,619.0] || equal(hAPP(u,v_x),v_x) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,t_a,tc_fun(w,tc_bool)),u),c_Set_Oinsert(x,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,t_a,tc_fun(w,tc_bool))))**.
% 299.79/300.47 91363[0:Rew:91288.1,91215.1] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) hBOOL(hAPP(hAPP(c_in(x),y),z)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,tc_fun(x,tc_bool))))*.
% 299.79/300.47 91364[0:Rew:91288.1,91053.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,tc_fun(y,tc_bool))))*.
% 299.79/300.47 91841[4:SpL:329.1,78747.0] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname),tc_fun(v,tc_bool))* equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)).
% 299.79/300.47 91885[4:Rew:104.0,91837.1] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),tc_Com_Opname),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))).
% 299.79/300.47 91919[0:SpR:79073.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,x),w,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oinsert(v_Procs,x),u,y),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.79/300.47 91918[0:SpR:79073.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,x),w,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oinsert(v_Procs,x),u,y),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.79/300.47 91907[0:SpR:79073.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_Procs,x),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_Procs,x),v,tc_fun(y,tc_bool))))*.
% 299.79/300.47 92071[7:SpR:79101.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(v),v_x)),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,x),w,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oinsert(v_x,x),u,y),hAPP(c_in(v),v_x)),hAPP(c_in(v),v_x))**.
% 299.79/300.47 92070[7:SpR:79101.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(v),v_x)),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,x),w,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oinsert(v_x,x),u,y),hAPP(c_in(v),v_x)),hAPP(c_in(v),v_x))**.
% 299.79/300.47 92051[7:SpR:79101.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_in(u),v_x),v),w),c_Set_Oinsert(v_x,x),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_in(u),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,x),v,tc_fun(y,tc_bool))))*.
% 299.79/300.47 92588[0:SpL:5227.1,12998.0] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,u),v,w,x) c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),y),t_a)* -> c_Hoare__Mirabelle_Ohoare__valids(z,y,t_a) c_Hoare__Mirabelle_Otriple__valid(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(u,c_Suc(w),v,x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(z,y),t_a)*.
% 299.79/300.47 92960[0:SpR:338.0,5876.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Oinsert(w,u),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)),tc_fun(y,tc_bool))*.
% 299.79/300.47 92893[0:SpR:339.0,5876.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),z,x1,x2),x),tc_fun(y,tc_bool))*.
% 299.79/300.47 92888[0:SpR:338.0,5876.0] || -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),z,x1,x2),hAPP(c_Set_Oinsert(u,v),x)),tc_fun(y,tc_bool))*.
% 299.79/300.47 92863[0:SpR:465.1,5876.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_Set_Oimage(x,u,y),w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Set_Oimage(c_Fun_Ofun__upd(x,v,x1,u,y),u,y),x2,x3,x4),w),tc_fun(z,tc_bool))*.
% 299.79/300.47 92831[0:SpR:71.2,5876.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Fun_Othe__inv__into(w,x,u,y),x1,x2,x3),hAPP(x,v)),tc_fun(z,tc_bool))*.
% 299.79/300.47 92830[0:SpR:373.2,5876.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Hilbert__Choice_Oinv__into(w,x,u,y),x1,x2,x3),hAPP(x,v)),tc_fun(z,tc_bool))*.
% 299.79/300.47 6659[0:SpR:329.1,687.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),tc_Com_Opname),tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v_x)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),tc_Com_Opname)).
% 299.79/300.47 6658[0:SpR:329.1,686.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),tc_Com_Opname),tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v_x)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),tc_Com_Opname)).
% 299.79/300.47 12681[0:Res:1103.1,519.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),t_a) hBOOL(hAPP(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))))* hBOOL(hAPP(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))))*.
% 299.79/300.47 17361[0:Res:172.2,148.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),u) -> equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMax(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),u)),v))*.
% 299.79/300.47 17479[0:Res:171.2,148.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),u) -> equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMin(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),u)),v))*.
% 299.79/300.47 18179[0:SpR:600.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.47 18167[0:SpR:188.1,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),w),y))* -> c_lessequals(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Ovimage(c_COMBK(v,u,z),z,u),x,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.47 18379[0:SpR:600.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),u,z),y)))*.
% 299.79/300.47 18367[0:SpR:188.1,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),w),y))* -> hBOOL(hAPP(hAPP(c_in(z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,x1),x1,u),x,z),y)))*.
% 299.79/300.47 19103[0:SpR:196.1,545.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),z)) -> hBOOL(hAPP(hAPP(c_in(x1),y),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,x1),z)))*.
% 299.79/300.47 19102[0:SpR:196.1,362.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),z)) -> c_lessequals(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Ovimage(u,v,w),x,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.47 19317[0:Res:304.3,251.1] class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || c_lessequals(w,x,tc_fun(u,v)) c_lessequals(y,x,tc_fun(u,v)) -> c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),w),y),z),hAPP(x,z),v)*.
% 299.79/300.47 19805[0:SpR:104.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(y,w,tc_fun(z,tc_bool)),tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_HOL_Ouminus__class_Ouminus(y,tc_fun(z,tc_bool))),v,u),u)*.
% 299.79/300.47 19792[0:SpR:104.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),u,y),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.47 19985[0:SpR:64.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool))),z))* -> c_lessequals(hAPP(c_Set_Oinsert(x,y),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oinsert(x,y),v,u),u)*.
% 299.79/300.47 19972[0:SpR:64.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool))),hAPP(c_Set_Ovimage(c_Set_Oinsert(w,x),u,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(w,x),v),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.47 20373[0:SpR:584.0,438.1] || c_Fun_Oinj__on(c_COMBS(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_COMBS(u,v,w,x,y),z,x1),hAPP(hAPP(u,x2),hAPP(v,x2))),x2)**.
% 299.79/300.47 20372[0:SpR:586.0,438.1] || c_Fun_Oinj__on(hAPP(c_COMBB(u,v,w,x),y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_COMBB(u,v,w,x),y),z,x1),hAPP(u,hAPP(y,x2))),x2)**.
% 299.79/300.47 20371[0:SpR:585.0,438.1] || c_Fun_Oinj__on(hAPP(c_COMBC(u,v,w,x),y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_COMBC(u,v,w,x),y),z,x1),hAPP(hAPP(u,x2),y)),x2)**.
% 299.79/300.47 20368[0:SpR:11499.0,438.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x,y),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.47 20331[0:SpR:14526.0,438.1] || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),x,y),c_Orderings_Obot__class_Obot(tc_bool)),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),u))**.
% 299.79/300.47 20283[0:SpR:438.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) hBOOL(hAPP(hAPP(c_in(y),hAPP(v,z)),x1)) -> c_lessequals(z,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,x),y,u),u)*.
% 299.79/300.47 20279[0:SpR:438.1,176.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),hAPP(c_Set_Ovimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,z),hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.47 20517[0:SpR:584.0,99.1] || c_Fun_Oinj__on(c_COMBS(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_COMBS(u,v,w,x,y),z,x1),hAPP(hAPP(u,x2),hAPP(v,x2))),x2)**.
% 299.79/300.47 20516[0:SpR:586.0,99.1] || c_Fun_Oinj__on(hAPP(c_COMBB(u,v,w,x),y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_COMBB(u,v,w,x),y),z,x1),hAPP(u,hAPP(y,x2))),x2)**.
% 299.79/300.47 20515[0:SpR:585.0,99.1] || c_Fun_Oinj__on(hAPP(c_COMBC(u,v,w,x),y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_COMBC(u,v,w,x),y),z,x1),hAPP(hAPP(u,x2),y)),x2)**.
% 299.79/300.47 20512[0:SpR:11499.0,99.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x,y),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.47 20508[0:SpR:336.0,99.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))**.
% 299.79/300.47 20475[0:SpR:14526.0,99.1] || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),x,y),c_Orderings_Obot__class_Obot(tc_bool)),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),u))**.
% 299.79/300.47 20464[0:SpR:331.0,99.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,w),x),x)**.
% 299.79/300.47 20425[0:SpR:99.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) hBOOL(hAPP(hAPP(c_in(y),hAPP(v,z)),x1)) -> c_lessequals(z,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,x),y,u),u)*.
% 299.79/300.47 20421[0:SpR:99.1,176.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),hAPP(c_Set_Ovimage(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,z),hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.47 20732[0:Res:313.1,402.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Oimage(x,w,y),v),hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool))* -> equal(hAPP(c_Set_Oimage(x,w,y),u),hAPP(c_Set_Oimage(x,w,y),v)).
% 299.79/300.47 20778[0:Res:129.1,402.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Ovimage(x,y,w),v),hAPP(c_Set_Ovimage(x,y,w),u),tc_fun(y,tc_bool))* -> equal(hAPP(c_Set_Ovimage(x,y,w),u),hAPP(c_Set_Ovimage(x,y,w),v)).
% 299.79/300.47 21007[0:SpR:584.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_COMBS(u,v,w,x,y),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(c_Set_Oinsert(hAPP(hAPP(u,x2),hAPP(v,x2)),x1),hAPP(c_Set_Oimage(c_COMBS(u,v,w,x,y),z,x1),x3)))*.
% 299.79/300.47 21006[0:SpR:586.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(c_Set_Oinsert(hAPP(u,hAPP(y,x2)),x1),hAPP(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),z,x1),x3)))*.
% 299.79/300.47 21005[0:SpR:585.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_COMBC(u,v,w,x),y),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(c_Set_Oinsert(hAPP(hAPP(u,x2),y),x1),hAPP(c_Set_Oimage(hAPP(c_COMBC(u,v,w,x),y),z,x1),x3)))*.
% 299.79/300.47 21002[0:SpR:11499.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x,y),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),z)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),y),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x,y),z)))*.
% 299.79/300.47 20998[0:SpR:336.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w),y)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),y)))*.
% 299.79/300.47 20965[0:SpR:14526.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),x,y),hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),u),x),z)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),y),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),x,y),z)))*.
% 299.79/300.47 20954[0:SpR:331.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,w),y)))*.
% 299.79/300.47 20933[0:SpR:353.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(y,v),z),w),x1)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(y,v),hAPP(c_Set_Oinsert(u,v),z)),x),hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),x1)))*.
% 299.79/300.47 20897[0:SpR:317.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oinsert(hAPP(u,v),w),x,y,z,x1),hAPP(c_Set_Oimage(u,x2,w),x3)),hAPP(hAPP(c_Set_Oimage(u,x2,w),hAPP(c_Set_Oinsert(v,x2),x3)),hAPP(x,hAPP(c_Set_Oimage(u,x2,w),x3))))*.
% 299.79/300.47 20896[0:SpR:317.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oinsert(hAPP(v,w),x),y,z,x1),hAPP(c_Set_Oimage(v,x2,x),x3)),hAPP(hAPP(u,hAPP(c_Set_Oimage(v,x2,x),x3)),hAPP(c_Set_Oimage(v,x2,x),hAPP(c_Set_Oinsert(w,x2),x3))))*.
% 299.79/300.47 20887[0:SpR:317.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Set_Oimage(w,x,y),z)),x1)) -> c_lessequals(hAPP(c_Set_Oimage(w,x,y),hAPP(c_Set_Oinsert(x2,x),z)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oinsert(hAPP(w,x2),y),v,u),u)*.
% 299.79/300.47 20875[0:SpR:317.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),hAPP(c_Set_Ovimage(c_Set_Oinsert(hAPP(v,z),x),u,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(z,w),y)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.79/300.47 20845[0:SpR:317.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Set_Oinsert(w,x),y)),z)) -> c_lessequals(hAPP(c_Set_Oinsert(hAPP(x1,w),x2),hAPP(c_Set_Oimage(x1,x,x2),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(x1,x,x2),v,u),u)*.
% 299.79/300.47 20838[0:SpR:317.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Ovimage(c_Set_Oimage(y,w,z),u,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(hAPP(y,v),z),hAPP(c_Set_Oimage(y,w,z),x)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.79/300.47 21277[0:Res:168.0,469.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x),t_a) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x)),w,tc_Hoare__Mirabelle_Otriple(t_a))),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x)))**.
% 299.79/300.47 21669[0:SpL:21267.0,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),w)) -> hBOOL(hAPP(v,w)) hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_Com_Opname,x),w))*.
% 299.79/300.47 21667[0:SpL:21267.0,324.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),w,tc_fun(u,tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_Com_Opname,x),w,tc_fun(u,tc_bool))*.
% 299.79/300.47 21610[0:SpL:21267.0,57.1] class_OrderedGroup_Olordered__ab__group__add(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),u)),c_HOL_Ozero__class_Ozero(u))** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),tc_Com_Opname,v),c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.47 21513[0:SpR:130.1,21267.0] class_HOL_Ominus(u) || -> equal(hAPP(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),tc_Com_Opname,x)),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))**.
% 299.79/300.47 21453[0:SpR:21267.0,517.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x),tc_Com_Opname,x)))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x)).
% 299.79/300.47 21451[0:SpR:21267.0,518.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x),tc_Com_Opname,x)))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x)).
% 299.79/300.47 21903[0:Res:168.0,464.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x),t_a) equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x)),v,w,tc_Hoare__Mirabelle_Otriple(t_a))),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x)))**.
% 299.79/300.47 22297[0:SpL:21893.0,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),w)) -> hBOOL(hAPP(v,w)) hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,x),w))*.
% 299.79/300.47 22295[0:SpL:21893.0,324.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),w,tc_fun(u,tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,x),w,tc_fun(u,tc_bool))*.
% 299.79/300.47 22238[0:SpL:21893.0,57.1] class_OrderedGroup_Olordered__ab__group__add(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),u)),c_HOL_Ozero__class_Ozero(u))** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.47 22140[0:SpR:130.1,21893.0] class_HOL_Ominus(u) || -> equal(hAPP(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_Com_Opname,x)),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))**.
% 299.79/300.47 22079[0:SpR:21893.0,517.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),tc_Com_Opname,x)))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x)).
% 299.79/300.47 22077[0:SpR:21893.0,518.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),tc_Com_Opname,x)))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x)).
% 299.79/300.47 22435[0:SpL:97.1,469.0] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(w),y),v)) -> equal(hAPP(c_Fun_Othe__inv__into(v,u,w,x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(hAPP(c_Set_Oimage(u,w,x),v),c_Fun_Othe__inv__into(v,u,w,x),y,x,w)),y)**.
% 299.79/300.47 22434[0:SpL:97.1,464.0] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(w),y),v)) -> equal(hAPP(c_Fun_Othe__inv__into(v,u,w,x),c_ATP__Linkup_Osko__Set__XimageE__1__1(hAPP(c_Set_Oimage(u,w,x),v),y,c_Fun_Othe__inv__into(v,u,w,x),x,w)),y)**.
% 299.79/300.47 22420[0:SpR:97.1,317.0] || c_Fun_Oinj__on(u,v,w,x) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),hAPP(c_Set_Oinsert(y,x),hAPP(c_Set_Oimage(u,w,x),v))),hAPP(c_Set_Oinsert(hAPP(c_Fun_Othe__inv__into(v,u,w,x),y),w),v))**.
% 299.79/300.47 22419[0:SpR:97.1,584.0] || c_Fun_Oinj__on(u,v,w,x) -> equal(hAPP(c_COMBS(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,z,x1,x2),hAPP(c_Set_Oimage(u,w,x),v)),hAPP(v,hAPP(y,hAPP(c_Set_Oimage(u,w,x),v))))**.
% 299.79/300.47 22418[0:SpR:97.1,584.0] || c_Fun_Oinj__on(u,v,w,x) -> equal(hAPP(c_COMBS(y,c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),z,x1,x2),hAPP(c_Set_Oimage(u,w,x),v)),hAPP(hAPP(y,hAPP(c_Set_Oimage(u,w,x),v)),v))**.
% 299.79/300.47 22408[0:SpR:97.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Fun_Oinj__on(v,w,x,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oimage(v,x,y),w)),x1)) -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oimage(c_Fun_Othe__inv__into(w,v,x,y),y,x),z,u),u)*.
% 299.79/300.47 22400[0:SpR:97.1,176.0] || c_Fun_Oinj__on(u,v,w,x) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oimage(u,w,x),v)),hAPP(c_Set_Ovimage(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,z),hAPP(c_Set_Oinsert(v,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.47 22627[0:SpR:158.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),hAPP(c_Set_Oimage(x2,x3,v),x4)),hAPP(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x2,v,w,x3),x3,w),x4),hAPP(x,hAPP(c_Set_Oimage(x2,x3,v),x4))))*.
% 299.79/300.47 22626[0:SpR:158.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oimage(v,w,x),y,z,x1),hAPP(c_Set_Oimage(x2,x3,w),x4)),hAPP(hAPP(u,hAPP(c_Set_Oimage(x2,x3,w),x4)),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,x2,w,x,x3),x3,x),x4)))*.
% 299.79/300.47 22616[0:SpR:158.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Set_Oimage(w,x,y),z)),x1)) -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(x2,w,y,x3,x),x,x3),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oimage(x2,y,x3),v,u),u)*.
% 299.79/300.47 22608[0:SpR:158.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),hAPP(c_Set_Ovimage(c_Set_Oimage(z,x,x1),u,x2),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(c_Fun_Ocomp(z,v,x,x1,w),w,x1),y),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))))))*.
% 299.79/300.47 22586[0:SpR:158.0,687.1] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)) -> hBOOL(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname))))*.
% 299.79/300.47 22585[0:SpR:158.0,686.1] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)) -> hBOOL(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,z,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname))))*.
% 299.79/300.47 22582[0:SpR:158.0,196.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,x) -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),z))),z)**.
% 299.79/300.47 22574[0:SpR:158.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(c_Set_Oimage(y,z,x1),hAPP(c_Set_Oimage(x2,x3,z),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oimage(c_Fun_Ocomp(y,x2,z,x1,x3),x3,x1),v,u),u)*.
% 299.79/300.47 22566[0:SpR:158.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_Set_Oimage(c_Fun_Ocomp(w,x,y,z,x1),x1,z),u,x2),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(w,y,z),hAPP(c_Set_Oimage(x,x1,y),v)),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))))))*.
% 299.79/300.47 22532[0:SpR:158.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w)),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w))**.
% 299.79/300.47 23006[0:SpR:131.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),hAPP(c_Set_Ovimage(x2,w,x3),x4)),hAPP(hAPP(c_Set_Ovimage(c_Fun_Ocomp(x2,u,w,x3,v),v,x3),x4),hAPP(x,hAPP(c_Set_Ovimage(x2,w,x3),x4))))*.
% 299.79/300.47 23005[0:SpR:131.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Ovimage(v,w,x),y,z,x1),hAPP(c_Set_Ovimage(x2,x,x3),x4)),hAPP(hAPP(u,hAPP(c_Set_Ovimage(x2,x,x3),x4)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x2,v,x,x3,w),w,x3),x4)))*.
% 299.79/300.47 22995[0:SpR:131.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Set_Ovimage(w,x,y),z)),x1)) -> c_lessequals(hAPP(c_Set_Ovimage(c_Fun_Ocomp(w,x2,x,y,x3),x3,y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Ovimage(x2,x3,x),v,u),u)*.
% 299.79/300.47 22988[0:SpR:131.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),hAPP(c_Set_Ovimage(c_Set_Ovimage(z,x1,w),u,x2),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,z,w,x,x1),x1,x),y),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))))))*.
% 299.79/300.47 22970[0:SpR:131.0,687.1] || hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)) -> hBOOL(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,v_Procs,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname))))*.
% 299.79/300.47 22969[0:SpR:131.0,686.1] || hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)) -> hBOOL(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,z,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname))))*.
% 299.79/300.47 22958[0:SpR:131.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(c_Set_Ovimage(y,z,x1),hAPP(c_Set_Ovimage(x2,x1,x3),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Ovimage(c_Fun_Ocomp(x2,y,x1,x3,z),z,x3),v,u),u)*.
% 299.79/300.47 22953[0:SpR:131.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_Set_Ovimage(c_Fun_Ocomp(w,x,y,z,x1),x1,z),u,x2),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(x,x1,y),hAPP(c_Set_Ovimage(w,y,z),v)),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))))))*.
% 299.79/300.47 22918[0:SpR:131.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_x)),tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y)),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y))**.
% 299.79/300.47 22911[0:SpR:131.0,196.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,x) -> equal(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z))),z)**.
% 299.79/300.47 23344[0:SpR:460.1,9268.0] || class_Lattices_Olattice(t_b) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g)).
% 299.79/300.47 23618[0:Rew:523.1,23533.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v_x),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),tc_Com_Opname,v),v_x)),hAPP(w,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v_x,v_x)),hAPP(w,v_x)))**.
% 299.79/300.47 23619[0:Rew:523.1,23532.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v_x),tc_Com_Opname,v),v_x)),hAPP(w,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v_x,v_x)),hAPP(w,v_x)))**.
% 299.79/300.47 23475[0:SpR:523.1,9268.0] class_Lattices_Olattice(u) || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w)).
% 299.79/300.47 24324[0:SpR:393.1,97.1] || c_Fun_Oinj__on(c_COMBK(u,v,w),x,w,v) -> equal(x,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(x,c_COMBK(u,v,w),w,v),v,w),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),x)**.
% 299.79/300.47 24809[0:SpR:614.2,584.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,y,z,x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x2,w,u)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x2,w,u),hAPP(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x2,w,u))))*.
% 299.79/300.47 24808[0:SpR:614.2,584.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(hAPP(c_COMBS(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),y,z,x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x2,w,u)),hAPP(hAPP(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x2,w,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x2,w,u)))*.
% 299.79/300.47 24905[0:SpL:21893.0,467.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> equal(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,x,u),v_x),c_Set_Oimage(w,x,u),tc_Com_Opname,y),w,x,u),v)),v)**.
% 299.79/300.47 24904[0:SpL:21267.0,467.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> equal(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),v_x),tc_Com_Opname,y),w,x,u),v)),v)**.
% 299.79/300.47 25441[0:SpL:512.0,19641.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oimage(hAPP(c_COMBB(u,v,w,y),x),y,w),z))))* -> c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oimage(hAPP(c_COMBB(u,v,w,y),x),y,w),z,t_a).
% 299.79/300.47 25364[0:SpR:512.0,96.1] || c_Fun_Oinj__on(hAPP(c_COMBB(u,v,w,x),y),z,x,w) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(z,hAPP(c_COMBB(u,v,w,x),y),x,w),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),z)),w,x)*.
% 299.79/300.47 25520[0:Rew:586.0,25443.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1))))* -> equal(hAPP(w,hAPP(y,hAPP(c_Hilbert__Choice_Oinv__into(x1,hAPP(c_COMBB(w,x,u,z),y),z,u),v))),v)**.
% 299.79/300.47 26013[0:Rew:339.0,25957.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),x)),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))**.
% 299.79/300.47 25953[0:SpR:317.0,339.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oinsert(x,w),y))),z),hAPP(c_Set_Oinsert(hAPP(v,x),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),y)),z)))*.
% 299.79/300.47 25930[0:SpR:339.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x)),t_a) hBOOL(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x))))))*.
% 299.79/300.47 25876[0:SpR:339.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x,hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)))**.
% 299.79/300.47 26167[0:SpR:64.0,338.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(u,v),x)))**.
% 299.79/300.47 26163[0:SpR:317.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oinsert(y,x),z))),hAPP(c_Set_Oinsert(hAPP(w,y),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oimage(w,x,u),z))))*.
% 299.79/300.47 26138[0:SpR:338.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(y,v),z))),hAPP(c_Set_Oinsert(hAPP(u,y),w),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z))))*.
% 299.79/300.47 26871[0:SpL:56.1,62.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(w,u),x),tc_fun(u,tc_bool)),u)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),x,tc_fun(u,tc_bool)),u)*.
% 299.79/300.47 26844[0:SpR:317.0,56.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(v,y,u),hAPP(c_Set_Oinsert(w,y),z)),x,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(v,y,u),z),x,tc_fun(u,tc_bool)))**.
% 299.79/300.47 26823[0:SpR:56.1,63.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),x,tc_fun(u,tc_bool)),u)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(w,u),x),tc_fun(u,tc_bool)),u)*.
% 299.79/300.47 26944[0:SpR:64.0,424.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)).
% 299.79/300.47 26939[0:SpR:317.0,424.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x)) c_lessequals(hAPP(c_Set_Oimage(v,y,u),z),x,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(v,y,u),hAPP(c_Set_Oinsert(w,y),z)),x,tc_fun(u,tc_bool))*.
% 299.79/300.47 27011[0:Res:168.0,175.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),t_a) equal(hAPP(v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))))),x)**.
% 299.79/300.47 27196[0:Res:450.0,501.0] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v,w,x)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(tc_Hoare__Mirabelle_Otriple(t_a))),w),v),t_a)* c_Hoare__Mirabelle_Otriple__valid(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v,w,x),t_a).
% 299.79/300.47 27184[0:SpR:586.0,450.0] || -> hBOOL(hAPP(u,hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_COMBB(u,v,w,x),y,z,x1),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_COMBB(u,v,w,x),y,z,x1))))* c_Hoare__Mirabelle_Otriple__valid(x1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBB(u,v,w,x)),z),y),t_a).
% 299.79/300.47 27183[0:SpR:585.0,450.0] || -> hBOOL(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_COMBC(u,v,w,x),y,z,x1)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_COMBC(u,v,w,x),y,z,x1)))* c_Hoare__Mirabelle_Otriple__valid(x1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBC(u,v,w,x)),z),y),t_a).
% 299.79/300.47 27176[0:SpR:538.0,450.0] || -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x)))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool))),w),v),t_a).
% 299.79/300.47 27172[0:SpR:297.2,450.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x),u)* -> hBOOL(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x)) c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Lattices_Oupper__semilattice__class_Osup(u)),w),v),t_a).
% 299.79/300.47 27169[0:SpR:299.2,450.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x),u)* -> hBOOL(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x)) c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Lattices_Oupper__semilattice__class_Osup(u)),w),v),t_a).
% 299.79/300.47 27637[0:SpR:9.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Fun_Ocomp(x,y,z,x1,x2),w,u,x3) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Fun_Ocomp(x,y,z,x1,x2),u,x3),hAPP(x,hAPP(y,v))),v)**.
% 299.79/300.47 27628[0:SpR:1196.1,373.2] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,x),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.47 27619[0:SpR:1195.1,373.2] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,x),c_Orderings_Otop__class_Otop(u)),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.47 27592[0:SpR:87.1,373.2] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ouminus__class_Ouminus(w,u)),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),c_Orderings_Otop__class_Otop(u)),c_HOL_Ouminus__class_Ouminus(w,u))**.
% 299.79/300.47 27591[0:SpR:88.1,373.2] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),x,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),v,y),c_Orderings_Otop__class_Otop(u)),w)**.
% 299.79/300.47 27582[0:SpR:540.1,373.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),x,v,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),w)**.
% 299.79/300.47 27581[0:SpR:539.1,373.2] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),x,v,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),w)**.
% 299.79/300.47 27580[0:SpR:297.2,373.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) hBOOL(hAPP(hAPP(c_in(x),w),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,x,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,z),w),w)**.
% 299.79/300.47 27577[0:SpR:2098.1,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,u,y) -> c_Hoare__Mirabelle_Ohoare__valids(x,v,t_a) equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,v),tc_Hoare__Mirabelle_Otriple(t_a)),u,y),v),v)**.
% 299.79/300.47 27571[0:SpR:299.2,373.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* hBOOL(hAPP(hAPP(c_in(x),v),y))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,x,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,z),w),v)*.
% 299.79/300.47 27790[0:SpR:9.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Fun_Ocomp(x,y,z,x1,x2),w,u,x3) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Fun_Ocomp(x,y,z,x1,x2),u,x3),hAPP(x,hAPP(y,v))),v)**.
% 299.79/300.47 27781[0:SpR:1196.1,71.2] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,x),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.47 27772[0:SpR:1195.1,71.2] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,x),c_Orderings_Otop__class_Otop(u)),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.47 27745[0:SpR:87.1,71.2] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ouminus__class_Ouminus(w,u)),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),c_Orderings_Otop__class_Otop(u)),c_HOL_Ouminus__class_Ouminus(w,u))**.
% 299.79/300.47 27744[0:SpR:88.1,71.2] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),x,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),v,y),c_Orderings_Otop__class_Otop(u)),w)**.
% 299.79/300.47 27735[0:SpR:540.1,71.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),x,v,z) -> equal(hAPP(c_Fun_Othe__inv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),w)**.
% 299.79/300.47 27734[0:SpR:539.1,71.2] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),x,v,z) -> equal(hAPP(c_Fun_Othe__inv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),w)**.
% 299.79/300.47 27733[0:SpR:297.2,71.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) hBOOL(hAPP(hAPP(c_in(x),w),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,x,z) -> equal(hAPP(c_Fun_Othe__inv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,z),w),w)**.
% 299.79/300.47 27730[0:SpR:2098.1,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,u,y) -> c_Hoare__Mirabelle_Ohoare__valids(x,v,t_a) equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,v),tc_Hoare__Mirabelle_Otriple(t_a)),u,y),v),v)**.
% 299.79/300.47 27724[0:SpR:299.2,71.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* hBOOL(hAPP(hAPP(c_in(x),v),y))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,x,z) -> equal(hAPP(c_Fun_Othe__inv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,z),w),v)*.
% 299.79/300.47 27944[0:Res:468.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,w),t_a)* -> equal(hAPP(c_Set_Oimage(x,tc_Hoare__Mirabelle_Otriple(t_a),y),v),hAPP(c_Set_Oimage(z,tc_Hoare__Mirabelle_Otriple(t_a),y),v)) c_Hoare__Mirabelle_Otriple__valid(w,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,x,z,tc_Hoare__Mirabelle_Otriple(t_a),y),t_a)*.
% 299.79/300.47 28245[0:SpL:465.1,470.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),z),y)) hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__XimageE__1__1(y,v,c_Fun_Ofun__upd(w,z,x1,x,u),x,u)),y))*.
% 299.79/300.47 28244[0:SpL:465.1,466.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),z),y)) hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(y,c_Fun_Ofun__upd(w,z,x1,x,u),v,x,u)),y))*.
% 299.79/300.47 28179[0:SpR:465.1,96.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),z,x,y) -> hBOOL(hAPP(hAPP(c_in(x),v),z)) c_Fun_Oinj__on(c_Fun_Othe__inv__into(z,c_Fun_Ofun__upd(u,v,w,x,y),x,y),hAPP(c_Set_Oimage(u,x,y),z),y,x)*.
% 299.79/300.47 28570[0:SpL:118.0,31.0] || equal(c_Fun_Ocomp(u,v,w,x,y),c_Fun_Ofun__upd(c_Fun_Ocomp(z,x1,x2,x,y),x3,hAPP(z,x4),y,x))* -> equal(hAPP(u,hAPP(v,x5)),hAPP(z,hAPP(c_Fun_Ofun__upd(x1,x3,x4,y,x2),x5)))*.
% 299.79/300.47 28548[0:SpR:9.0,118.0] || -> equal(c_Fun_Ocomp(c_Fun_Ocomp(u,v,w,x,y),c_Fun_Ofun__upd(z,x1,x2,x3,x4),x4,x5,x3),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Fun_Ocomp(u,v,w,x,y),z,x4,x5,x3),x1,hAPP(u,hAPP(v,x2)),x3,x5))*.
% 299.79/300.47 28528[0:SpR:11695.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),c_Fun_Ofun__upd(x,y,c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),w),z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),x,x1,x2,z),y,c_Orderings_Otop__class_Otop(tc_bool),z,x2))*.
% 299.79/300.47 28502[0:SpR:88.1,118.0] class_Lattices_Oboolean__algebra(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),c_Fun_Ofun__upd(w,x,v,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),w,z,x1,y),x,c_Orderings_Otop__class_Otop(u),y,x1))*.
% 299.79/300.47 28492[0:SpR:540.1,118.0] class_Lattices_Olattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Fun_Ofun__upd(w,x,y,z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x1,x2,z),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v),z,x2))*.
% 299.79/300.47 28491[0:SpR:539.1,118.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Fun_Ofun__upd(w,x,y,z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x1,x2,z),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v),z,x2))*.
% 299.79/300.47 28490[0:SpR:297.2,118.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Fun_Ofun__upd(x,y,w,z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,x1,x2,z),y,w,z,x2))*.
% 299.79/300.47 28487[0:SpR:2098.1,118.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) equal(c_Fun_Ocomp(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),c_Fun_Ofun__upd(w,x,v,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,z,x1,y),x,v,y,x1))*.
% 299.79/300.47 28481[0:SpR:299.2,118.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Fun_Ofun__upd(x,y,v,z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,x1,x2,z),y,w,z,x2))*.
% 299.79/300.47 28433[0:SpR:118.0,118.0] || -> equal(c_Fun_Ocomp(u,c_Fun_Ocomp(v,c_Fun_Ofun__upd(w,x,y,z,x1),x1,x2,z),x2,x3,z),c_Fun_Ofun__upd(c_Fun_Ocomp(u,c_Fun_Ocomp(v,w,x1,x2,z),x2,x3,z),x,hAPP(u,hAPP(v,y)),z,x3))*.
% 299.79/300.47 28424[0:SpR:118.0,118.0] || -> equal(c_Fun_Ocomp(u,c_Fun_Ofun__upd(c_Fun_Ofun__upd(v,w,x,y,z),x1,x2,y,z),z,x3,y),c_Fun_Ofun__upd(c_Fun_Ofun__upd(c_Fun_Ocomp(u,v,z,x3,y),w,hAPP(u,x),y,x3),x1,hAPP(u,x2),y,x3))*.
% 299.79/300.47 28585[0:Rew:9.0,28564.0] || -> equal(c_Fun_Ocomp(c_Fun_Ocomp(u,v,w,x,y),c_Fun_Ofun__upd(z,x1,x2,x3,y),y,x,x3),c_Fun_Ofun__upd(c_Fun_Ocomp(u,c_Fun_Ocomp(v,z,y,w,x3),w,x,x3),x1,hAPP(u,hAPP(v,x2)),x3,x))*.
% 299.79/300.47 29182[0:SpL:537.1,57.1] class_Lattices_Olattice(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u))),c_HOL_Ozero__class_Ozero(u))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.47 29098[0:SpR:537.1,1103.1] class_Lattices_Olattice(u) || -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),t_a) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))))))*.
% 299.79/300.47 29029[0:SpR:537.1,415.0] class_Lattices_Olattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))**.
% 299.79/300.47 29707[0:SpL:534.1,57.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Olordered__ab__group__add(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u))),c_HOL_Ozero__class_Ozero(u))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.47 29622[0:SpR:534.1,1103.1] class_Lattices_Oupper__semilattice(u) || -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),t_a) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))))))*.
% 299.79/300.47 29551[0:SpR:534.1,415.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))**.
% 299.79/300.47 31407[0:SpL:12944.0,449.0] || hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)),z,x1))) -> c_Hoare__Mirabelle_Otriple__valid(x1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),z),hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y))),t_a)*.
% 299.79/300.47 31401[0:SpL:11473.0,449.0] || hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),x,y))) -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),x),hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))),t_a)*.
% 299.79/300.47 31386[0:SpL:17045.0,449.0] || hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)),y,z))) -> c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool))),t_a)*.
% 299.79/300.47 31513[0:SpL:393.1,473.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* -> equal(x,c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))) hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Hilbert__Choice_Oinv__into(x,c_COMBK(w,u,y),y,u),v)),x))*.
% 299.79/300.47 32061[0:Res:151.2,280.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(x,v),y))* -> hBOOL(hAPP(hAPP(c_in(u),v),z))* hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_HOL_Ominus__class_Ominus(w,z,tc_fun(u,tc_bool)),x,u,tc_fun(x1,tc_bool)),y))*.
% 299.79/300.47 32384[0:Res:8369.1,477.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y),c_HOL_Ouminus__class_Ouminus(z,tc_fun(x,tc_bool)),u)),z))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(z,tc_fun(x,tc_bool)),v))*.
% 299.79/300.47 32383[0:Res:10930.1,477.0] || equal(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Set_Oinsert(y,u),v_x),v)),v_Procs)** hBOOL(hAPP(hAPP(c_in(v),z),w))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,u),v_x),z))*.
% 299.79/300.47 32404[0:Rew:586.0,32367.2] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),hAPP(c_COMBB(u,z,x1,x2),v),w))))* hBOOL(hAPP(hAPP(c_in(w),x3),x))* -> hBOOL(hAPP(u,hAPP(v,x3)))*.
% 299.79/300.47 32405[0:Rew:585.0,32366.2] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_COMBC(u,y,z,x1),x2),v)),x2))* hBOOL(hAPP(hAPP(c_in(v),x3),w))* -> hBOOL(hAPP(hAPP(u,x3),x2))*.
% 299.79/300.47 32564[0:Res:8369.1,476.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w),c_HOL_Ouminus__class_Ouminus(z,tc_fun(x,tc_bool)),u)),z))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(z,tc_fun(x,tc_bool)),v))*.
% 299.79/300.47 32563[0:Res:10930.1,476.0] || equal(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Set_Oinsert(y,u),v_x),v)),v_Procs)** hBOOL(hAPP(hAPP(c_in(v),z),x))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,u),v_x),z))*.
% 299.79/300.47 32582[0:Rew:586.0,32547.2] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),hAPP(c_COMBB(u,z,x1,x2),v),w))))* hBOOL(hAPP(hAPP(c_in(w),x3),y))* -> hBOOL(hAPP(u,hAPP(v,x3)))*.
% 299.79/300.47 32583[0:Rew:585.0,32546.2] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_COMBC(u,y,z,x1),x2),v)),x2))* hBOOL(hAPP(hAPP(c_in(v),x3),x))* -> hBOOL(hAPP(hAPP(u,x3),x2))*.
% 299.79/300.47 33029[0:SpR:27043.1,475.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,x),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,x),u,w),v))**.
% 299.79/300.47 33023[0:SpR:10063.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),u,w),v))**.
% 299.79/300.47 33006[0:SpR:105.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(c_Set_Ovimage(z,x,v),u,y),w)),hAPP(c_Set_Oimage(c_Set_Ovimage(z,x,v),u,y),w))**.
% 299.79/300.47 32999[0:SpR:38.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(c_Set_Ovimage(z,x,v),u,y),w)),hAPP(c_Set_Oimage(c_Set_Ovimage(z,x,v),u,y),w))**.
% 299.79/300.47 32998[0:SpR:321.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(c_Set_Oimage(z,v,x),u,y),w)),hAPP(c_Set_Oimage(c_Set_Oimage(z,v,x),u,y),w))**.
% 299.79/300.47 32963[0:SpR:87.1,475.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ouminus__class_Ouminus(w,u)),x)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),x))**.
% 299.79/300.47 32944[0:SpR:302.1,475.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y),x))**.
% 299.79/300.47 32930[0:SpR:15476.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool),x),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,tc_bool)),u,x),v)),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,tc_bool)),u,x),v))**.
% 299.79/300.47 32915[0:SpR:369.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),x),z),hAPP(c_Set_Oimage(c_Set_Oinsert(v,w),u,z),y)),hAPP(c_Set_Oimage(c_Set_Oinsert(v,w),u,z),y))**.
% 299.79/300.47 32914[0:SpR:2089.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,x),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),u,x),w))**.
% 299.79/300.47 32853[0:SpR:475.1,446.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(x,hAPP(c_Set_Oimage(y,u,z),w),tc_fun(z,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(hAPP(y,v),z),x),hAPP(c_Set_Oimage(y,u,z),w),tc_fun(z,tc_bool))*.
% 299.79/300.47 34423[0:SpL:24914.0,469.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,x,u),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,x,u),v_x)),w,v,x,u)),v)**.
% 299.79/300.47 34422[0:SpL:24914.0,464.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,x,u),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,x,u),v_x)),v,w,x,u)),v)**.
% 299.79/300.47 34404[0:SpL:24914.0,8513.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x)) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_Com_Opname,w),hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_x)),u)**.
% 299.79/300.47 34377[0:SpL:24914.0,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname,w),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.47 34262[0:SpL:24914.0,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),u))* c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* c_Hoare__Mirabelle_Otriple__valid(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,x),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x)),t_a)*.
% 299.79/300.47 34222[0:SpR:188.1,24914.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.79/300.47 34183[0:SpR:24914.0,338.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,x),hAPP(c_Set_Oinsert(u,v),v_x)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(u,v),v_x)))**.
% 299.79/300.47 34182[0:SpR:24914.0,424.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,x),hAPP(c_Set_Oinsert(v,u),v_x)),w,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,u),v_x),w,tc_fun(u,tc_bool)).
% 299.79/300.47 34176[0:SpR:24914.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,y),hAPP(c_Set_Oimage(u,v,w),v_x)))),hAPP(c_Set_Oinsert(hAPP(u,x),w),hAPP(c_Set_Oimage(u,v,w),v_x)))**.
% 299.79/300.47 34170[0:SpR:24914.0,131.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(u,w,x),tc_Com_Opname,z),hAPP(c_Set_Ovimage(u,w,x),v_x))),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)))**.
% 299.79/300.47 34168[0:SpR:24914.0,158.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(v,y,w),tc_Com_Opname,z),hAPP(c_Set_Oimage(v,y,w),v_x))),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))**.
% 299.79/300.47 34157[0:SpR:24914.0,31323.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v_x),hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),tc_Com_Opname,u),hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v_x))),tc_bool)*.
% 299.79/300.47 34114[0:SpR:24914.0,9568.0] || -> c_lessequals(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),tc_Com_Opname,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x))),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x),tc_bool)*.
% 299.79/300.47 34112[0:SpR:24914.0,9569.0] || -> c_lessequals(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),tc_Com_Opname,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x))),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x),tc_bool)*.
% 299.79/300.47 34511[0:Rew:339.0,34046.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x))),x)),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),x)))**.
% 299.79/300.47 34040[0:SpR:24914.0,129.1] || c_lessequals(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(v,w,x),tc_Com_Opname,y),hAPP(c_Set_Ovimage(v,w,x),v_x)),tc_fun(x,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),u),hAPP(c_Set_Ovimage(v,w,x),v_x),tc_fun(w,tc_bool))*.
% 299.79/300.47 34032[0:SpR:24914.0,313.1] || c_lessequals(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(v,w,x),tc_Com_Opname,y),hAPP(c_Set_Oimage(v,w,x),v_x)),tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),u),hAPP(c_Set_Oimage(v,w,x),v_x),tc_fun(x,tc_bool))*.
% 299.79/300.47 33956[0:SpR:24914.0,129.1] || c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Ovimage(u,v,w),v_x)),y,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),v_x),hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool))*.
% 299.79/300.47 33929[0:SpR:24914.0,313.1] || c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),y,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),v_x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))*.
% 299.79/300.47 34525[7:MRR:34194.0,27297.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_COMBK(u,v,w),w,v),tc_Com_Opname,x),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.79/300.48 34659[0:SpL:55.1,215.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),x),y,tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),w)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(w)),v),y)) c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w).
% 299.79/300.48 34747[0:SpR:34428.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v,w),hAPP(c_Set_Oinsert(v_x,v),x)),hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v,w),x)))*.
% 299.79/300.48 34746[0:SpR:34428.0,99.1] || c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v,w),v_x),v_x)**.
% 299.79/300.48 34745[0:SpR:34428.0,438.1] || c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v,w),v_x),v_x)**.
% 299.79/300.48 35389[0:SpR:10090.1,410.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),v),w),hAPP(u,v_x),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 35382[0:SpR:303.1,410.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,tc_fun(y,tc_bool))))*.
% 299.79/300.48 35366[0:SpR:11176.1,410.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,tc_fun(y,tc_bool))))*.
% 299.79/300.48 35362[0:SpR:11177.1,410.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v,tc_fun(y,tc_bool))))*.
% 299.79/300.48 35317[0:SpR:300.1,410.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,tc_fun(y,tc_bool))))*.
% 299.79/300.48 35312[0:SpR:3586.1,410.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,w),x),c_Set_Oinsert(v,u),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v,u),w,tc_fun(y,tc_bool))))*.
% 299.79/300.48 35311[7:SpR:27278.1,410.0] || equal(hAPP(c_in(u),v),v_x) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,w),x),c_Set_Oinsert(v,u),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v,u),w,tc_fun(y,tc_bool))))*.
% 299.79/300.48 35282[0:SpR:9493.1,410.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 35280[0:SpR:8498.1,410.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,w),x),c_Set_Oinsert(y,v),w,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(y,v),w,tc_fun(z,tc_bool))))*.
% 299.79/300.48 35509[0:SpR:196.1,113.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool))),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool)))**.
% 299.79/300.48 35494[0:SpR:196.1,113.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(u,v,w),x),y,tc_fun(v,tc_bool)))**.
% 299.79/300.48 35552[0:Rew:113.0,35517.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Ovimage(u,v,w),v_x)),y,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(v_x,y,tc_fun(w,tc_bool))))**.
% 299.79/300.48 35553[0:Rew:113.0,35502.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(u,v,w),tc_Com_Opname,y),hAPP(c_Set_Ovimage(u,v,w),v_x)),tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,v_x,tc_fun(w,tc_bool))))**.
% 299.79/300.48 35599[7:Res:29397.1,477.0] || equal(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Set_Oinsert(y,u),v_x),v)),v_x)** hBOOL(hAPP(hAPP(c_in(v),z),w))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,u),v_x),z))*.
% 299.79/300.48 35598[7:Res:29397.1,476.0] || equal(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Set_Oinsert(y,u),v_x),v)),v_x)** hBOOL(hAPP(hAPP(c_in(v),z),x))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,u),v_x),z))*.
% 299.79/300.48 36155[0:SpL:339.0,516.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y))))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x))) hBOOL(hAPP(hAPP(c_in(u),v),y)).
% 299.79/300.48 36151[0:SpL:338.0,516.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y))))* -> hBOOL(hAPP(hAPP(c_in(u),v),x)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),y))).
% 299.79/300.48 36116[0:SpL:8415.2,516.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(v_x,w)))* -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(u),v),w)).
% 299.79/300.48 36924[0:Rew:66.0,36849.0] || -> equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oinsert(y,w),v)),tc_fun(w,tc_bool)))**.
% 299.79/300.48 37128[0:SpL:8415.2,471.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(hAPP(c_in(v),x),v_x))* c_lessequals(v_x,y,tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,x)),y))*.
% 299.79/300.48 37500[0:SpL:205.1,390.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(x,y,tc_fun(v,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,v,w),y),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,v,w)*.
% 299.79/300.48 37483[0:SpR:8415.2,205.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),v_x),v_x)**.
% 299.79/300.48 37470[0:SpR:205.1,20881.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),z),x),x1)),z))*.
% 299.79/300.48 37450[0:SpR:205.1,9569.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v)),hAPP(c_Set_Oimage(u,v,w),x)),tc_bool)*.
% 299.79/300.48 37449[0:SpR:205.1,9568.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v)),z),hAPP(c_Set_Oimage(u,v,w),x)),tc_bool)*.
% 299.79/300.48 37688[0:SpL:198.1,95.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(x,y,v,z) -> c_Fun_Oinj__on(c_Fun_Ocomp(x,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),v,z,w),hAPP(c_Set_Oimage(u,v,w),y),w,z)*.
% 299.79/300.48 38224[0:Res:13.2,430.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,y,tc_fun(w,tc_bool))* c_lessequals(c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),z,tc_fun(w,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool)),z,tc_fun(w,tc_bool))*.
% 299.79/300.48 38234[0:SSi:38230.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,y,tc_fun(w,tc_bool))* c_lessequals(z,c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> c_lessequals(z,c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.48 38344[0:SSi:38323.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || hBOOL(hAPP(hAPP(c_in(tc_bool),u),v))* c_Finite__Set_Ofinite(v,tc_bool) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,v,tc_bool,tc_bool),c_Orderings_Obot__class_Obot(tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w,v,tc_bool,tc_bool))*.
% 299.79/300.48 38404[0:SpL:584.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(x,y)),hAPP(c_Set_Oimage(u,v,w),y)) c_Fun_Oinj__on(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,z,x1,x2),y),v,w)* -> equal(hAPP(x,y),y).
% 299.79/300.48 39314[0:SpL:533.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_Procs) -> .
% 299.79/300.48 39313[7:SpL:533.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_x) -> .
% 299.79/300.48 39312[0:SpL:533.0,3929.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.79/300.48 39188[0:SpR:533.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,tc_fun(y,tc_bool)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z)),tc_bool)*.
% 299.79/300.48 39164[0:SpR:533.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),z,x1,x2),x))*.
% 299.79/300.48 39141[0:SpR:533.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),tc_Com_Opname,u),u)*.
% 299.79/300.48 39134[0:SpR:533.0,23902.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Orderings_Obot__class_Obot(tc_bool)),v_x)**.
% 299.79/300.48 39614[0:SpR:532.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z)),tc_bool)*.
% 299.79/300.48 39590[0:SpR:532.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))*.
% 299.79/300.48 40459[0:Res:10500.2,529.0] || hBOOL(hAPP(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x))) -> c_Hoare__Mirabelle_Ohoare__valids(u,y,t_a) c_Hoare__Mirabelle_Otriple__valid(c_Suc(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(u,y)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),hAPP(c_Com_Ocom_OBODY,w)),x),t_a)*.
% 299.79/300.48 40953[0:Rew:339.0,40919.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,t_a),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,u,t_a)),hAPP(c_Set_Oinsert(v,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x))))*.
% 299.79/300.48 40913[0:Res:15262.1,479.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),w,v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w)))*.
% 299.79/300.48 40912[0:Res:3285.1,479.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),x,v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),x)))*.
% 299.79/300.48 40911[0:Res:3317.1,479.1] || equal(c_in(u),c_in(v)) hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v_x,u),x),y,w,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(v_x,u),x)),y)))*.
% 299.79/300.48 40954[0:Rew:339.0,40907.1] || hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,v),hAPP(c_in(tc_Com_Opname),v_x)),x,u,v)),hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),x))))*.
% 299.79/300.48 40955[0:Rew:533.0,40884.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs),w,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w))))*.
% 299.79/300.48 40956[0:Rew:533.0,40883.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v),w,u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),w))))*.
% 299.79/300.48 41200[0:Res:19451.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(w,t_a),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),hAPP(c_Set_Oinsert(w,t_a),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))))*.
% 299.79/300.48 41194[0:Res:15262.1,478.1] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))))*.
% 299.79/300.48 41193[0:Res:3285.1,478.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs),v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs))))*.
% 299.79/300.48 41192[0:Res:3317.1,478.1] || equal(c_in(u),c_in(v)) hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(v_x,u),y),w,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(v_x,u),y))))*.
% 299.79/300.48 41188[0:Res:19440.0,478.1] || hBOOL(hAPP(u,v_Procs)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oinsert(x,v),hAPP(c_in(tc_Com_Opname),v_x)),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),hAPP(c_in(tc_Com_Opname),v_x)))))*.
% 299.79/300.48 41165[0:Res:649.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs))))*.
% 299.79/300.48 41164[0:Res:650.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w))))*.
% 299.79/300.48 41361[0:SpL:9987.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w))* hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41359[0:SpL:2095.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(z,v),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41356[0:SpL:303.1,275.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(u))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41354[0:SpL:23902.1,275.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_bool)),w)) hBOOL(hAPP(hAPP(c_in(x),y),v_x)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41348[0:SpL:330.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) hBOOL(hAPP(hAPP(c_in(x),y),z)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41343[0:SpL:14216.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(z,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool))),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41340[0:SpL:11176.1,275.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),w),x))* hBOOL(hAPP(hAPP(c_in(y),z),u)) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(y,tc_bool))))*.
% 299.79/300.48 41336[0:SpL:11177.1,275.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(x),y),u))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41292[0:SpL:331.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),v))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41291[0:SpL:302.1,275.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* hBOOL(hAPP(hAPP(c_in(y),z),c_Orderings_Otop__class_Otop(u))) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(y,tc_bool))))*.
% 299.79/300.48 41283[0:SpL:34428.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,y),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 41276[0:SpL:15476.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) hBOOL(hAPP(hAPP(c_in(w),x),c_HOL_Ouminus__class_Ouminus(hAPP(y,v_x),tc_bool))) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_HOL_Ouminus__class_Ouminus(y,tc_fun(t_a,tc_bool)),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 41257[0:SpL:34427.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,y),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 41256[0:SpL:2093.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(tc_Com_Opname),v_x)),v)) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_in(tc_Com_Opname),v_x))) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_Procs,y),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 41254[0:SpL:3744.1,275.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) hBOOL(hAPP(hAPP(c_in(x),y),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,u),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41488[4:SpR:533.0,38236.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_Com_Opname,tc_bool))*.
% 299.79/300.48 41646[0:SpL:9925.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,u),x)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u)* -> hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Otop__class_Otop(tc_bool)),x)).
% 299.79/300.48 41621[0:SpL:23682.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,u),x)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u)* -> hBOOL(hAPP(hAPP(c_in(w),v),x)).
% 299.79/300.48 41744[0:Res:10500.2,494.1] || hBOOL(hAPP(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),x)))* hBOOL(hAPP(hAPP(v,y),z))* c_Natural_Oevaln(w,z,v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(u,x1),x2)* -> c_Hoare__Mirabelle_Ohoare__valids(u,x1,t_a) hBOOL(hAPP(hAPP(x,y),x2))*.
% 299.79/300.48 41835[4:Res:38631.1,199.0] || c_lessequals(v_x,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v,u,w)),tc_bool)* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),y))*.
% 299.79/300.48 41833[0:Res:526.1,199.0] || hBOOL(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_in(x),y),v,u,w)),y))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(hAPP(c_in(x),y),z))*.
% 299.79/300.48 42017[0:Res:37962.1,477.0] || hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x,y,z,x1),u))* hBOOL(hAPP(hAPP(c_in(u),x2),v))* -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x,y,z,x1),x2))*.
% 299.79/300.48 42016[0:Res:37962.1,476.0] || hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x,y,z,x1),u))* hBOOL(hAPP(hAPP(c_in(u),x2),w))* -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x,y,z,x1),x2))*.
% 299.79/300.48 42087[0:SpR:180.2,9567.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,tc_fun(y,tc_bool)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),z,v,u,u)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),z,hAPP(c_Set_Oinsert(w,u),v),u,u),tc_bool)*.
% 299.79/300.48 42063[0:SpR:180.2,5875.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z,x1,x2),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u)))*.
% 299.79/300.48 42062[0:SpR:180.2,415.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(w,u),v),u,u),y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))**.
% 299.79/300.48 42230[0:Obv:42159.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u))** -> c_lessequals(x,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u),u).
% 299.79/300.48 42233[0:Obv:42094.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,x,u) c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),y,v,u,u),x,u) -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),y,hAPP(c_Set_Oinsert(w,u),v),u,u),x,u)*.
% 299.79/300.48 42234[0:Obv:42077.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u),u) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(w,u),v),u,u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u))**.
% 299.79/300.48 42237[0:SSi:42169.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(x,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> equal(x,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.79/300.48 42497[0:SpL:9936.1,315.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x,y)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Set_Oimage(v,x,y),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x,y),w)).
% 299.79/300.48 42456[0:SpL:9936.1,315.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,x,y)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x,y),w),hAPP(c_Set_Oimage(v,x,y),w)).
% 299.79/300.48 42743[0:SpL:161.0,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,tc_fun(v,tc_bool)),u,v)))* hBOOL(hAPP(hAPP(c_in(v),z),c_HOL_Ominus__class_Ominus(w,y,tc_fun(v,tc_bool))))* -> hBOOL(hAPP(u,z))*.
% 299.79/300.48 42742[0:SpL:161.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,tc_fun(v,tc_bool)),u,v)))* hBOOL(hAPP(hAPP(c_in(v),z),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))))* -> hBOOL(hAPP(u,z))*.
% 299.79/300.48 42732[0:SpL:161.0,327.0] || equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))) -> c_lessequals(c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.48 42688[0:SpR:161.0,329.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(x,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(x,v,tc_fun(w,tc_bool))).
% 299.79/300.48 42684[0:SpR:161.0,328.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(x,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),v,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(x,v,tc_fun(w,tc_bool))).
% 299.79/300.48 42655[0:SpR:161.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(w,y,tc_fun(v,tc_bool))),z,u),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.48 42635[0:SpR:161.0,9566.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool)))),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))),tc_bool)*.
% 299.79/300.48 43078[0:SpR:23840.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u,tc_fun(w,tc_bool)))**.
% 299.79/300.48 43019[0:SpR:10463.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),u,tc_fun(x,tc_bool)))**.
% 299.79/300.48 43018[0:SpR:9911.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),u,tc_fun(x,tc_bool)))**.
% 299.79/300.48 42899[0:SpR:486.1,9566.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,v))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))),tc_bool)*.
% 299.79/300.48 43562[0:SpL:507.0,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)),u,x)))* hBOOL(hAPP(hAPP(c_in(x),x1),hAPP(c_Set_Oimage(v,w,x),y)))* -> hBOOL(hAPP(u,x1))*.
% 299.79/300.48 43561[0:SpL:507.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)),u,x)))* hBOOL(hAPP(hAPP(c_in(x),x1),hAPP(c_Set_Oimage(v,w,x),z)))* -> hBOOL(hAPP(u,x1))*.
% 299.79/300.48 43551[0:SpL:507.0,327.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(c_Set_Oimage(u,v,w),y)) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))*.
% 299.79/300.48 43506[0:SpR:507.0,329.1] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))* -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(c_Set_Oimage(u,v,w),y)).
% 299.79/300.48 43502[0:SpR:507.0,328.1] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))* -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x)),hAPP(c_Set_Oimage(u,v,w),y)).
% 299.79/300.48 43473[0:SpR:507.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y)),x1,u),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.79/300.48 43452[0:SpR:507.0,9566.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x))),hAPP(c_Set_Oimage(u,v,w),y)),tc_bool)*.
% 299.79/300.48 43784[0:SpL:162.0,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),x1),hAPP(c_Set_Ovimage(v,w,x),y)))* -> hBOOL(hAPP(u,x1))*.
% 299.79/300.48 43783[0:SpL:162.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),x1),hAPP(c_Set_Ovimage(v,w,x),z)))* -> hBOOL(hAPP(u,x1))*.
% 299.79/300.48 43773[0:SpL:162.0,327.0] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),hAPP(c_Set_Ovimage(u,v,w),y)) -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool))*.
% 299.79/300.48 43728[0:SpR:162.0,329.1] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),hAPP(c_Set_Ovimage(u,v,w),y)).
% 299.79/300.48 43724[0:SpR:162.0,328.1] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),x)),hAPP(c_Set_Ovimage(u,v,w),y)).
% 299.79/300.48 43695[0:SpR:162.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),y)),x1,u),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.79/300.48 43674[0:SpR:162.0,9566.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x))),hAPP(c_Set_Ovimage(u,v,w),y)),tc_bool)*.
% 299.79/300.48 44174[0:SpR:2267.1,232.1] || equal(u,v) c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> c_lessequals(hAPP(c_Set_Oimage(w,x,y),c_HOL_Ouminus__class_Ouminus(v,tc_fun(x,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(w,x,y),u),tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.48 44152[0:SpR:2267.1,232.1] || equal(hAPP(c_Set_Oimage(u,v,w),x),y) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.48 44137[0:SpR:3229.1,232.1] || equal(u,c_Set_Oimage(v,w,x)) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.48 44334[0:Res:19436.1,268.0] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),u)))* equal(hAPP(x,v_x),hAPP(x,v))* c_Fun_Oinj__on(x,hAPP(c_Set_Oinsert(w,tc_Com_Opname),u),tc_Com_Opname,y)* -> equal(v_x,v).
% 299.79/300.48 44326[0:Res:11030.1,268.0] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(hAPP(c_in(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))* equal(hAPP(x,v_x),hAPP(x,v))* c_Fun_Oinj__on(x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,y)* -> equal(v_x,v).
% 299.79/300.48 44322[0:Res:3316.1,268.0] || equal(c_in(u),c_in(v)) hBOOL(hAPP(hAPP(c_in(v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))* equal(hAPP(x,v_x),hAPP(x,w))* c_Fun_Oinj__on(x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,y)* -> equal(v_x,w).
% 299.79/300.48 44309[0:Res:9246.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))))* equal(hAPP(x,y),hAPP(x,v))* c_Fun_Oinj__on(x,c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),u,z)* -> hBOOL(hAPP(w,y))* equal(y,v).
% 299.79/300.48 44283[0:SpL:3229.1,268.0] || equal(u,hAPP(c_in(v),w))* hBOOL(hAPP(u,v_x))* hBOOL(hAPP(hAPP(c_in(v),x),v_x))* equal(hAPP(y,w),hAPP(y,x))* c_Fun_Oinj__on(y,v_x,v,z)* -> equal(w,x).
% 299.79/300.48 44277[0:SpL:3229.1,268.0] || equal(u,c_in(v))* hBOOL(hAPP(hAPP(u,v_x),w))* hBOOL(hAPP(hAPP(c_in(v),x),w))* equal(hAPP(y,v_x),hAPP(y,x))* c_Fun_Oinj__on(y,w,v,z)* -> equal(v_x,x).
% 299.79/300.48 44396[0:SpR:3229.1,90.0] || equal(u,c_COMBB(c_Set_Oimage(v,w,x),tc_fun(w,tc_bool),tc_fun(x,tc_bool),y))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(u,v_x),y,tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,v_x,y,tc_fun(w,tc_bool))))*.
% 299.79/300.48 44450[0:SpR:3229.1,30.0] || equal(u,c_COMBB(c_Set_Ovimage(v,w,x),tc_fun(x,tc_bool),tc_fun(w,tc_bool),y))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(u,v_x),y,tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,v_x,y,tc_fun(x,tc_bool))))*.
% 299.79/300.48 44584[0:SpR:3229.1,240.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(v,c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w))* c_Finite__Set_Ofinite(x,w) -> equal(c_Finite__Set_Ofold(hAPP(v,v_x),y,x,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v_x,w,u)))*.
% 299.79/300.48 45122[0:Res:326.2,436.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,y,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),z))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),z))*.
% 299.79/300.48 45050[0:SpR:10090.1,326.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(v,v_x,tc_fun(u,tc_bool)) c_lessequals(w,c_Orderings_Otop__class_Otop(tc_bool),tc_fun(u,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_bool),tc_fun(u,tc_bool))*.
% 299.79/300.48 45459[0:Res:45357.1,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname)))* c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.48 45898[0:Res:8376.2,482.2] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_Procs)** hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)))* -> hBOOL(hAPP(x,v_x)).
% 299.79/300.48 46143[0:Res:3284.1,481.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(v,v_Procs)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(u,v_x)),x),v,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(u,v_x)),x)))*.
% 299.79/300.48 46461[0:Res:3284.1,480.0] || equal(c_in(tc_Com_Opname),u) -> hBOOL(hAPP(v,v_Procs)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(u,v_x)),v,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(u,v_x))))*.
% 299.79/300.48 47196[0:Res:13387.1,242.1] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** hBOOL(hAPP(hAPP(c_in(w),v),u)) -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool))*.
% 299.79/300.48 48807[0:Res:13238.1,619.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,t_a,tc_fun(w,tc_bool)),u),c_Set_Oinsert(x,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,t_a,tc_fun(w,tc_bool))))**.
% 299.79/300.48 48800[0:Res:8375.1,619.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,v,tc_fun(x,tc_bool)),u),c_Set_Oinsert(y,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,w,v,tc_fun(x,tc_bool))))**.
% 299.79/300.48 48778[0:Res:652.1,619.0] || c_lessequals(v_Procs,u,tc_fun(tc_Com_Opname,tc_bool)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,tc_Com_Opname,tc_fun(w,tc_bool)),u),c_Set_Oinsert(x,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,tc_Com_Opname,tc_fun(w,tc_bool))))**.
% 299.79/300.48 48982[0:Res:9258.0,483.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),tc_bool))* hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)),u))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)),v))*.
% 299.79/300.48 49087[0:SpR:49017.1,118.0] || -> hBOOL(hAPP(u,v_x)) equal(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),c_Fun_Ofun__upd(v,w,v_Procs,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,y,z,x),w,v_Procs,x,z))*.
% 299.79/300.48 49064[0:SpR:49017.1,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,w,tc_Com_Opname),tc_Com_Opname),v,u,x) -> hBOOL(hAPP(w,v_x)) equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,w,tc_Com_Opname),tc_Com_Opname),u,x),v_Procs),v_Procs)**.
% 299.79/300.48 49063[0:SpR:49017.1,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,w,tc_Com_Opname),tc_Com_Opname),v,u,x) -> hBOOL(hAPP(w,v_x)) equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,w,tc_Com_Opname),tc_Com_Opname),u,x),v_Procs),v_Procs)**.
% 299.79/300.48 49187[0:Res:9258.0,239.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,u,w,t_a) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(x,w,t_a),u),v_x),tc_bool)) hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(u,x,w,t_a),v_x)),v))*.
% 299.79/300.48 49302[0:Res:526.1,488.1] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x))* hBOOL(hAPP(y,x))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,y,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,y,u)),w))*.
% 299.79/300.48 49688[0:Rew:49662.2,49506.2] || equal(u,v) c_Fun_Oinj__on(v,w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(u,v_x)),hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oinsert(v_x,x),w))))* c_Fun_Oinj__on(v,hAPP(c_Set_Oinsert(v_x,x),w),x,y).
% 299.79/300.48 49733[0:Rew:49662.2,49479.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),u,v,w) -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,v),u))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,v),u),v,w).
% 299.79/300.48 51859[4:Res:40792.1,477.0] || c_lessequals(v_x,hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Set_Oinsert(y,z),u),v)),tc_bool)* hBOOL(hAPP(hAPP(c_in(v),x1),w))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,z),u),x1))*.
% 299.79/300.48 51858[4:Res:40792.1,476.0] || c_lessequals(v_x,hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Set_Oinsert(y,z),u),v)),tc_bool)* hBOOL(hAPP(hAPP(c_in(v),x1),x))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,z),u),x1))*.
% 299.79/300.48 52746[0:SpR:24019.2,410.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),v_x,u,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 52991[0:Res:23739.1,481.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(u,v_Procs)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),w)))*.
% 299.79/300.48 52990[0:Res:23739.1,480.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(u,v_Procs)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)))*.
% 299.79/300.48 53058[0:SpR:23955.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Fun_Ofun__upd(u,v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,y,z,x),v,v_x,x,z))*.
% 299.79/300.48 53190[0:SpR:23958.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_Fun_Ofun__upd(u,v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,y,z,x),v,v_x,x,z))*.
% 299.79/300.48 53358[0:Res:31543.0,481.0] || -> hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w)))*.
% 299.79/300.48 53357[0:Res:31543.0,480.0] || -> hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)))*.
% 299.79/300.48 53788[0:SpR:53771.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Option_Othe(w),u,x),y),z),c_Option_Othe(w),y,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Option_Othe(w),y,tc_fun(x1,tc_bool))))*.
% 299.79/300.48 53819[0:SpR:53772.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Option_Othe(v),w,u,x),y),z),c_Option_Othe(v),y,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Option_Othe(v),y,tc_fun(x1,tc_bool))))*.
% 299.79/300.48 54308[0:Rew:20024.0,54224.1] || c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v) -> equal(c_Suc(c_Finite__Set_Ocard(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v)),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v))**.
% 299.79/300.48 54748[0:SpR:13749.2,118.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Fun_Ofun__upd(w,x,c_Orderings_Otop__class_Otop(u),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,z,x1,y),x,c_Orderings_Otop__class_Otop(u),y,x1))*.
% 299.79/300.48 55222[0:SpR:14043.2,118.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Fun_Ofun__upd(w,x,c_Orderings_Otop__class_Otop(u),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,z,x1,y),x,c_Orderings_Otop__class_Otop(u),y,x1))*.
% 299.79/300.48 58486[0:SpL:533.0,58248.0] || equal(c_COMBK(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),x,y),c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_fun(t_a,tc_bool)))** -> .
% 299.79/300.48 58740[0:SpL:180.2,15629.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)))*.
% 299.79/300.48 58683[0:SpL:99.1,15629.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(x)* -> hBOOL(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),y)))*.
% 299.79/300.48 58682[0:SpL:438.1,15629.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(x)* -> hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),y)))*.
% 299.79/300.48 59248[0:SpL:180.2,15857.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) hBOOL(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z)))*.
% 299.79/300.48 59191[0:SpL:99.1,15857.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(x)* -> hBOOL(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z)))*.
% 299.79/300.48 59190[0:SpL:438.1,15857.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(x)* -> hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z)))*.
% 299.79/300.48 59934[0:SSi:59864.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool))) -> c_lessequals(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.48 59935[0:SSi:59863.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),hAPP(c_Set_Ovimage(u,v,w),x)) -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),y),hAPP(c_Set_Ovimage(u,v,w),x),tc_fun(v,tc_bool))*.
% 299.79/300.48 59936[0:SSi:59862.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(c_Set_Oimage(u,v,w),x)) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),y),hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool))*.
% 299.79/300.48 60430[7:Res:58968.1,371.0] || equal(hAPP(c_Set_Oinsert(u,v),w),v_x) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Set_Oinsert(u,v),w),x)))* equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Set_Oinsert(u,v),w),x),u).
% 299.79/300.48 60388[7:SpR:297.2,58968.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)).
% 299.79/300.48 60543[0:Res:58969.1,371.0] || equal(hAPP(c_Set_Oinsert(u,v),w),v_Procs) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Set_Oinsert(u,v),w),x)))* equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Set_Oinsert(u,v),w),x),u).
% 299.79/300.48 60501[0:SpR:297.2,58969.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)).
% 299.79/300.48 60616[7:Res:59476.1,371.0] || equal(hAPP(c_Set_Oinsert(u,v),w),v_x) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),y)))* equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),y),u).
% 299.79/300.48 60574[7:SpR:297.2,59476.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),u)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)).
% 299.79/300.48 60689[0:Res:59477.1,371.0] || equal(hAPP(c_Set_Oinsert(u,v),w),v_Procs) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),y)))* equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),y),u).
% 299.79/300.48 60647[0:SpR:297.2,59477.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),u)* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)).
% 299.79/300.48 60787[0:Rew:584.0,60735.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(v,v_x)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(v,v_x)),tc_fun(u,tc_bool))*.
% 299.79/300.48 60788[0:Rew:584.0,60734.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(v,v_x)),tc_Com_Opname,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(v,v_x)),tc_fun(u,tc_bool))*.
% 299.79/300.48 60874[0:Res:59017.1,371.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,w),x),t_a)* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Set_Oinsert(v,w),x),y)))* equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Set_Oinsert(v,w),x),y),v).
% 299.79/300.48 60832[0:SpR:297.2,59017.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u)* -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)).
% 299.79/300.48 60947[0:Res:59525.1,371.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oinsert(v,w),x),t_a)* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),z)))* equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),z),v).
% 299.79/300.48 60905[0:SpR:297.2,59525.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),u)* -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)).
% 299.79/300.48 62443[0:SSi:62238.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) equal(hAPP(c_Set_Ovimage(x,y,w),v),hAPP(c_Set_Ovimage(x,y,w),u)) -> c_lessequals(hAPP(c_Set_Ovimage(x,y,w),v),hAPP(c_Set_Ovimage(x,y,w),u),tc_fun(y,tc_bool))*.
% 299.79/300.48 62444[0:SSi:62237.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) equal(hAPP(c_Set_Oimage(x,w,y),v),hAPP(c_Set_Oimage(x,w,y),u)) -> c_lessequals(hAPP(c_Set_Oimage(x,w,y),v),hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool))*.
% 299.79/300.48 64214[0:SpR:181.1,646.1] || c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_Procs,tc_Com_Opname,x) -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Set_Ovimage(c_COMBK(u,v,w),w,v),tc_Com_Opname,x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),v_x)**.
% 299.79/300.48 64171[0:SpR:646.1,317.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,x),hAPP(c_Set_Oinsert(hAPP(u,v_x),w),y)),hAPP(c_Set_Oinsert(v_x,x),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,x),y)))*.
% 299.79/300.48 64170[0:SpR:646.1,99.1] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) c_Fun_Oinj__on(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,x),v_x),hAPP(u,v_x))**.
% 299.79/300.48 64169[0:SpR:646.1,438.1] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) c_Fun_Oinj__on(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,x),v_x),hAPP(u,v_x))**.
% 299.79/300.48 64381[0:SpR:181.1,645.1] || c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(u,v,w),w,v),v_Procs,tc_Com_Opname,x) -> hBOOL(hAPP(hAPP(c_in(v),u),v_x)) equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_COMBK(u,v,w),w,v),tc_Com_Opname,x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),v_x)**.
% 299.79/300.48 64338[0:SpR:645.1,317.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,x),hAPP(c_Set_Oinsert(hAPP(u,v_x),w),y)),hAPP(c_Set_Oinsert(v_x,x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,x),y)))*.
% 299.79/300.48 64337[0:SpR:645.1,99.1] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,x),v_x),hAPP(u,v_x))**.
% 299.79/300.48 64336[0:SpR:645.1,438.1] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,x),v_x),hAPP(u,v_x))**.
% 299.79/300.48 64473[0:SpR:24914.0,662.1] || hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),tc_Com_Opname,w),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),v_x))))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(v,tc_bool)),v_x)).
% 299.79/300.48 64694[0:Res:27986.0,481.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))*.
% 299.79/300.48 64693[0:Res:27986.0,480.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs)))*.
% 299.79/300.48 64714[0:Res:27987.0,481.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))*.
% 299.79/300.48 64713[0:Res:27987.0,480.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs)))*.
% 299.79/300.48 64734[0:Res:28288.0,481.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))*.
% 299.79/300.48 64733[0:Res:28288.0,480.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs)))*.
% 299.79/300.48 64754[0:Res:28289.0,481.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))*.
% 299.79/300.48 64753[0:Res:28289.0,480.0] || -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),v_Procs)))*.
% 299.79/300.48 66727[0:SpR:1188.2,317.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,w),hAPP(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(u),v),x)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,w),x)))*.
% 299.79/300.48 67482[0:SpR:1189.2,317.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,w),hAPP(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(u),v),x)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,w),x)))*.
% 299.79/300.48 74118[7:SpL:71835.1,268.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,v)) hBOOL(hAPP(hAPP(c_in(u),w),v))* equal(hAPP(x,v_x),hAPP(x,w))* c_Fun_Oinj__on(x,v,u,y)* -> equal(v_x,w).
% 299.79/300.48 73899[7:SpR:71835.1,30.0] || equal(c_COMBB(c_Set_Ovimage(u,v,w),tc_fun(w,tc_bool),tc_fun(v,tc_bool),x),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v_x,x,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v_x,x,tc_fun(v,tc_bool)))**.
% 299.79/300.48 73898[7:SpR:71835.1,90.0] || equal(c_COMBB(c_Set_Oimage(u,v,w),tc_fun(v,tc_bool),tc_fun(w,tc_bool),x),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v_x,x,tc_fun(v,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v_x,x,tc_fun(w,tc_bool)))**.
% 299.79/300.48 73713[7:SpR:71835.1,240.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),v),c_Set_Oinsert(v_x,t_a))** c_Finite__Set_Ofinite(w,v) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,v_x,v,u)),c_Finite__Set_Ofold(v_x,x,w,v,u))**.
% 299.79/300.48 73708[7:SpR:71835.1,232.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.48 74524[7:MRR:74254.1,6340.0] || equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(w,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),x),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),x)))*.
% 299.79/300.48 74525[7:MRR:74253.1,6340.0] || equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(w,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v_x),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v_x)))*.
% 299.79/300.48 75718[7:SpR:71883.1,486.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_fun(w,tc_bool)))**.
% 299.79/300.48 77371[0:Res:2399.2,363.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool)) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.48 77474[7:SpL:71894.1,275.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 77734[0:SpL:600.0,5892.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))))* -> hBOOL(hAPP(c_COMBS(c_in(x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y,z,x1),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))))*.
% 299.79/300.48 77675[0:SpL:71.2,5892.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(v,hAPP(x,v)))* -> hBOOL(hAPP(c_COMBS(c_in(z),c_Fun_Othe__inv__into(w,x,u,y),x1,x2,x3),hAPP(x,v)))*.
% 299.79/300.48 77674[0:SpL:373.2,5892.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(v,hAPP(x,v)))* -> hBOOL(hAPP(c_COMBS(c_in(z),c_Hilbert__Choice_Oinv__into(w,x,u,y),x1,x2,x3),hAPP(x,v)))*.
% 299.79/300.48 77666[0:SpL:196.1,5892.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(x,hAPP(c_Set_Oimage(u,v,w),x)))* -> hBOOL(hAPP(c_COMBS(c_in(y),c_Set_Ovimage(u,v,w),z,x1,x2),hAPP(c_Set_Oimage(u,v,w),x)))*.
% 299.79/300.48 77663[0:SpL:317.0,5892.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),y)),hAPP(c_Set_Oinsert(v,x),y)))* -> hBOOL(hAPP(c_COMBS(c_in(z),c_Set_Oimage(u,x,w),x1,x2,x3),hAPP(c_Set_Oinsert(v,x),y)))*.
% 299.79/300.48 78684[4:Res:78665.1,481.0] || equal(hAPP(hAPP(c_in(u),v),w),v_x)** -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)))*.
% 299.79/300.48 78683[4:Res:78665.1,480.0] || equal(hAPP(hAPP(c_in(u),v),w),v_x)** -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w)))*.
% 299.79/300.48 79029[0:Res:15630.1,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) c_Hoare__Mirabelle_Ohoare__valids(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,x),y),z,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x),t_a)* c_Hoare__Mirabelle_Otriple__valid(x1,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x1),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x1,u,t_a)*.
% 299.79/300.48 79018[0:Res:15630.1,279.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,hAPP(c_in(u),v),x)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,hAPP(c_in(u),v),x))**.
% 299.79/300.48 79014[0:Res:15630.1,356.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oimage(c_COMBK(x,y,u),u,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,z),x1),x2,hAPP(c_in(u),v),z)),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.48 78983[0:SpR:181.1,15630.1] || hBOOL(hAPP(c_Set_Ovimage(c_COMBK(u,v,w),w,v),x)) -> hBOOL(hAPP(hAPP(c_in(v),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(x,y),z),x1,c_Set_Ovimage(c_COMBK(u,v,w),w,v),y)))* hBOOL(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.48 79249[0:Res:15858.1,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) c_Hoare__Mirabelle_Ohoare__valids(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(v,y),z),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),y),t_a)* c_Hoare__Mirabelle_Otriple__valid(x1,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x1),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x1,u,t_a)*.
% 299.79/300.48 79238[0:Res:15858.1,279.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(w,y),z),hAPP(c_in(u),v),y)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(w,y),z),hAPP(c_in(u),v),y))**.
% 299.79/300.48 79234[0:Res:15858.1,356.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oimage(c_COMBK(x,y,u),u,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,hAPP(c_Set_Oinsert(w,x1),x2),hAPP(c_in(u),v),x1)),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.48 79203[0:SpR:181.1,15858.1] || hBOOL(hAPP(c_Set_Ovimage(c_COMBK(u,v,w),w,v),x)) -> hBOOL(hAPP(hAPP(c_in(v),u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(x,z),x1),c_Set_Ovimage(c_COMBK(u,v,w),w,v),z)))* hBOOL(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.48 80306[0:SpL:21268.0,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_in(w),hAPP(c_in(w),x),v,y)),z))* hBOOL(hAPP(hAPP(c_in(w),x),x1))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,u,w,tc_fun(x2,tc_bool)),z))*.
% 299.79/300.48 80287[0:SpL:21268.0,390.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),z,x1),v,w,x),u,x,w)*.
% 299.79/300.48 80264[0:SpL:21268.0,514.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),z),x1))* -> equal(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),z),x2,x3))*.
% 299.79/300.48 80237[0:SpL:21268.0,6582.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,y),v,tc_fun(u,tc_bool))*.
% 299.79/300.48 80213[0:SpL:21268.0,278.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(w),v),hAPP(hAPP(c_in(w),v),x),y,z),x1,u,w)))*.
% 299.79/300.48 80212[0:SpL:21268.0,277.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(w),v),hAPP(hAPP(c_in(w),v),x),z,x1),u,w)))*.
% 299.79/300.48 80191[0:SpL:21268.0,12554.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),y,z)),u))*.
% 299.79/300.48 80123[0:SpL:21268.0,5892.0] || hBOOL(hAPP(hAPP(u,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,hAPP(u,v),w,x)))* -> hBOOL(hAPP(c_COMBS(c_in(y),u,z,x1,x2),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,hAPP(u,v),w,x)))*.
% 299.79/300.48 80089[0:SpL:21268.0,175.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),hAPP(c_Set_Oinsert(y,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))* -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1)),y)*.
% 299.79/300.48 80085[0:SpL:21268.0,470.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__XimageE__1__1(y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1),w,x,u)),y))*.
% 299.79/300.48 80084[0:SpL:21268.0,466.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(y,w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1),x,u)),y))*.
% 299.79/300.48 80010[0:SpL:21268.0,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,v)),v))* c_Hoare__Mirabelle_Otriple__valid(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x,y),t_a)*.
% 299.79/300.48 79963[0:SpR:128.0,21268.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool)),x,z)),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool)))**.
% 299.79/300.48 79911[0:SpR:538.0,21268.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v),w,y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v))**.
% 299.79/300.48 79796[0:SpR:21268.0,317.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(v,x),hAPP(c_Set_Oinsert(v,x),z),y,x1))),hAPP(c_Set_Oimage(u,x,w),hAPP(c_Set_Oinsert(v,x),z)))**.
% 299.79/300.48 79756[0:SpR:21268.0,10746.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),y),u,z),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),y),tc_bool)*.
% 299.79/300.48 79710[0:SpR:21268.0,328.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,y),w,tc_fun(v,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),w).
% 299.79/300.48 79709[0:SpR:21268.0,7830.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,y),hAPP(c_Set_Oinsert(z,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),tc_fun(v,tc_bool))*.
% 299.79/300.48 79641[0:SpR:21268.0,128.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),y),x,z),tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool)))**.
% 299.79/300.48 79555[0:SpR:21268.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(w,x),v,y)),z))* -> equal(hAPP(c_Set_Oinsert(hAPP(w,x),x1),hAPP(c_Set_Oimage(w,u,x1),z)),hAPP(c_Set_Oimage(w,u,x1),z))**.
% 299.79/300.48 79543[0:SpR:21268.0,5887.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1),v,x2),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1),u)*.
% 299.79/300.48 79542[0:SpR:21268.0,5888.1] class_Lattices_Olattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1),v,x2),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1),u)*.
% 299.79/300.48 79541[0:SpR:21268.0,37898.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,w,x,y),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,w,x,y),z),v,x1)))* -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,w,x,y),z)).
% 299.79/300.48 79442[4:SpR:21268.0,40244.1] || c_lessequals(v_x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),z),u,x1),tc_bool)* -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),z)).
% 299.79/300.48 81501[0:SpL:21894.0,280.1] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(w),x),c_in(w),v,y)),z))* hBOOL(hAPP(hAPP(c_in(w),x),x1))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,u,w,tc_fun(x2,tc_bool)),z))*.
% 299.79/300.48 81482[0:SpL:21894.0,390.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),z,x1),v,w,x),u,x,w)*.
% 299.79/300.48 81459[0:SpL:21894.0,514.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),z),x1))* -> equal(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),z),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),x2,x3))*.
% 299.79/300.48 81432[0:SpL:21894.0,6582.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,y),v,tc_fun(u,tc_bool))*.
% 299.79/300.48 81408[0:SpL:21894.0,278.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_in(w),v),x),hAPP(c_in(w),v),y,z),x1,u,w)))*.
% 299.79/300.48 81407[0:SpL:21894.0,277.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),x)) -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_in(w),v),x),hAPP(c_in(w),v),z,x1),u,w)))*.
% 299.79/300.48 81386[0:SpL:21894.0,12554.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),y,z)),u))*.
% 299.79/300.48 81318[0:SpL:21894.0,5892.0] || hBOOL(hAPP(hAPP(u,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(u,v),u,w,x)))* -> hBOOL(hAPP(c_COMBS(c_in(y),u,z,x1,x2),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(u,v),u,w,x)))*.
% 299.79/300.48 81284[0:SpL:21894.0,175.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),hAPP(c_Set_Oinsert(y,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))* -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1)),y)*.
% 299.79/300.48 81280[0:SpL:21894.0,470.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__XimageE__1__1(y,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1),w,x,u)),y))*.
% 299.79/300.48 81279[0:SpL:21894.0,466.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(y,w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1),x,u)),y))*.
% 299.79/300.48 81205[0:SpL:21894.0,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,v)),v))* c_Hoare__Mirabelle_Otriple__valid(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x,y),t_a)*.
% 299.79/300.48 81157[0:SpR:128.0,21894.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool)),c_Set_Ovimage(u,v,w),x,z)),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool)))**.
% 299.79/300.48 81105[0:SpR:538.0,21894.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v))**.
% 299.79/300.48 80990[0:SpR:21894.0,317.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(v,x),z),c_Set_Oinsert(v,x),y,x1))),hAPP(c_Set_Oimage(u,x,w),hAPP(c_Set_Oinsert(v,x),z)))**.
% 299.79/300.48 80950[0:SpR:21894.0,10746.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),y),hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),u,z),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),y),tc_bool)*.
% 299.79/300.48 80904[0:SpR:21894.0,328.1] || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,y),w,tc_fun(v,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),w).
% 299.79/300.48 80903[0:SpR:21894.0,7830.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,y),hAPP(c_Set_Oinsert(z,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),tc_fun(v,tc_bool))*.
% 299.79/300.48 80835[0:SpR:21894.0,128.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),y),c_Set_Ovimage(u,v,w),x,z),tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool)))**.
% 299.79/300.48 80748[0:SpR:21894.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(w,x),w,v,y)),z))* -> equal(hAPP(c_Set_Oinsert(hAPP(w,x),x1),hAPP(c_Set_Oimage(w,u,x1),z)),hAPP(c_Set_Oimage(w,u,x1),z))**.
% 299.79/300.48 80736[0:SpR:21894.0,5887.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),v,x2),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1),u)*.
% 299.79/300.48 80735[0:SpR:21894.0,5888.1] class_Lattices_Olattice(u) || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),v,x2),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1),u)*.
% 299.79/300.48 80734[0:SpR:21894.0,37898.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,w,x,y),z),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,w,x,y),v,x1)))* -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,w,x,y),z)).
% 299.79/300.48 80635[4:SpR:21894.0,40244.1] || c_lessequals(v_x,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),z),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),u,x1),tc_bool)* -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v,w,x,y),z)).
% 299.79/300.48 83795[0:SpR:5899.0,21894.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_COMBS(u,v,x1,x2,x3),x4),c_COMBS(u,v,x1,x2,x3),z,x5)),hAPP(c_COMBS(u,v,x1,x2,x3),x4))**.
% 299.79/300.48 83793[0:SpR:5899.0,21268.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_COMBS(u,v,x1,x2,x3),hAPP(c_COMBS(u,v,x1,x2,x3),x4),z,x5)),hAPP(c_COMBS(u,v,x1,x2,x3),x4))**.
% 299.79/300.48 83758[0:SpR:5899.0,21894.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_COMBS(u,v,x1,x2,x3),x4),c_COMBS(u,v,w,x,y),z,x5)),hAPP(c_COMBS(u,v,x1,x2,x3),x4))**.
% 299.79/300.48 83757[0:SpR:5899.0,21268.0] || -> equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_COMBS(u,v,w,x,y),hAPP(c_COMBS(u,v,x1,x2,x3),x4),z,x5)),hAPP(c_COMBS(u,v,x1,x2,x3),x4))**.
% 299.79/300.48 84908[4:SpL:104.0,78744.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),w),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),w,t_a).
% 299.79/300.48 85520[4:SpL:78507.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,y),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 85929[0:SpL:197.1,13582.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),z))* hBOOL(hAPP(hAPP(c_in(w),z),hAPP(c_Set_Oimage(u,v,w),y)))* -> .
% 299.79/300.48 86570[0:SpR:197.1,19823.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),x),y)) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(z,x,tc_fun(v,tc_bool))),tc_fun(w,tc_bool)),y))*.
% 299.79/300.48 87147[7:Res:82177.0,268.0] || hBOOL(hAPP(hAPP(c_in(t_a),u),hAPP(c_Set_Oinsert(v,t_a),c_Set_Oinsert(v_x,w))))* equal(hAPP(x,v_x),hAPP(x,u))* c_Fun_Oinj__on(x,hAPP(c_Set_Oinsert(v,t_a),c_Set_Oinsert(v_x,w)),t_a,y)* -> equal(v_x,u).
% 299.79/300.48 87322[7:SpR:533.0,71492.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),x))*.
% 299.79/300.48 87470[7:SpR:533.0,71493.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),x,t_a)*.
% 299.79/300.48 87600[7:SpR:533.0,71679.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.48 88427[0:Res:8176.1,231.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),c_HOL_Ominus__class_Ominus(u,z,tc_fun(x,tc_bool))),y,tc_fun(w,tc_bool))*.
% 299.79/300.48 88415[0:SpR:197.1,8176.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,z,tc_fun(v,tc_bool))),y,tc_fun(w,tc_bool))*.
% 299.79/300.48 88559[0:Res:340.2,8306.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* c_lessequals(y,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),y),v,tc_fun(x,tc_bool))*.
% 299.79/300.48 88547[0:SpL:197.1,8306.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(x,hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(y,z,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))* -> c_lessequals(x,hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)).
% 299.79/300.48 88904[0:SpR:537.1,14196.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),z))*.
% 299.79/300.48 88903[0:SpR:534.1,14196.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),z))*.
% 299.79/300.48 88901[0:SpR:536.1,14196.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)))*.
% 299.79/300.48 88900[0:SpR:535.1,14196.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)))*.
% 299.79/300.48 89043[0:Res:78099.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))* equal(hAPP(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),hAPP(x,v))* c_Fun_Oinj__on(x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),u,z)* -> equal(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),v).
% 299.79/300.48 89042[0:Res:78099.0,481.0] || -> hBOOL(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),y),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),y)))*.
% 299.79/300.48 89041[0:Res:78099.0,480.0] || -> hBOOL(hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))*.
% 299.79/300.48 89538[7:SpL:78590.1,275.1] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(x),y),u))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 89708[7:Res:89344.1,239.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),w),c_Set_Oinsert(v_x,t_a)) c_lessequals(w,x,tc_fun(v,tc_bool)) c_Fun_Oinj__on(u,w,v,t_a) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Fun_Othe__inv__into(w,u,v,t_a),v_x)),x))*.
% 299.79/300.48 89691[7:Res:89344.1,483.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),c_Set_Oinsert(v_x,t_a))** -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)),u))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)),v))*.
% 299.79/300.48 90329[4:SpL:78660.1,275.1] || equal(hAPP(u,v_x),v_x) hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(x),y),u))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 90778[0:Res:84.1,26480.0] || c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool)),x,tc_fun(v,tc_bool))* -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)).
% 299.79/300.48 90852[4:Res:90134.1,239.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),v_x) c_lessequals(w,x,tc_fun(v,tc_bool)) c_Fun_Oinj__on(u,w,v,t_a) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Fun_Othe__inv__into(w,u,v,t_a),v_x)),x))*.
% 299.79/300.48 90835[4:Res:90134.1,483.0] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),v_x)** -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)),u))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)),v))*.
% 299.79/300.48 91855[4:SpL:131.0,78747.0] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),tc_Com_Opname))),v_x)** -> hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_x)).
% 299.79/300.48 91854[4:SpL:158.0,78747.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),tc_Com_Opname))),v_x)** -> hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x)).
% 299.79/300.48 91984[0:SpL:79073.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w))* hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_Procs,z),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 92146[7:SpL:79101.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(v),v_x)),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_in(v),v_x)))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,z),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 92212[0:Res:4019.2,251.1] class_Orderings_Olinorder(tc_fun(u,v)) class_OrderedGroup_Opordered__ab__group__add(tc_fun(u,v)) class_HOL_Oord(v) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),w,tc_fun(u,v)) c_lessequals(hAPP(c_HOL_Ozero__class_Ozero(tc_fun(u,v)),x),hAPP(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,v)),x),v)*.
% 299.79/300.48 92646[7:SpR:533.0,82151.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Set_Oinsert(v_x,x)))*.
% 299.79/300.48 92881[0:SpR:537.1,5876.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),z,x1,x2),x),tc_fun(y,tc_bool))*.
% 299.79/300.48 92880[0:SpR:534.1,5876.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),z,x1,x2),x),tc_fun(y,tc_bool))*.
% 299.79/300.48 92878[0:SpR:536.1,5876.0] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)),tc_fun(y,tc_bool))*.
% 299.79/300.48 92877[0:SpR:535.1,5876.0] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)),tc_fun(y,tc_bool))*.
% 299.79/300.48 93306[4:SpR:533.0,85556.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),x),tc_bool)*.
% 299.79/300.48 93494[0:SpR:533.0,86147.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),x))*.
% 299.79/300.48 93645[0:SpR:533.0,86148.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),x,t_a)*.
% 299.79/300.48 93789[0:SpR:533.0,86342.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.48 16796[0:Res:47.2,390.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x),tc_fun(u,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(x,v,w,u),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(v,w,u),x),tc_fun(u,tc_bool)),u,w)*.
% 299.79/300.48 17362[0:Res:172.2,147.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),u) hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMax(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),u)),w))* -> equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.79/300.48 17480[0:Res:171.2,147.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),u) hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMin(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),u)),w))* -> equal(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.79/300.48 19357[0:SSi:19316.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool))* c_lessequals(z,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool))* c_Finite__Set_Ofinite(y,w) -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),z),x)*.
% 299.79/300.48 19358[0:SSi:19308.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,v,tc_fun(w,tc_bool)) c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),tc_fun(w,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v).
% 299.79/300.48 19794[0:SpR:104.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(y,v,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_HOL_Ouminus__class_Ouminus(y,tc_fun(z,tc_bool))),u,x),w)))*.
% 299.79/300.48 19793[0:SpR:104.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(y,tc_bool))),u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.48 19756[0:SpR:104.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))))**.
% 299.79/300.48 19977[0:SpR:64.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool))),y))* -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oinsert(w,x),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(w,x),u,z),y)))*.
% 299.79/300.48 19976[0:SpR:64.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool))),y))* -> c_lessequals(hAPP(c_Set_Oinsert(w,x),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(w,x),u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.48 19966[0:SpR:64.0,9493.1] || equal(hAPP(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v_x,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),tc_fun(t_a,tc_bool)),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v_x,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),tc_fun(t_a,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),u)).
% 299.79/300.48 19959[0:SpR:64.0,8498.1] || equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** -> equal(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),u)).
% 299.79/300.48 20281[0:SpR:438.1,545.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),z)) -> hBOOL(hAPP(hAPP(c_in(x1),y),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,x1),z)))*.
% 299.79/300.48 20280[0:SpR:438.1,362.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),z)) -> c_lessequals(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.48 20488[0:SpR:329.1,99.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y),v),v)**.
% 299.79/300.48 20423[0:SpR:99.1,545.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),z)) -> hBOOL(hAPP(hAPP(c_in(x1),y),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,x1),z)))*.
% 299.79/300.48 20422[0:SpR:99.1,362.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),z)) -> c_lessequals(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.48 21008[0:SpR:12944.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y,z),hAPP(c_Set_Oinsert(x1,y),x2)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),z),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y,z),x2)))*.
% 299.79/300.48 20986[0:SpR:11473.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,x),hAPP(c_Set_Oinsert(y,w),z)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,x),z)))*.
% 299.79/300.48 20978[0:SpR:329.1,317.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y),hAPP(c_Set_Oinsert(v,x),z)),hAPP(c_Set_Oinsert(v,y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y),z)))*.
% 299.79/300.48 20977[0:SpR:328.1,317.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,y),hAPP(c_Set_Oinsert(u,x),z)),hAPP(c_Set_Oinsert(v,y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,y),z)))*.
% 299.79/300.48 20975[0:SpR:538.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(y,w),z)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),z)))*.
% 299.79/300.48 20967[0:SpR:17045.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x,y),hAPP(c_Set_Oinsert(z,x),x1)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),y),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x,y),x1)))*.
% 299.79/300.48 20880[0:SpR:317.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) -> hBOOL(hAPP(hAPP(c_in(x1),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(x2,w),y))),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(v,x2),x),u,x1),z)))*.
% 299.79/300.48 20879[0:SpR:317.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(x1,w),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oinsert(hAPP(v,x1),x),u,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.79/300.48 20843[0:SpR:317.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oinsert(hAPP(x1,v),x2),hAPP(c_Set_Oimage(x1,w,x2),x))),hAPP(c_Set_Oimage(c_Set_Oimage(x1,w,x2),u,z),y)))*.
% 299.79/300.48 20842[0:SpR:317.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> c_lessequals(hAPP(c_Set_Oinsert(hAPP(z,v),x1),hAPP(c_Set_Oimage(z,w,x1),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oimage(z,w,x1),u,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.79/300.48 21658[0:SpL:21267.0,513.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),v_x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),x),y),z))* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),v_x),tc_Com_Opname,x1),z)*.
% 299.79/300.48 22286[0:SpL:21893.0,513.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),v_x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),x),y),z))* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),v_x),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),tc_Com_Opname,x1),z)*.
% 299.79/300.48 22406[0:SpR:97.1,545.1] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oimage(u,w,x),v)),z)) -> hBOOL(hAPP(hAPP(c_in(x1),v),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,x1),z)))*.
% 299.79/300.48 22405[0:SpR:97.1,362.1] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oimage(u,w,x),v)),z)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.48 22614[0:SpR:158.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) -> hBOOL(hAPP(hAPP(c_in(x1),hAPP(c_Set_Oimage(c_Fun_Ocomp(x2,v,x,x3,w),w,x3),y)),hAPP(c_Set_Oimage(c_Set_Oimage(x2,x,x3),u,x1),z)))*.
% 299.79/300.48 22613[0:SpR:158.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(x1,v,x,x2,w),w,x2),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(x1,x,x2),u,tc_fun(x3,tc_bool)),tc_fun(x3,tc_bool))*.
% 299.79/300.48 22572[0:SpR:158.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,z,x1),hAPP(c_Set_Oimage(x2,x3,z),v))),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(y,x2,z,x1,x3),x3,x1),u,x),w)))*.
% 299.79/300.48 22571[0:SpR:158.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oimage(x,y,z),hAPP(c_Set_Oimage(x1,x2,y),v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_Fun_Ocomp(x,x1,y,z,x2),x2,z),u,tc_fun(x3,tc_bool)),tc_fun(x3,tc_bool))*.
% 299.79/300.48 22569[0:SpR:158.0,97.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),z,y,x) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(z,c_Fun_Ocomp(u,v,w,x,y),y,x),x,y),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),z))),z)**.
% 299.79/300.48 22990[0:SpR:131.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),z)) -> hBOOL(hAPP(hAPP(c_in(x1),hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,x2,w,x,x3),x3,x),y)),hAPP(c_Set_Oimage(c_Set_Ovimage(x2,x3,w),u,x1),z)))*.
% 299.79/300.48 22989[0:SpR:131.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),z)) -> c_lessequals(hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,x1,w,x,x2),x2,x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Ovimage(x1,x2,w),u,tc_fun(x3,tc_bool)),tc_fun(x3,tc_bool))*.
% 299.79/300.48 22955[0:SpR:131.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Ovimage(y,z,x1),hAPP(c_Set_Ovimage(x2,x1,x3),v))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(x2,y,x1,x3,z),z,x3),u,x),w)))*.
% 299.79/300.48 22954[0:SpR:131.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Ovimage(x,y,z),hAPP(c_Set_Ovimage(x1,z,x2),v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(c_Fun_Ocomp(x1,x,z,x2,y),y,x2),u,tc_fun(x3,tc_bool)),tc_fun(x3,tc_bool))*.
% 299.79/300.48 23383[0:SpR:460.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || class_Lattices_Olattice(t_b) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v,u),u)*.
% 299.79/300.48 23379[0:SpR:460.1,176.0] || class_Lattices_Olattice(t_b) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,v),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))))*.
% 299.79/300.48 23514[0:SpR:523.1,361.2] class_Lattices_Olattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(y,v_x)),hAPP(z,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),y),z),w,v),v)*.
% 299.79/300.48 23510[0:SpR:523.1,176.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Ovimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x),v,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.48 24150[0:SpR:542.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),z)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v,u),u)*.
% 299.79/300.48 24139[0:SpR:542.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))))*.
% 299.79/300.48 24329[0:SpR:393.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))* c_lessequals(hAPP(c_Set_Oinsert(z,x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oimage(c_COMBK(z,x1,y),y,x1),v,u),u)*.
% 299.79/300.48 24321[0:SpR:393.1,176.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),u),hAPP(c_Set_Ovimage(c_Set_Oimage(c_COMBK(x,y,v),v,y),w,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.48 24782[0:SpR:614.2,361.2] class_Complete__Lattice_Ocomplete__lattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || c_Finite__Set_Ofinite(w,x) hBOOL(hAPP(hAPP(c_in(y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,z,x,u)),x1)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,z,x,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),y,v),v)*.
% 299.79/300.48 24771[0:SpR:614.2,176.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,z),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.48 24924[0:Res:168.0,467.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x),t_a) equal(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x)))),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Set_Oimage(v,w,tc_Hoare__Mirabelle_Otriple(t_a)),x)))**.
% 299.79/300.48 24897[0:SpL:97.1,467.0] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(w),y),v)) -> equal(hAPP(c_Fun_Othe__inv__into(v,u,w,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,w,x),v),c_Fun_Othe__inv__into(v,u,w,x),x,w),y)),y)**.
% 299.79/300.48 25370[0:SpR:512.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(c_Set_Oimage(y,z,x1),hAPP(c_Set_Oimage(x2,x3,z),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oimage(hAPP(c_COMBB(y,z,x1,x3),x2),x3,x1),v,u),u)*.
% 299.79/300.48 25362[0:SpR:512.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_Set_Oimage(hAPP(c_COMBB(w,x,y,z),x1),z,y),u,x2),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(w,x,y),hAPP(c_Set_Oimage(x1,z,x),v)),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))))))*.
% 299.79/300.48 25510[0:Rew:25273.0,25410.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBB(u,v,w,x),v_x),c_COMBB(u,v,w,x),tc_Com_Opname,y),x,v),z)),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v_x,v,w,x),x,w),z))**.
% 299.79/300.48 25511[0:Rew:25273.0,25409.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBB(u,v,w,x),hAPP(c_COMBB(u,v,w,x),v_x),tc_Com_Opname,y),x,v),z)),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v_x,v,w,x),x,w),z))**.
% 299.79/300.48 25512[0:Rew:25273.0,25382.0] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)) -> hBOOL(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,v_Procs,c_Set_Oimage(hAPP(c_COMBB(u,w,x,y),v),y,x),tc_Com_Opname))))*.
% 299.79/300.48 25513[0:Rew:25273.0,25381.0] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x)) -> hBOOL(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,z,c_Set_Oimage(hAPP(c_COMBB(u,w,x,y),v),y,x),tc_Com_Opname))))*.
% 299.79/300.48 25994[0:SpL:339.0,19641.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),x))))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),x,t_a).
% 299.79/300.48 26250[0:SpL:338.0,208.0] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),y)),tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),x),u)) c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y),tc_fun(v,tc_bool)).
% 299.79/300.48 26093[0:SpR:338.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y,z),hAPP(c_Set_Oinsert(x1,u),x2)),hAPP(hAPP(c_Set_Oinsert(x1,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x2)),hAPP(w,hAPP(c_Set_Oinsert(x1,u),x2))))*.
% 299.79/300.48 26092[0:SpR:338.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y,z),hAPP(c_Set_Oinsert(x1,v),x2)),hAPP(hAPP(u,hAPP(c_Set_Oinsert(x1,v),x2)),hAPP(c_Set_Oinsert(x1,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x2))))*.
% 299.79/300.48 26954[0:Res:424.2,390.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) c_lessequals(z,hAPP(c_Set_Oimage(w,x,u),y),tc_fun(u,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(y,w,x,u),hAPP(c_Set_Oinsert(v,u),z),u,x)*.
% 299.79/300.48 27068[0:SpL:21893.0,280.1] || hBOOL(hAPP(hAPP(u,v),w)) hBOOL(hAPP(hAPP(c_in(x),v),v_x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(x),v),v_x),hAPP(c_in(x),v),tc_Com_Opname,y),u,x,tc_fun(z,tc_bool)),w))*.
% 299.79/300.48 27067[0:SpL:21267.0,280.1] || hBOOL(hAPP(hAPP(u,v),w)) hBOOL(hAPP(hAPP(c_in(x),v),v_x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(x),v),hAPP(hAPP(c_in(x),v),v_x),tc_Com_Opname,y),u,x,tc_fun(z,tc_bool)),w))*.
% 299.79/300.48 27192[0:Res:450.0,371.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Set_Oinsert(v,w)),x),y),t_a) hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oinsert(v,w),y,x,u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Set_Oinsert(v,w),y,x,u)))* equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Set_Oinsert(v,w),y,x,u),v).
% 299.79/300.48 27168[0:SpR:15172.0,450.0] || -> hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y,z,x1))) c_Hoare__Mirabelle_Otriple__valid(x1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool))),z),y),t_a)*.
% 299.79/300.48 27138[0:SpR:300.1,450.0] class_Lattices_Obounded__lattice(u) || -> hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w,x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w,x)))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u))),w),v),t_a).
% 299.79/300.48 27629[0:SpR:105.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_Set_Ovimage(x,y,v),w,u,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Ovimage(x,y,v),u,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.79/300.48 27622[0:SpR:38.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_Set_Ovimage(x,y,v),w,u,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Ovimage(x,y,v),u,z),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.48 27621[0:SpR:321.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_Set_Oimage(x,v,y),w,u,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oimage(x,v,y),u,z),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.48 27615[0:SpR:14216.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),w,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Set_Oinsert(x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),u,x1),c_Orderings_Otop__class_Otop(tc_bool)),v)*.
% 299.79/300.48 27613[0:SpR:584.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x)) c_Fun_Oinj__on(hAPP(y,w),x,u,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,hAPP(y,w),u,z),hAPP(c_COMBS(y,v,x1,x2,x3),w)),hAPP(v,w))**.
% 299.79/300.48 27560[0:SpR:25.1,373.2] class_HOL_Ouminus(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,u)),w,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,u)),v,y),c_HOL_Ouminus__class_Ouminus(hAPP(x,v_x),u)),v_x)**.
% 299.79/300.48 27545[0:SpR:653.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,w),w,tc_Com_Opname),v,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,w),w,tc_Com_Opname),u,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_Procs)**.
% 299.79/300.48 27542[0:SpR:445.1,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Fun_Ofun__upd(x,y,z,x1,x2),w,u,x3) -> equal(v,y) equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Fun_Ofun__upd(x,y,z,x1,x2),u,x3),hAPP(x,v)),v)**.
% 299.79/300.48 27782[0:SpR:105.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_Set_Ovimage(x,y,v),w,u,z) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Ovimage(x,y,v),u,z),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.79/300.48 27775[0:SpR:38.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_Set_Ovimage(x,y,v),w,u,z) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Ovimage(x,y,v),u,z),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.48 27774[0:SpR:321.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_Set_Oimage(x,v,y),w,u,z) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oimage(x,v,y),u,z),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.48 27768[0:SpR:14216.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),w,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Set_Oinsert(x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),u,x1),c_Orderings_Otop__class_Otop(tc_bool)),v)*.
% 299.79/300.48 27766[0:SpR:584.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x)) c_Fun_Oinj__on(hAPP(y,w),x,u,z) -> equal(hAPP(c_Fun_Othe__inv__into(x,hAPP(y,w),u,z),hAPP(c_COMBS(y,v,x1,x2,x3),w)),hAPP(v,w))**.
% 299.79/300.48 27713[0:SpR:25.1,71.2] class_HOL_Ouminus(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,u)),w,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,u)),v,y),c_HOL_Ouminus__class_Ouminus(hAPP(x,v_x),u)),v_x)**.
% 299.79/300.48 27697[0:SpR:653.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,w),w,tc_Com_Opname),v,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,w),w,tc_Com_Opname),u,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_Procs)**.
% 299.79/300.48 27694[0:SpR:445.1,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Fun_Ofun__upd(x,y,z,x1,x2),w,u,x3) -> equal(v,y) equal(hAPP(c_Fun_Othe__inv__into(w,c_Fun_Ofun__upd(x,y,z,x1,x2),u,x3),hAPP(x,v)),v)**.
% 299.79/300.48 27930[0:Res:468.0,150.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),w,x,u,y)),v))* -> equal(hAPP(c_Set_Oimage(w,u,y),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(x,u,y),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)))).
% 299.79/300.48 28128[0:SpR:465.1,83.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),z)))* c_lessequals(hAPP(c_Set_Oimage(w,u,y),hAPP(c_Set_Ovimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),z)),z,tc_fun(y,tc_bool))*.
% 299.79/300.48 28526[0:SpR:14216.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Fun_Ofun__upd(x,y,z,x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,x2,x3,x1),y,c_Orderings_Otop__class_Otop(tc_bool),x1,x3))*.
% 299.79/300.48 28470[0:SpR:25.1,118.0] class_HOL_Ouminus(u) || -> equal(c_Fun_Ocomp(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),c_Fun_Ofun__upd(w,x,v_x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w,z,x1,y),x,c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u),y,x1))*.
% 299.79/300.48 28453[0:SpR:653.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),c_Fun_Ofun__upd(v,w,v_Procs,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),v,y,z,x),w,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),x,z))*.
% 299.79/300.48 28450[0:SpR:445.1,118.0] || -> equal(u,v) equal(c_Fun_Ocomp(c_Fun_Ofun__upd(w,v,x,y,z),c_Fun_Ofun__upd(x1,x2,u,x3,x4),x4,x5,x3),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Fun_Ofun__upd(w,v,x,y,z),x1,x4,x5,x3),x2,hAPP(w,u),x3,x5))*.
% 299.79/300.48 28621[0:SpR:353.0,177.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x))) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(v,u),x)),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(w,u),x))**.
% 299.79/300.48 29197[0:SpL:537.1,19641.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x))))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,t_a).
% 299.79/300.48 29294[0:SSi:29077.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))**.
% 299.79/300.48 29722[0:SpL:534.1,19641.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x))))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,t_a).
% 299.79/300.48 30481[0:SSi:30307.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x))** -> c_lessequals(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),tc_fun(u,tc_bool)).
% 299.79/300.48 30483[0:SSi:30133.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))**.
% 299.79/300.48 31424[0:SpL:586.0,449.0] || hBOOL(hAPP(u,hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,c_COMBB(u,w,x,y),z,x1),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,c_COMBB(u,w,x,y),z,x1))))* -> c_Hoare__Mirabelle_Otriple__valid(x1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),z),c_COMBB(u,w,x,y)),t_a).
% 299.79/300.48 31423[0:SpL:585.0,449.0] || hBOOL(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,c_COMBC(u,w,x,y),z,x1)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,c_COMBC(u,w,x,y),z,x1)))* -> c_Hoare__Mirabelle_Otriple__valid(x1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),z),c_COMBC(u,w,x,y)),t_a).
% 299.79/300.48 31416[0:SpL:538.0,449.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w,x)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w,x)))* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool))),t_a).
% 299.79/300.48 31412[0:SpL:297.2,449.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,c_Lattices_Oupper__semilattice__class_Osup(u),w,x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,c_Lattices_Oupper__semilattice__class_Osup(u),w,x),u)* hBOOL(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,c_Lattices_Oupper__semilattice__class_Osup(u),w,x)) -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),c_Lattices_Oupper__semilattice__class_Osup(u)),t_a).
% 299.79/300.48 31409[0:SpL:299.2,449.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,c_Lattices_Oupper__semilattice__class_Osup(u),w,x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,c_Lattices_Oupper__semilattice__class_Osup(u),w,x),u)* hBOOL(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,c_Lattices_Oupper__semilattice__class_Osup(u),w,x)) -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),c_Lattices_Oupper__semilattice__class_Osup(u)),t_a).
% 299.79/300.48 31520[0:SpL:465.1,473.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),z),y)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Hilbert__Choice_Oinv__into(y,c_Fun_Ofun__upd(w,z,x1,x,u),x,u),v)),y))*.
% 299.79/300.48 31999[0:SpR:118.0,383.1] || -> equal(u,v) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(c_Fun_Ocomp(w,x,y,z,x1),u,x2,x1,z),v,hAPP(w,x3),x1,z),c_Fun_Ofun__upd(c_Fun_Ocomp(w,c_Fun_Ofun__upd(x,v,x3,x1,y),y,z,x1),u,x2,x1,z))*.
% 299.79/300.48 31975[0:SpR:383.1,118.0] || -> equal(u,v) equal(c_Fun_Ocomp(w,c_Fun_Ofun__upd(c_Fun_Ofun__upd(x,u,y,z,x1),v,x2,z,x1),x1,x3,z),c_Fun_Ofun__upd(c_Fun_Ocomp(w,c_Fun_Ofun__upd(x,v,x2,z,x1),x1,x3,z),u,hAPP(w,y),z,x3))*.
% 299.79/300.48 31969[0:SpR:383.1,465.1] || -> equal(u,v) hBOOL(hAPP(hAPP(c_in(w),u),x)) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(c_Fun_Ofun__upd(y,u,z,w,x1),v,x2,w,x1),w,x1),x),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,x2,w,x1),w,x1),x))**.
% 299.79/300.48 32056[0:Res:151.2,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),u) -> hBOOL(hAPP(hAPP(c_in(u),v),x)) c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),u),v,u)*.
% 299.79/300.48 32055[0:Res:151.2,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),u) -> hBOOL(hAPP(hAPP(c_in(u),v),x)) c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),u),u)*.
% 299.79/300.48 32053[0:Res:151.2,356.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(u),v),x))* equal(hAPP(c_Set_Oimage(c_COMBK(y,z,u),u,z),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))**.
% 299.79/300.48 33005[0:SpR:1196.1,475.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,x),w))**.
% 299.79/300.48 33001[0:SpR:3294.1,475.1] || equal(c_in(t_a),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x),hAPP(c_Set_Oimage(hAPP(u,v_x),v,x),w)),hAPP(c_Set_Oimage(hAPP(u,v_x),v,x),w))**.
% 299.79/300.48 32997[0:SpR:330.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> equal(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),u,y),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),u,y),w))**.
% 299.79/300.48 32996[0:SpR:1195.1,475.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,x),w))**.
% 299.79/300.48 32990[0:SpR:584.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_COMBS(y,v,z,x1,x2),w),x3),hAPP(c_Set_Oimage(hAPP(y,w),u,x3),x)),hAPP(c_Set_Oimage(hAPP(y,w),u,x3),x))**.
% 299.79/300.48 32988[0:SpR:9936.1,475.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),w),x))* -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,y),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,y),x))**.
% 299.79/300.48 32984[0:SpR:9935.1,475.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),u),w))* -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v,x),w))**.
% 299.79/300.48 33434[0:Res:171.2,453.0] class_Orderings_Olinorder(tc_Hoare__Mirabelle_Otriple(t_a)) || c_Finite__Set_Ofinite(u,tc_Hoare__Mirabelle_Otriple(t_a)) c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,c_Finite__Set_Olinorder__class_OMin(u,tc_Hoare__Mirabelle_Otriple(t_a)),t_a)*.
% 299.79/300.48 33433[0:Res:172.2,453.0] class_Orderings_Olinorder(tc_Hoare__Mirabelle_Otriple(t_a)) || c_Finite__Set_Ofinite(u,tc_Hoare__Mirabelle_Otriple(t_a)) c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,c_Finite__Set_Olinorder__class_OMax(u,tc_Hoare__Mirabelle_Otriple(t_a)),t_a)*.
% 299.79/300.48 34421[0:SpL:24914.0,467.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> equal(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,x,u),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,x,u),v_x)),w,x,u),v)),v)**.
% 299.79/300.48 34394[0:SpL:24914.0,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),w)) -> hBOOL(hAPP(v,w)) hBOOL(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),w))*.
% 299.79/300.48 34392[0:SpL:24914.0,324.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),w,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),w,tc_fun(u,tc_bool))*.
% 299.79/300.48 34200[0:SpR:130.1,24914.0] class_HOL_Ominus(u) || -> equal(hAPP(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),tc_Com_Opname,x),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))**.
% 299.79/300.48 34513[0:Rew:523.1,34189.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),tc_Com_Opname,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v_x)),v_x)),hAPP(w,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v_x,v_x)),hAPP(w,v_x)))**.
% 299.79/300.48 34113[0:SpR:24914.0,517.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),tc_Com_Opname,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x))))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),v_x)).
% 299.79/300.48 34111[0:SpR:24914.0,518.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),tc_Com_Opname,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x))))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u),v_x)).
% 299.79/300.48 33917[0:SpR:24914.0,8498.1] || equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))** -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),hAPP(c_Set_Oinsert(u,v),v_x)).
% 299.79/300.48 33911[0:SpR:24914.0,463.1] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Obody,tc_Com_Opname,u),hAPP(c_Com_Obody,v_x))),v,w,x) -> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x)),v,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Obody,tc_Com_Opname,u),hAPP(c_Com_Obody,v_x)),w,v,x),x)*.
% 299.79/300.48 34556[0:SpR:34427.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)) -> equal(hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,x),u,w),v)),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,x),u,w),v))**.
% 299.79/300.48 34662[0:SpL:55.1,62.0] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,w),x),y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),w)* -> hBOOL(hAPP(hAPP(c_in(w),v),y)) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),w).
% 299.79/300.48 34596[0:SpR:55.1,63.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),x) -> hBOOL(hAPP(hAPP(c_in(x),y),w)) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(y,x),v),w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),x)*.
% 299.79/300.48 34595[0:SpR:55.1,446.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(x),y),w)) c_lessequals(hAPP(c_Set_Oinsert(y,x),u),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(y,x),v),w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.48 34576[0:SpR:55.1,446.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),y),v)) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(y,w),u),v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(y,w),x),tc_fun(w,tc_bool))*.
% 299.79/300.48 34677[0:MRR:34593.0,56.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),tc_Hoare__Mirabelle_Otriple(t_a)),v),w,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)))**.
% 299.79/300.48 35409[0:SpR:27043.1,410.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),c_Set_Oinsert(v_Procs,w),u,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_Procs,w),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 35403[0:SpR:10063.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u),v),c_Set_Oinsert(v_x,t_a),u,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,t_a),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 35384[0:SpR:105.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v),w),c_Set_Ovimage(x,y,u),v,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(x,y,u),v,tc_fun(z,tc_bool))))*.
% 299.79/300.48 35376[0:SpR:38.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),w),c_Set_Ovimage(x,y,u),v,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(x,y,u),v,tc_fun(z,tc_bool))))*.
% 299.79/300.48 35375[0:SpR:321.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),w),c_Set_Oimage(x,u,y),v,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(x,u,y),v,tc_fun(z,tc_bool))))*.
% 299.79/300.48 35340[0:SpR:87.1,410.0] class_Lattices_Oboolean__algebra(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(v,u),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,tc_fun(y,tc_bool))))*.
% 299.79/300.48 35321[0:SpR:302.1,410.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,tc_fun(y,tc_bool))))*.
% 299.79/300.48 35306[0:SpR:15476.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,tc_bool)),u,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,tc_bool)),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 35291[0:SpR:369.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),w),x),y),c_Set_Oinsert(u,v),x,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(u,v),x,tc_fun(z,tc_bool))))*.
% 299.79/300.48 35290[0:SpR:2089.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),v),w),c_Set_Oinsert(v_x,tc_Com_Opname),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,tc_Com_Opname),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 35245[0:SpR:410.0,340.2] || c_lessequals(hAPP(u,v),w,tc_fun(x,tc_bool)) c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,u,z,tc_fun(x,tc_bool)),w,tc_fun(x,tc_bool)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,z),y),u,z,tc_fun(x,tc_bool)),w,tc_fun(x,tc_bool))*.
% 299.79/300.48 35193[0:SpR:410.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,y,tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,y),x),v,y,tc_fun(u,tc_bool)),z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)))**.
% 299.79/300.48 35510[0:SpR:131.0,113.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(c_Set_Ovimage(v,y,w),x1),tc_fun(y,tc_bool)),hAPP(c_Set_Ovimage(v,y,w),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(u,w,x),z),x1,tc_fun(w,tc_bool))))*.
% 299.79/300.48 35495[0:SpR:131.0,113.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(c_Set_Ovimage(c_Fun_Ocomp(y,u,w,z,v),v,z),x1),tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Ovimage(y,w,z),x1),tc_fun(w,tc_bool))))*.
% 299.79/300.48 35640[0:SpR:158.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,hAPP(c_COMBB(v,w,tc_fun(x,tc_bool),y),c_Fun_Ocomp(z,x1,x2,w,y)),y,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(z,x2,w),hAPP(c_Set_Oimage(x1,y,x2),u)),v,w,tc_fun(x,tc_bool)))*.
% 299.79/300.48 35633[0:SpR:158.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_COMBB(y,z,tc_fun(x1,tc_bool),w),x2),w,tc_fun(x1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(c_Fun_Ocomp(x2,u,w,z,v),v,z),x),y,z,tc_fun(x1,tc_bool)))*.
% 299.79/300.48 35632[0:SpR:97.1,89.0] || c_Fun_Oinj__on(u,v,w,x) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,w,x),v),hAPP(c_COMBB(y,w,tc_fun(z,tc_bool),x),c_Fun_Othe__inv__into(v,u,w,x)),x,tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,tc_fun(z,tc_bool)))**.
% 299.79/300.48 35631[0:SpR:317.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_COMBB(x,y,tc_fun(z,tc_bool),v),x1),v,tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(x1,u),y),hAPP(c_Set_Oimage(x1,v,y),w)),x,y,tc_fun(z,tc_bool)))*.
% 299.79/300.48 35902[0:Res:114.1,282.0] || c_Fun_Oinj__on(u,v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(u,w,x),c_HOL_Ominus__class_Ominus(v,z,tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Fun_Ofun__upd(u,x1,y,w,x),c_HOL_Ominus__class_Ominus(v,z,tc_fun(w,tc_bool)),w,x)*.
% 299.79/300.48 36726[0:SpR:67.0,600.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,u),v),tc_fun(u,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),v))*.
% 299.79/300.48 37464[0:SpR:205.1,475.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oimage(u,v,w),y)))* -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x),v),y),y)**.
% 299.79/300.48 37463[0:SpR:205.1,545.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oimage(u,v,w),y)))* -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x)),y))*.
% 299.79/300.48 38316[0:Res:201.3,427.1] class_Lattices_Oupper__semilattice(u) class_Orderings_Opreorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Finite__Set_Ofinite(w,u) c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,w,u,u),y,u)* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),y,u)*.
% 299.79/300.48 38240[0:SpR:8415.2,201.3] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Finite__Set_Ofinite(v,u) -> c_lessequals(hAPP(v_x,w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u),u)*.
% 299.79/300.48 38367[0:SpL:8415.2,493.1] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(hAPP(c_Set_Oimage(w,u,x),v),hAPP(c_Set_Oimage(w,u,x),v_x))* c_Fun_Oinj__on(w,v_x,u,x) -> equal(v,v_x).
% 299.79/300.48 38361[0:SpL:8415.2,493.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(hAPP(c_Set_Oimage(v,u,w),v_x),hAPP(c_Set_Oimage(v,u,w),x)) c_Fun_Oinj__on(v,hAPP(v_x,x),u,w)* -> equal(v_x,x).
% 299.79/300.48 38647[0:SpL:8415.2,184.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x))) c_Fun_Oinj__on(v,x,w,u) -> equal(hAPP(v,hAPP(c_Fun_Othe__inv__into(x,v,w,u),v_x)),v_x)**.
% 299.79/300.48 38638[0:SpL:8415.2,184.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) c_Fun_Oinj__on(u,v_x,v,w) -> equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(v_x,u,v,w),x)),x)**.
% 299.79/300.48 38677[0:MRR:38635.2,96.1] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(w),y),v)) -> equal(hAPP(c_Fun_Othe__inv__into(v,u,w,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,w,x),v),c_Fun_Othe__inv__into(v,u,w,x),x,w),y)),y)**.
% 299.79/300.48 39005[0:SpL:354.2,390.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_lessequals(z,u,tc_fun(w,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,w,y),u),c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,w,y)*.
% 299.79/300.48 38987[0:SpR:8415.2,354.2] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(v_x,x,tc_fun(v,tc_bool)) c_Fun_Oinj__on(u,x,v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(x,u,v,w),w,v),v_x),v_x)**.
% 299.79/300.48 38973[0:SpR:354.2,20881.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,w,y),u),z),x2)),u))*.
% 299.79/300.48 38953[0:SpR:354.2,9569.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w)),hAPP(c_Set_Oimage(x,w,y),u)),tc_bool)*.
% 299.79/300.48 38952[0:SpR:354.2,9568.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> c_lessequals(u,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w)),x1),hAPP(c_Set_Oimage(x,w,y),u)),tc_bool)*.
% 299.79/300.48 39017[0:MRR:39000.2,20734.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_Fun_Oinj__on(z,u,w,x1) -> c_Fun_Oinj__on(c_Fun_Ocomp(z,c_Hilbert__Choice_Oinv__into(v,x,w,y),w,x1,y),hAPP(c_Set_Oimage(x,w,y),u),y,x1)*.
% 299.79/300.48 39325[0:SpL:533.0,3698.2] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.48 39317[0:SpL:533.0,3493.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_in(tc_Com_Opname)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* -> .
% 299.79/300.48 39187[0:SpR:533.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z))))*.
% 299.79/300.48 39146[0:SpR:533.0,3339.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),y,z),u)**.
% 299.79/300.48 39145[0:SpR:533.0,3316.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.79/300.48 39142[0:SpR:533.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),tc_Com_Opname,u),v_Procs)))*.
% 299.79/300.48 39131[0:SpR:533.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.48 39129[0:SpR:533.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.48 39125[0:SpR:533.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_Com_Opname,x),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.48 39123[0:SpR:533.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_Com_Opname,x)),v_Procs))*.
% 299.79/300.48 39122[0:SpR:533.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),t_a,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.48 39120[0:SpR:533.0,11030.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))*.
% 299.79/300.48 39119[0:SpR:533.0,10090.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.48 39112[0:SpR:533.0,3284.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.48 39107[2:SpR:533.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool))*.
% 299.79/300.48 39105[0:SpR:533.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_fun(t_a,tc_bool)),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool))*.
% 299.79/300.48 39104[7:SpR:533.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_fun(t_a,tc_bool)),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool))*.
% 299.79/300.48 39101[0:SpR:533.0,651.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.79/300.48 39097[0:SpR:533.0,21130.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,y),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_Procs))))*.
% 299.79/300.48 39769[0:SpR:542.0,532.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))**.
% 299.79/300.48 39933[0:Rew:39932.1,39190.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z)),z)**.
% 299.79/300.48 40189[0:Res:399.1,430.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),v),x,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),u),x,tc_fun(w,tc_bool))*.
% 299.79/300.48 40201[0:SSi:40195.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),u),tc_fun(w,tc_bool))* -> c_lessequals(x,hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),v),tc_fun(w,tc_bool))*.
% 299.79/300.48 40443[0:SpL:21893.0,529.0] || c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),x),v) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Obody,v_x),c_Com_Obody,tc_Com_Opname,y))),x),v)*.
% 299.79/300.48 40442[0:SpL:21267.0,529.0] || c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),x),v) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Obody,hAPP(c_Com_Obody,v_x),tc_Com_Opname,y))),x),v)*.
% 299.79/300.48 40692[0:SpR:21893.0,530.1] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Obody,v_x),c_Com_Obody,tc_Com_Opname,x))),y),v)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),y),v).
% 299.79/300.48 40691[0:SpR:21267.0,530.1] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Obody,hAPP(c_Com_Obody,v_x),tc_Com_Opname,x))),y),v)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),y),v).
% 299.79/300.48 40934[0:Res:171.2,479.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(w,c_Finite__Set_Olinorder__class_OMin(v,u))) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,x,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))*.
% 299.79/300.48 40933[0:Res:172.2,479.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(w,c_Finite__Set_Olinorder__class_OMax(v,u))) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,x,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))*.
% 299.79/300.48 40872[0:SpL:584.0,479.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(c_COMBS(c_in(w),x,y,z,x1),v))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(x,v),x2,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(x,v)),x2)))*.
% 299.79/300.48 41215[0:Res:171.2,478.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(w,c_Finite__Set_Olinorder__class_OMin(v,u))) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v)))*.
% 299.79/300.48 41214[0:Res:172.2,478.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(w,c_Finite__Set_Olinorder__class_OMax(v,u))) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v)))*.
% 299.79/300.48 41153[0:SpL:584.0,478.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(c_COMBS(c_in(w),x,y,z,x1),v))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x2,hAPP(x,v),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x2),hAPP(x,v))))*.
% 299.79/300.48 41388[0:SpL:21893.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)),x))* hBOOL(hAPP(hAPP(c_in(y),z),hAPP(v,v_x))) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,u,tc_fun(y,tc_bool))))*.
% 299.79/300.48 41387[0:SpL:21267.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)),x))* hBOOL(hAPP(hAPP(c_in(y),z),hAPP(v,v_x))) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,u,tc_fun(y,tc_bool))))*.
% 299.79/300.48 41383[0:SpL:28334.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,y,hAPP(y,v_x),tc_Com_Opname,z),tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 41380[0:SpL:28031.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(y,v_x),y,tc_Com_Opname,z),tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 41372[0:SpL:12944.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(z,x1),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x2,x3)),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41366[0:SpL:9.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(z,hAPP(x1,v))))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ocomp(z,x1,x2,x3,x4),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41364[0:SpL:11499.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),v)) hBOOL(hAPP(hAPP(c_in(w),x),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x1)),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 41363[0:SpL:10090.1,275.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41358[0:SpL:105.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(x1,z,v),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41357[0:SpL:1196.1,275.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(u))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41350[0:SpL:38.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(x1,z,v),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41349[0:SpL:321.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(x1,v,z),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41347[0:SpL:1195.1,275.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(u))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41345[0:SpL:11695.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),v)),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(z,x1),c_Option_Othe(v)),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41344[0:SpL:11473.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41310[0:SpL:87.1,275.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ouminus__class_Ouminus(w,u)),x)) hBOOL(hAPP(hAPP(c_in(y),z),c_Orderings_Otop__class_Otop(u))) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(y,tc_bool))))*.
% 299.79/300.48 41309[0:SpL:88.1,275.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) hBOOL(hAPP(hAPP(c_in(y),z),c_Orderings_Otop__class_Otop(u))) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),v,tc_fun(y,tc_bool))))*.
% 299.79/300.48 41306[0:SpL:17045.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)),x1,tc_fun(x2,tc_bool)),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41294[0:SpL:2098.1,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),y),v)) -> c_Hoare__Mirabelle_Ohoare__valids(z,v,t_a) hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(z,v),tc_Hoare__Mirabelle_Otriple(t_a)),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41282[0:SpL:3586.1,275.1] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) hBOOL(hAPP(hAPP(c_in(y),z),v_x)) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v,u),w,tc_fun(y,tc_bool))))*.
% 299.79/300.48 41281[7:SpL:27278.1,275.1] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) hBOOL(hAPP(hAPP(c_in(y),z),v_x)) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v,u),w,tc_fun(y,tc_bool))))*.
% 299.79/300.48 41255[0:SpL:653.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,y),y,tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 41250[0:SpL:9493.1,275.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(x),y),u))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41248[0:SpL:8498.1,275.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))* hBOOL(hAPP(hAPP(c_in(w),u),x))* hBOOL(hAPP(hAPP(c_in(y),z),u))* -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(x1,v),w,tc_fun(y,tc_bool))))*.
% 299.79/300.48 41686[0:Rew:30495.2,41583.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y,v),z)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,v)* -> hBOOL(hAPP(hAPP(c_in(y),w),z)).
% 299.79/300.48 41687[0:Rew:31042.2,41582.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y,v),z)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,v)* -> hBOOL(hAPP(hAPP(c_in(y),w),z)).
% 299.79/300.48 41854[0:Res:12687.1,199.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(x,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_HOL_Ouminus__class_Ouminus(x,tc_fun(y,tc_bool)),u,v,w))))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(x,tc_fun(y,tc_bool)),z))*.
% 299.79/300.48 41841[0:Res:9258.0,199.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_in(t_a),v_x),u,v,w)),v_x),tc_bool))* hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.48 41864[0:MRR:41817.1,820.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v,u,w)),tc_bool)* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),y))*.
% 299.79/300.48 41990[0:Res:82.0,430.0] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),z,tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),z,tc_fun(w,tc_bool))*.
% 299.79/300.48 42005[0:SSi:41998.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(v,w,x),y),hAPP(c_Set_Oimage(v,w,x),z),tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* -> c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),c_HOL_Ominus__class_Ominus(y,z,tc_fun(w,tc_bool))),tc_fun(x,tc_bool)).
% 299.79/300.48 42263[0:Rew:31043.2,42088.3] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y)* -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),z,hAPP(c_Set_Oinsert(w,u),v),u,u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),z,v,u,u))**.
% 299.79/300.48 42658[0:SpR:161.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),x,tc_fun(y,tc_bool)),c_HOL_Ominus__class_Ominus(z,w,tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z),w,tc_fun(u,tc_bool)),tc_bool)*.
% 299.79/300.48 42634[0:SpR:161.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool))),z,x1,x2),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))))*.
% 299.79/300.48 43087[0:SpR:9925.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),u,tc_fun(w,tc_bool)))**.
% 299.79/300.48 43062[0:SpR:23682.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(x,tc_bool)))**.
% 299.79/300.48 42972[0:SpR:8385.1,486.1] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,tc_Com_Opname),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,tc_Com_Opname),v,tc_fun(x,tc_bool)))**.
% 299.79/300.48 42948[0:SpR:486.1,339.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(x,y),u,tc_fun(y,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(x,y),u,tc_fun(y,tc_bool)))**.
% 299.79/300.48 42923[0:SpR:486.1,9567.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),z,tc_fun(x1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)),tc_bool)*.
% 299.79/300.48 42898[0:SpR:486.1,5875.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,v)),x1,x2,x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))))*.
% 299.79/300.48 43509[0:SpR:507.0,584.0] || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,u),x,y,z),hAPP(c_Set_Oimage(v,w,u),x1)),hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),hAPP(c_Set_Oimage(v,w,u),x1))))*.
% 299.79/300.48 43476[0:SpR:507.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),y,tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x1)),hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x1)),tc_bool)*.
% 299.79/300.48 43451[0:SpR:507.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x)),x1,x2,x3),hAPP(c_Set_Oimage(u,v,w),y)))*.
% 299.79/300.48 43731[0:SpR:162.0,584.0] || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Ovimage(v,u,w),x,y,z),hAPP(c_Set_Ovimage(v,u,w),x1)),hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),hAPP(c_Set_Ovimage(v,u,w),x1))))*.
% 299.79/300.48 43698[0:SpR:162.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),y,tc_fun(z,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x1)),hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x1)),tc_bool)*.
% 299.79/300.48 43673[0:SpR:162.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x)),x1,x2,x3),hAPP(c_Set_Ovimage(u,v,w),y)))*.
% 299.79/300.48 44180[0:Res:232.1,431.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(x,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),w,z)* -> c_Fun_Oinj__on(x,hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(y,tc_fun(v,tc_bool))),w,z)*.
% 299.79/300.48 44361[4:MRR:44281.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(hAPP(c_in(u),w),v_x))* equal(hAPP(x,v),hAPP(x,w))* c_Fun_Oinj__on(x,v_x,u,y)* -> equal(v,w).
% 299.79/300.48 44412[0:Rew:90.0,44387.0,507.0,44387.0,586.0,44387.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,y),z),x1,y,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(x1,x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x1,y,tc_fun(v,tc_bool)))))*.
% 299.79/300.48 44466[0:Rew:30.0,44441.0,162.0,44441.0,586.0,44441.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,y),z),x1,y,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(x1,x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x1,y,tc_fun(w,tc_bool)))))*.
% 299.79/300.48 45061[0:SpR:3229.1,326.2] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* c_lessequals(w,x,tc_fun(v,tc_bool))* c_lessequals(v_x,y,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y),tc_fun(v,tc_bool))*.
% 299.79/300.48 45055[0:SpR:3229.1,326.2] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) c_lessequals(v_x,w,tc_fun(v,tc_bool)) c_lessequals(x,y,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(hAPP(u,v_x),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y),tc_fun(v,tc_bool))*.
% 299.79/300.48 44996[0:SpR:3229.1,326.2] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* c_lessequals(x,w,tc_fun(v,tc_bool))* c_lessequals(y,v_x,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y),hAPP(u,v_x),tc_fun(v,tc_bool))*.
% 299.79/300.48 44990[0:SpR:3229.1,326.2] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) c_lessequals(w,v_x,tc_fun(v,tc_bool)) c_lessequals(x,y,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(hAPP(u,v_x),y),tc_fun(v,tc_bool))*.
% 299.79/300.48 45334[0:SpL:3229.1,487.1] || equal(u,c_in(v)) hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,w,v)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,w,v)))*.
% 299.79/300.48 45275[0:SpL:3229.1,487.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,y))* hBOOL(hAPP(hAPP(c_in(v),y),hAPP(u,v_x)))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,v)))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,x,v)))*.
% 299.79/300.48 45269[0:SpL:3229.1,487.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) hBOOL(hAPP(w,x))* hBOOL(hAPP(hAPP(c_in(v),x),hAPP(hAPP(u,v_x),y)))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,w,v)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,w,v)))*.
% 299.79/300.48 45492[0:SpL:3229.1,237.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(w,x,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,v) -> equal(hAPP(w,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v_x,w,v,x)),v_x)**.
% 299.79/300.48 45621[0:SpL:323.0,519.0] || hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),z))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool)),z)) hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),z)).
% 299.79/300.48 46178[0:Res:8376.2,481.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(v,v_Procs) -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))*.
% 299.79/300.48 46173[0:Res:168.0,481.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) hBOOL(hAPP(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v)))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),x),w,tc_Hoare__Mirabelle_Otriple(t_a))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),x)))*.
% 299.79/300.48 46144[0:Res:3346.1,481.0] || equal(c_Set_Oinsert(u,v),w)* -> hBOOL(hAPP(x,u))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(w,v_x)),y),x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(w,v_x)),y)))*.
% 299.79/300.48 46496[0:Res:8376.2,480.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(v,v_Procs) -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v)))*.
% 299.79/300.48 46491[0:Res:168.0,480.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) hBOOL(hAPP(w,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v)))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),x),v),w,tc_Hoare__Mirabelle_Otriple(t_a))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),x),v)))*.
% 299.79/300.48 46462[0:Res:3346.1,480.0] || equal(c_Set_Oinsert(u,v),w)* -> hBOOL(hAPP(x,u))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),hAPP(w,v_x)),x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),hAPP(w,v_x))))*.
% 299.79/300.48 46593[7:MRR:46581.2,27297.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,c_Set_Oinsert(x,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,u,v,tc_fun(w,tc_bool))))*.
% 299.79/300.48 46652[4:SpL:533.0,46565.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))* -> .
% 299.79/300.48 46937[0:Res:241.2,437.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool))* c_Finite__Set_Ofinite(x,u) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),u)*.
% 299.79/300.48 47190[0:Res:7539.0,242.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(w,hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(x,u),hAPP(c_Set_Oinsert(y,u),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))),tc_fun(u,tc_bool))*.
% 299.79/300.48 47393[0:SpL:584.0,485.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(c_COMBS(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y,z,x1),v))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)),x))*.
% 299.79/300.48 47624[0:SpL:584.0,484.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(c_COMBS(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y,z,x1),v))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,u,w)),v))*.
% 299.79/300.48 47962[0:SpL:584.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(c_COMBS(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y,z,x1),v))* -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)),x))*.
% 299.79/300.48 48074[0:SpL:584.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(c_COMBS(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,y,z),x1))* -> hBOOL(hAPP(u,x1)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x1,u,w)),x1))*.
% 299.79/300.48 48810[0:Res:15261.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,t_a,tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Set_Oinsert(w,v),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,t_a,tc_fun(v,tc_bool))))**.
% 299.79/300.48 48783[0:Res:267.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,v),y)),c_Set_Oinsert(z,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(z,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,v),y),u,v,tc_fun(w,tc_bool))))**.
% 299.79/300.48 48981[0:Res:13238.1,483.0] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,t_a)),u))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,t_a)),v))*.
% 299.79/300.48 48980[0:Res:8375.1,483.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** -> hBOOL(hAPP(x,y))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.79/300.48 48974[0:Res:652.1,483.0] || c_lessequals(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(u,w,tc_Com_Opname)),u))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,w,tc_Com_Opname)),v))*.
% 299.79/300.48 49107[0:SpL:49017.1,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_Procs)) -> hBOOL(hAPP(y,v_x)) hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,y,tc_Com_Opname),tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 49186[0:Res:13238.1,239.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),c_Orderings_Otop__class_Otop(tc_bool)) c_lessequals(w,x,tc_fun(v,tc_bool)) c_Fun_Oinj__on(u,w,v,t_a) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Fun_Othe__inv__into(w,u,v,t_a),v_x)),x))*.
% 299.79/300.48 49185[0:Res:8375.1,239.0] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) c_lessequals(x,y,tc_fun(v,tc_bool)) c_Fun_Oinj__on(u,x,v,w) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Fun_Othe__inv__into(x,u,v,w),z)),y))*.
% 299.79/300.48 49177[0:Res:652.1,239.0] || c_lessequals(v_Procs,hAPP(c_Set_Oimage(u,v,tc_Com_Opname),w),tc_fun(tc_Com_Opname,tc_bool)) c_lessequals(w,x,tc_fun(v,tc_bool)) c_Fun_Oinj__on(u,w,v,tc_Com_Opname) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Fun_Othe__inv__into(w,u,v,tc_Com_Opname),v_x)),x))*.
% 299.79/300.48 49307[0:Res:9258.0,488.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w),v_x),tc_bool))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,u,t_a)),v))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,u,t_a)),w))*.
% 299.79/300.48 49410[0:SpR:49342.1,118.0] || hBOOL(hAPP(u,v_x)) -> equal(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),c_Fun_Ofun__upd(v,w,v_Procs,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,y,z,x),w,v_Procs,x,z))*.
% 299.79/300.48 49387[0:SpR:49342.1,71.2] || hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,x),v_Procs),v_Procs)**.
% 299.79/300.48 49386[0:SpR:49342.1,373.2] || hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,x),v_Procs),v_Procs)**.
% 299.79/300.48 49715[0:Rew:49662.2,49529.1] || c_Fun_Oinj__on(c_Option_Othe(u),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Option_Othe(u),w,x),hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(y,u),w),v))))* c_Fun_Oinj__on(c_Option_Othe(u),hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(y,u),w),v),w,x).
% 299.79/300.48 50503[0:SpL:223.1,215.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,tc_Hoare__Mirabelle_Otriple(x1)),u,tc_Hoare__Mirabelle_Otriple(x1)),w),x1)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(z,tc_Hoare__Mirabelle_Otriple(x1)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(x1),tc_bool))),x1).
% 299.79/300.48 54113[0:SpR:52997.1,475.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,x),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,x),u,w),v))**.
% 299.79/300.48 54725[0:SpR:13749.2,71.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.48 54724[0:SpR:13749.2,373.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.48 55199[0:SpR:14043.2,71.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.48 55198[0:SpR:14043.2,373.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),w,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,y),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.48 56005[0:SpL:533.0,55174.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)))* -> .
% 299.79/300.48 55923[0:SpL:533.0,55174.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool),hAPP(x,v_x))* -> .
% 299.79/300.48 56226[0:SpR:30368.2,118.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Fun_Ofun__upd(v,w,x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,z,x1,y),w,c_Orderings_Otop__class_Otop(u),y,x1))*.
% 299.79/300.48 56203[0:SpR:30368.2,71.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y),c_Orderings_Otop__class_Otop(u)),w)*.
% 299.79/300.48 56202[0:SpR:30368.2,373.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y),c_Orderings_Otop__class_Otop(u)),w)*.
% 299.79/300.48 56668[0:SpR:30928.2,118.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Fun_Ofun__upd(v,w,x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,z,x1,y),w,c_Orderings_Otop__class_Otop(u),y,x1))*.
% 299.79/300.48 56645[0:SpR:30928.2,71.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,v,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y),c_Orderings_Otop__class_Otop(u)),w)*.
% 299.79/300.48 56644[0:SpR:30928.2,373.2] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,v,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y),c_Orderings_Otop__class_Otop(u)),w)*.
% 299.79/300.48 58603[0:Res:10771.1,477.0] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Set_Oinsert(y,u),z),v)),z))* hBOOL(hAPP(hAPP(c_in(v),x1),w))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,u),z),x1))*.
% 299.79/300.48 58602[0:Res:10771.1,476.0] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Set_Oinsert(y,u),z),v)),z))* hBOOL(hAPP(hAPP(c_in(v),x1),x))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,u),z),x1))*.
% 299.79/300.48 58761[0:SpL:410.0,15629.0] || hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,u)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,u)),z)))*.
% 299.79/300.48 58754[0:SpL:532.0,15629.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)))*.
% 299.79/300.48 59269[0:SpL:410.0,15857.0] || hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,u)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,u)),x1)))*.
% 299.79/300.48 59262[0:SpL:532.0,15857.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z)))*.
% 299.79/300.48 60435[7:Res:58968.1,453.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,y)),v))* c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.48 60471[0:SpR:5882.1,317.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),z),x2)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x1),hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1),x2)))*.
% 299.79/300.48 60470[0:SpR:5882.1,99.1] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.48 60469[0:SpR:5882.1,438.1] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.48 60548[0:Res:58969.1,453.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Procs) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,y)),v))* c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.48 60621[7:Res:59476.1,453.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,y)),v))* c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.48 60694[0:Res:59477.1,453.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Procs) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,y)),v))* c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.48 60789[0:Rew:584.0,60731.0] || -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(v,v_x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(v,v_x)),tc_fun(u,tc_bool))*.
% 299.79/300.48 60879[0:Res:59017.1,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x),v),t_a)* -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x),t_a)* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,z)),u))* c_Hoare__Mirabelle_Otriple__valid(z,x,t_a)*.
% 299.79/300.48 60822[0:SpR:393.1,59017.1] || -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Set_Oimage(c_COMBK(w,x,y),y,x),u),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))** c_Hoare__Mirabelle_Ohoare__valids(z,c_Set_Oimage(c_COMBK(w,x,y),y,x),t_a)* hBOOL(hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))).
% 299.79/300.48 60952[0:Res:59525.1,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x),w),t_a)* -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),x),t_a)* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,z)),u))* c_Hoare__Mirabelle_Otriple__valid(z,x,t_a)*.
% 299.79/300.48 60895[0:SpR:393.1,59525.1] || -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oimage(c_COMBK(w,x,y),y,x),v),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))** c_Hoare__Mirabelle_Ohoare__valids(z,c_Set_Oimage(c_COMBK(w,x,y),y,x),t_a)* hBOOL(hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))).
% 299.79/300.48 61793[0:SpR:11167.1,317.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> equal(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),hAPP(c_Set_Oinsert(v_Procs,x),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),w,x),y)))*.
% 299.79/300.48 61792[0:SpR:11167.1,99.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),w,x),v_Procs),v_Procs)**.
% 299.79/300.48 61791[0:SpR:11167.1,438.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),w,x),v_Procs),v_Procs)**.
% 299.79/300.48 64213[0:SpR:188.1,646.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x)**.
% 299.79/300.48 64380[0:SpR:188.1,645.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),v_x)**.
% 299.79/300.48 70903[0:SpL:533.0,6582.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w))** -> c_lessequals(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_fun(u,tc_bool)).
% 299.79/300.48 71603[7:SpR:71455.1,486.1] || equal(u,v_x) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)))**.
% 299.79/300.48 74239[7:SpL:71835.1,487.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),w),hAPP(v_x,x)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,v,u)))* hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)))*.
% 299.79/300.48 74154[7:SpL:71835.1,487.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,v,u)))* hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)))*.
% 299.79/300.48 74144[7:SpL:71835.1,237.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u) -> equal(hAPP(v,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v_x,v,u,w)),v_x)**.
% 299.79/300.48 73906[7:SpR:71835.1,326.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,t_a))** c_lessequals(w,v,tc_fun(u,tc_bool))* c_lessequals(x,v_x,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),v_x,tc_fun(u,tc_bool))*.
% 299.79/300.48 73533[7:SpR:71835.1,326.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) c_lessequals(v,v_x,tc_fun(u,tc_bool)) c_lessequals(w,x,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(v_x,x),tc_fun(u,tc_bool))*.
% 299.79/300.48 73245[7:SpR:71835.1,326.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) c_lessequals(v_x,v,tc_fun(u,tc_bool)) c_lessequals(w,x,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(v_x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),tc_fun(u,tc_bool))*.
% 299.79/300.48 75037[0:Res:340.2,6845.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,v,tc_fun(w,tc_bool)) equal(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x)) -> c_lessequals(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),tc_fun(w,tc_bool))*.
% 299.79/300.48 76728[0:SSi:76598.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),x,tc_fun(u,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),x).
% 299.79/300.48 76729[0:SSi:76593.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),x) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),x,tc_fun(u,tc_bool))*.
% 299.79/300.48 77098[0:SSi:76953.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),w,tc_fun(u,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),w).
% 299.79/300.48 77099[0:SSi:76948.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),w) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),w,tc_fun(u,tc_bool))*.
% 299.79/300.48 77370[0:Res:2399.2,214.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool))))*.
% 299.79/300.48 77456[7:SpR:71894.1,486.1] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_fun(w,tc_bool)))**.
% 299.79/300.48 77802[0:SpL:317.0,5892.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oimage(u,v,w),y)))* -> hBOOL(hAPP(c_COMBS(c_in(z),c_Set_Oinsert(hAPP(u,x),w),x1,x2,x3),hAPP(c_Set_Oimage(u,v,w),y)))*.
% 299.79/300.48 77730[0:SpL:614.2,5892.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u)))* -> hBOOL(hAPP(c_COMBS(c_in(y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),z,x1,x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u)))*.
% 299.79/300.48 77673[0:SpL:131.0,5892.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(c_Set_Ovimage(u,w,x),z)))* -> hBOOL(hAPP(c_COMBS(c_in(x1),c_Set_Ovimage(v,y,w),x2,x3,x4),hAPP(c_Set_Ovimage(u,w,x),z)))*.
% 299.79/300.48 77671[0:SpL:158.0,5892.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(c_Set_Oimage(v,y,w),z)))* -> hBOOL(hAPP(c_COMBS(c_in(x1),c_Set_Oimage(u,w,x),x2,x3,x4),hAPP(c_Set_Oimage(v,y,w),z)))*.
% 299.79/300.48 78723[4:Res:78665.1,485.1] || equal(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),v_x)** hBOOL(hAPP(y,v))* -> hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,y,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,y,u)),w))*.
% 299.79/300.48 78722[4:Res:78665.1,484.1] || equal(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),v_x)** hBOOL(hAPP(y,v))* -> hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,y,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,y,u)),x))*.
% 299.79/300.48 78711[4:Res:78665.1,489.1] || equal(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),v_x)** hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,y,u)))* -> hBOOL(hAPP(y,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,y,u)),x))*.
% 299.79/300.48 78710[4:Res:78665.1,490.1] || equal(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),v_x)** hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,y,u)))* -> hBOOL(hAPP(y,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,y,u)),w))*.
% 299.79/300.48 78708[4:Res:78665.1,224.0] || equal(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(v,x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))),v_x)** c_Fun_Oinj__on(v,hAPP(c_Set_Oinsert(w,x),y),x,u) -> .
% 299.79/300.48 78792[0:Rew:584.0,78790.1,584.0,78790.0] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(v,v_x)),u) -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(v,v_x)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),tc_Com_Opname,z),u)*.
% 299.79/300.48 78793[0:Rew:584.0,78789.1,584.0,78789.0] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(v,v_x)),u) -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(v,v_x)),tc_Com_Opname,z),u)*.
% 299.79/300.48 78982[0:SpR:188.1,15630.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,c_Set_Ovimage(c_COMBK(v,u,x1),x1,u),x)))* hBOOL(hAPP(c_Set_Ovimage(c_COMBK(v,u,x1),x1,u),w)) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))).
% 299.79/300.48 79202[0:SpR:188.1,15858.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oinsert(x,y),z),c_Set_Ovimage(c_COMBK(v,u,x1),x1,u),y)))* hBOOL(hAPP(c_Set_Ovimage(c_COMBK(v,u,x1),x1,u),x)) -> hBOOL(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))).
% 299.79/300.48 80301[0:SpL:21268.0,156.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y))) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,v)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Ovimage(w,u,x),hAPP(c_Set_Ovimage(w,u,x),y),z,x1)))*.
% 299.79/300.48 80242[0:SpL:21268.0,346.0] || c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v,y) -> c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),z,x1),v,y)*.
% 299.79/300.48 80205[0:SpL:21268.0,255.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),x,y),z,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),z)).
% 299.79/300.48 80181[0:SpL:21268.0,208.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),v),u)) c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),y,z),tc_fun(w,tc_bool))*.
% 299.79/300.48 80083[0:SpL:21268.0,473.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1))),y))*.
% 299.79/300.48 79757[0:SpR:21268.0,38131.1] || hBOOL(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),y),u,z))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),y)).
% 299.79/300.48 79676[0:SpR:21268.0,304.3] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),x,z),w,u)* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),w,u).
% 299.79/300.48 79643[0:SpR:21268.0,153.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(v,y,u),hAPP(c_Set_Ovimage(v,y,u),z),x,x1)))* -> hBOOL(hAPP(hAPP(c_in(y),w),hAPP(c_Set_Ovimage(v,y,u),z))).
% 299.79/300.48 79616[0:SpR:21268.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oimage(x,u,y),hAPP(c_Set_Oimage(x,u,y),z),w,x1)))* -> hBOOL(hAPP(hAPP(c_in(y),hAPP(x,v)),hAPP(c_Set_Oimage(x,u,y),z))).
% 299.79/300.48 79584[0:SpR:21268.0,335.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),x),w,y),v)* -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),x),v).
% 299.79/300.48 79441[0:SpR:21268.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(v,w),u,x),y),z),v,y,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(v,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,v,y,tc_fun(x1,tc_bool))))*.
% 299.79/300.48 81496[0:SpL:21894.0,156.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y))) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,v)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Ovimage(w,u,x),y),c_Set_Ovimage(w,u,x),z,x1)))*.
% 299.79/300.48 81437[0:SpL:21894.0,346.0] || c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v,y) -> c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),z,x1),v,y)*.
% 299.79/300.48 81400[0:SpL:21894.0,255.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),x,y),z,tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),v),z)).
% 299.79/300.48 81376[0:SpL:21894.0,208.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),v),u)) c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),y,z),tc_fun(w,tc_bool))*.
% 299.79/300.48 81278[0:SpL:21894.0,473.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1))),y))*.
% 299.79/300.48 80951[0:SpR:21894.0,38131.1] || hBOOL(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),y),hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),u,z))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),y)).
% 299.79/300.48 80870[0:SpR:21894.0,304.3] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,z),w,u)* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),w,u).
% 299.79/300.48 80837[0:SpR:21894.0,153.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Ovimage(v,y,u),z),c_Set_Ovimage(v,y,u),x,x1)))* -> hBOOL(hAPP(hAPP(c_in(y),w),hAPP(c_Set_Ovimage(v,y,u),z))).
% 299.79/300.48 80810[0:SpR:21894.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(x,u,y),z),c_Set_Oimage(x,u,y),w,x1)))* -> hBOOL(hAPP(hAPP(c_in(y),hAPP(x,v)),hAPP(c_Set_Oimage(x,u,y),z))).
% 299.79/300.48 80777[0:SpR:21894.0,335.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w,y),v)* -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),x),v).
% 299.79/300.48 80634[0:SpR:21894.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(v,w),v,u,x),y),z),v,y,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(v,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,v,y,tc_fun(x1,tc_bool))))*.
% 299.79/300.48 81925[0:SpR:55.1,5879.1] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),x)) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(w,v),y),x,tc_fun(v,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oinsert(w,v),z,x1,x2),c_HOL_Ominus__class_Ominus(y,x,tc_fun(v,tc_bool))),u)*.
% 299.79/300.48 81875[0:SpR:410.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),y,w,tc_fun(z,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x1,x2,x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,w,tc_fun(z,tc_bool))),u)*.
% 299.79/300.48 82143[7:SpR:78597.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Set_Oinsert(v_x,v)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Set_Oinsert(v_x,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),u,tc_fun(x,tc_bool)))**.
% 299.79/300.48 82397[0:SpR:55.1,5880.1] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),x)) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(w,v),y),x,tc_fun(v,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oinsert(w,v),z,x1,x2),c_HOL_Ominus__class_Ominus(y,x,tc_fun(v,tc_bool))),u)*.
% 299.79/300.48 82347[0:SpR:410.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),y,w,tc_fun(z,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x1,x2,x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,w,tc_fun(z,tc_bool))),u)*.
% 299.79/300.48 82833[7:Res:77991.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,y),v_x)),c_Set_Oinsert(z,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(z,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,y),v_x),u,v,tc_fun(w,tc_bool))))**.
% 299.79/300.48 83767[0:SpR:5899.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_COMBS(u,v,w,x,y),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(c_Set_Oinsert(hAPP(c_COMBS(u,v,x4,x5,x6),x2),x1),hAPP(c_Set_Oimage(c_COMBS(u,v,w,x,y),z,x1),x3)))*.
% 299.79/300.48 83766[0:SpR:5899.0,99.1] || c_Fun_Oinj__on(c_COMBS(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_COMBS(u,v,w,x,y),z,x1),hAPP(c_COMBS(u,v,x2,x3,x4),x5)),x5)**.
% 299.79/300.48 83765[0:SpR:5899.0,438.1] || c_Fun_Oinj__on(c_COMBS(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_COMBS(u,v,w,x,y),z,x1),hAPP(c_COMBS(u,v,x2,x3,x4),x5)),x5)**.
% 299.79/300.48 84989[0:Res:84957.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,y),x)),c_Set_Oinsert(z,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(z,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,y),x),u,v,tc_fun(w,tc_bool))))**.
% 299.79/300.48 84975[0:SpR:55.1,84957.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),w)) hBOOL(hAPP(hAPP(c_in(x),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),u),v),w,tc_fun(u,tc_bool))))*.
% 299.79/300.48 85268[0:SpR:1250.3,824.1] class_Lattices_Oboolean__algebra(tc_fun(t_a,u)) class_OrderedGroup_Ogroup__add(tc_fun(t_a,u)) class_Orderings_Obot(u) || equal(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_HOL_Ozero__class_Ozero(tc_fun(t_a,u))) -> equal(c_Fun_Ofun__upd(c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)),v_x,c_Orderings_Obot__class_Obot(u),v,w),c_HOL_Ozero__class_Ozero(tc_fun(t_a,u)))**.
% 299.79/300.48 85942[0:SpL:21894.0,13582.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),y,z)),v))* -> .
% 299.79/300.48 85940[0:SpL:21268.0,13582.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),y,z)),v))* -> .
% 299.79/300.48 86256[0:SpR:86109.1,486.1] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)))**.
% 299.79/300.48 88328[0:Res:7227.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Oimage(c_COMBK(v,w,x),y,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))))),hAPP(c_Set_Oimage(c_COMBK(v,w,x),y,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))))* c_Hoare__Mirabelle_Otriple__valid(u,v,t_a).
% 299.79/300.48 88978[0:SpR:475.1,14196.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(hAPP(x,v),y),z,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,u,y),w),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),hAPP(c_Set_Oimage(x,u,y),w)))*.
% 299.79/300.48 89189[0:SpL:21894.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),v)* -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y,z),v)*.
% 299.79/300.48 89187[0:SpL:21268.0,25984.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),v)* -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,z),v)*.
% 299.79/300.48 89736[7:Res:89344.1,199.0] || equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_in(t_a),v_x),v,u,w)),c_Set_Oinsert(v_x,t_a))** c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.48 89725[7:Res:89344.1,488.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)),u))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)),v))*.
% 299.79/300.48 90764[0:SpL:113.0,26480.0] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(c_Set_Ovimage(u,v,w),y),tc_fun(v,tc_bool)).
% 299.79/300.48 90880[4:Res:90134.1,199.0] || equal(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_in(t_a),v_x),v,u,w)),v_x),v_x)** c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.48 90869[4:Res:90134.1,488.1] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),v_x)** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)),u))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)),v))*.
% 299.79/300.48 92425[0:MRR:92424.1,56.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool))).
% 299.79/300.48 92686[7:Res:82151.1,481.0] || equal(c_in(t_a),c_in(u)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,w)),x),v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,w)),x)))*.
% 299.79/300.48 92685[7:Res:82151.1,480.0] || equal(c_in(t_a),c_in(u)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_Set_Oinsert(v_x,x)),v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_Set_Oinsert(v_x,x))))*.
% 299.79/300.48 94086[0:Rew:223.1,94054.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),hAPP(c_Set_Oinsert(y,z),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,x1,u,z),u,z),w)),tc_fun(z,tc_bool))*.
% 299.79/300.48 94154[0:Res:14364.3,85.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x))) c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))*.
% 299.79/300.48 12079[0:Res:49.2,325.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) -> c_lessequals(v,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.48 12430[0:Res:49.2,324.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) -> c_lessequals(w,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.48 18459[0:Res:171.2,156.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(v,u,w),x),u) -> equal(hAPP(c_Set_Ovimage(v,u,w),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),hAPP(v,c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Ovimage(v,u,w),x),u))),x))*.
% 299.79/300.48 18458[0:Res:172.2,156.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(v,u,w),x),u) -> equal(hAPP(c_Set_Ovimage(v,u,w),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),hAPP(v,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Ovimage(v,u,w),x),u))),x))*.
% 299.79/300.48 19684[0:Res:687.1,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname)))* c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.48 19683[0:Res:686.1,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,w,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname)))* c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.48 19659[0:Res:510.1,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),x)))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.48 19658[0:Res:511.1,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),x),v))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),x),v)))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a)*.
% 299.79/300.48 20101[0:SpR:353.0,246.2] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v) -> hBOOL(hAPP(hAPP(c_in(v),x),hAPP(c_Set_Oinsert(u,v),w))) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(x,v),w)),v),c_Suc(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(u,v),w),v)))**.
% 299.79/300.48 21470[0:SpR:21267.0,11177.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),tc_Com_Opname,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x)).
% 299.79/300.48 21460[0:SpR:21267.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x),tc_Com_Opname,x)))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))).
% 299.79/300.48 22096[0:SpR:21893.0,11177.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x)).
% 299.79/300.48 22086[0:SpR:21893.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),tc_Com_Opname,x)))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))).
% 299.79/300.48 23381[0:SpR:460.1,545.1] || class_Lattices_Olattice(t_b) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,w),v)))*.
% 299.79/300.48 23380[0:SpR:460.1,362.1] || class_Lattices_Olattice(t_b) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.48 23512[0:SpR:523.1,545.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(y,v_x)),hAPP(z,v_x))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),y),z),v,x),w)))*.
% 299.79/300.48 23511[0:SpR:523.1,362.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(x,v_x)),hAPP(y,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),x),y),v,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.48 24141[0:SpR:542.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,z),y)))*.
% 299.79/300.48 24140[0:SpR:542.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.48 24327[0:SpR:393.1,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oinsert(z,x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(z,x1,x),x,x1),u,y),w)))*.
% 299.79/300.48 24326[0:SpR:393.1,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* c_lessequals(hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_COMBK(y,z,x),x,z),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.48 24459[0:Res:20152.0,208.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))* c_lessequals(c_HOL_Ominus__class_Ominus(w,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))*.
% 299.79/300.48 24773[0:SpR:614.2,545.1] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),z)) -> hBOOL(hAPP(hAPP(c_in(x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,x1),z)))*.
% 299.79/300.48 24772[0:SpR:614.2,362.1] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),z)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.48 25378[0:SpR:512.0,196.1] || c_Fun_Oinj__on(hAPP(c_COMBB(u,v,w,x),y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w) -> equal(hAPP(c_Set_Ovimage(hAPP(c_COMBB(u,v,w,x),y),x,w),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),z))),z)**.
% 299.79/300.48 25368[0:SpR:512.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,z,x1),hAPP(c_Set_Oimage(x2,x3,z),v))),hAPP(c_Set_Oimage(c_Set_Oimage(hAPP(c_COMBB(y,z,x1,x3),x2),x3,x1),u,x),w)))*.
% 299.79/300.48 25367[0:SpR:512.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oimage(x,y,z),hAPP(c_Set_Oimage(x1,x2,y),v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(hAPP(c_COMBB(x,y,z,x2),x1),x2,z),u,tc_fun(x3,tc_bool)),tc_fun(x3,tc_bool))*.
% 299.79/300.48 25325[0:SpR:512.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_x)),tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Set_Oimage(hAPP(c_COMBB(u,v,w,y),x),y,w)),c_Set_Oimage(hAPP(c_COMBB(u,v,w,y),x),y,w))**.
% 299.79/300.48 25894[0:SpR:339.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(c_Set_Oinsert(y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(y,z),x1)),v,u),u)*.
% 299.79/300.48 25881[0:SpR:339.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),y)),u,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.48 26143[0:SpR:338.0,10931.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w),t_a) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(t_a)),w)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w))))*.
% 299.79/300.48 26141[0:SpR:338.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(x,u),y))),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y))))*.
% 299.79/300.48 26126[0:SpR:338.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),z)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(x1,w),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oinsert(x1,w),v,u),u)*.
% 299.79/300.48 26112[0:SpR:338.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Ovimage(c_Set_Oinsert(y,v),u,z),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(y,v),x)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.48 26059[0:SpR:338.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Set_Oinsert(w,x),y)),z)) -> c_lessequals(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),v,u),u)*.
% 299.79/300.48 26046[0:SpR:338.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),u,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),x)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.48 26295[0:Rew:20386.1,26133.1] || c_Fun_Oinj__on(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(u,v),w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z))**.
% 299.79/300.48 26296[0:Rew:20386.1,26132.1] || c_Fun_Oinj__on(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(u,v),w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z))**.
% 299.79/300.48 26297[0:Rew:24251.1,26063.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(y,u),z)),hAPP(c_Set_Oinsert(y,u),z))**.
% 299.79/300.48 26848[0:SpR:338.0,56.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(c_Set_Oinsert(v,u),y)),w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y),w,tc_fun(u,tc_bool)))**.
% 299.79/300.48 26943[0:SpR:338.0,424.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y),w,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(c_Set_Oinsert(v,u),y)),w,tc_fun(u,tc_bool))*.
% 299.79/300.48 27190[0:Res:450.0,280.1] || hBOOL(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(v),w,x,y)),z)) -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(v)),x),w),t_a) hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),w,x,y),u,v,tc_fun(x1,tc_bool)),z))*.
% 299.79/300.48 27155[0:SpR:9935.1,450.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x),tc_bool) -> hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x))) c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),w),v),t_a)*.
% 299.79/300.48 27134[0:SpR:8385.1,450.0] || equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oinsert(v_x,tc_Com_Opname),u,v,w),v_Procs) -> hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oinsert(v_x,tc_Com_Opname),u,v,w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Set_Oinsert(v_x,tc_Com_Opname),u,v,w)))* c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Set_Oinsert(v_x,tc_Com_Opname)),v),u),t_a).
% 299.79/300.48 27363[0:SpL:317.0,470.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(hAPP(w,x),u),hAPP(c_Set_Oimage(w,y,u),z))))* -> hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__XimageE__1__1(hAPP(c_Set_Oinsert(x,y),z),v,w,y,u)),hAPP(c_Set_Oinsert(x,y),z)))*.
% 299.79/300.48 27423[0:SpL:317.0,466.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(hAPP(w,x),u),hAPP(c_Set_Oimage(w,y,u),z))))* -> hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(hAPP(c_Set_Oinsert(x,y),z),w,v,y,u)),hAPP(c_Set_Oinsert(x,y),z)))*.
% 299.79/300.48 27652[0:SpR:21893.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)),x))* c_Fun_Oinj__on(v,x,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,v,u,y),hAPP(v,v_x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w))*.
% 299.79/300.48 27651[0:SpR:21267.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)),x))* c_Fun_Oinj__on(v,x,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,v,u,y),hAPP(v,v_x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w))*.
% 299.79/300.48 27646[0:SpR:10063.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),v,u,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(v_x,t_a),u,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.79/300.48 27640[0:SpR:584.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_COMBS(x,y,z,x1,x2),w,u,x3) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_COMBS(x,y,z,x1,x2),u,x3),hAPP(hAPP(x,v),hAPP(y,v))),v)**.
% 299.79/300.48 27639[0:SpR:586.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_COMBB(x,y,z,x1),x2),w,u,x3) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_COMBB(x,y,z,x1),x2),u,x3),hAPP(x,hAPP(x2,v))),v)**.
% 299.79/300.48 27638[0:SpR:585.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_COMBC(x,y,z,x1),x2),w,u,x3) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_COMBC(x,y,z,x1),x2),u,x3),hAPP(hAPP(x,v),x2)),v)**.
% 299.79/300.48 27624[0:SpR:3294.1,373.2] || equal(c_in(t_a),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),w)) c_Fun_Oinj__on(hAPP(u,v_x),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(u,v_x),v,x),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))**.
% 299.79/300.48 27620[0:SpR:330.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),w,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),u,y),x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.48 27575[0:SpR:331.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),w,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),u,y),v),v)**.
% 299.79/300.48 27548[0:SpR:369.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) c_Fun_Oinj__on(c_Set_Oinsert(v,w),y,u,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,c_Set_Oinsert(v,w),u,z),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Oinsert(v,w),x))**.
% 299.79/300.48 27547[0:SpR:2089.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),w,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oinsert(v_x,tc_Com_Opname),u,x),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))**.
% 299.79/300.48 27528[0:SpR:373.2,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(y,x,v,z) hBOOL(hAPP(hAPP(c_in(x1),hAPP(y,w)),x2)) -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,c_Hilbert__Choice_Oinv__into(x,y,v,z),x1,u),u)*.
% 299.79/300.48 27523[0:SpR:373.2,176.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),hAPP(c_Set_Ovimage(c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x1),hAPP(c_Set_Oinsert(v,x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.79/300.48 27805[0:SpR:21893.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)),x))* c_Fun_Oinj__on(v,x,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,v,u,y),hAPP(v,v_x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w))*.
% 299.79/300.48 27804[0:SpR:21267.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)),x))* c_Fun_Oinj__on(v,x,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,v,u,y),hAPP(v,v_x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w))*.
% 299.79/300.48 27799[0:SpR:10063.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),v,u,w) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(v_x,t_a),u,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))**.
% 299.79/300.48 27793[0:SpR:584.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_COMBS(x,y,z,x1,x2),w,u,x3) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_COMBS(x,y,z,x1,x2),u,x3),hAPP(hAPP(x,v),hAPP(y,v))),v)**.
% 299.79/300.48 27792[0:SpR:586.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_COMBB(x,y,z,x1),x2),w,u,x3) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_COMBB(x,y,z,x1),x2),u,x3),hAPP(x,hAPP(x2,v))),v)**.
% 299.79/300.48 27791[0:SpR:585.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_COMBC(x,y,z,x1),x2),w,u,x3) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_COMBC(x,y,z,x1),x2),u,x3),hAPP(hAPP(x,v),x2)),v)**.
% 299.79/300.48 27777[0:SpR:3294.1,71.2] || equal(c_in(t_a),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),w)) c_Fun_Oinj__on(hAPP(u,v_x),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(u,v_x),v,x),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))**.
% 299.79/300.48 27773[0:SpR:330.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),w,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),u,y),x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.48 27728[0:SpR:331.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),w,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),u,y),v),v)**.
% 299.79/300.48 27700[0:SpR:369.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) c_Fun_Oinj__on(c_Set_Oinsert(v,w),y,u,z) -> equal(hAPP(c_Fun_Othe__inv__into(y,c_Set_Oinsert(v,w),u,z),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Oinsert(v,w),x))**.
% 299.79/300.48 27699[0:SpR:2089.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),w)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),w,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oinsert(v_x,tc_Com_Opname),u,x),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs))**.
% 299.79/300.48 27680[0:SpR:71.2,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(y,x,v,z) hBOOL(hAPP(hAPP(c_in(x1),hAPP(y,w)),x2)) -> c_lessequals(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,c_Fun_Othe__inv__into(x,y,v,z),x1,u),u)*.
% 299.79/300.48 27674[0:SpR:71.2,176.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),hAPP(c_Set_Ovimage(c_Fun_Othe__inv__into(w,x,u,y),z,x1),hAPP(c_Set_Oinsert(v,x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.79/300.48 28196[0:SpR:465.1,196.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> hBOOL(hAPP(hAPP(c_in(x),v),z)) equal(hAPP(c_Set_Ovimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),hAPP(c_Set_Oimage(u,x,y),z)),z)**.
% 299.79/300.48 28187[0:SpR:465.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> hBOOL(hAPP(hAPP(c_in(y),z),w)) c_lessequals(hAPP(c_Set_Oimage(x1,y,x2),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oimage(c_Fun_Ofun__upd(x1,z,x3,y,x2),y,x2),v,u),u)*.
% 299.79/300.48 28177[0:SpR:465.1,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),w),hAPP(c_Set_Ovimage(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),x,x2),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(y,u,x1),w),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))))))*.
% 299.79/300.48 28138[0:SpR:465.1,9268.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(w,u,x),v_x),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Set_Oimage(c_Fun_Ofun__upd(w,v,y,u,x),u,x)),c_Set_Oimage(c_Fun_Ofun__upd(w,v,y,u,x),u,x))**.
% 299.79/300.48 28551[0:SpR:584.0,118.0] || -> equal(c_Fun_Ocomp(c_COMBS(u,v,w,x,y),c_Fun_Ofun__upd(z,x1,x2,x3,x4),x4,x5,x3),c_Fun_Ofun__upd(c_Fun_Ocomp(c_COMBS(u,v,w,x,y),z,x4,x5,x3),x1,hAPP(hAPP(u,x2),hAPP(v,x2)),x3,x5))*.
% 299.79/300.48 28550[0:SpR:586.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_COMBB(u,v,w,x),y),c_Fun_Ofun__upd(z,x1,x2,x3,x4),x4,x5,x3),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_COMBB(u,v,w,x),y),z,x4,x5,x3),x1,hAPP(u,hAPP(y,x2)),x3,x5))*.
% 299.79/300.48 28549[0:SpR:585.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_COMBC(u,v,w,x),y),c_Fun_Ofun__upd(z,x1,x2,x3,x4),x4,x5,x3),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_COMBC(u,v,w,x),y),z,x4,x5,x3),x1,hAPP(hAPP(u,x2),y),x3,x5))*.
% 299.79/300.48 28546[0:SpR:11499.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),c_Fun_Ofun__upd(x,y,c_Orderings_Otop__class_Otop(tc_bool),z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x,x1,x2,z),y,c_Orderings_Otop__class_Otop(tc_bool),z,x2))*.
% 299.79/300.48 28542[0:SpR:336.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Fun_Ofun__upd(w,x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,z,x1,y),x,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),y,x1))*.
% 299.79/300.48 28497[0:SpR:14526.0,118.0] || -> equal(c_Fun_Ocomp(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),c_Fun_Ofun__upd(x,y,c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),u),z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),x,x1,x2,z),y,c_Orderings_Obot__class_Obot(tc_bool),z,x2))*.
% 299.79/300.48 28485[0:SpR:331.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),c_Fun_Ofun__upd(v,w,x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,z,x1,y),w,x,y,x1))*.
% 299.79/300.48 28458[0:SpR:353.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,hAPP(c_Set_Oinsert(y,v),z),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(u,v),w,x2,x3,x1),x,hAPP(c_Set_Oinsert(y,v),hAPP(c_Set_Oinsert(u,v),z)),x1,x3))*.
% 299.79/300.48 28710[0:SpR:28031.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),hAPP(c_Set_Oinsert(v_Procs,x),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),w,x),y)))*.
% 299.79/300.48 28709[0:SpR:28031.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),w,x),v_Procs),v_Procs)**.
% 299.79/300.48 28708[0:SpR:28031.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),w,x),v_Procs),v_Procs)**.
% 299.79/300.48 28865[0:SpR:28334.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),hAPP(c_Set_Oinsert(v_Procs,x),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),w,x),y)))*.
% 299.79/300.48 28864[0:SpR:28334.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),w,x),v_Procs),v_Procs)**.
% 299.79/300.48 28863[0:SpR:28334.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),w,x),v_Procs),v_Procs)**.
% 299.79/300.48 29273[0:Rew:537.1,29159.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w)),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),x)))**.
% 299.79/300.48 29274[0:Rew:537.1,29158.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,w)),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),x)))**.
% 299.79/300.48 29295[0:SSi:29193.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),tc_fun(v,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)),y,tc_fun(v,tc_bool)).
% 299.79/300.48 29298[0:SSi:29081.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)),y,tc_fun(v,tc_bool)) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),tc_fun(v,tc_bool))*.
% 299.79/300.48 29777[0:Rew:534.1,29684.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w)),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),x)))**.
% 299.79/300.48 29778[0:Rew:534.1,29683.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,w)),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),x)))**.
% 299.79/300.48 30269[0:SpR:21893.0,536.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)))**.
% 299.79/300.48 30268[0:SpR:21267.0,536.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)))**.
% 299.79/300.48 30485[0:SSi:30315.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),tc_fun(v,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,x,tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y),tc_fun(v,tc_bool)).
% 299.79/300.48 30487[0:SSi:30486.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y))))*.
% 299.79/300.48 30488[0:SSi:30241.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(x,u),y))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y))))*.
% 299.79/300.48 30490[0:SSi:30134.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),tc_fun(w,tc_bool)) -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y)),tc_fun(w,tc_bool))*.
% 299.79/300.48 30833[0:SpR:21893.0,535.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)))**.
% 299.79/300.48 30832[0:SpR:21267.0,535.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)))**.
% 299.79/300.48 31252[0:SpL:21893.0,356.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,u),u,x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,y)),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.79/300.48 31251[0:SpL:21267.0,356.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,u),u,x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,y)),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.79/300.48 31429[0:Res:518.1,449.0] || hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y)))* -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)),t_a).
% 299.79/300.48 31408[0:SpL:15172.0,449.0] || hBOOL(hAPP(c_Orderings_Obot__class_Obot(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)),z,x1))) -> c_Hoare__Mirabelle_Otriple__valid(x1,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),z),c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool))),t_a)*.
% 299.79/300.48 31375[0:SpL:300.1,449.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,x)))* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u))),t_a).
% 299.79/300.48 31978[0:SpR:383.1,383.1] || -> equal(u,v) equal(w,u) equal(c_Fun_Ofun__upd(c_Fun_Ofun__upd(c_Fun_Ofun__upd(x,v,y,z,x1),w,x2,z,x1),u,x3,z,x1),c_Fun_Ofun__upd(c_Fun_Ofun__upd(c_Fun_Ofun__upd(x,u,x3,z,x1),v,y,z,x1),w,x2,z,x1))*.
% 299.79/300.48 32066[0:Res:151.2,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w)) c_Hoare__Mirabelle_Ohoare__valids(c_HOL_Ominus__class_Ominus(v,w,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),x,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_HOL_Ominus__class_Ominus(v,w,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),x),u,t_a)*.
% 299.79/300.48 32063[0:Res:151.2,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Ohoare__valids(w,c_HOL_Ominus__class_Ominus(v,x,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,y),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x))* c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.48 32043[0:SpR:56.1,151.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(u),x),hAPP(c_Set_Oinsert(v,u),y)))* -> hBOOL(hAPP(hAPP(c_in(u),x),w)) hBOOL(hAPP(hAPP(c_in(u),x),c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool))))*.
% 299.79/300.48 32376[0:Res:34.1,477.0] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),hAPP(c_Set_Ovimage(v,z,x1),u),w))))* hBOOL(hAPP(hAPP(c_in(w),x2),x))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,z,x1),u),x2))*.
% 299.79/300.48 32339[0:SpL:299.2,477.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v),y,u)* hBOOL(y) hBOOL(hAPP(hAPP(c_in(v),z),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z))*.
% 299.79/300.48 32556[0:Res:34.1,476.0] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),hAPP(c_Set_Ovimage(v,z,x1),u),w))))* hBOOL(hAPP(hAPP(c_in(w),x2),y))* -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,z,x1),u),x2))*.
% 299.79/300.48 32519[0:SpL:299.2,476.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v),y,u)* hBOOL(y) hBOOL(hAPP(hAPP(c_in(v),z),x))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z))*.
% 299.79/300.48 32795[0:SpR:56.1,35.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(w,x,tc_fun(u,tc_bool)) c_lessequals(x,hAPP(c_Set_Oinsert(v,u),y),tc_fun(u,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(x,c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),w)**.
% 299.79/300.48 33014[0:SpR:9.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(x,hAPP(y,v)),z),hAPP(c_Set_Oimage(c_Fun_Ocomp(x,y,x1,x2,x3),u,z),w)),hAPP(c_Set_Oimage(c_Fun_Ocomp(x,y,x1,x2,x3),u,z),w))**.
% 299.79/300.48 32994[0:SpR:11695.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),v)),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(y,z),c_Option_Othe(v)),u,x),w)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(y,z),c_Option_Othe(v)),u,x),w))**.
% 299.79/300.48 32962[0:SpR:88.1,475.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),v,y),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),v,y),x))**.
% 299.79/300.48 32952[0:SpR:540.1,475.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y),z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,z),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,z),x))**.
% 299.79/300.48 32951[0:SpR:539.1,475.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y),z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,z),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,z),x))**.
% 299.79/300.48 32950[0:SpR:297.2,475.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) hBOOL(hAPP(hAPP(c_in(x),w),y)) -> equal(hAPP(c_Set_Oinsert(w,z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,z),y)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,z),y))**.
% 299.79/300.48 32947[0:SpR:2098.1,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(x,v,t_a) equal(hAPP(c_Set_Oinsert(v,y),hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,v),tc_Hoare__Mirabelle_Otriple(t_a)),u,y),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,v),tc_Hoare__Mirabelle_Otriple(t_a)),u,y),w))**.
% 299.79/300.48 32941[0:SpR:299.2,475.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* hBOOL(hAPP(hAPP(c_in(x),v),y))* -> equal(hAPP(c_Set_Oinsert(w,z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,z),y)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,z),y))**.
% 299.79/300.48 32899[0:SpR:465.1,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),x),w)) equal(hAPP(c_Set_Oinsert(hAPP(c_Fun_Ofun__upd(y,x,z,u,x1),v),x1),hAPP(c_Set_Oimage(y,u,x1),w)),hAPP(c_Set_Oimage(y,u,x1),w))**.
% 299.79/300.48 32882[0:SpR:475.1,317.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(x,hAPP(y,v)),z),hAPP(c_Set_Oimage(x,x1,z),hAPP(c_Set_Oimage(y,u,x1),w))),hAPP(c_Set_Oimage(x,x1,z),hAPP(c_Set_Oimage(y,u,x1),w)))**.
% 299.79/300.48 33386[0:SpL:21893.0,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),u))* c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,x),t_a)*.
% 299.79/300.48 33385[0:SpL:21267.0,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),u))* c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),tc_Com_Opname,x),t_a)*.
% 299.79/300.48 33802[0:Res:248.4,405.1] class_Orderings_Olinorder(u) class_Orderings_Oorder(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,v,tc_fun(u,tc_bool)) c_lessequals(c_Finite__Set_Olinorder__class_OMin(w,u),c_Finite__Set_Olinorder__class_OMin(v,u),u)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(c_Finite__Set_Olinorder__class_OMin(w,u),c_Finite__Set_Olinorder__class_OMin(v,u)).
% 299.79/300.48 33882[0:Res:247.4,405.1] class_Orderings_Olinorder(u) class_Orderings_Oorder(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,v,tc_fun(u,tc_bool)) c_lessequals(c_Finite__Set_Olinorder__class_OMax(v,u),c_Finite__Set_Olinorder__class_OMax(w,u),u)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(c_Finite__Set_Olinorder__class_OMax(v,u),c_Finite__Set_Olinorder__class_OMax(w,u)).
% 299.79/300.48 34412[0:SpL:24914.0,280.1] || hBOOL(hAPP(hAPP(u,v),w)) hBOOL(hAPP(hAPP(c_in(x),v),v_x)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(x),v),tc_Com_Opname,y),hAPP(hAPP(c_in(x),v),v_x)),u,x,tc_fun(z,tc_bool)),w))*.
% 299.79/300.48 34383[0:SpL:24914.0,513.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),v_x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),x),y),z))* -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),tc_Com_Opname,x1),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),v_x)),z)*.
% 299.79/300.48 34324[0:SpL:24914.0,57.1] class_OrderedGroup_Olordered__ab__group__add(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),c_HOL_Ouminus__class_Ouminus(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x)),u)),c_HOL_Ozero__class_Ozero(u))** -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(u),tc_Com_Opname,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x)),c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.48 34555[0:SpR:34427.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,w),v,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,w),u,x),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))**.
% 299.79/300.48 34554[0:SpR:34427.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,w),v,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,w),u,x),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))**.
% 299.79/300.48 34665[0:SpL:55.1,263.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(w,u),x),y,tc_fun(u,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(u),w),y)) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(x,y,tc_fun(u,tc_bool)))) equal(v,w).
% 299.79/300.48 34749[0:SpR:34428.0,118.0] || -> equal(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),c_Fun_Ofun__upd(v,w,v_x,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v,y,z,x),w,v_x,x,z))*.
% 299.79/300.48 34738[0:SpR:34428.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,w),v,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,w),u,x),v_x),v_x)**.
% 299.79/300.48 34737[0:SpR:34428.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,w),v,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,w),u,x),v_x),v_x)**.
% 299.79/300.48 35383[0:SpR:1196.1,410.0] class_Lattices_Oboolean__algebra(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 35378[0:SpR:3294.1,410.0] || equal(c_in(t_a),u) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v),w),hAPP(u,v_x),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 35374[0:SpR:330.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v,tc_fun(y,tc_bool))))*.
% 299.79/300.48 35373[0:SpR:1195.1,410.0] class_Lattices_Oboolean__algebra(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 35367[0:SpR:584.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(u,v),w),x),hAPP(y,v),w,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_COMBS(y,u,x1,x2,x3),v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(y,v),w,tc_fun(z,tc_bool))))*.
% 299.79/300.48 35365[0:SpR:9936.1,410.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,tc_fun(y,tc_bool))))*.
% 299.79/300.48 35361[0:SpR:9935.1,410.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x),v,tc_fun(y,tc_bool))))*.
% 299.79/300.48 35289[0:SpR:34427.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u),v),c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,w),u,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,w),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 35276[0:SpR:21893.0,410.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(w,x),v_x),c_Set_Oinsert(w,x),tc_Com_Opname,y),v,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),v_x),v,x,tc_fun(u,tc_bool)))**.
% 299.79/300.48 35275[0:SpR:21267.0,410.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(w,x),hAPP(c_Set_Oinsert(w,x),v_x),tc_Com_Opname,y),v,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),v_x),v,x,tc_fun(u,tc_bool)))**.
% 299.79/300.48 36729[0:SpR:67.0,64.0] || -> equal(hAPP(c_Set_Oinsert(u,v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),tc_fun(v,tc_bool))),hAPP(c_Set_Oinsert(u,v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))))**.
% 299.79/300.48 37127[0:SpL:158.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(z,w,u,x1,x),x,x1),y),x2,tc_fun(x1,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(x1),hAPP(z,v)),x2))*.
% 299.79/300.48 37125[0:SpL:317.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* c_lessequals(hAPP(c_Set_Oinsert(hAPP(y,w),z),hAPP(c_Set_Oimage(y,u,z),x)),x1,tc_fun(z,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(z),hAPP(y,v)),x1))*.
% 299.79/300.48 37482[0:SpR:158.0,205.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z)),hAPP(c_Set_Oimage(x,y,v),z))**.
% 299.79/300.48 37477[0:SpR:205.1,158.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(x,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),v,y,w),w,y),hAPP(c_Set_Oimage(u,v,w),z)),hAPP(c_Set_Oimage(x,v,y),z))**.
% 299.79/300.48 37455[0:SpR:205.1,313.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(x,hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x),y,tc_fun(v,tc_bool))*.
% 299.79/300.48 37452[0:SpR:205.1,98.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Set_Oimage(u,v,w),x),w,v)* -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),x),w),c_Finite__Set_Ocard(x,v)).
% 299.79/300.48 37440[0:SpR:205.1,313.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool)) -> c_lessequals(x,hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),y),tc_fun(v,tc_bool))*.
% 299.79/300.48 37685[0:SpR:23.0,198.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Fun_Ocomp(c_Fun_Ocomp(x,c_Fun_Ocomp(y,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),v,z,w),z,x1,w),u,w,x1,v),c_Fun_Ocomp(x,y,z,x1,v))**.
% 299.79/300.48 37678[0:SpR:198.1,23.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Fun_Ocomp(c_Fun_Ocomp(x,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),v,y,w),c_Fun_Ocomp(u,z,v,w,x1),w,y,x1),c_Fun_Ocomp(x,z,v,y,x1))**.
% 299.79/300.48 37677[0:SpR:198.1,131.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),v,y,w),w,y),z)),hAPP(c_Set_Ovimage(x,v,y),z))**.
% 299.79/300.48 38967[0:SpR:354.2,475.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(y),z),hAPP(c_Set_Oimage(x,w,y),u)))* -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v,x,w,y),z),w),u),u)**.
% 299.79/300.48 38966[0:SpR:354.2,545.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(y),z),hAPP(c_Set_Oimage(x,w,y),u)))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(v,x,w,y),z)),u))*.
% 299.79/300.48 39018[0:MRR:38957.2,20734.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,w,y),u),c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),w,y),u),hAPP(c_Set_Oimage(x,w,y),u))**.
% 299.79/300.48 39329[0:SpL:533.0,3507.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v_x)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.79/300.48 39328[0:SpL:533.0,16327.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_Procs) -> .
% 299.79/300.48 39327[7:SpL:533.0,31886.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),c_Orderings_Obot__class_Obot(tc_bool))** equal(u,v_x) -> .
% 299.79/300.48 39326[0:SpL:533.0,3499.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.79/300.48 39324[0:SpL:533.0,24254.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Com_Ocom_OBODY)** equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.79/300.48 39319[0:SpL:533.0,13272.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x)* -> hBOOL(hAPP(x,v_x))*.
% 299.79/300.48 39318[0:SpL:533.0,3484.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Com_Ocom_OBODY) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),hAPP(c_Com_Ocom_OBODY,x))* -> equal(v_x,x).
% 299.79/300.48 39258[0:SpR:8415.2,533.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),w))**.
% 299.79/300.48 39192[0:SpR:533.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,y),hAPP(c_Set_Oinsert(z,x),x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z))))*.
% 299.79/300.48 39167[0:SpR:533.0,9569.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w))),x),tc_bool)*.
% 299.79/300.48 39166[0:SpR:533.0,9568.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w))),z),x),tc_bool)*.
% 299.79/300.48 39154[0:SpR:533.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y))) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v_x))))*.
% 299.79/300.48 39153[0:SpR:533.0,28356.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),tc_Com_Opname,y)))*.
% 299.79/300.48 39152[0:SpR:533.0,28053.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),u,tc_Com_Opname,y)))*.
% 299.79/300.48 39151[0:SpR:533.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),tc_Com_Opname,y)))*.
% 299.79/300.48 39150[0:SpR:533.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),tc_Com_Opname,y)))*.
% 299.79/300.48 39149[0:SpR:533.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),tc_Com_Opname,y),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x))))*.
% 299.79/300.48 39148[0:SpR:533.0,3317.1] || equal(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),hAPP(c_Set_Oinsert(v_x,u),y)))*.
% 299.79/300.48 39147[0:SpR:533.0,3305.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,y),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x))))*.
% 299.79/300.48 39143[0:SpR:533.0,2771.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.79/300.48 39137[0:SpR:533.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.79/300.48 39135[0:SpR:533.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))),v_Procs))*.
% 299.79/300.48 39128[0:SpR:533.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname,x),hAPP(c_Set_Oinsert(y,tc_Com_Opname),v_Procs)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.48 39127[0:SpR:533.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),t_a,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.79/300.48 39121[0:SpR:533.0,15262.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_in(t_a)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))*.
% 299.79/300.48 39118[0:SpR:533.0,8376.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_in(tc_Com_Opname)) equal(x,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),x))*.
% 299.79/300.48 39116[0:SpR:533.0,8415.2] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),v_x)**.
% 299.79/300.48 39115[0:SpR:533.0,3291.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),v_Procs))*.
% 299.79/300.48 39114[0:SpR:533.0,3285.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)))*.
% 299.79/300.48 39110[0:SpR:533.0,3279.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool))) -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),v_Procs),v_x))*.
% 299.79/300.48 39741[0:SpR:8415.2,532.0] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))**.
% 299.79/300.48 39618[0:SpR:532.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),z),w),x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z))))*.
% 299.79/300.48 39593[0:SpR:532.0,9569.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)),tc_bool)*.
% 299.79/300.48 39592[0:SpR:532.0,9568.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)),tc_bool)*.
% 299.79/300.48 39589[0:SpR:532.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)),y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v))**.
% 299.79/300.48 39939[0:Rew:39938.1,20486.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w,x),y),y)**.
% 299.79/300.48 40182[0:SpR:8415.2,399.1] || equal(v_Procs,v_x) equal(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(v_x,v,tc_fun(u,tc_bool)) -> c_lessequals(v_x,hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),tc_fun(u,tc_bool))*.
% 299.79/300.48 40176[0:SpR:8415.2,399.1] || equal(v_Procs,v_x) equal(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(v,v_x,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),v_x,tc_fun(u,tc_bool))*.
% 299.79/300.48 40277[0:SpL:8415.2,398.0] || equal(v_Procs,v_x) equal(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(v_x,hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),tc_fun(u,tc_bool))* -> c_lessequals(v_x,v,tc_fun(u,tc_bool)).
% 299.79/300.48 40271[0:SpL:8415.2,398.0] || equal(v_Procs,v_x) equal(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),v_x,tc_fun(u,tc_bool))* -> c_lessequals(v,v_x,tc_fun(u,tc_bool)).
% 299.79/300.48 40451[0:SpL:8415.2,529.0] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Hoare__Mirabelle_Otriple__valid(x,v_x,u) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),u)*.
% 299.79/300.48 40441[0:SpL:24914.0,529.0] || c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),x),v) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Obody,tc_Com_Opname,y),hAPP(c_Com_Obody,v_x)))),x),v)*.
% 299.79/300.48 40438[0:SpL:8415.2,529.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Com_Obody) c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),v_x)),x),v) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,v_x)),x),v)*.
% 299.79/300.48 40700[0:SpR:8415.2,530.1] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),u)* -> c_Hoare__Mirabelle_Otriple__valid(x,v_x,u).
% 299.79/300.48 40690[0:SpR:24914.0,530.1] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Obody,tc_Com_Opname,x),hAPP(c_Com_Obody,v_x)))),y),v)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),y),v).
% 299.79/300.48 40687[0:SpR:8415.2,530.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Com_Obody) c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,v_x)),x),v)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),v_x)),x),v).
% 299.79/300.48 40924[0:Res:23961.0,479.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_Procs),w,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_Procs)),w)))*.
% 299.79/300.48 40958[0:Rew:339.0,40921.1,339.0,40921.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),x,u,tc_Com_Opname)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))))*.
% 299.79/300.48 40959[0:Rew:339.0,40920.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,u,t_a)),hAPP(c_Set_Oinsert(v,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w))))*.
% 299.79/300.48 40960[0:Rew:339.0,40906.1,339.0,40906.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oinsert(v,w),y)),z,u,w)),hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)))))*.
% 299.79/300.48 40899[0:Res:9071.0,479.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,tc_fun(w,tc_bool)),x,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,tc_fun(w,tc_bool))),x)))*.
% 299.79/300.48 40893[0:Res:1157.0,479.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(c_COMBK(v,x,y),tc_Com_Opname,w),v_Procs),z,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_COMBK(v,x,y),tc_Com_Opname,w),v_Procs)),z)))*.
% 299.79/300.48 40961[0:Rew:339.0,40892.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(y,u),w),z,x,u)),hAPP(c_Set_Oinsert(y,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z))))*.
% 299.79/300.48 40863[0:SpL:8415.2,479.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,w)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,x,v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))*.
% 299.79/300.48 40963[0:Rew:104.0,40923.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),w,u,tc_Com_Opname)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),w,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.79/300.48 41205[0:Res:23961.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_Procs),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_Procs))))*.
% 299.79/300.48 41202[0:Res:19441.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(w,tc_Com_Opname),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)))))*.
% 299.79/300.48 41201[0:Res:19452.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))))*.
% 299.79/300.48 41187[0:Res:9067.0,478.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(y,w),hAPP(c_Set_Oinsert(v,w),z)),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(y,w),hAPP(c_Set_Oinsert(v,w),z)))))*.
% 299.79/300.48 41180[0:Res:9071.0,478.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,tc_fun(w,tc_bool)),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,tc_fun(w,tc_bool)))))*.
% 299.79/300.48 41174[0:Res:1157.0,478.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oimage(c_COMBK(v,y,z),tc_Com_Opname,w),v_Procs),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(c_COMBK(v,y,z),tc_Com_Opname,w),v_Procs))))*.
% 299.79/300.48 41173[0:Res:254.1,478.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(z,u),w),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(c_Set_Oinsert(z,u),w))))*.
% 299.79/300.48 41144[0:SpL:8415.2,478.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,w)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,w,v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w)))*.
% 299.79/300.48 41233[0:Rew:19819.0,41204.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),u,tc_Com_Opname)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(w,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),v,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.79/300.48 41386[0:SpL:32668.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,y,tc_Com_Opname,z),hAPP(y,v_x)),tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 41385[0:SpL:28910.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(y,z,x1),y,tc_Com_Opname,x2),tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 41384[0:SpL:28926.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,y),tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 41382[0:SpL:28755.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,y,c_COMBK(y,z,x1),tc_Com_Opname,x2),tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 41381[0:SpL:28771.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,y),tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 41379[0:SpL:27043.1,275.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_Procs,y),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 41377[0:SpL:10063.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v)) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,t_a),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 41373[0:SpL:15172.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),z,x1),x2,tc_fun(x3,tc_bool)),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41368[0:SpL:586.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(z,hAPP(x1,v))))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_COMBB(z,x2,x3,x4),x1),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41367[0:SpL:585.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(hAPP(z,v),x1)))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_COMBC(z,x2,x3,x4),x1),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41355[0:SpL:24914.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))),x))* hBOOL(hAPP(hAPP(c_in(y),z),hAPP(v,v_x))) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,u,tc_fun(y,tc_bool))))*.
% 299.79/300.48 41339[0:SpL:9936.1,275.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),w),x))* hBOOL(hAPP(hAPP(c_in(y),z),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(y,tc_bool))))*.
% 299.79/300.48 41335[0:SpL:9935.1,275.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41304[0:SpL:14526.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v)),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(c_Option_Othe(v),z,tc_fun(x1,tc_bool)),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41278[0:SpL:8415.2,275.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) hBOOL(hAPP(hAPP(c_in(x),y),v_x)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,u,v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41259[0:SpL:369.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y))* hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(c_Set_Oinsert(v,w),x)))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(v,w),u,tc_fun(z,tc_bool))))*.
% 299.79/300.48 41258[0:SpL:2089.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41252[0:SpL:445.1,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(z,v)))* -> equal(v,x1)* hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ofun__upd(z,x1,x2,x3,x4),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41635[0:SpL:2935.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_in(t_a),v_x),v,u),w)))* c_Fun_Oinj__on(hAPP(c_in(t_a),v_x),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,u)* -> hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),w)).
% 299.79/300.48 41630[0:SpL:301.1,284.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),y)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,v)* -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(u)),y)).
% 299.79/300.48 41577[0:SpL:414.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,x,v,y,z),x1,u),x2)))* c_Fun_Oinj__on(c_Fun_Ofun__upd(w,x,v,y,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x1,u)* -> hBOOL(hAPP(hAPP(c_in(x1),x),x2)).
% 299.79/300.48 41562[0:SpL:8415.2,284.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(u,w,v),x)))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v)* -> hBOOL(hAPP(hAPP(c_in(w),v_x),x)).
% 299.79/300.48 41558[0:SpL:365.1,284.0] class_Orderings_Obot(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),w,v),x)))* c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v)* -> hBOOL(hAPP(hAPP(c_in(w),v_x),x)).
% 299.79/300.48 41557[0:SpL:397.1,284.0] class_Orderings_Otop(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),w,v),x)))* c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v)* -> hBOOL(hAPP(hAPP(c_in(w),v_x),x)).
% 299.79/300.48 41522[0:SpL:8415.2,284.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,x)),v_x))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> hBOOL(hAPP(hAPP(c_in(v),x),v_x))*.
% 299.79/300.48 41695[0:Rew:39934.1,41610.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y,u),z)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,u)* -> hBOOL(hAPP(hAPP(c_in(y),v),z)).
% 299.79/300.48 41747[0:Res:530.1,494.1] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),hAPP(c_Com_Ocom_OBODY,w)),x),t_a)* hBOOL(hAPP(hAPP(v,y),z))* c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w)),z,u,x1)* -> hBOOL(hAPP(hAPP(x,y),x1))*.
% 299.79/300.48 41731[0:SpL:8415.2,494.1] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** hBOOL(hAPP(hAPP(u,w),x))* c_Hoare__Mirabelle_Otriple__valid(y,v_x,t_a) c_Natural_Oevaln(v,x,y,z)* -> hBOOL(hAPP(hAPP(v_x,w),z))*.
% 299.79/300.48 41720[0:SpL:8415.2,494.1] || equal(v_Procs,v_x) equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(v_x,y),t_a)* c_Natural_Oevaln(v_x,w,x,z)* -> hBOOL(hAPP(hAPP(y,v),z))*.
% 299.79/300.48 41714[0:SpL:8415.2,494.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(t_a)) hBOOL(hAPP(hAPP(v_x,u),v))* c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(v_x,x),y),t_a)* c_Natural_Oevaln(x,v,w,z)* -> hBOOL(hAPP(hAPP(y,u),z))*.
% 299.79/300.48 41849[0:Res:8376.2,199.0] || equal(c_in(tc_Com_Opname),u) equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(u,v_x),w,v,x)),v_Procs)** c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(hAPP(u,v_x),y))*.
% 299.79/300.48 41843[0:Res:212.1,199.0] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Set_Oinsert(y,z),u),w,v,x))))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,z),u),x1))*.
% 299.79/300.48 41840[0:Res:13238.1,199.0] || equal(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_in(t_a),v_x),v,u,w)),v_x),c_Orderings_Otop__class_Otop(tc_bool))** c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),x))*.
% 299.79/300.48 41834[0:Res:8375.1,199.0] || equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_in(x),y),v,u,w)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))** c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(hAPP(c_in(x),y),z))*.
% 299.79/300.48 41832[0:Res:652.1,199.0] || c_lessequals(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_in(tc_Com_Opname),v_x),v,u,w)),tc_fun(tc_Com_Opname,tc_bool))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),x))*.
% 299.79/300.48 41976[0:SpR:8415.2,82.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> c_lessequals(c_HOL_Ominus__class_Ominus(v_x,hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(v_x,x,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.48 41961[0:SpR:8415.2,82.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),v_x,tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,v_x,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.48 42149[0:SpR:8415.2,180.2] class_Lattices_Oupper__semilattice(u) || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(u)) c_Finite__Set_Ofinite(v,u) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(v_x,u),v),u,u),hAPP(v_x,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u)))**.
% 299.79/300.48 42091[0:SpR:180.2,20881.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y),hAPP(c_Set_Oinsert(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),z,v,u,u),x),x1)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),z,hAPP(c_Set_Oinsert(w,u),v),u,u)))*.
% 299.79/300.48 42066[0:SpR:180.2,9569.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u)),tc_bool)*.
% 299.79/300.48 42065[0:SpR:180.2,9568.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x)),z),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u)),tc_bool)*.
% 299.79/300.48 42238[0:SSi:42113.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(hAPP(c_in(v),w),x)) -> hBOOL(hAPP(hAPP(c_in(v),w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,hAPP(c_Set_Oinsert(x,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool))))*.
% 299.79/300.48 42310[0:SpR:8415.2,221.1] class_Complete__Lattice_Ocomplete__lattice(u) || equal(v_Procs,v_x) equal(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(c_List_Ofoldl(c_COMBC(v_x,v,u,u),c_Orderings_Obot__class_Obot(u),w,u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(w,v),v_x,v,u))**.
% 299.79/300.48 42316[0:Rew:221.1,42315.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),v_x),c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),tc_Com_Opname,x),w,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(v,w),v_x,w,u))**.
% 299.79/300.48 42317[0:Rew:221.1,42314.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),v_x),tc_Com_Opname,x),w,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(v,w),v_x,w,u))**.
% 299.79/300.48 42499[0:SpL:14216.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_Set_Oinsert(w,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),z,x1)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Set_Oimage(u,z,x1),v),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(w,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),z,x1),v)).
% 299.79/300.48 42458[0:SpL:14216.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u,z,x1)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(w,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),z,x1),v),hAPP(c_Set_Oimage(u,z,x1),v)).
% 299.79/300.48 42777[0:Rew:39935.1,42659.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z),w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(z,w,tc_fun(u,tc_bool)))**.
% 299.79/300.48 43113[0:SpR:21893.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)),x))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(v,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,u,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,u,tc_fun(y,tc_bool)))**.
% 299.79/300.48 43112[0:SpR:21267.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)),x))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(v,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,u,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,u,tc_fun(y,tc_bool)))**.
% 299.79/300.48 43067[0:SpR:24020.1,486.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool)))**.
% 299.79/300.48 43059[0:SpR:9924.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,tc_fun(x,tc_bool)))**.
% 299.79/300.48 43009[0:SpR:525.1,486.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(y,tc_bool)))**.
% 299.79/300.48 42970[0:SpR:2097.1,486.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),u),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v,z),w,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v,z),w,tc_fun(y,tc_bool)))**.
% 299.79/300.48 43335[0:SpL:8385.1,406.0] || equal(hAPP(c_Set_Oinsert(u,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v_Procs) equal(hAPP(c_Set_Oinsert(u,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))))* -> equal(v_x,v) equal(v_x,w).
% 299.79/300.48 43593[0:Rew:39935.1,43477.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,z)* -> equal(hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x1)),hAPP(c_Set_Oimage(v,w,u),x1))**.
% 299.79/300.48 43821[0:Rew:39935.1,43699.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,z)* -> equal(hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x1)),hAPP(c_Set_Ovimage(v,u,w),x1))**.
% 299.79/300.48 43879[0:Res:38131.1,477.0] || hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z)),u))* hBOOL(hAPP(hAPP(c_in(u),x1),v))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z)),x1))*.
% 299.79/300.48 43878[0:Res:38131.1,476.0] || hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z)),u))* hBOOL(hAPP(hAPP(c_in(u),x1),w))* -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z)),x1))*.
% 299.79/300.48 44016[0:Rew:19109.1,43980.3] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x),tc_fun(u,tc_bool))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u)* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))*.
% 299.79/300.48 44184[0:Res:232.1,471.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* hBOOL(hAPP(hAPP(c_in(v),x),c_HOL_Ouminus__class_Ouminus(y,tc_fun(v,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,x)),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))))*.
% 299.79/300.48 44198[0:SSi:44144.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.48 44353[0:Res:27441.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))* equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,hAPP(w,v_x),tc_Com_Opname,x)),hAPP(v,u))* c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,y)* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,hAPP(w,v_x),tc_Com_Opname,x),u).
% 299.79/300.48 44350[0:Res:27381.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))* equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(w,v_x),w,tc_Com_Opname,x)),hAPP(v,u))* c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,y)* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(w,v_x),w,tc_Com_Opname,x),u).
% 299.79/300.48 44331[0:Res:19451.0,268.0] || hBOOL(hAPP(hAPP(c_in(t_a),u),hAPP(c_Set_Oinsert(v,t_a),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))* equal(hAPP(x,v_x),hAPP(x,u))* c_Fun_Oinj__on(x,hAPP(c_Set_Oinsert(v,t_a),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),t_a,y)* -> equal(v_x,u).
% 299.79/300.48 44325[0:Res:15262.1,268.0] || equal(c_in(t_a),c_in(u)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))* equal(hAPP(w,v_x),hAPP(w,v))* c_Fun_Oinj__on(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,x)* -> equal(v_x,v).
% 299.79/300.48 44324[0:Res:3285.1,268.0] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))* equal(hAPP(x,v_x),hAPP(x,v))* c_Fun_Oinj__on(x,hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs),u,y)* -> equal(v_x,v).
% 299.79/300.48 44323[0:Res:3317.1,268.0] || equal(c_in(u),c_in(v)) hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oinsert(v_x,u),x)))* equal(hAPP(y,v_x),hAPP(y,w))* c_Fun_Oinj__on(y,hAPP(c_Set_Oinsert(v_x,u),x),v,z)* -> equal(v_x,w).
% 299.79/300.48 44319[0:Res:19440.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_in(tc_Com_Opname),v_x))))* equal(hAPP(x,v_Procs),hAPP(x,v))* c_Fun_Oinj__on(x,hAPP(c_Set_Oinsert(w,u),hAPP(c_in(tc_Com_Opname),v_x)),u,y)* -> equal(v_Procs,v).
% 299.79/300.48 44300[0:Res:648.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,tc_Com_Opname,u),v_Procs)))* equal(hAPP(x,hAPP(w,v_x)),hAPP(x,v))* c_Fun_Oinj__on(x,hAPP(c_Set_Oimage(w,tc_Com_Opname,u),v_Procs),u,y)* -> equal(hAPP(w,v_x),v).
% 299.79/300.48 44296[0:Res:649.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs)))* equal(hAPP(w,v_x),hAPP(w,u))* c_Fun_Oinj__on(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),v_Procs),tc_Com_Opname,x)* -> equal(v_x,u).
% 299.79/300.48 44295[0:Res:650.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v)))* equal(hAPP(w,v_x),hAPP(w,u))* c_Fun_Oinj__on(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),v),tc_Com_Opname,x)* -> equal(v_x,u).
% 299.79/300.48 44409[0:Rew:586.0,44402.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(hAPP(c_Set_Oimage(x,y,z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x1,u,tc_fun(y,tc_bool))),x2,tc_fun(z,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(x,y,z),hAPP(x1,v)),x2,tc_fun(z,tc_bool))*.
% 299.79/300.48 44410[0:Rew:586.0,44401.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(hAPP(c_Set_Oimage(x,y,z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x1,u,tc_fun(y,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))** -> equal(hAPP(c_Set_Oimage(x,y,z),hAPP(x1,v)),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))**.
% 299.79/300.48 44463[0:Rew:586.0,44456.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(hAPP(c_Set_Ovimage(x,y,z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x1,u,tc_fun(z,tc_bool))),x2,tc_fun(y,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(x,y,z),hAPP(x1,v)),x2,tc_fun(y,tc_bool))*.
% 299.79/300.48 44464[0:Rew:586.0,44455.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(hAPP(c_Set_Ovimage(x,y,z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x1,u,tc_fun(z,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))** -> equal(hAPP(c_Set_Ovimage(x,y,z),hAPP(x1,v)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))**.
% 299.79/300.48 44801[0:MRR:44787.3,3591.0] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname)))),hAPP(v_Q,c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname))),t_a)*.
% 299.79/300.48 44802[0:MRR:44786.3,3591.0] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname)))),hAPP(v_Q,c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname))),t_a)*.
% 299.79/300.48 45120[0:Res:326.2,431.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,y,tc_fun(w,tc_bool))* c_Fun_Oinj__on(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),w,x1)* -> c_Fun_Oinj__on(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),w,x1)*.
% 299.79/300.48 45109[0:SpR:3294.1,326.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_lessequals(v_x,v,tc_fun(u,tc_bool)) c_lessequals(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),w,tc_fun(u,tc_bool)) -> c_lessequals(c_Orderings_Obot__class_Obot(tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_fun(u,tc_bool))*.
% 299.79/300.48 45104[0:SpR:584.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(hAPP(x,u),y,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,z,x1,x2),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),tc_fun(w,tc_bool))*.
% 299.79/300.48 45087[0:SpR:600.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),y,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),tc_fun(w,tc_bool))*.
% 299.79/300.48 45044[0:SpR:3294.1,326.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_lessequals(v,v_x,tc_fun(u,tc_bool)) c_lessequals(w,c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),tc_fun(u,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_bool),tc_fun(u,tc_bool))*.
% 299.79/300.48 45039[0:SpR:584.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,hAPP(y,v),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y,z,x1,x2),v),tc_fun(w,tc_bool))*.
% 299.79/300.48 45022[0:SpR:600.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,c_HOL_Ominus__class_Ominus(y,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v),tc_fun(w,tc_bool))*.
% 299.79/300.48 45323[0:SpL:3294.1,487.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),w),c_Orderings_Obot__class_Obot(tc_bool)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,v,u))) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v,u)))*.
% 299.79/300.48 45318[0:SpL:584.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,y,z,x1),x2)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x2,u,w))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(x,x2),u,w)))*.
% 299.79/300.48 45301[0:SpL:600.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),u,w)))*.
% 299.79/300.48 45483[0:Rew:339.0,45425.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x))) -> hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),tc_Com_Opname))))*.
% 299.79/300.48 45484[0:Rew:537.1,45422.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname))))*.
% 299.79/300.48 45485[0:Rew:534.1,45421.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname))))*.
% 299.79/300.48 45627[0:SpL:323.0,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,v,tc_fun(z,tc_bool)),u,z)))* hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,v,tc_fun(z,tc_bool))))* -> hBOOL(hAPP(u,x1))*.
% 299.79/300.48 45626[0:SpL:323.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,v,tc_fun(z,tc_bool)),u,z)))* hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,tc_fun(z,tc_bool))))* -> hBOOL(hAPP(u,x1))*.
% 299.79/300.48 45552[0:SpR:323.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,v,tc_fun(z,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,v,tc_fun(z,tc_bool))),x1,u),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))))*.
% 299.79/300.48 45643[0:SSi:45589.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(t_a,tc_bool)),v_x)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,w,tc_fun(t_a,tc_bool)),v_x)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v,w,tc_fun(t_a,tc_bool)),v_x))**.
% 299.79/300.48 45876[0:SpL:3229.1,482.2] || equal(u,c_in(v)) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,w,v)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,w,v)))* hBOOL(hAPP(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(w,v_x)).
% 299.79/300.48 45816[0:SpL:3229.1,482.2] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,v)))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,x,v)))* hBOOL(hAPP(hAPP(c_in(v),y),hAPP(u,v_x)))* -> hBOOL(hAPP(x,y))*.
% 299.79/300.48 45810[0:SpL:3229.1,482.2] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,w,v)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,w,v)))* hBOOL(hAPP(hAPP(c_in(v),y),hAPP(hAPP(u,v_x),x)))* -> hBOOL(hAPP(w,y))*.
% 299.79/300.48 46006[0:Rew:339.0,45940.1] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),tc_Com_Opname))))* -> hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x))).
% 299.79/300.48 46007[0:Rew:537.1,45937.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname))))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))).
% 299.79/300.48 46008[0:Rew:534.1,45936.2] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname))))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))).
% 299.79/300.48 46199[0:Rew:104.0,46139.2] || -> hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),x,u)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))*.
% 299.79/300.48 46938[0:Res:241.2,44639.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v)) c_lessequals(v,hAPP(c_Set_Oinsert(u,tc_Com_Opname),w),tc_fun(tc_Com_Opname,tc_bool))* equal(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(u,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> hBOOL(hAPP(w,v_x)).
% 299.79/300.48 46930[0:Res:241.2,18625.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),y),hAPP(x,y),tc_bool)*.
% 299.79/300.48 47192[0:Res:1145.0,242.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(w,hAPP(c_Set_Oinsert(v,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),x,y),tc_Com_Opname,tc_fun(u,tc_bool))),tc_fun(u,tc_bool))*.
% 299.79/300.48 47411[0:Res:8376.2,485.1] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_Procs)** hBOOL(hAPP(x,v_x)) -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)),v))*.
% 299.79/300.48 47642[0:Res:8376.2,484.1] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_Procs)** hBOOL(hAPP(x,v_x)) -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)),w))*.
% 299.79/300.48 47980[0:Res:8376.2,490.1] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_Procs)** hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)))* -> hBOOL(hAPP(x,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)),v))*.
% 299.79/300.48 48092[0:Res:8376.2,489.1] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_Procs)** hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)))* -> hBOOL(hAPP(x,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.79/300.48 48146[4:SpR:533.0,39023.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),z))*.
% 299.79/300.48 48261[4:SpR:533.0,39064.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),z,t_a)*.
% 299.79/300.48 48320[0:SpL:659.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,u),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v_Procs,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,v),w),v,u) -> .
% 299.79/300.48 48310[0:SpL:66.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(v,x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(w,x),z),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(v,hAPP(c_Set_Oinsert(w,x),c_HOL_Ominus__class_Ominus(y,z,tc_fun(x,tc_bool))),x,u) -> .
% 299.79/300.48 48679[0:SpL:197.1,148.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(y,z,tc_fun(v,tc_bool)))))* -> hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oimage(u,v,w),y))).
% 299.79/300.48 48794[0:Res:3284.1,619.0] || equal(c_in(tc_Com_Opname),u) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(x,tc_bool)),hAPP(u,v_x)),c_Set_Oinsert(y,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(u,v_x),v,w,tc_fun(x,tc_bool))))**.
% 299.79/300.48 49008[0:Res:48989.1,593.0] || c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> hBOOL(hAPP(v,v_x)) c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,v,tc_Com_Opname))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,v,tc_Com_Opname)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,v,tc_Com_Opname))),t_a)*.
% 299.79/300.48 49065[0:SpR:49017.1,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(w,v_x)) equal(hAPP(c_Set_Oinsert(v_Procs,x),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,w,tc_Com_Opname),tc_Com_Opname),u,x),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,w,tc_Com_Opname),tc_Com_Opname),u,x),v))**.
% 299.79/300.48 49306[0:Res:13238.1,488.1] || equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,t_a)),u))* hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,t_a)),v))*.
% 299.79/300.48 49305[0:Res:8375.1,488.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))** hBOOL(hAPP(x,y))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)),w))*.
% 299.79/300.48 49299[0:Res:652.1,488.1] || c_lessequals(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),v),tc_fun(tc_Com_Opname,tc_bool))* hBOOL(hAPP(w,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(u,w,tc_Com_Opname)),u))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,w,tc_Com_Opname)),v))*.
% 299.79/300.48 49430[0:SpL:49342.1,275.1] || hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) hBOOL(hAPP(hAPP(c_in(x),y),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 50516[0:Rew:223.1,50438.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,x1,u,y),u,y),w)),hAPP(c_Set_Oinsert(x1,y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,x,u,y),u,y),w)))*.
% 299.79/300.48 51359[0:SpR:533.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),hAPP(hAPP(c_Set_Oinsert(x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.48 51790[4:Res:40244.1,477.0] || c_lessequals(v_x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x,y,z,x1),u),tc_bool)* hBOOL(hAPP(hAPP(c_in(u),x2),v))* -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x,y,z,x1),x2))*.
% 299.79/300.48 51789[4:Res:40244.1,476.0] || c_lessequals(v_x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x,y,z,x1),u),tc_bool)* hBOOL(hAPP(hAPP(c_in(u),x2),w))* -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x,y,z,x1),x2))*.
% 299.79/300.48 52481[0:Res:37898.1,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,y,z,x1),v)))* hBOOL(hAPP(hAPP(c_in(v),x2),w))* -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,y,z,x1),x2))*.
% 299.79/300.48 52480[0:Res:37898.1,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,y,z,x1),v)))* hBOOL(hAPP(hAPP(c_in(v),x2),x))* -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,y,z,x1),x2))*.
% 299.79/300.48 53040[0:SpR:23955.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)),w))* -> equal(hAPP(c_Set_Oinsert(v_x,x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,x),w))**.
% 299.79/300.48 53172[0:SpR:23958.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)),w))* -> equal(hAPP(c_Set_Oinsert(v_x,x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,x),w))**.
% 299.79/300.48 53813[0:SpL:53771.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Option_Othe(x),v,y)),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),w))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Option_Othe(x),u,tc_fun(x1,tc_bool))))*.
% 299.79/300.48 53844[0:SpL:53772.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(w),x,v,y)),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),x))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Option_Othe(w),u,tc_fun(x1,tc_bool))))*.
% 299.79/300.48 54034[0:SpR:52997.1,410.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),c_Set_Oinsert(v_Procs,w),u,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_Procs,w),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 54309[0:MRR:54218.0,208.1] || c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),tc_fun(v,tc_bool))* -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool)).
% 299.79/300.48 54726[0:SpR:13749.2,475.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,x),w))**.
% 299.79/300.48 55200[0:SpR:14043.2,475.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,x),w))**.
% 299.79/300.48 56404[0:SpL:30368.2,315.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,y)),c_Orderings_Otop__class_Otop(u))** -> equal(hAPP(c_Set_Oimage(v,x,y),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,y),w)).
% 299.79/300.48 56396[0:SpL:30368.2,315.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,x,y)),c_Orderings_Otop__class_Otop(u))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,y),w),hAPP(c_Set_Oimage(v,x,y),w)).
% 299.79/300.48 56846[0:SpL:30928.2,315.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,y)),c_Orderings_Otop__class_Otop(u))** -> equal(hAPP(c_Set_Oimage(v,x,y),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,y),w)).
% 299.79/300.48 56838[0:SpL:30928.2,315.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,x,y)),c_Orderings_Otop__class_Otop(u))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,y),w),hAPP(c_Set_Oimage(v,x,y),w)).
% 299.79/300.48 57952[0:SpL:533.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),v_x)))* -> .
% 299.79/300.48 58109[0:SpL:533.0,55992.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_COMBK(x,y,z))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool),x)* -> .
% 299.79/300.48 59128[0:Rew:104.0,58751.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),x),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)))*.
% 299.79/300.48 59638[0:Rew:104.0,59259.1] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),y),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)))*.
% 299.79/300.48 60221[0:SpL:533.0,58170.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),tc_bool),y,z),u)* -> .
% 299.79/300.48 60414[7:SpR:131.0,58968.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x) -> hBOOL(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z))))*.
% 299.79/300.48 60413[7:SpR:158.0,58968.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x) -> hBOOL(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z))))*.
% 299.79/300.48 60527[0:SpR:131.0,58969.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs) -> hBOOL(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z))))*.
% 299.79/300.48 60526[0:SpR:158.0,58969.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs) -> hBOOL(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z))))*.
% 299.79/300.48 60600[7:SpR:131.0,59476.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x) -> hBOOL(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),x1))))*.
% 299.79/300.48 60599[7:SpR:158.0,59476.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_x) -> hBOOL(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),x1))))*.
% 299.79/300.48 60673[0:SpR:131.0,59477.1] || equal(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs) -> hBOOL(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),x1))))*.
% 299.79/300.48 60672[0:SpR:158.0,59477.1] || equal(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs) -> hBOOL(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),x1))))*.
% 299.79/300.48 60858[0:SpR:131.0,59017.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y),t_a)* hBOOL(hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1))))*.
% 299.79/300.48 60857[0:SpR:158.0,59017.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y),t_a)* hBOOL(hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1))))*.
% 299.79/300.48 60931[0:SpR:131.0,59525.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y),t_a)* hBOOL(hAPP(c_Set_Ovimage(w,z,x),hAPP(c_Set_Ovimage(v,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x2))))*.
% 299.79/300.48 60930[0:SpR:158.0,59525.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y),t_a)* hBOOL(hAPP(c_Set_Oimage(v,x,y),hAPP(c_Set_Oimage(w,z,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x2))))*.
% 299.79/300.48 62656[0:Res:247.4,4340.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,v,tc_fun(u,tc_bool)) c_lessequals(c_Finite__Set_Olinorder__class_OMax(v,u),c_Finite__Set_Olinorder__class_OMax(w,u),u)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(c_Finite__Set_Olinorder__class_OMax(v,u),c_Finite__Set_Olinorder__class_OMax(w,u)).
% 299.79/300.48 62655[0:Res:248.4,4340.1] class_Orderings_Olinorder(u) class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) c_lessequals(w,v,tc_fun(u,tc_bool)) c_lessequals(c_Finite__Set_Olinorder__class_OMin(w,u),c_Finite__Set_Olinorder__class_OMin(v,u),u)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(c_Finite__Set_Olinorder__class_OMin(w,u),c_Finite__Set_Olinorder__class_OMin(v,u)).
% 299.79/300.48 64173[0:SpR:646.1,118.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(c_Fun_Ocomp(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),c_Fun_Ofun__upd(w,x,hAPP(u,v_x),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,z,x1,y),x,v_x,y,x1))*.
% 299.79/300.48 64340[0:SpR:645.1,118.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),c_Fun_Ofun__upd(w,x,hAPP(u,v_x),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,z,x1,y),x,v_x,y,x1))*.
% 299.79/300.48 66031[0:SpR:65404.1,486.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(y,tc_bool)))**.
% 299.79/300.48 66729[0:SpR:1188.2,118.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),c_Fun_Ofun__upd(v,w,c_HOL_Ozero__class_Ozero(u),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,y,z,x),w,c_Orderings_Otop__class_Otop(u),x,z))*.
% 299.79/300.48 67484[0:SpR:1189.2,118.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),c_Fun_Ofun__upd(v,w,c_HOL_Ozero__class_Ozero(u),x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,y,z,x),w,c_Orderings_Otop__class_Otop(u),x,z))*.
% 299.79/300.48 71816[7:SpL:71455.1,406.0] || equal(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x) equal(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Set_Oinsert(w,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))))* -> equal(v_x,v) equal(v_x,w).
% 299.79/300.48 71638[7:SpR:71455.1,450.0] || equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oinsert(v_x,t_a),u,v,w),v_x) -> hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oinsert(v_x,t_a),u,v,w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Set_Oinsert(v_x,t_a),u,v,w)))* c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Set_Oinsert(v_x,t_a)),v),u),t_a).
% 299.79/300.48 74370[7:SpL:71835.1,482.2] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,v,u)))* hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,v,u)))* hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(v,v_x)).
% 299.79/300.48 74165[7:SpL:71835.1,482.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,v,u)))* hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,v,u)))* hBOOL(hAPP(hAPP(c_in(u),x),hAPP(v_x,w)))* -> hBOOL(hAPP(v,x))*.
% 299.79/300.48 77736[0:SpL:338.0,5892.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Oinsert(u,v),x)))* -> hBOOL(hAPP(c_COMBS(c_in(y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),z,x1,x2),hAPP(c_Set_Oinsert(u,v),x)))*.
% 299.79/300.48 78436[7:SpL:78167.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,v),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,v),hAPP(c_Set_Oinsert(v_x,w),x),w,u) -> .
% 299.79/300.48 78682[4:Res:78665.1,619.0] || equal(hAPP(hAPP(c_in(u),v),w),v_x)** -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,u,tc_fun(y,tc_bool)),w),c_Set_Oinsert(z,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(z,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))))**.
% 299.79/300.48 78794[0:Rew:584.0,78786.1,584.0,78786.0] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(v,v_x)),u) -> c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),hAPP(v,v_x))),u)*.
% 299.79/300.48 80297[0:SpL:21268.0,469.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),y),z,x1),w,v,x,u)),v)**.
% 299.79/300.48 80296[0:SpL:21268.0,464.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),y),z,x1),v,w,x,u)),v)**.
% 299.79/300.48 80258[0:SpL:21268.0,8513.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w),x,y),u)**.
% 299.79/300.48 80217[0:SpL:21268.0,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),x,y)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,u,t_a).
% 299.79/300.48 80009[0:SpL:21268.0,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),y,z),t_a)*.
% 299.79/300.48 79976[0:SpR:338.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(u,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(u,v),y)),w,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(u,v),y)))**.
% 299.79/300.48 79974[0:SpR:475.1,21268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(x,v),y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oinsert(hAPP(x,v),y),hAPP(c_Set_Oimage(x,u,y),w),z,x1)),hAPP(c_Set_Oimage(x,u,y),w))**.
% 299.79/300.48 79973[0:SpR:317.0,21268.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,y,w),hAPP(c_Set_Oinsert(v,y),z)),x,x1)),hAPP(c_Set_Oimage(u,y,w),hAPP(c_Set_Oinsert(v,y),z)))**.
% 299.79/300.48 79849[0:SpR:131.0,21268.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(c_Fun_Ocomp(y,u,w,z,v),v,z),x1),x,x2)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(y,u,w,z,v),v,z),x1))**.
% 299.79/300.48 79847[0:SpR:158.0,21268.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,y,v,w,z),z,w),x1),x,x2)),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,y,v,w,z),z,w),x1))**.
% 299.79/300.48 79809[0:SpR:21268.0,338.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),y),x,z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(u,v),y)))**.
% 299.79/300.48 79800[0:SpR:21268.0,424.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v,u),y),x,z),w,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool)).
% 299.79/300.48 79789[0:SpR:21268.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),z),y,x1))),hAPP(c_Set_Oinsert(hAPP(u,x),w),hAPP(c_Set_Oimage(u,v,w),z)))**.
% 299.79/300.48 79775[0:SpR:21268.0,131.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Ovimage(u,w,x),hAPP(c_Set_Ovimage(u,w,x),x1),z,x2)),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x1)))**.
% 299.79/300.48 79773[0:SpR:21268.0,158.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(v,y,w),hAPP(c_Set_Oimage(v,y,w),x1),z,x2)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x1)))**.
% 299.79/300.48 79762[0:SpR:21268.0,31323.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u),hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u),v,w)),tc_bool)*.
% 299.79/300.48 79673[0:SpR:21268.0,9568.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),y),v,z)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),y),tc_bool)*.
% 299.79/300.48 79671[0:SpR:21268.0,9569.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),y),v,z)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),y),tc_bool)*.
% 299.79/300.48 80409[0:Rew:339.0,79571.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),x),w,y)),z)),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z)))**.
% 299.79/300.48 79563[0:SpR:21268.0,662.1] || hBOOL(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(w,tc_bool)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(w,tc_bool)),x),v,y)))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(w,tc_bool)),x)).
% 299.79/300.48 79558[0:SpR:21268.0,129.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Ovimage(w,x,y),hAPP(c_Set_Ovimage(w,x,y),z),v,x1),tc_fun(y,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(w,x,y),u),hAPP(c_Set_Ovimage(w,x,y),z),tc_fun(x,tc_bool))*.
% 299.79/300.48 79549[0:SpR:21268.0,313.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oimage(w,x,y),hAPP(c_Set_Oimage(w,x,y),z),v,x1),tc_fun(x,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(w,x,y),u),hAPP(c_Set_Oimage(w,x,y),z),tc_fun(y,tc_bool))*.
% 299.79/300.48 79439[0:SpR:21268.0,129.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Ovimage(v,w,x),hAPP(c_Set_Ovimage(v,w,x),y),u,z),x1,tc_fun(x,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),y),hAPP(c_Set_Ovimage(v,w,x),x1),tc_fun(w,tc_bool))*.
% 299.79/300.48 79389[0:SpR:21268.0,313.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),u,z),x1,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),y),hAPP(c_Set_Oimage(v,w,x),x1),tc_fun(x,tc_bool))*.
% 299.79/300.48 79377[7:SpR:21268.0,71455.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v),u,w),v_x)** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v),u,w),hAPP(c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.48 79371[0:SpR:21268.0,8385.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),u,w),v_Procs)** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),u,w),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v)).
% 299.79/300.48 80430[0:Rew:113.0,79794.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),z),y,x1),tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,z,tc_fun(w,tc_bool))))**.
% 299.79/300.48 80432[0:Rew:113.0,79642.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),y),x,z),x1,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(y,x1,tc_fun(w,tc_bool))))**.
% 299.79/300.48 80434[0:AED:24.0,79828.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),x,y)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.79/300.48 81492[0:SpL:21894.0,469.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(w,x,u),y),c_Set_Oimage(w,x,u),z,x1),w,v,x,u)),v)**.
% 299.79/300.48 81491[0:SpL:21894.0,464.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(w,x,u),y),c_Set_Oimage(w,x,u),z,x1),v,w,x,u)),v)**.
% 299.79/300.48 81453[0:SpL:21894.0,8513.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),x,y),u)**.
% 299.79/300.48 81412[0:SpL:21894.0,501.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) c_Hoare__Mirabelle_Otriple__valid(c_Suc(w),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x,y)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(w,u,t_a).
% 299.79/300.48 81204[0:SpL:21894.0,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),y,z),t_a)*.
% 299.79/300.48 81170[0:SpR:338.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(u,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(u,v),y)),c_Set_Oinsert(u,v),w,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(u,v),y)))**.
% 299.79/300.48 81168[0:SpR:475.1,21894.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(x,v),y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(x,u,y),w),c_Set_Oinsert(hAPP(x,v),y),z,x1)),hAPP(c_Set_Oimage(x,u,y),w))**.
% 299.79/300.48 81167[0:SpR:317.0,21894.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(u,v),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(u,y,w),hAPP(c_Set_Oinsert(v,y),z)),c_Set_Oinsert(hAPP(u,v),w),x,x1)),hAPP(c_Set_Oimage(u,y,w),hAPP(c_Set_Oinsert(v,y),z)))**.
% 299.79/300.48 81043[0:SpR:131.0,21894.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(y,u,w,z,v),v,z),x1),c_Set_Ovimage(u,v,w),x,x2)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(y,u,w,z,v),v,z),x1))**.
% 299.79/300.48 81041[0:SpR:158.0,21894.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,y,v,w,z),z,w),x1),c_Set_Oimage(u,v,w),x,x2)),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,y,v,w,z),z,w),x1))**.
% 299.79/300.48 81003[0:SpR:21894.0,338.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),y),c_Set_Oinsert(u,v),x,z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(u,v),y)))**.
% 299.79/300.48 80994[0:SpR:21894.0,424.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(v,u),y),c_Set_Oinsert(v,u),x,z),w,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool)).
% 299.79/300.48 80983[0:SpR:21894.0,317.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(u,v,w),z),c_Set_Oimage(u,v,w),y,x1))),hAPP(c_Set_Oinsert(hAPP(u,x),w),hAPP(c_Set_Oimage(u,v,w),z)))**.
% 299.79/300.48 80969[0:SpR:21894.0,131.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Ovimage(u,w,x),x1),c_Set_Ovimage(u,w,x),z,x2)),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x1)))**.
% 299.79/300.48 80967[0:SpR:21894.0,158.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(v,y,w),x1),c_Set_Oimage(v,y,w),z,x2)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x1)))**.
% 299.79/300.48 80956[0:SpR:21894.0,31323.0] || -> c_lessequals(hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u),hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),v,w)),tc_bool)*.
% 299.79/300.48 80867[0:SpR:21894.0,9568.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v,z)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),y),tc_bool)*.
% 299.79/300.48 80865[0:SpR:21894.0,9569.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),v,z)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),y),tc_bool)*.
% 299.79/300.48 81604[0:Rew:339.0,80764.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(u,v),x),c_Set_Oinsert(u,v),w,y)),z)),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z)))**.
% 299.79/300.48 80756[0:SpR:21894.0,662.1] || hBOOL(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(w,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(w,tc_bool)),v,y)))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(w,tc_bool)),x)).
% 299.79/300.48 80751[0:SpR:21894.0,129.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(w,x,y),z),c_Set_Ovimage(w,x,y),v,x1),tc_fun(y,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(w,x,y),u),hAPP(c_Set_Ovimage(w,x,y),z),tc_fun(x,tc_bool))*.
% 299.79/300.48 80742[0:SpR:21894.0,313.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(w,x,y),z),c_Set_Oimage(w,x,y),v,x1),tc_fun(x,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(w,x,y),u),hAPP(c_Set_Oimage(w,x,y),z),tc_fun(y,tc_bool))*.
% 299.79/300.48 80632[0:SpR:21894.0,129.1] || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),y),c_Set_Ovimage(v,w,x),u,z),x1,tc_fun(x,tc_bool))* -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),y),hAPP(c_Set_Ovimage(v,w,x),x1),tc_fun(w,tc_bool))*.
% 299.79/300.48 80582[0:SpR:21894.0,313.1] || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),u,z),x1,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),y),hAPP(c_Set_Oimage(v,w,x),x1),tc_fun(x,tc_bool))*.
% 299.79/300.48 80570[7:SpR:21894.0,71455.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v),c_Set_Oinsert(v_x,t_a),u,w),v_x)** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v),c_Set_Oinsert(v_x,t_a),u,w),hAPP(c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.48 80564[0:SpR:21894.0,8385.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),c_Set_Oinsert(v_x,tc_Com_Opname),u,w),v_Procs)** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),c_Set_Oinsert(v_x,tc_Com_Opname),u,w),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v)).
% 299.79/300.48 81625[0:Rew:113.0,80988.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),z),c_Set_Ovimage(u,v,w),y,x1),tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,z,tc_fun(w,tc_bool))))**.
% 299.79/300.48 81627[0:Rew:113.0,80836.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),y),c_Set_Ovimage(u,v,w),x,z),x1,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(y,x1,tc_fun(w,tc_bool))))**.
% 299.79/300.48 81629[0:AED:24.0,81022.0] || -> equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),c_Set_Oimage(c_COMBK(u,v,w),w,v),x,y)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.79/300.48 81755[0:SpR:465.1,5075.1] || c_Finite__Set_Ofinite(u,v) -> hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Ovimage(c_Fun_Ofun__upd(y,x,z,w,v),w,v),u)))* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(y,w,v),hAPP(c_Set_Ovimage(c_Fun_Ofun__upd(y,x,z,w,v),w,v),u)),v)*.
% 299.79/300.48 81801[0:SpR:205.1,5879.1] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_lessequals(y,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,x),x,w),z,x1,x2),hAPP(c_Set_Oimage(v,w,x),y)),u)*.
% 299.79/300.48 81775[0:SpR:21894.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),x1),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),w,x2)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),x1),u)*.
% 299.79/300.48 81773[0:SpR:21268.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),x1),w,x2)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),x1),u)*.
% 299.79/300.48 82273[0:SpR:205.1,5880.1] class_Lattices_Olattice(u) || c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_lessequals(y,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,x),x,w),z,x1,x2),hAPP(c_Set_Oimage(v,w,x),y)),u)*.
% 299.79/300.48 82247[0:SpR:21894.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),x1),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),w,x2)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),x1),u)*.
% 299.79/300.48 82245[0:SpR:21268.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),x1),w,x2)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,x,y,z),x1),u)*.
% 299.79/300.48 83165[0:Rew:5924.0,83127.2] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),c_COMBS(u,c_COMBK(y,z,x1),x2,x3,x4),v)),y))* hBOOL(hAPP(hAPP(c_in(v),x5),w))* -> hBOOL(hAPP(hAPP(u,x5),y))*.
% 299.79/300.48 83166[0:Rew:5924.0,83126.2] || hBOOL(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),c_COMBS(u,c_COMBK(y,z,x1),x2,x3,x4),v)),y))* hBOOL(hAPP(hAPP(c_in(v),x5),x))* -> hBOOL(hAPP(hAPP(u,x5),y))*.
% 299.79/300.48 83475[0:Rew:5961.0,83446.2] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),c_COMBS(c_COMBK(u,z,x1),v,x2,x3,x4),w))))* hBOOL(hAPP(hAPP(c_in(w),x5),x))* -> hBOOL(hAPP(u,hAPP(v,x5)))*.
% 299.79/300.48 83476[0:Rew:5961.0,83445.2] || hBOOL(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),c_COMBS(c_COMBK(u,z,x1),v,x2,x3,x4),w))))* hBOOL(hAPP(hAPP(c_in(w),x5),y))* -> hBOOL(hAPP(u,hAPP(v,x5)))*.
% 299.79/300.48 84909[4:SpL:339.0,78744.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),x))),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),x,t_a).
% 299.79/300.48 84906[4:SpL:537.1,78744.0] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x))),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,t_a).
% 299.79/300.48 84905[4:SpL:534.1,78744.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x))),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,t_a).
% 299.79/300.48 85074[0:SpR:644.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),w),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),c_HOL_Ominus__class_Ominus(w,v_Procs,tc_fun(tc_Com_Opname,tc_bool))),tc_fun(v,tc_bool))*.
% 299.79/300.48 85067[0:SpR:644.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),w),tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),c_HOL_Ominus__class_Ominus(v_Procs,w,tc_fun(tc_Com_Opname,tc_bool))),tc_fun(v,tc_bool))*.
% 299.79/300.48 86503[0:SpL:86109.1,406.0] || equal(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_Procs) equal(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Set_Oinsert(w,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))))* -> equal(v_x,v) equal(v_x,w).
% 299.79/300.48 86393[0:SpR:86109.1,21894.0] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v),c_Set_Oinsert(v_x,t_a),u,w),v_Procs)** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v),c_Set_Oinsert(v_x,t_a),u,w),hAPP(c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.48 86391[0:SpR:86109.1,21268.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v),u,w),v_Procs)** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v),u,w),hAPP(c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.48 86296[0:SpR:86109.1,450.0] || equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oinsert(v_x,t_a),u,v,w),v_Procs) -> hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oinsert(v_x,t_a),u,v,w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Set_Oinsert(v_x,t_a),u,v,w)))* c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Set_Oinsert(v_x,t_a)),v),u),t_a).
% 299.79/300.48 89022[0:Res:14196.0,15629.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(u,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(u,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),y)))*.
% 299.79/300.48 89021[0:Res:14196.0,15857.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(u,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(u,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),z)))*.
% 299.79/300.48 88976[0:SpR:55.1,14196.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(v,u),x,y),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),z),w,tc_fun(u,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),c_HOL_Ominus__class_Ominus(z,w,tc_fun(u,tc_bool))))*.
% 299.79/300.48 88925[0:SpR:410.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),x,y),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,z),x1),v,z,tc_fun(u,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,v,z,tc_fun(u,tc_bool))))*.
% 299.79/300.48 89829[0:SpR:26183.0,533.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))**.
% 299.79/300.48 89795[0:SpR:26183.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(y,u),v),w),z)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(y,u),v),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),z)))*.
% 299.79/300.48 91365[0:Rew:91288.1,91222.3] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),y)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,v)* -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(u)),y)).
% 299.79/300.48 92393[0:Res:362.1,5022.0] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(w,x),u,tc_fun(x,tc_bool))),v))* -> equal(hAPP(c_Set_Oinsert(w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(w,x),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(w,x),u,tc_fun(x,tc_bool)))**.
% 299.79/300.48 92955[0:SpR:55.1,5876.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Oinsert(v,u),z,x1,x2),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool))),tc_fun(y,tc_bool))*.
% 299.79/300.48 92902[0:SpR:410.0,5876.0] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,u)),x1,x2,x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool))),tc_fun(z,tc_bool))*.
% 299.79/300.48 93095[0:Rew:584.0,92795.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),hAPP(u,v_x)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u,w,x,y),tc_Com_Opname,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),hAPP(u,v_x)),tc_fun(v,tc_bool))*.
% 299.79/300.48 93096[0:Rew:584.0,92793.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u,w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),hAPP(u,v_x)),tc_Com_Opname,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),hAPP(u,v_x)),tc_fun(v,tc_bool))*.
% 299.79/300.48 94271[0:Res:14491.3,5022.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Set_Oinsert(w,u),c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)))))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> equal(hAPP(c_Set_Oinsert(w,u),c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool))),c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool))).
% 299.79/300.48 14198[0:Res:176.0,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Ovimage(u,tc_Hoare__Mirabelle_Otriple(t_a),v),hAPP(c_Set_Oinsert(hAPP(u,w),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),x,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Ovimage(u,tc_Hoare__Mirabelle_Otriple(t_a),v),hAPP(c_Set_Oinsert(hAPP(u,w),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),x),w,t_a)*.
% 299.79/300.48 14718[0:SpR:128.0,49.2] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(hAPP(c_Set_Ovimage(v,u,w),x),c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(v,u,w),x),hAPP(c_Set_Ovimage(v,u,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),tc_fun(u,tc_bool))*.
% 299.79/300.48 14716[0:SpR:128.0,47.2] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x),tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(v,u,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(v,u,w),x),tc_fun(u,tc_bool))*.
% 299.79/300.48 19322[0:Res:304.3,50.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Olordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),u)* c_lessequals(w,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),u)* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_HOL_Ozero__class_Ozero(u),u).
% 299.79/300.48 19321[0:Res:304.3,46.1] class_Lattices_Oupper__semilattice(u) class_OrderedGroup_Oordered__ab__group__add(u) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),u)* c_lessequals(w,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u),u)* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),c_HOL_Ozero__class_Ozero(u),u).
% 299.79/300.48 19360[0:SSi:19310.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) c_lessequals(z,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(y,v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),z),x,w)*.
% 299.79/300.48 20369[0:SpR:128.0,438.1] || c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),x,y),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),z),tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(z,tc_fun(w,tc_bool)))**.
% 299.79/300.48 20513[0:SpR:128.0,99.1] || c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),x,y),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),z),tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(z,tc_fun(w,tc_bool)))**.
% 299.79/300.48 21013[0:SpL:317.0,193.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(hAPP(x,u),y),hAPP(c_Set_Oimage(x,v,y),w)),y),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(u,v),w),v))* -> c_Fun_Oinj__on(x,hAPP(c_Set_Oinsert(u,v),w),v,y)*.
% 299.79/300.48 21009[0:SpR:15172.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y,z),hAPP(c_Set_Oinsert(x1,y),x2)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),z),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y,z),x2)))*.
% 299.79/300.48 21003[0:SpR:128.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(z,tc_fun(w,tc_bool)),x),x1)),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),z),tc_fun(v,tc_bool)),y),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),x1)))*.
% 299.79/300.48 20974[0:SpR:337.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,w),y)))*.
% 299.79/300.48 20971[0:SpR:544.1,317.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),w),z)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),z)))*.
% 299.79/300.48 20970[0:SpR:543.1,317.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),w),z)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),z)))*.
% 299.79/300.48 21420[0:SpR:21267.0,181.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x),tc_Com_Opname,x)))* equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.48 22046[0:SpR:21893.0,181.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x),c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x)))* equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.48 24179[0:SpR:542.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x1)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x1),hAPP(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x1))))*.
% 299.79/300.48 24178[0:SpR:542.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x1)),hAPP(hAPP(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x1)))*.
% 299.79/300.48 25365[0:SpR:512.0,97.1] || c_Fun_Oinj__on(hAPP(c_COMBB(u,v,w,x),y),z,x,w) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(z,hAPP(c_COMBB(u,v,w,x),y),x,w),w,x),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),z))),z)**.
% 299.79/300.48 25698[0:SpL:21893.0,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname,w),t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.79/300.48 25697[0:SpL:21267.0,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x),tc_Com_Opname,w),t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.79/300.48 26014[0:Rew:339.0,25927.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x))) -> hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),tc_Com_Opname))))*.
% 299.79/300.48 26015[0:Rew:339.0,25926.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x))) -> hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),tc_Com_Opname))))*.
% 299.79/300.48 25883[0:SpR:339.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oinsert(y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),v))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(y,z),x1)),u,x),w)))*.
% 299.79/300.48 25882[0:SpR:339.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(x,y),z)),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.48 25836[0:SpR:339.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w))).
% 299.79/300.48 26118[0:SpR:338.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x1,v),x))),hAPP(c_Set_Oimage(c_Set_Oinsert(x1,v),u,z),y)))*.
% 299.79/300.48 26117[0:SpR:338.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(z,v),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(z,v),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.48 26048[0:SpR:338.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),x))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),u,z),y)))*.
% 299.79/300.48 26047[0:SpR:338.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> c_lessequals(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.48 27187[0:Res:450.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(u),v,w,x),u) -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(u)),w),v),t_a) c_lessequals(c_Finite__Set_Olinorder__class_OMin(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(u),v,w,x),u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(u),v,w,x),u)*.
% 299.79/300.48 27186[0:Res:450.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(u),v,w,x),u) -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(u)),w),v),t_a) c_lessequals(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(u),v,w,x),c_Finite__Set_Olinorder__class_OMax(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(u),v,w,x),u),u)*.
% 299.79/300.48 27139[0:SpR:299.2,450.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y),v,u)* -> hBOOL(hAPP(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y)))* c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),x),w),t_a)*.
% 299.79/300.48 27132[0:SpR:2097.1,450.0] || hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oinsert(u,v),w,x,y),u)) -> hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oinsert(u,v),w,x,y),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Set_Oinsert(u,v),w,x,y)))* c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Set_Oinsert(u,v)),x),w),t_a).
% 299.79/300.48 27365[0:SpL:158.0,470.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Fun_Ocomp(w,x,y,u,z),z,u),x1)))* -> hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__XimageE__1__1(hAPP(c_Set_Oimage(x,z,y),x1),v,w,y,u)),hAPP(c_Set_Oimage(x,z,y),x1)))*.
% 299.79/300.48 27364[0:SpL:97.1,470.0] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(w),y),v)) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__XimageE__1__1(hAPP(c_Set_Oimage(u,w,x),v),y,c_Fun_Othe__inv__into(v,u,w,x),x,w)),hAPP(c_Set_Oimage(u,w,x),v)))*.
% 299.79/300.48 27425[0:SpL:158.0,466.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Fun_Ocomp(w,x,y,u,z),z,u),x1)))* -> hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(hAPP(c_Set_Oimage(x,z,y),x1),w,v,y,u)),hAPP(c_Set_Oimage(x,z,y),x1)))*.
% 299.79/300.48 27424[0:SpL:97.1,466.0] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(w),y),v)) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(hAPP(c_Set_Oimage(u,w,x),v),c_Fun_Othe__inv__into(v,u,w,x),y,x,w)),hAPP(c_Set_Oimage(u,w,x),v)))*.
% 299.79/300.48 27643[0:SpR:12944.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(x,y),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),z,x1)),w,u,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Set_Oinsert(x,y),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),z,x1)),u,x2),c_Orderings_Otop__class_Otop(tc_bool)),v)*.
% 299.79/300.48 27635[0:SpR:11499.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),v)) c_Fun_Oinj__on(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y)),v,u,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y)),u,z),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.48 27617[0:SpR:11695.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),v)),w)) c_Fun_Oinj__on(hAPP(c_Set_Oinsert(x,y),c_Option_Othe(v)),w,u,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Set_Oinsert(x,y),c_Option_Othe(v)),u,z),c_Orderings_Otop__class_Otop(tc_bool)),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),v))**.
% 299.79/300.48 27616[0:SpR:11473.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,u,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u,z),c_Orderings_Otop__class_Otop(tc_bool)),v)*.
% 299.79/300.48 27605[0:SpR:329.1,373.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) hBOOL(hAPP(hAPP(c_in(x),v),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y,x,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,z),v),v)**.
% 299.79/300.48 27604[0:SpR:328.1,373.2] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(x),u),y))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y,x,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,z),v),u)*.
% 299.79/300.48 27601[0:SpR:538.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),w,u,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),y)),v)**.
% 299.79/300.48 27588[0:SpR:17045.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y,tc_fun(z,tc_bool)),w,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y,tc_fun(z,tc_bool)),u,x1),c_Orderings_Obot__class_Obot(tc_bool)),v)*.
% 299.79/300.48 27526[0:SpR:373.2,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),x1)) -> hBOOL(hAPP(hAPP(c_in(x2),v),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x2),x1)))*.
% 299.79/300.48 27524[0:SpR:373.2,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),x1)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Hilbert__Choice_Oinv__into(w,x,u,y),z,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.79/300.48 27796[0:SpR:12944.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(x,y),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),z,x1)),w,u,x2) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Set_Oinsert(x,y),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),z,x1)),u,x2),c_Orderings_Otop__class_Otop(tc_bool)),v)*.
% 299.79/300.48 27788[0:SpR:11499.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),v)) c_Fun_Oinj__on(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y)),v,u,z) -> equal(hAPP(c_Fun_Othe__inv__into(v,hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y)),u,z),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool))**.
% 299.79/300.48 27770[0:SpR:11695.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),v)),w)) c_Fun_Oinj__on(hAPP(c_Set_Oinsert(x,y),c_Option_Othe(v)),w,u,z) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Set_Oinsert(x,y),c_Option_Othe(v)),u,z),c_Orderings_Otop__class_Otop(tc_bool)),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),v))**.
% 299.79/300.48 27769[0:SpR:11473.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,u,z) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u,z),c_Orderings_Otop__class_Otop(tc_bool)),v)*.
% 299.79/300.48 27758[0:SpR:329.1,71.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) hBOOL(hAPP(hAPP(c_in(x),v),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y,x,z) -> equal(hAPP(c_Fun_Othe__inv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,z),v),v)**.
% 299.79/300.48 27757[0:SpR:328.1,71.2] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(x),u),y))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y,x,z) -> equal(hAPP(c_Fun_Othe__inv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,z),v),u)*.
% 299.79/300.48 27754[0:SpR:538.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),w,u,z) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),y)),v)**.
% 299.79/300.48 27741[0:SpR:17045.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y,tc_fun(z,tc_bool)),w,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y,tc_fun(z,tc_bool)),u,x1),c_Orderings_Obot__class_Obot(tc_bool)),v)*.
% 299.79/300.48 27678[0:SpR:71.2,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),x1)) -> hBOOL(hAPP(hAPP(c_in(x2),v),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(w,x,u,y),z,x2),x1)))*.
% 299.79/300.48 27675[0:SpR:71.2,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),x1)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Fun_Othe__inv__into(w,x,u,y),z,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.79/300.48 27931[0:Res:468.0,148.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(z,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)))) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)),u,z,v,w)),x))*.
% 299.79/300.48 28248[0:SpL:465.1,469.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),z),y)) equal(hAPP(c_Fun_Ofun__upd(w,z,x1,x,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(y,c_Fun_Ofun__upd(w,z,x1,x,u),v,x,u)),v)**.
% 299.79/300.48 28247[0:SpL:465.1,464.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),z),y)) equal(hAPP(c_Fun_Ofun__upd(w,z,x1,x,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(y,v,c_Fun_Ofun__upd(w,z,x1,x,u),x,u)),v)**.
% 299.79/300.48 28209[0:SpR:465.1,317.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),hAPP(c_Set_Oinsert(x1,u),w)),hAPP(c_Set_Oinsert(hAPP(c_Fun_Ofun__upd(x,v,y,u,z),x1),z),hAPP(c_Set_Oimage(x,u,z),w)))*.
% 299.79/300.48 28185[0:SpR:465.1,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),y),v)) hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oimage(x1,x,x2),v)),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(x1,y,x3,x,x2),x,x2),u,z),w)))*.
% 299.79/300.48 28182[0:SpR:465.1,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),y),v)) c_lessequals(hAPP(c_Set_Oimage(z,x,x1),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_Fun_Ofun__upd(z,y,x2,x,x1),x,x1),u,tc_fun(x3,tc_bool)),tc_fun(x3,tc_bool))*.
% 299.79/300.48 28180[0:SpR:465.1,97.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),z,x,y) -> hBOOL(hAPP(hAPP(c_in(x),v),z)) equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(z,c_Fun_Ofun__upd(u,v,w,x,y),x,y),y,x),hAPP(c_Set_Oimage(u,x,y),z)),z)**.
% 299.79/300.48 28130[0:SpR:465.1,158.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(c_Fun_Ofun__upd(z,v,x1,u,x2),w,u,x2,x),x,x2),y),hAPP(c_Set_Oimage(z,u,x2),hAPP(c_Set_Oimage(w,x,u),y)))**.
% 299.79/300.48 28554[0:SpR:12944.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),c_Fun_Ofun__upd(y,z,x1,x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y,x3,x4,x2),z,c_Orderings_Otop__class_Otop(tc_bool),x2,x4))*.
% 299.79/300.48 28527[0:SpR:11473.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Fun_Ofun__upd(w,x,y,z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,x1,x2,z),x,c_Orderings_Otop__class_Otop(tc_bool),z,x2))*.
% 299.79/300.48 28516[0:SpR:329.1,118.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),c_Fun_Ofun__upd(x,y,v,z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,x1,x2,z),y,v,z,x2))*.
% 299.79/300.48 28515[0:SpR:328.1,118.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),c_Fun_Ofun__upd(x,y,u,z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,x1,x2,z),y,v,z,x2))*.
% 299.79/300.48 28512[0:SpR:538.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Fun_Ofun__upd(w,x,y,z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x1,x2,z),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v),z,x2))*.
% 299.79/300.48 28499[0:SpR:17045.0,118.0] || -> equal(c_Fun_Ocomp(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),c_Fun_Ofun__upd(x,y,z,x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x,x2,x3,x1),y,c_Orderings_Obot__class_Obot(tc_bool),x1,x3))*.
% 299.79/300.48 29283[0:Rew:537.1,29093.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname))))*.
% 299.79/300.48 29284[0:Rew:537.1,29092.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname))))*.
% 299.79/300.48 29050[0:SpR:537.1,361.2] class_Lattices_Olattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),x),y)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1)),w,v),v)*.
% 299.79/300.48 29034[0:SpR:537.1,176.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),v,z),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.48 28983[0:SpR:537.1,9268.0] class_Lattices_Olattice(u) || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))).
% 299.79/300.48 29789[0:Rew:534.1,29617.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname))))*.
% 299.79/300.48 29790[0:Rew:534.1,29616.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname))))*.
% 299.79/300.48 29573[0:SpR:534.1,361.2] class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),x),y)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1)),w,v),v)*.
% 299.79/300.48 29556[0:SpR:534.1,176.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),v,z),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.48 29505[0:SpR:534.1,9268.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))).
% 299.79/300.48 30146[0:SpR:536.1,584.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x2)),hAPP(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x2))))*.
% 299.79/300.48 30145[0:SpR:536.1,584.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x2)),hAPP(hAPP(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x2))))*.
% 299.79/300.48 30097[0:SpR:536.1,361.2] class_Lattices_Olattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),z)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),w,v),v)*.
% 299.79/300.48 30080[0:SpR:536.1,176.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,z),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),x)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.48 30493[0:Rew:20404.2,30101.2] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z))**.
% 299.79/300.48 30706[0:SpR:535.1,584.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x2)),hAPP(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x2))))*.
% 299.79/300.48 30705[0:SpR:535.1,584.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_COMBS(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x2)),hAPP(hAPP(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x2))))*.
% 299.79/300.48 30653[0:SpR:535.1,361.2] class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || hBOOL(hAPP(hAPP(c_in(w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),z)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),w,v),v)*.
% 299.79/300.48 30636[0:SpR:535.1,176.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,z),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),x)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.48 31040[0:Rew:20405.2,30657.2] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z))**.
% 299.79/300.48 31395[0:SpL:9935.1,449.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),tc_bool) hBOOL(hAPP(c_Orderings_Otop__class_Otop(tc_bool),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x))) -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v)),t_a)*.
% 299.79/300.48 31514[0:SpL:317.0,473.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(hAPP(w,x),u),hAPP(c_Set_Oimage(w,y,u),z))))* -> hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oinsert(x,y),z),w,y,u),v)),hAPP(c_Set_Oinsert(x,y),z)))*.
% 299.79/300.48 31743[0:SpL:97.1,389.0] || c_Fun_Oinj__on(u,v,w,x) equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y),v)** c_Fun_Oinj__on(c_Fun_Othe__inv__into(v,u,w,x),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w)* -> equal(y,hAPP(c_Set_Oimage(u,w,x),v)).
% 299.79/300.48 32044[0:SpR:177.1,151.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* -> hBOOL(hAPP(hAPP(c_in(u),w),x)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* hBOOL(hAPP(hAPP(c_in(u),v),x)).
% 299.79/300.48 32992[0:SpR:14216.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(y,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),u,x),w)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(y,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),u,x),w))**.
% 299.79/300.48 32929[0:SpR:25.1,475.1] class_HOL_Ouminus(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(hAPP(x,v_x),u),y),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,u)),v,y),w)),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,u)),v,y),w))**.
% 299.79/300.48 32912[0:SpR:653.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,w),w,tc_Com_Opname),u,x),v)),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,w),w,tc_Com_Opname),u,x),v))**.
% 299.79/300.48 32909[0:SpR:445.1,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(v,x) equal(hAPP(c_Set_Oinsert(hAPP(y,v),z),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,x,x1,x2,x3),u,z),w)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,x,x1,x2,x3),u,z),w))**.
% 299.79/300.48 32903[0:SpR:21893.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,u,x),v_x),c_Set_Oimage(w,u,x),tc_Com_Opname,y)))* -> equal(hAPP(c_Set_Oinsert(hAPP(w,v),x),hAPP(c_Set_Oimage(w,u,x),v_x)),hAPP(c_Set_Oimage(w,u,x),v_x)).
% 299.79/300.48 32902[0:SpR:21267.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,u,x),hAPP(c_Set_Oimage(w,u,x),v_x),tc_Com_Opname,y)))* -> equal(hAPP(c_Set_Oinsert(hAPP(w,v),x),hAPP(c_Set_Oimage(w,u,x),v_x)),hAPP(c_Set_Oimage(w,u,x),v_x)).
% 299.79/300.48 33358[0:SpR:21893.0,23789.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),v_x),c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),tc_Com_Opname,w),tc_bool)*.
% 299.79/300.48 33357[0:SpR:21267.0,23789.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),v_x),tc_Com_Opname,w),tc_bool)*.
% 299.79/300.48 33435[0:Res:468.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a)* -> equal(hAPP(c_Set_Oimage(w,tc_Hoare__Mirabelle_Otriple(t_a),x),v),hAPP(c_Set_Oimage(y,tc_Hoare__Mirabelle_Otriple(t_a),x),v)) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,z)),u))* c_Hoare__Mirabelle_Otriple__valid(z,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,w,y,tc_Hoare__Mirabelle_Otriple(t_a),x),t_a)*.
% 299.79/300.48 33525[0:Rew:64.0,33510.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),w) -> equal(c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),w)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(v,w),u),w))**.
% 299.79/300.48 34365[0:SpL:24914.0,356.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Oimage(c_COMBK(w,x,u),u,x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,y),hAPP(hAPP(c_in(u),v),v_x))),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))**.
% 299.79/300.48 34261[0:SpL:24914.0,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x),u))* c_Hoare__Mirabelle_Ohoare__valids(v,u,t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,w)),v))* c_Hoare__Mirabelle_Otriple__valid(w,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,x),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_x)),t_a)*.
% 299.79/300.48 34127[0:SpR:24914.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))).
% 299.79/300.48 34121[0:SpR:24914.0,536.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)))**.
% 299.79/300.48 34120[0:SpR:24914.0,535.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)))**.
% 299.79/300.48 34519[0:Rew:537.1,34057.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x))),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),x)))**.
% 299.79/300.48 34520[0:Rew:534.1,34056.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x))),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v_x),x)))**.
% 299.79/300.48 34625[0:SpR:55.1,317.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),z),w,tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(hAPP(x,v),y),hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(z,w,tc_fun(u,tc_bool)))))*.
% 299.79/300.48 34676[0:Rew:66.0,34608.2] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)))) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)))**.
% 299.79/300.48 35392[0:SpR:9.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Fun_Ocomp(x,y,z,x1,x2),v,tc_fun(x3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x3,tc_bool)),hAPP(x,hAPP(y,u))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ocomp(x,y,z,x1,x2),v,tc_fun(x3,tc_bool))))*.
% 299.79/300.48 35371[0:SpR:11695.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),u),v),w),hAPP(c_Set_Oinsert(x,y),c_Option_Othe(u)),v,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(x,y),c_Option_Othe(u)),v,tc_fun(z,tc_bool))))*.
% 299.79/300.48 35339[0:SpR:88.1,410.0] class_Lattices_Oboolean__algebra(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),w,tc_fun(y,tc_bool))))*.
% 299.79/300.48 35329[0:SpR:540.1,410.0] class_Lattices_Olattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w,tc_fun(z,tc_bool))))*.
% 299.79/300.48 35328[0:SpR:539.1,410.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w,tc_fun(z,tc_bool))))*.
% 299.79/300.48 35327[0:SpR:297.2,410.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,tc_fun(z,tc_bool))))*.
% 299.79/300.48 35324[0:SpR:2098.1,410.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,tc_fun(y,tc_bool))))*.
% 299.79/300.48 35318[0:SpR:299.2,410.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,tc_fun(z,tc_bool))))*.
% 299.79/300.48 35273[0:SpR:64.0,410.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(w,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)),v,y,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,y),x),v,y,tc_fun(u,tc_bool)))**.
% 299.79/300.48 35267[0:SpR:317.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),z,w,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(z,hAPP(u,x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,w),y),z,w,tc_fun(x1,tc_bool))))*.
% 299.79/300.48 35264[0:SpR:24914.0,410.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(w,x),tc_Com_Opname,y),hAPP(c_Set_Oinsert(w,x),v_x)),v,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),v_x),v,x,tc_fun(u,tc_bool)))**.
% 299.79/300.48 35637[0:SpR:465.1,89.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_COMBB(x,y,tc_fun(z,tc_bool),u),c_Fun_Ofun__upd(x1,v,x2,u,y)),u,tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x1,u,y),w),x,y,tc_fun(z,tc_bool)))**.
% 299.79/300.48 35904[0:Res:16776.0,282.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(w,x,u,y),y,u),hAPP(c_Set_Oimage(x,u,y),w))))* c_Fun_Oinj__on(c_Fun_Ofun__upd(c_Hilbert__Choice_Oinv__into(w,x,u,y),z,v,y,u),hAPP(c_Set_Oimage(x,u,y),w),y,u)*.
% 299.79/300.48 36158[0:SpL:410.0,516.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),y),z,x,tc_fun(u,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(z,w))) hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,z,x,tc_fun(u,tc_bool)))).
% 299.79/300.48 36794[0:Rew:67.0,36753.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),hAPP(c_Set_Oinsert(w,u),y),tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(w,u),y),tc_fun(u,tc_bool)))**.
% 299.79/300.48 38004[0:Res:124.0,441.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w,tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w,tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.79/300.48 38346[0:Obv:38269.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x)) c_Finite__Set_Ofinite(x,u) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),y,x,u,u),u)*.
% 299.79/300.48 38347[0:Obv:38267.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y),w,u,u),u)*.
% 299.79/300.48 38399[0:SpL:104.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(u,v,w),y)) c_Fun_Oinj__on(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),v,w)* -> equal(c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool)),y).
% 299.79/300.48 38394[0:SpL:600.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(u,v,w),y)) c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y),v,w)* -> equal(c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)),y).
% 299.79/300.48 38980[0:SpR:354.2,158.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(z,c_Hilbert__Choice_Oinv__into(v,x,w,y),w,x1,y),y,x1),hAPP(c_Set_Oimage(x,w,y),u)),hAPP(c_Set_Oimage(z,w,x1),u))**.
% 299.79/300.48 38958[0:SpR:354.2,313.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_lessequals(z,hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z),u,tc_fun(w,tc_bool))*.
% 299.79/300.48 38949[0:SpR:354.2,415.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(c_Fun_Ofun__upd(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),hAPP(c_Set_Oimage(x,w,y),u),u,z,x1),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w))**.
% 299.79/300.48 38941[0:SpR:354.2,313.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_lessequals(hAPP(c_Set_Oimage(x,w,y),u),z,tc_fun(y,tc_bool)) -> c_lessequals(u,hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z),tc_fun(w,tc_bool))*.
% 299.79/300.48 39323[0:SpL:533.0,3489.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool))))* -> .
% 299.79/300.48 39322[0:SpL:533.0,3487.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Set_Oinsert(v_x,tc_Com_Opname)) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs)** -> .
% 299.79/300.48 39249[0:SpR:533.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,y,z,x1),x2),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x2)),hAPP(x,x2)))*.
% 299.79/300.48 39248[0:SpR:533.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y,z,x1),x2),hAPP(hAPP(u,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),x2))))*.
% 299.79/300.48 39133[0:SpR:533.0,3294.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_in(t_a)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.48 40947[0:Res:1103.1,479.1] || hBOOL(hAPP(u,v)) -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(x),v),t_a) hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,hAPP(c_in(x),v)),y,u,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,hAPP(c_in(x),v))),y)))*.
% 299.79/300.48 40868[0:SpL:21893.0,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(v),v_x),c_in(v),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,y,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))*.
% 299.79/300.48 40867[0:SpL:21267.0,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(v),hAPP(c_in(v),v_x),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,y,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))*.
% 299.79/300.48 41228[0:Res:1103.1,478.1] || hBOOL(hAPP(u,v)) -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(x),v),t_a) hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,hAPP(c_in(x),v)),u,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,hAPP(c_in(x),v)))))*.
% 299.79/300.48 41149[0:SpL:21893.0,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(v),v_x),c_in(v),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,x,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x)))*.
% 299.79/300.48 41148[0:SpL:21267.0,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(v),hAPP(c_in(v),v_x),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,x,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x)))*.
% 299.79/300.48 41369[0:SpL:584.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(hAPP(z,v),hAPP(x1,v))))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(z,x1,x2,x3,x4),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41360[0:SpL:336.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41352[0:SpL:3294.1,275.1] || equal(c_in(t_a),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41341[0:SpL:584.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* hBOOL(hAPP(hAPP(c_in(y),z),hAPP(c_COMBS(x1,v,x2,x3,x4),w)))* -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(x1,w),u,tc_fun(y,tc_bool))))*.
% 299.79/300.48 41325[0:SpL:337.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41299[0:SpL:540.1,275.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* hBOOL(hAPP(hAPP(c_in(y),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1)))* -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),v,tc_fun(y,tc_bool))))*.
% 299.79/300.48 41298[0:SpL:539.1,275.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* hBOOL(hAPP(hAPP(c_in(y),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1)))* -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),v,tc_fun(y,tc_bool))))*.
% 299.79/300.48 41297[0:SpL:297.2,275.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* hBOOL(hAPP(hAPP(c_in(x),w),y))* hBOOL(hAPP(hAPP(c_in(z),x1),w))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,tc_fun(z,tc_bool))))*.
% 299.79/300.48 41288[0:SpL:299.2,275.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* hBOOL(hAPP(hAPP(c_in(x),v),y))* hBOOL(hAPP(hAPP(c_in(z),x1),w)) -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,tc_fun(z,tc_bool))))*.
% 299.79/300.48 41275[0:SpL:25.1,275.1] class_HOL_Ouminus(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_HOL_Ouminus__class_Ouminus(hAPP(z,v_x),u))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ouminus__class_Ouminus(z,tc_fun(t_a,u)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 41640[0:SpL:303.1,284.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),y)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,v)* -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(u)),y)).
% 299.79/300.48 41620[0:SpL:11177.1,284.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,v),y)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,v)* -> hBOOL(hAPP(hAPP(c_in(x),u),y)).
% 299.79/300.48 41571[0:SpL:300.1,284.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,v),y)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,v)* -> hBOOL(hAPP(hAPP(c_in(x),w),y)).
% 299.79/300.48 41719[0:SpL:21893.0,494.1] || hBOOL(hAPP(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_x),c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_Com_Opname,u),v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_x),y),z),t_a)* c_Natural_Oevaln(y,w,x,x1)* -> hBOOL(hAPP(hAPP(z,v),x1))*.
% 299.79/300.48 41718[0:SpL:21267.0,494.1] || hBOOL(hAPP(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_x),tc_Com_Opname,u),v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_x),y),z),t_a)* c_Natural_Oevaln(y,w,x,x1)* -> hBOOL(hAPP(hAPP(z,v),x1))*.
% 299.79/300.48 41865[0:Rew:9.0,41824.2] || hBOOL(hAPP(u,hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,y),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Fun_Ocomp(u,v,z,x1,x2),x,w,y)))))* c_Fun_Oinj__on(x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,y) -> hBOOL(hAPP(u,hAPP(v,x3)))*.
% 299.79/300.48 42241[0:Rew:180.2,42240.2] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(y,u),v),u,u)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y),u),v),u,u))**.
% 299.79/300.48 42248[0:Rew:42241.2,42247.2,42241.2,42247.2] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y),u),v),u,u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),x),u),v),u,u))*.
% 299.79/300.48 42256[0:Rew:42241.2,42255.2,42209.2,42255.2] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u)),y),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y),u),v),u,u))**.
% 299.79/300.48 42318[0:Rew:221.1,42313.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(v,w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),tc_Com_Opname,x),hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),v_x)),w,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(v,w),v_x,w,u))**.
% 299.79/300.48 42741[0:SpL:161.0,85.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(w,y,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.79/300.48 42689[0:SpR:161.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(y,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* -> c_lessequals(u,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),y),w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)).
% 299.79/300.48 42679[0:SpR:161.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(x,u),c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool)))),hAPP(c_Set_Oinsert(x,u),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),w,tc_fun(u,tc_bool))))**.
% 299.79/300.48 42662[0:SpR:161.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),x,y),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(z,w,tc_fun(u,tc_bool)),x),x1)),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z),w,tc_fun(u,tc_bool))))*.
% 299.79/300.48 42637[0:SpR:161.0,9569.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool)))),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))),tc_bool)*.
% 299.79/300.48 42636[0:SpR:161.0,9568.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool)))),z),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))),tc_bool)*.
% 299.79/300.48 43086[0:SpR:9987.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),u,tc_fun(x,tc_bool)))**.
% 299.79/300.48 43084[0:SpR:2095.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(y,v),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(y,v),u,tc_fun(x,tc_bool)))**.
% 299.79/300.48 43080[0:SpR:24914.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))),x))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(v,v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,u,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v,u,tc_fun(y,tc_bool)))**.
% 299.79/300.48 43079[0:SpR:23902.1,486.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_bool)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool)))**.
% 299.79/300.48 43076[0:SpR:2935.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_in(t_a),v_x),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_in(t_a),v_x),u,tc_fun(w,tc_bool)))**.
% 299.79/300.48 43071[0:SpR:301.1,486.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,tc_fun(x,tc_bool)))**.
% 299.79/300.48 43016[0:SpR:414.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ofun__upd(z,v,y,x1,x2),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ofun__upd(z,v,y,x1,x2),u,tc_fun(x,tc_bool)))**.
% 299.79/300.48 43007[0:SpR:524.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),u,tc_fun(x,tc_bool)))**.
% 299.79/300.48 43001[0:SpR:8415.2,486.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,u,v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,u,v,tc_fun(x,tc_bool)))**.
% 299.79/300.48 42997[0:SpR:365.1,486.1] class_Orderings_Obot(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,tc_fun(x,tc_bool)))**.
% 299.79/300.48 42996[0:SpR:397.1,486.1] class_Orderings_Otop(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,tc_fun(x,tc_bool)))**.
% 299.79/300.48 42979[0:SpR:2093.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(tc_Com_Opname),v_x)),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_Procs,x),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_Procs,x),u,tc_fun(w,tc_bool)))**.
% 299.79/300.48 42977[0:SpR:3744.1,486.1] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,u),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,u),v,tc_fun(x,tc_bool)))**.
% 299.79/300.48 42959[0:SpR:486.1,84.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_HOL_Ominus__class_Ominus(x,hAPP(y,v),tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))* -> c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool)).
% 299.79/300.48 42950[0:SpR:486.1,338.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),hAPP(c_Set_Oinsert(z,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)))),hAPP(c_Set_Oinsert(z,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool))))**.
% 299.79/300.48 42927[0:SpR:486.1,20881.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),z,x1),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)),z),x2)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 42901[0:SpR:486.1,9569.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,v))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))),tc_bool)*.
% 299.79/300.48 42900[0:SpR:486.1,9568.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,v))),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))),tc_bool)*.
% 299.79/300.48 43333[0:SpL:2097.1,406.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w))* equal(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(y,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))))* -> equal(w,x)* equal(w,y)*.
% 299.79/300.48 43560[0:SpL:507.0,85.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)),tc_fun(x,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),z),tc_fun(x,tc_bool))*.
% 299.79/300.48 43533[0:SpR:8415.2,507.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),hAPP(c_Set_Oimage(u,v,w),x)),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),x)))*.
% 299.79/300.48 43579[0:Rew:538.0,43518.2] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),hAPP(c_Set_Oimage(u,v,w),x)),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)))*.
% 299.79/300.48 43507[0:SpR:507.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),z),tc_fun(x,tc_bool))* -> c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)),tc_fun(x,tc_bool)).
% 299.79/300.48 43497[0:SpR:507.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),hAPP(c_Set_Oinsert(y,u),hAPP(c_Set_Oimage(v,w,u),z))),hAPP(c_Set_Oinsert(y,u),hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z))))**.
% 299.79/300.48 43480[0:SpR:507.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),y,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(v,w,u),x1),y),x2)),hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x1))))*.
% 299.79/300.48 43454[0:SpR:507.0,9569.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x))),hAPP(c_Set_Oimage(u,v,w),y)),tc_bool)*.
% 299.79/300.48 43453[0:SpR:507.0,9568.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x))),x1),hAPP(c_Set_Oimage(u,v,w),y)),tc_bool)*.
% 299.79/300.48 43584[0:Rew:507.0,43541.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x)),y)),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),y)))**.
% 299.79/300.48 43585[0:Rew:507.0,43540.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x)),y)),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),y)))**.
% 299.79/300.48 43586[0:Rew:507.0,43526.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,y))),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)))**.
% 299.79/300.48 43587[0:Rew:507.0,43525.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,y))),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)))**.
% 299.79/300.48 43782[0:SpL:162.0,85.0] || c_lessequals(u,hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),z),tc_fun(w,tc_bool))*.
% 299.79/300.48 43752[0:SpR:8415.2,162.0] || equal(v_Procs,v_x) equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),hAPP(c_Set_Ovimage(u,v,w),x)),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),x)))*.
% 299.79/300.48 43808[0:Rew:538.0,43737.2] || equal(v_Procs,v_x) equal(c_Set_Ovimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),hAPP(c_Set_Ovimage(u,v,w),x)),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))*.
% 299.79/300.48 43729[0:SpR:162.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),z),tc_fun(w,tc_bool))* -> c_lessequals(u,hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),tc_fun(w,tc_bool)).
% 299.79/300.48 43719[0:SpR:162.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),hAPP(c_Set_Oinsert(y,u),hAPP(c_Set_Ovimage(v,u,w),z))),hAPP(c_Set_Oinsert(y,u),hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z))))**.
% 299.79/300.48 43702[0:SpR:162.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),y,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(v,u,w),x1),y),x2)),hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x1))))*.
% 299.79/300.48 43676[0:SpR:162.0,9569.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x))),hAPP(c_Set_Ovimage(u,v,w),y)),tc_bool)*.
% 299.79/300.48 43675[0:SpR:162.0,9568.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x))),x1),hAPP(c_Set_Ovimage(u,v,w),y)),tc_bool)*.
% 299.79/300.48 43815[0:Rew:162.0,43763.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),v_x),c_Set_Ovimage(u,v,w),tc_Com_Opname,x)),y)),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),y)))**.
% 299.79/300.48 43816[0:Rew:162.0,43762.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x),tc_Com_Opname,x)),y)),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),y)))**.
% 299.79/300.48 43817[0:Rew:162.0,43748.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(u,v,w),v_x),c_Set_Ovimage(u,v,w),tc_Com_Opname,y))),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))**.
% 299.79/300.48 43818[0:Rew:162.0,43747.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),v_x),tc_Com_Opname,y))),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))**.
% 299.79/300.48 43946[0:SpL:8415.2,231.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(x,v_x,tc_fun(w,tc_bool)) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),v_x,tc_fun(v,tc_bool))*.
% 299.79/300.48 44067[0:SpL:8415.2,358.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(v_x,hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> c_lessequals(v_x,x,tc_fun(v,tc_bool)).
% 299.79/300.48 44052[0:SpL:8415.2,358.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),v_x,tc_fun(w,tc_bool))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* -> c_lessequals(x,v_x,tc_fun(v,tc_bool)).
% 299.79/300.48 44179[0:Res:232.1,430.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),y,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool))),y,tc_fun(w,tc_bool))*.
% 299.79/300.48 44199[0:SSi:44186.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(x,hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(y,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))* -> c_lessequals(x,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.48 44310[0:Res:149.1,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))))* equal(hAPP(x,y),hAPP(x,v))* c_Fun_Oinj__on(x,c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),u,z)* -> hBOOL(hAPP(hAPP(c_in(u),y),w))* equal(y,v).
% 299.79/300.48 44284[0:SpL:584.0,268.0] || hBOOL(hAPP(c_COMBS(c_in(u),v,w,x,y),z))* hBOOL(hAPP(hAPP(c_in(u),x1),hAPP(v,z)))* equal(hAPP(x2,z),hAPP(x2,x1))* c_Fun_Oinj__on(x2,hAPP(v,z),u,x3)* -> equal(z,x1).
% 299.79/300.48 45093[0:SpR:104.0,326.2] || c_lessequals(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w,tc_fun(v,tc_bool)) c_lessequals(x,y,tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y),tc_fun(v,tc_bool))*.
% 299.79/300.48 45028[0:SpR:104.0,326.2] || c_lessequals(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)) c_lessequals(x,y,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.48 45307[0:SpL:104.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)))*.
% 299.79/300.48 45467[0:Res:45357.1,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_Com_Opname)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_Com_Opname)))*.
% 299.79/300.48 45531[0:SpR:323.0,9566.0] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Set_Oinsert(z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))),tc_bool)*.
% 299.79/300.48 45865[0:SpL:3294.1,482.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,v,u))) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v,u)))* hBOOL(hAPP(hAPP(c_in(u),w),c_Orderings_Obot__class_Obot(tc_bool)))* -> hBOOL(hAPP(v,w))*.
% 299.79/300.48 45860[0:SpL:584.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(x,v),u,w)))* hBOOL(hAPP(hAPP(c_in(w),y),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,z,x1,x2),v)))* -> hBOOL(hAPP(u,y))*.
% 299.79/300.48 45842[0:SpL:600.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ominus__class_Ominus(x,v,tc_fun(w,tc_bool)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v)))* -> hBOOL(hAPP(u,y))*.
% 299.79/300.48 46193[0:Rew:339.0,46163.2] || equal(u,v_Procs) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(w,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),x)),v,tc_Com_Opname)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),x))))*.
% 299.79/300.48 46155[0:Res:11030.1,481.0] || equal(c_in(t_a),c_in(u)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x),v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)))*.
% 299.79/300.48 46151[0:Res:3316.1,481.0] || equal(c_in(u),c_in(v)) -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),x),w,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),x)))*.
% 299.79/300.48 46129[0:Res:648.0,481.0] || -> hBOOL(hAPP(u,hAPP(v,v_x))) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs)),x),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs)),x)))*.
% 299.79/300.48 46112[0:SpL:3229.1,481.0] || equal(u,hAPP(c_in(v),w))* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(x,w))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),y),x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),y)))*.
% 299.79/300.48 46106[0:SpL:3229.1,481.0] || equal(u,c_in(v))* hBOOL(hAPP(hAPP(u,v_x),w))* -> hBOOL(hAPP(x,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y),x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)))*.
% 299.79/300.48 46481[0:Res:19436.1,480.0] || equal(u,v_Procs) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),u)),v,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),u))))*.
% 299.79/300.48 46473[0:Res:11030.1,480.0] || equal(c_in(t_a),c_in(u)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.79/300.48 46469[0:Res:3316.1,480.0] || equal(c_in(u),c_in(v)) -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),w,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)))))*.
% 299.79/300.48 46447[0:Res:648.0,480.0] || -> hBOOL(hAPP(u,hAPP(v,v_x))) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs)),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs))))*.
% 299.79/300.48 46430[0:SpL:3229.1,480.0] || equal(u,hAPP(c_in(v),w))* hBOOL(hAPP(u,v_x))* -> hBOOL(hAPP(x,w))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),v_x),x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),v_x)))*.
% 299.79/300.48 46424[0:SpL:3229.1,480.0] || equal(u,c_in(v))* hBOOL(hAPP(hAPP(u,v_x),w))* -> hBOOL(hAPP(x,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),w),x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),w)))*.
% 299.79/300.48 46934[0:Res:241.2,436.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool))* hBOOL(hAPP(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),y))* -> hBOOL(hAPP(x,y))*.
% 299.79/300.48 47268[0:SSi:47222.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(w,hAPP(c_Set_Oinsert(v,u),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x,y,z,x1),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),tc_fun(u,tc_bool))*.
% 299.79/300.48 48681[0:SpL:197.1,103.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(y,x,tc_fun(v,tc_bool))),w)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),y),w).
% 299.79/300.48 48680[0:SpL:197.1,147.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oimage(u,v,w),y))) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(z,y,tc_fun(v,tc_bool)))))* -> .
% 299.79/300.48 48829[0:Res:8376.2,619.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(v,v_Procs) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,u,tc_fun(x,tc_bool)),v),c_Set_Oinsert(y,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,u,tc_fun(x,tc_bool))))**.
% 299.79/300.48 48795[0:Res:3346.1,619.0] || equal(c_Set_Oinsert(u,v),w)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,v,tc_fun(y,tc_bool)),hAPP(w,v_x)),c_Set_Oinsert(z,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(z,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(w,v_x),x,v,tc_fun(y,tc_bool))))**.
% 299.79/300.48 48780[0:Res:648.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(x,tc_Com_Opname,v),v_Procs)),c_Set_Oinsert(y,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(y,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,tc_Com_Opname,v),v_Procs),u,v,tc_fun(w,tc_bool))))**.
% 299.79/300.48 48970[0:SpL:584.0,483.0] || hBOOL(hAPP(c_COMBS(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y),z))* -> hBOOL(hAPP(x1,z)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x1,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(z,x1,u)),z))*.
% 299.79/300.48 49041[0:SpR:49017.1,410.0] || -> hBOOL(hAPP(u,v_x)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,v),w),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 49175[0:SpL:584.0,239.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(v,w,u),x,y,z),x1))* c_lessequals(x1,x2,tc_fun(w,tc_bool)) c_Fun_Oinj__on(v,x1,w,u) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(x1,v,w,u),x1)),x2))*.
% 299.79/300.48 49333[0:Res:49314.1,593.0] || hBOOL(hAPP(u,v_x)) c_Hoare__Mirabelle_Otriple__valid(v,v_n(v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname))),t_a)*.
% 299.79/300.48 49388[0:SpR:49342.1,475.1] || hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> equal(hAPP(c_Set_Oinsert(v_Procs,x),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,x),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,x),w))**.
% 299.79/300.48 49672[0:Rew:49662.2,49531.1] || c_Fun_Oinj__on(c_COMBK(u,v,w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),u),hAPP(c_Set_Oimage(c_COMBK(u,v,w),y,z),hAPP(c_Set_Oinsert(x1,y),x))))* c_Fun_Oinj__on(c_COMBK(u,v,w),hAPP(c_Set_Oinsert(x1,y),x),y,z).
% 299.79/300.48 49716[0:Rew:49662.2,49570.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,x),hAPP(c_Set_Oinsert(u,w),v))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(c_Set_Oinsert(u,w),v),w,x).
% 299.79/300.48 50172[7:MRR:50163.1,27297.0] || equal(u,c_Set_Oimage(v,w,tc_fun(x,tc_bool))) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(u,v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,v,w,tc_fun(x,tc_bool))))*.
% 299.79/300.48 52845[0:SpL:24019.2,284.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v_x,v,u),w)))* c_Fun_Oinj__on(v_x,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,u)* -> hBOOL(hAPP(hAPP(c_in(v),v_x),w)).
% 299.79/300.48 52844[0:SpL:24019.2,275.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 53092[0:SpL:23955.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)),w))* hBOOL(hAPP(hAPP(c_in(x),y),v_x)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 53027[0:SpR:23955.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 53224[0:SpL:23958.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)),w))* hBOOL(hAPP(hAPP(c_in(x),y),v_x)) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(x,tc_bool))))*.
% 299.79/300.48 53159[0:SpR:23958.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 53475[0:SpL:33303.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,y),v_x),tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 54174[0:SpL:52997.1,275.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_Procs,y),u,tc_fun(w,tc_bool))))*.
% 299.79/300.48 54839[0:SpL:13749.2,275.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(u))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 54704[0:SpR:13749.2,410.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,tc_fun(y,tc_bool))))*.
% 299.79/300.48 55314[0:SpL:14043.2,275.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(u))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 55178[0:SpR:14043.2,410.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),v,tc_fun(y,tc_bool))))*.
% 299.79/300.48 56353[0:SpL:30368.2,275.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* hBOOL(hAPP(hAPP(c_in(y),z),c_Orderings_Otop__class_Otop(u))) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(y,tc_bool))))*.
% 299.79/300.48 56204[0:SpR:30368.2,475.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y),x))**.
% 299.79/300.48 56795[0:SpL:30928.2,275.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* hBOOL(hAPP(hAPP(c_in(y),z),c_Orderings_Otop__class_Otop(u))) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(y,tc_bool))))*.
% 299.79/300.48 56646[0:SpR:30928.2,475.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,y),x))**.
% 299.79/300.48 58802[0:SpL:131.0,15629.0] || hBOOL(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),z)))* -> hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x1)))*.
% 299.79/300.48 58801[0:SpL:158.0,15629.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)))* -> hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x1)))*.
% 299.79/300.48 58730[0:SpL:523.1,15629.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x)))*.
% 299.79/300.48 58729[0:SpL:460.1,15629.0] || class_Lattices_Olattice(t_b) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u)))*.
% 299.79/300.48 59310[0:SpL:131.0,15857.0] || hBOOL(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),z)))* -> hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x2)))*.
% 299.79/300.48 59309[0:SpL:158.0,15857.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)))* -> hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x2)))*.
% 299.79/300.48 59238[0:SpL:523.1,15857.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),y)))*.
% 299.79/300.48 59237[0:SpL:460.1,15857.0] || class_Lattices_Olattice(t_b) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v)))*.
% 299.79/300.48 60439[7:Res:58968.1,454.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),x,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),x),u,t_a)*.
% 299.79/300.48 60425[7:Res:58968.1,170.1] class_Orderings_Olinorder(u) || equal(hAPP(c_in(u),v),v_x) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w),u),v,u)*.
% 299.79/300.48 60424[7:Res:58968.1,169.1] class_Orderings_Olinorder(u) || equal(hAPP(c_in(u),v),v_x) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w),u),u)*.
% 299.79/300.48 60397[7:SpR:104.0,58968.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w),tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))*.
% 299.79/300.48 60379[7:SpR:445.1,58968.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),v_x) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Fun_Ofun__upd(u,v,w,x,y),z),v) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Fun_Ofun__upd(u,v,w,x,y),z)))*.
% 299.79/300.48 60482[0:SpL:5882.1,275.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(u))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),z,x1,x2,x3),v,tc_fun(x,tc_bool))))*.
% 299.79/300.48 60473[0:SpR:5882.1,118.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Fun_Ocomp(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_Fun_Ofun__upd(z,x1,c_Orderings_Otop__class_Otop(u),x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x3,x4,x2),x1,c_Orderings_Otop__class_Otop(u),x2,x4))*.
% 299.79/300.48 60552[0:Res:58969.1,454.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),x,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),x),u,t_a)*.
% 299.79/300.48 60538[0:Res:58969.1,170.1] class_Orderings_Olinorder(u) || equal(hAPP(c_in(u),v),v_Procs) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w),u),v,u)*.
% 299.79/300.48 60537[0:Res:58969.1,169.1] class_Orderings_Olinorder(u) || equal(hAPP(c_in(u),v),v_Procs) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),v),w),u),u)*.
% 299.79/300.48 60510[0:SpR:104.0,58969.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w),tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))*.
% 299.79/300.48 60492[0:SpR:445.1,58969.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),v_Procs) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Fun_Ofun__upd(u,v,w,x,y),z),v) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Fun_Ofun__upd(u,v,w,x,y),z)))*.
% 299.79/300.49 60625[7:Res:59476.1,454.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x) -> c_Hoare__Mirabelle_Ohoare__valids(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w),x,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w),x),u,t_a)*.
% 299.79/300.49 60611[7:Res:59476.1,170.1] class_Orderings_Olinorder(u) || equal(hAPP(c_in(u),v),v_x) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x),u),v,u)*.
% 299.79/300.49 60610[7:Res:59476.1,169.1] class_Orderings_Olinorder(u) || equal(hAPP(c_in(u),v),v_x) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x),u),u)*.
% 299.79/300.49 60583[7:SpR:104.0,59476.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),x),tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))*.
% 299.79/300.49 60565[7:SpR:445.1,59476.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),v_x) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Fun_Ofun__upd(u,v,w,x,y),x1),v) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Fun_Ofun__upd(u,v,w,x,y),x1)))*.
% 299.79/300.49 60698[0:Res:59477.1,454.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Procs) -> c_Hoare__Mirabelle_Ohoare__valids(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w),x,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w),x),u,t_a)*.
% 299.79/300.49 60684[0:Res:59477.1,170.1] class_Orderings_Olinorder(u) || equal(hAPP(c_in(u),v),v_Procs) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x),u),v,u)*.
% 299.79/300.49 60683[0:Res:59477.1,169.1] class_Orderings_Olinorder(u) || equal(hAPP(c_in(u),v),v_Procs) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),x),u),u)*.
% 299.79/300.49 60656[0:SpR:104.0,59477.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_Procs) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),x),tc_fun(u,tc_bool)),tc_fun(u,tc_bool)))*.
% 299.79/300.49 60638[0:SpR:445.1,59477.1] || equal(c_Fun_Ofun__upd(u,v,w,x,y),v_Procs) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Fun_Ofun__upd(u,v,w,x,y),x1),v) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Fun_Ofun__upd(u,v,w,x,y),x1)))*.
% 299.79/300.49 60883[0:Res:59017.1,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v),t_a)* c_Hoare__Mirabelle_Ohoare__valids(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v),w),y,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v),w),y),v,t_a)*.
% 299.79/300.49 60869[0:Res:59017.1,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_in(u),x),v),u) -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_in(u),x),t_a)* c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_in(u),x),v),u),x,u)*.
% 299.79/300.49 60868[0:Res:59017.1,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_in(u),x),v),u) -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_in(u),x),t_a)* c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_in(u),x),v),u),u)*.
% 299.79/300.49 60841[0:SpR:104.0,59017.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))),t_a)* hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))),x),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))*.
% 299.79/300.49 60823[0:SpR:445.1,59017.1] || -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Fun_Ofun__upd(w,x,y,z,x1),u),x) c_Hoare__Mirabelle_Ohoare__valids(x2,c_Fun_Ofun__upd(w,x,y,z,x1),t_a)* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,c_Fun_Ofun__upd(w,x,y,z,x1),u)))*.
% 299.79/300.49 60956[0:Res:59525.1,454.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v),t_a)* c_Hoare__Mirabelle_Ohoare__valids(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v),x),y,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v),x),y),v,t_a)*.
% 299.79/300.49 60942[0:Res:59525.1,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(u),x),w),u) -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_in(u),x),t_a)* c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(u),x),w),u),x,u)*.
% 299.79/300.49 60941[0:Res:59525.1,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(u),x),w),u) -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_in(u),x),t_a)* c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(u),x),w),u),u)*.
% 299.79/300.49 60914[0:SpR:104.0,59525.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))),t_a)* hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(v,tc_bool))),y),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))*.
% 299.79/300.49 60896[0:SpR:445.1,59525.1] || -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Fun_Ofun__upd(w,x,y,z,x1),v),x) c_Hoare__Mirabelle_Ohoare__valids(x2,c_Fun_Ofun__upd(w,x,y,z,x1),t_a)* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Fun_Ofun__upd(w,x,y,z,x1),v)))*.
% 299.79/300.49 61808[0:SpL:11167.1,275.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Set_Oinsert(y,z),c_Set_Oinsert(v_x,tc_Com_Opname)),u,tc_fun(w,tc_bool))))*.
% 299.79/300.49 61795[0:SpR:11167.1,118.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> equal(c_Fun_Ocomp(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),c_Fun_Ofun__upd(w,x,v_Procs,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Set_Oinsert(u,v),c_Set_Oinsert(v_x,tc_Com_Opname)),w,z,x1,y),x,v_Procs,y,x1))*.
% 299.79/300.49 61783[0:SpR:11167.1,71.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(hAPP(c_Set_Oinsert(w,x),c_Set_Oinsert(v_x,tc_Com_Opname)),v,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(v,hAPP(c_Set_Oinsert(w,x),c_Set_Oinsert(v_x,tc_Com_Opname)),u,y),v_Procs),v_Procs)**.
% 299.79/300.49 61782[0:SpR:11167.1,373.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(hAPP(c_Set_Oinsert(w,x),c_Set_Oinsert(v_x,tc_Com_Opname)),v,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,hAPP(c_Set_Oinsert(w,x),c_Set_Oinsert(v_x,tc_Com_Opname)),u,y),v_Procs),v_Procs)**.
% 299.79/300.49 61947[0:SpL:533.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY) equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool),c_Com_Ocom_OSKIP)** -> .
% 299.79/300.49 64541[0:SpL:533.0,24257.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(v_x,v_Procs)).
% 299.79/300.49 64618[0:SpL:26782.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) hBOOL(hAPP(hAPP(c_in(w),x),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),y,tc_fun(z,tc_bool)),u,tc_fun(w,tc_bool))))*.
% 299.79/300.49 64863[0:SpL:28747.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),tc_Com_Opname,z),tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.49 64983[0:SpL:28748.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),tc_Com_Opname,z),tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.49 65103[0:SpL:28902.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,z),tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.49 65223[0:SpL:28903.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,z),tc_Com_Opname),u,tc_fun(w,tc_bool))))*.
% 299.79/300.49 66706[0:SpR:1188.2,71.2] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,x),c_Orderings_Otop__class_Otop(u)),c_HOL_Ozero__class_Ozero(u))**.
% 299.79/300.49 66705[0:SpR:1188.2,373.2] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,x),c_Orderings_Otop__class_Otop(u)),c_HOL_Ozero__class_Ozero(u))**.
% 299.79/300.49 67461[0:SpR:1189.2,71.2] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),w,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,x),c_Orderings_Otop__class_Otop(u)),c_HOL_Ozero__class_Ozero(u))**.
% 299.79/300.49 67460[0:SpR:1189.2,373.2] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),w,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,x),c_Orderings_Otop__class_Otop(u)),c_HOL_Ozero__class_Ozero(u))**.
% 299.79/300.49 67673[0:SpR:67115.3,221.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_List_Ofoldl(c_COMBC(hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),v),w),v,u,u),c_HOL_Ozero__class_Ozero(u),x,u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(x,v),w,v,u))**.
% 299.79/300.49 67960[0:SpR:67416.3,221.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oupper__semilattice(u) class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_List_Ofoldl(c_COMBC(hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),v),w),v,u,u),c_HOL_Ozero__class_Ozero(u),x,u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(x,v),w,v,u))**.
% 299.79/300.49 69147[0:SpR:67573.3,221.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_List_Ofoldl(c_COMBC(hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),v),w),v,u,u),c_HOL_Ozero__class_Ozero(u),x,u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(x,v),w,v,u))**.
% 299.79/300.49 69439[0:SpR:68745.3,221.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Olattice(u) class_Lattices_Oboolean__algebra(u) class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_List_Ofoldl(c_COMBC(hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),v),w),v,u,u),c_HOL_Ozero__class_Ozero(u),x,u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(x,v),w,v,u))**.
% 299.79/300.49 74117[7:SpL:71835.1,481.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))*.
% 299.79/300.49 74116[7:SpL:71835.1,480.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v)))*.
% 299.79/300.49 74530[7:MRR:73229.1,27297.0] || equal(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,u,v,tc_fun(w,tc_bool))))*.
% 299.79/300.49 78698[4:Res:78665.1,239.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)),v_x)** c_lessequals(y,z,tc_fun(x,tc_bool)) c_Fun_Oinj__on(w,y,x,u) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Fun_Othe__inv__into(y,w,x,u),v)),z))*.
% 299.79/300.49 78680[4:Res:78665.1,483.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),v_x)** -> hBOOL(hAPP(y,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,y,u)),w))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,y,u)),x))*.
% 299.79/300.49 79028[0:Res:15630.1,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) c_Hoare__Mirabelle_Ohoare__valids(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,x),y),z,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x1)),w))* c_Hoare__Mirabelle_Otriple__valid(x1,u,t_a)*.
% 299.79/300.49 79022[0:Res:15630.1,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(x,y),z),x1,hAPP(c_Set_Oinsert(u,v),w),y)))* equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(x,y),z),x1,hAPP(c_Set_Oinsert(u,v),w),y),u).
% 299.79/300.49 78981[0:SpR:297.2,15630.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),u)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)).
% 299.79/300.49 78971[0:SpR:393.1,15630.1] || hBOOL(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),x)) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(x,y),z),x1,c_Set_Oimage(c_COMBK(u,v,w),w,v),y),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** hBOOL(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))).
% 299.79/300.49 79056[0:Rew:104.0,78990.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,x),y),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),x),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)))*.
% 299.79/300.49 79248[0:Res:15858.1,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) c_Hoare__Mirabelle_Ohoare__valids(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(v,y),z),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),y),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x1)),w))* c_Hoare__Mirabelle_Otriple__valid(x1,u,t_a)*.
% 299.79/300.49 79242[0:Res:15858.1,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(x,z),x1),hAPP(c_Set_Oinsert(u,v),w),z)))* equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(x,z),x1),hAPP(c_Set_Oinsert(u,v),w),z),u).
% 299.79/300.49 79201[0:SpR:297.2,15858.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oinsert(x,y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),u)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oinsert(x,y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)).
% 299.79/300.49 79191[0:SpR:393.1,15858.1] || hBOOL(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),x)) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(x,z),x1),c_Set_Oimage(c_COMBK(u,v,w),w,v),z),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** hBOOL(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))).
% 299.79/300.49 79276[0:Rew:104.0,79210.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(v,y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),y),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)))*.
% 299.79/300.49 80295[0:SpL:21268.0,467.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> equal(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),y),z,x1),w,x,u),v)),v)**.
% 299.79/300.49 80236[0:SpL:21268.0,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)) -> hBOOL(hAPP(v,x)) hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),y,z),x))*.
% 299.79/300.49 80234[0:SpL:21268.0,324.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),y,z),x,tc_fun(u,tc_bool))*.
% 299.79/300.49 80232[0:SpL:21268.0,344.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,y),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))**.
% 299.79/300.49 79856[0:SpR:130.1,21268.0] class_HOL_Ominus(u) || -> equal(hAPP(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),x,y)),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))**.
% 299.79/300.49 79846[0:SpR:354.2,21268.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),u,z,x1)),u)**.
% 299.79/300.49 80411[0:Rew:523.1,79818.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),v,x),v_x)),hAPP(y,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(y,v_x)))**.
% 299.79/300.49 79672[0:SpR:21268.0,517.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),y),v,z)))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),y)).
% 299.79/300.49 79670[0:SpR:21268.0,518.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),y),v,z)))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),y)).
% 299.79/300.49 79358[0:SpR:21268.0,2097.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),v))* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),hAPP(c_Set_Oinsert(v,w),x)).
% 299.79/300.49 81490[0:SpL:21894.0,467.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> equal(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(w,x,u),y),c_Set_Oimage(w,x,u),z,x1),w,x,u),v)),v)**.
% 299.79/300.49 81431[0:SpL:21894.0,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)) -> hBOOL(hAPP(v,x)) hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y,z),x))*.
% 299.79/300.49 81429[0:SpL:21894.0,324.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y,z),x,tc_fun(u,tc_bool))*.
% 299.79/300.49 81427[0:SpL:21894.0,344.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,y),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))**.
% 299.79/300.49 81050[0:SpR:130.1,21894.0] class_HOL_Ominus(u) || -> equal(hAPP(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x,y)),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u))**.
% 299.79/300.49 81040[0:SpR:354.2,21894.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),u,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x1)),u)**.
% 299.79/300.49 81606[0:Rew:523.1,81012.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v,x),v_x)),hAPP(y,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(y,v_x)))**.
% 299.79/300.49 80866[0:SpR:21894.0,517.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v,z)))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),y)).
% 299.79/300.49 80864[0:SpR:21894.0,518.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),v,z)))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u),y)).
% 299.79/300.49 80551[0:SpR:21894.0,2097.1] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),v))* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),hAPP(c_Set_Oinsert(v,w),x)).
% 299.79/300.49 81799[0:SpR:354.2,5879.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,tc_fun(x,tc_bool)) c_Fun_Oinj__on(y,w,x,z) -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(w,y,x,z),z,x),x1,x2,x3),hAPP(c_Set_Oimage(y,x,z),v)),u)*.
% 299.79/300.49 82271[0:SpR:354.2,5880.1] class_Lattices_Olattice(u) || c_lessequals(v,w,tc_fun(x,tc_bool)) c_Fun_Oinj__on(y,w,x,z) -> c_lessequals(v,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(w,y,x,z),z,x),x1,x2,x3),hAPP(c_Set_Oimage(y,x,z),v)),u)*.
% 299.79/300.49 83769[0:SpR:5899.0,118.0] || -> equal(c_Fun_Ocomp(c_COMBS(u,v,w,x,y),c_Fun_Ofun__upd(z,x1,x2,x3,x4),x4,x5,x3),c_Fun_Ofun__upd(c_Fun_Ocomp(c_COMBS(u,v,w,x,y),z,x4,x5,x3),x1,hAPP(c_COMBS(u,v,x6,x7,x8),x2),x3,x5))*.
% 299.79/300.49 83750[0:SpR:5899.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_COMBS(x,y,z,x1,x2),w,u,x3) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_COMBS(x,y,z,x1,x2),u,x3),hAPP(c_COMBS(x,y,x4,x5,x6),v)),v)**.
% 299.79/300.49 83749[0:SpR:5899.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_COMBS(x,y,z,x1,x2),w,u,x3) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_COMBS(x,y,z,x1,x2),u,x3),hAPP(c_COMBS(x,y,x4,x5,x6),v)),v)**.
% 299.79/300.49 85062[0:SpR:644.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),x),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),w,x),y)))*.
% 299.79/300.49 85061[0:SpR:644.0,99.1] || c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),w,x),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),v_Procs)**.
% 299.79/300.49 85060[0:SpR:644.0,438.1] || c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),w,x),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),v_Procs)**.
% 299.79/300.49 85444[4:SpR:78507.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,x),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,x),u,tc_fun(w,tc_bool)))**.
% 299.79/300.49 85843[0:Res:9066.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x))))* c_Hoare__Mirabelle_Otriple__valid(u,w,t_a).
% 299.79/300.49 87166[7:Rew:339.0,87146.1] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,w)),x)),u,t_a)),hAPP(c_Set_Oinsert(v,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,w)),x))))*.
% 299.79/300.49 87145[7:Res:82177.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),hAPP(c_Set_Oinsert(w,t_a),c_Set_Oinsert(v_x,x))),u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),hAPP(c_Set_Oinsert(w,t_a),c_Set_Oinsert(v_x,x)))))*.
% 299.79/300.49 88435[0:Res:8176.1,441.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.79/300.49 88851[0:SpR:205.1,14196.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,y),hAPP(c_Set_Oinsert(z,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),hAPP(c_Set_Oimage(u,v,w),z)))*.
% 299.79/300.49 89339[7:SpR:78590.1,486.1] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)))**.
% 299.79/300.49 90129[4:SpR:78660.1,486.1] || equal(hAPP(u,v_x),v_x) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)))**.
% 299.79/300.49 91367[0:Rew:91288.1,91079.1] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,tc_fun(x,tc_bool)))**.
% 299.79/300.49 91886[4:Rew:339.0,91838.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),tc_Com_Opname))),v_x)** -> hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x))).
% 299.79/300.49 91887[4:Rew:537.1,91835.2] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname))),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))).
% 299.79/300.49 91888[4:Rew:534.1,91834.2] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname))),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))).
% 299.79/300.49 91922[0:SpR:79073.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_Procs,y),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_Procs,y),u,tc_fun(x,tc_bool)))**.
% 299.79/300.49 92074[7:SpR:79101.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(v),v_x)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_in(v),v_x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,y),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,y),u,tc_fun(x,tc_bool)))**.
% 299.79/300.49 92355[0:SpL:317.0,5022.0] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))* -> equal(hAPP(c_Set_Oinsert(hAPP(u,x),w),hAPP(c_Set_Oimage(u,v,w),y)),hAPP(c_Set_Oimage(u,v,w),y)).
% 299.79/300.49 92426[0:Rew:21893.0,92383.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),tc_fun(v,tc_bool))* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)).
% 299.79/300.49 92427[0:Rew:21267.0,92381.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),tc_fun(v,tc_bool))* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)).
% 299.79/300.49 92684[7:Res:82151.1,619.0] || equal(c_in(t_a),c_in(u)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(w,tc_bool)),c_Set_Oinsert(v_x,x)),c_Set_Oinsert(y,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(y,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Set_Oinsert(v_x,x),v,u,tc_fun(w,tc_bool))))**.
% 299.79/300.49 92828[0:SpR:205.1,5876.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),z,x1,x2),hAPP(c_Set_Oimage(u,v,w),x)),tc_fun(y,tc_bool))*.
% 299.79/300.49 93097[0:Rew:584.0,92789.0] || -> c_lessequals(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u,w,x,y),tc_Com_Opname,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),hAPP(u,v_x)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),hAPP(u,v_x)),tc_fun(v,tc_bool))*.
% 299.79/300.49 93219[0:SpR:5878.1,317.0] class_Lattices_Obounded__lattice(u) || -> equal(hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),z),x2)),hAPP(c_Set_Oinsert(hAPP(v,c_Orderings_Obot__class_Obot(u)),x1),hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1),x2)))*.
% 299.79/300.49 93218[0:SpR:5878.1,99.1] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1),hAPP(v,c_Orderings_Obot__class_Obot(u))),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.49 93217[0:SpR:5878.1,438.1] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x1),hAPP(v,c_Orderings_Obot__class_Obot(u))),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.49 670[0:Res:589.0,487.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))* -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,hAPP(c_in(tc_Com_Opname),v_x),u))) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,hAPP(c_in(tc_Com_Opname),v_x),u))).
% 299.79/300.49 668[0:Res:589.0,485.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,hAPP(c_in(tc_Com_Opname),v_x),u)),v))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,hAPP(c_in(tc_Com_Opname),v_x),u))).
% 299.79/300.49 669[0:Res:589.0,484.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,hAPP(c_in(tc_Com_Opname),v_x),u)),w))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,hAPP(c_in(tc_Com_Opname),v_x),u))).
% 299.79/300.49 667[0:Res:589.0,488.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,hAPP(c_in(tc_Com_Opname),v_x),u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,hAPP(c_in(tc_Com_Opname),v_x),u)),w))*.
% 299.79/300.49 14361[0:Res:176.0,170.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(hAPP(v,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(hAPP(v,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),u),x,u)*.
% 299.79/300.49 14488[0:Res:176.0,169.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(hAPP(v,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),u) -> c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(hAPP(v,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),u),u)*.
% 299.79/300.49 20307[0:SpR:130.1,438.1] class_HOL_Ominus(u) || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x,y),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)),v_x)**.
% 299.79/300.49 20302[0:SpR:196.1,438.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),x,y),z),hAPP(c_Set_Oimage(u,v,w),z))**.
% 299.79/300.49 20451[0:SpR:130.1,99.1] class_HOL_Ominus(u) || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x,y),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)),v_x)**.
% 299.79/300.49 20445[0:SpR:196.1,99.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),x,y),z),hAPP(c_Set_Oimage(u,v,w),z))**.
% 299.79/300.49 21012[0:SpR:64.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),w),z)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),y),x),hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),z)))*.
% 299.79/300.49 20941[0:SpR:130.1,317.0] class_HOL_Ominus(u) || -> equal(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x,y),hAPP(c_Set_Oinsert(v_x,x),z)),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),y),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x,y),z)))*.
% 299.79/300.49 20934[0:SpR:196.1,317.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),z),x),x1)),hAPP(c_Set_Oinsert(z,y),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),x1)))*.
% 299.79/300.49 21646[0:SpL:21267.0,279.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,w))**.
% 299.79/300.49 21594[0:SpL:21267.0,469.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y),w,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y))**.
% 299.79/300.49 21501[0:SpR:21267.0,10931.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),v_x),tc_Com_Opname,w),t_a) hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),v_x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),v_x),tc_Com_Opname,w))))*.
% 299.79/300.49 21421[0:SpR:21267.0,188.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x),tc_Com_Opname,x)))* -> equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))).
% 299.79/300.49 21889[0:SpL:21267.0,464.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y),v,w,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y))**.
% 299.79/300.49 22274[0:SpL:21893.0,279.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,w))**.
% 299.79/300.49 22222[0:SpL:21893.0,469.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y),w,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y))**.
% 299.79/300.49 22221[0:SpL:21893.0,464.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y),v,w,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y))**.
% 299.79/300.49 22127[0:SpR:21893.0,10931.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),v_x),c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,w),t_a) hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),v_x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),v_x),c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,w))))*.
% 299.79/300.49 22047[0:SpR:21893.0,188.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x),c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x)))* -> equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))).
% 299.79/300.49 22421[0:SpR:317.0,97.1] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),x),w,y) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(hAPP(c_Set_Oinsert(v,w),x),u,w,y),y,w),hAPP(c_Set_Oinsert(hAPP(u,v),y),hAPP(c_Set_Oimage(u,w,y),x))),hAPP(c_Set_Oinsert(v,w),x))**.
% 299.79/300.49 23620[0:Rew:523.1,23570.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),tc_Com_Opname,w),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(v_x,v_x)))**.
% 299.79/300.49 23621[0:Rew:523.1,23569.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),v_x),tc_Com_Opname,w),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(v_x,v_x)))**.
% 299.79/300.49 24457[0:Res:83.0,208.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Ovimage(w,x,u),hAPP(c_Set_Oinsert(v,u),y)))))* c_lessequals(hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Ovimage(w,x,u),hAPP(c_Set_Oinsert(v,u),y))),y,tc_fun(u,tc_bool))*.
% 299.79/300.49 24802[0:SpR:614.2,523.1] class_Complete__Lattice_Ocomplete__lattice(tc_fun(t_a,u)) class_Lattices_Olattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v_x)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,tc_fun(t_a,u)),v_x)),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,tc_fun(t_a,u)),v_x))**.
% 299.79/300.49 26137[0:SpR:338.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),x2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),hAPP(c_Set_Oinsert(u,v),x2)),hAPP(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),x2))))*.
% 299.79/300.49 26136[0:SpR:338.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oinsert(v,w),x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),x2)),hAPP(hAPP(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),x2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),hAPP(c_Set_Oinsert(v,w),x2))))*.
% 299.79/300.49 26687[0:SpR:353.0,244.2] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x))) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,u),x),u),c_HOL_Ozero__class_Ozero(tc_nat)) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(v,u),x)),u),c_Suc(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,u),x),u)))**.
% 299.79/300.49 27197[0:Res:450.0,454.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(tc_Hoare__Mirabelle_Otriple(t_a))),v),w),t_a) c_Hoare__Mirabelle_Ohoare__valids(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),w,v,u),x,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),w,v,u),x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),w,v,u),t_a)*.
% 299.79/300.49 27194[0:Res:450.0,455.0] || c_Hoare__Mirabelle_Ohoare__valids(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v,w,x),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,y),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(tc_Hoare__Mirabelle_Otriple(t_a))),w),v),t_a)* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v,w,x),t_a)*.
% 299.79/300.49 27932[0:Res:468.0,147.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)),x,y,u,z)),w))* -> equal(hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool)))).
% 299.79/300.49 28246[0:SpL:465.1,467.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),z),y)) equal(hAPP(c_Fun_Ofun__upd(w,z,x1,x,u),hAPP(c_Hilbert__Choice_Oinv__into(y,c_Fun_Ofun__upd(w,z,x1,x,u),x,u),v)),v)**.
% 299.79/300.49 28712[0:SpR:28031.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),c_Fun_Ofun__upd(w,x,v_Procs,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),w,z,x1,y),x,v_Procs,y,x1))*.
% 299.79/300.49 28691[0:SpR:28031.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(w,v_x),w,tc_Com_Opname,x),tc_Com_Opname),v,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(w,v_x),w,tc_Com_Opname,x),tc_Com_Opname),u,y),v_Procs),v_Procs)**.
% 299.79/300.49 28690[0:SpR:28031.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(w,v_x),w,tc_Com_Opname,x),tc_Com_Opname),v,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(w,v_x),w,tc_Com_Opname,x),tc_Com_Opname),u,y),v_Procs),v_Procs)**.
% 299.79/300.49 28867[0:SpR:28334.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),c_Fun_Ofun__upd(w,x,v_Procs,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),w,z,x1,y),x,v_Procs,y,x1))*.
% 299.79/300.49 28846[0:SpR:28334.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,hAPP(w,v_x),tc_Com_Opname,x),tc_Com_Opname),v,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,hAPP(w,v_x),tc_Com_Opname,x),tc_Com_Opname),u,y),v_Procs),v_Procs)**.
% 299.79/300.49 28845[0:SpR:28334.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,hAPP(w,v_x),tc_Com_Opname,x),tc_Com_Opname),v,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,hAPP(w,v_x),tc_Com_Opname,x),tc_Com_Opname),u,y),v_Procs),v_Procs)**.
% 299.79/300.49 29038[0:SpR:537.1,545.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),w))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1)),v,y),x)))*.
% 299.79/300.49 29035[0:SpR:537.1,362.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),v,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.49 29560[0:SpR:534.1,545.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),w))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1)),v,y),x)))*.
% 299.79/300.49 29557[0:SpR:534.1,362.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),v,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.49 30084[0:SpR:536.1,545.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),v,z),y)))*.
% 299.79/300.49 30081[0:SpR:536.1,362.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.49 30640[0:SpR:535.1,545.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),v,z),y)))*.
% 299.79/300.49 30637[0:SpR:535.1,362.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.49 31097[0:SpR:28771.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,v),x)),hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v,w),x)))*.
% 299.79/300.49 31096[0:SpR:28771.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v,w),v_Procs),v_Procs)**.
% 299.79/300.49 31095[0:SpR:28771.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v,w),v_Procs),v_Procs)**.
% 299.79/300.49 31183[0:SpR:28926.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,v),x)),hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v,w),x)))*.
% 299.79/300.49 31182[0:SpR:28926.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v,w),v_Procs),v_Procs)**.
% 299.79/300.49 31181[0:SpR:28926.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v,w),v_Procs),v_Procs)**.
% 299.79/300.49 31376[0:SpL:299.2,449.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y),w,u)* hBOOL(hAPP(w,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y)))* -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w)),t_a)*.
% 299.79/300.49 31516[0:SpL:158.0,473.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Fun_Ocomp(w,x,y,u,z),z,u),x1)))* -> hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,z,y),x1),w,y,u),v)),hAPP(c_Set_Oimage(x,z,y),x1)))*.
% 299.79/300.49 31515[0:SpL:97.1,473.0] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(w),y),v)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,w,x),v),c_Fun_Othe__inv__into(v,u,w,x),x,w),y)),hAPP(c_Set_Oimage(u,w,x),v)))*.
% 299.79/300.49 31750[0:SpL:158.0,389.0] || equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x1)))* c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,x)* -> equal(z,x1).
% 299.79/300.49 32169[0:SSi:32114.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)) c_lessequals(y,x,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)),x,tc_fun(u,tc_bool))*.
% 299.79/300.49 32170[0:SSi:32112.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),v,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y)),v,tc_fun(w,tc_bool))*.
% 299.79/300.49 32381[0:Res:517.1,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),z),v)))* hBOOL(hAPP(hAPP(c_in(v),x1),w))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),z),x1))*.
% 299.79/300.49 32380[0:Res:518.1,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),u),v)))* hBOOL(hAPP(hAPP(c_in(v),x1),w))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),u),x1))*.
% 299.79/300.49 32407[0:SSi:32307.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),u,v)))* hBOOL(hAPP(hAPP(c_in(v),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))* -> hBOOL(hAPP(u,z))*.
% 299.79/300.49 32561[0:Res:517.1,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),z),v)))* hBOOL(hAPP(hAPP(c_in(v),x1),x))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),z),x1))*.
% 299.79/300.49 32560[0:Res:518.1,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),u),v)))* hBOOL(hAPP(hAPP(c_in(v),x1),x))* -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),u),x1))*.
% 299.79/300.49 32585[0:SSi:32485.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),u,v)))* hBOOL(hAPP(hAPP(c_in(v),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)))* -> hBOOL(hAPP(u,z))*.
% 299.79/300.49 32767[0:SpR:35.2,151.2] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(v,x,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(w),y),v))* -> hBOOL(hAPP(hAPP(c_in(w),y),c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool))))* hBOOL(hAPP(hAPP(c_in(w),y),u)).
% 299.79/300.49 33017[0:SpR:584.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(x,v),hAPP(y,v)),z),hAPP(c_Set_Oimage(c_COMBS(x,y,x1,x2,x3),u,z),w)),hAPP(c_Set_Oimage(c_COMBS(x,y,x1,x2,x3),u,z),w))**.
% 299.79/300.49 33016[0:SpR:586.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(x,hAPP(y,v)),z),hAPP(c_Set_Oimage(hAPP(c_COMBB(x,x1,x2,x3),y),u,z),w)),hAPP(c_Set_Oimage(hAPP(c_COMBB(x,x1,x2,x3),y),u,z),w))**.
% 299.79/300.49 33015[0:SpR:585.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(x,v),y),z),hAPP(c_Set_Oimage(hAPP(c_COMBC(x,x1,x2,x3),y),u,z),w)),hAPP(c_Set_Oimage(hAPP(c_COMBC(x,x1,x2,x3),y),u,z),w))**.
% 299.79/300.49 33012[0:SpR:11499.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),v)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z)),u,w),v)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z)),u,w),v))**.
% 299.79/300.49 33008[0:SpR:336.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),u,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),u,x),w))**.
% 299.79/300.49 32957[0:SpR:14526.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v)),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Option_Othe(v),y,tc_fun(z,tc_bool)),u,x),w)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Option_Othe(v),y,tc_fun(z,tc_bool)),u,x),w))**.
% 299.79/300.49 32945[0:SpR:331.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(v,x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),u,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),u,x),w))**.
% 299.79/300.49 32917[0:SpR:353.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(z,w),x)),x1),hAPP(c_Set_Oimage(c_Set_Oinsert(z,w),u,x1),y)),hAPP(c_Set_Oimage(c_Set_Oinsert(z,w),u,x1),y))**.
% 299.79/300.49 32889[0:SpR:475.1,338.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(x,v),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Set_Oimage(x,u,y),w))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Set_Oimage(x,u,y),w)))**.
% 299.79/300.49 32881[0:SpR:475.1,584.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_COMBS(c_Set_Oinsert(hAPP(x,v),y),z,x1,x2,x3),hAPP(c_Set_Oimage(x,u,y),w)),hAPP(hAPP(c_Set_Oimage(x,u,y),w),hAPP(z,hAPP(c_Set_Oimage(x,u,y),w))))*.
% 299.79/300.49 32880[0:SpR:475.1,584.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_COMBS(x,c_Set_Oinsert(hAPP(y,v),z),x1,x2,x3),hAPP(c_Set_Oimage(y,u,z),w)),hAPP(hAPP(x,hAPP(c_Set_Oimage(y,u,z),w)),hAPP(c_Set_Oimage(y,u,z),w)))*.
% 299.79/300.49 32869[0:SpR:475.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oimage(z,v,x1),x)),x2)) -> c_lessequals(hAPP(c_Set_Oimage(z,v,x1),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,c_Set_Oinsert(hAPP(z,w),x1),y,u),u)*.
% 299.79/300.49 32864[0:SpR:475.1,339.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(x,v),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,u,y),w)),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,u,y),w)),z))**.
% 299.79/300.49 32851[0:SpR:475.1,176.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),w)),hAPP(c_Set_Ovimage(c_Set_Oinsert(hAPP(y,v),z),x,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(y,u,z),w),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.79/300.49 33073[0:SpL:317.0,94.1] || c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v,w),x),w,y) c_Fun_Oinj__on(z,hAPP(c_Set_Oinsert(hAPP(u,v),y),hAPP(c_Set_Oimage(u,w,y),x)),y,x1)* -> c_Fun_Oinj__on(c_Fun_Ocomp(z,u,y,x1,w),hAPP(c_Set_Oinsert(v,w),x),w,x1)*.
% 299.79/300.49 33239[0:SpR:32668.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),hAPP(c_Set_Oinsert(v_Procs,x),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),w,x),y)))*.
% 299.79/300.49 33238[0:SpR:32668.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),w,x),v_Procs),v_Procs)**.
% 299.79/300.49 33237[0:SpR:32668.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),w,x),v_Procs),v_Procs)**.
% 299.79/300.49 34375[0:SpL:24914.0,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname,w),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)),t_a)* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.79/300.49 34143[0:SpR:24914.0,11177.1] || equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),tc_Com_Opname,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v_x)).
% 299.79/300.49 34082[0:SpR:24914.0,23789.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),v_x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),tc_Com_Opname,w),hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),v_x)),tc_bool)*.
% 299.79/300.49 34081[0:SpR:24914.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,u,x),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,u,x),v_x))))* -> equal(hAPP(c_Set_Oinsert(hAPP(w,v),x),hAPP(c_Set_Oimage(w,u,x),v_x)),hAPP(c_Set_Oimage(w,u,x),v_x)).
% 299.79/300.49 34076[0:SpR:24914.0,181.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x))))* equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.49 34037[0:SpR:24914.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))),x))* c_Fun_Oinj__on(v,x,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,v,u,y),hAPP(v,v_x)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x)))*.
% 299.79/300.49 34036[0:SpR:24914.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))),x))* c_Fun_Oinj__on(v,x,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,v,u,y),hAPP(v,v_x)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x)))*.
% 299.79/300.49 34663[0:SpL:55.1,208.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,w),x),y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),v),y)) hBOOL(hAPP(hAPP(c_in(w),v),u)) c_lessequals(u,c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)).
% 299.79/300.49 34632[0:SpR:55.1,10931.1] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) c_Hoare__Mirabelle_Ohoare__valids(w,c_HOL_Ominus__class_Ominus(x,v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(t_a)),x),v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,c_HOL_Ominus__class_Ominus(x,v,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)))))*.
% 299.79/300.49 34739[0:SpR:34428.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,x),u,w),v)),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,x),u,w),v))**.
% 299.79/300.49 35055[0:SpR:28755.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),y,z),hAPP(c_Set_Oinsert(v_Procs,y),x1)),hAPP(c_Set_Oinsert(v_Procs,z),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),y,z),x1)))*.
% 299.79/300.49 35054[0:SpR:28755.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,z) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),y,z),v_Procs),v_Procs)**.
% 299.79/300.49 35053[0:SpR:28755.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),y,z),v_Procs),v_Procs)**.
% 299.79/300.49 35144[0:SpR:28910.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),y,z),hAPP(c_Set_Oinsert(v_Procs,y),x1)),hAPP(c_Set_Oinsert(v_Procs,z),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),y,z),x1)))*.
% 299.79/300.49 35143[0:SpR:28910.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,z) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),y,z),v_Procs),v_Procs)**.
% 299.79/300.49 35142[0:SpR:28910.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),y,z),v_Procs),v_Procs)**.
% 299.79/300.49 35369[0:SpR:14216.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),v,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),v,tc_fun(x1,tc_bool))))*.
% 299.79/300.49 35305[0:SpR:25.1,410.0] class_HOL_Ouminus(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,v),w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,u)),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(x,v_x),u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,u)),v,tc_fun(y,tc_bool))))*.
% 299.79/300.49 35287[0:SpR:653.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,w),w,tc_Com_Opname),u,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,w),w,tc_Com_Opname),u,tc_fun(x,tc_bool))))*.
% 299.79/300.49 35284[0:SpR:445.1,410.0] || -> equal(u,v) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,w),x),c_Fun_Ofun__upd(y,v,z,x1,x2),w,tc_fun(x3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x3,tc_bool)),hAPP(y,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Fun_Ofun__upd(y,v,z,x1,x2),w,tc_fun(x3,tc_bool))))*.
% 299.79/300.49 35181[0:SpR:410.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),x)),y,v,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,tc_fun(z,tc_bool)))))*.
% 299.79/300.49 35642[0:SpR:21893.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_COMBB(y,w,tc_fun(z,tc_bool),v),u),v,tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,w),v_x),y,w,tc_fun(z,tc_bool)))**.
% 299.79/300.49 35641[0:SpR:21267.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),hAPP(c_COMBB(y,w,tc_fun(z,tc_bool),v),u),v,tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,w),v_x),y,w,tc_fun(z,tc_bool)))**.
% 299.79/300.49 35620[0:SpR:89.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,hAPP(c_COMBB(hAPP(c_COMBB(v,w,tc_fun(x,tc_bool),y),z),y,tc_fun(x,tc_bool),x1),x2),x1,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(z,y,w),hAPP(c_Set_Oimage(x2,x1,y),u)),v,w,tc_fun(x,tc_bool)))*.
% 299.79/300.49 35618[0:SpR:89.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oimage(w,x,v),y)),z,v,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(z,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_COMBB(z,v,tc_fun(x1,tc_bool),x),w),x,tc_fun(x1,tc_bool))))*.
% 299.79/300.49 36982[0:Res:84.1,375.1] || c_lessequals(c_HOL_Ominus__class_Ominus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),y,tc_fun(x,tc_bool)),z,tc_fun(x,tc_bool))* hBOOL(hAPP(hAPP(c_in(w),x1),u))* -> c_lessequals(hAPP(v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),tc_fun(x,tc_bool))*.
% 299.79/300.49 37150[0:Res:84.1,471.1] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool)),z,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(v),x1),x))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)))*.
% 299.79/300.49 37131[0:SpL:465.1,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(hAPP(c_Set_Oimage(x,u,y),w),z,tc_fun(y,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),x1),w))* hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Fun_Ofun__upd(x,x1,x2,u,y),v)),z))*.
% 299.79/300.49 37296[0:SpL:353.0,274.0] || equal(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(u,v),y)))* -> hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oinsert(x,v),y)))* equal(w,hAPP(c_Set_Oinsert(x,v),y)).
% 299.79/300.49 39185[0:SpR:533.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),z,u),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))*.
% 299.79/300.49 40454[0:SpL:584.0,529.0] || c_Hoare__Mirabelle_Otriple__valid(u,hAPP(c_COMBS(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x,y,z,x1),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x2))),v)* -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x2)),hAPP(x,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x2)))),v)*.
% 299.79/300.49 40703[0:SpR:584.0,530.1] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),hAPP(y,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x)))),v)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(c_COMBS(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),y,z,x1,x2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v)*.
% 299.79/300.49 40935[0:Res:468.0,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,w,x,y,z)))* -> equal(hAPP(c_Set_Oimage(w,y,z),v),hAPP(c_Set_Oimage(x,y,z),v)) hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,x1,u,y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),x1)))*.
% 299.79/300.49 40889[0:Res:474.0,479.1] || hBOOL(hAPP(u,hAPP(v,w)))* -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(v,y,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),z,u,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,y,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),z)))*.
% 299.79/300.49 40866[0:SpL:24914.0,479.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(v),tc_Com_Opname,w),hAPP(c_in(v),v_x))))* hBOOL(hAPP(hAPP(c_in(v),v_x),x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,y,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))*.
% 299.79/300.49 41216[0:Res:468.0,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,w,x,y,z)))* -> equal(hAPP(c_Set_Oimage(w,y,z),v),hAPP(c_Set_Oimage(x,y,z),v)) hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,v,u,y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),x1),v)))*.
% 299.79/300.49 41170[0:Res:474.0,478.1] || hBOOL(hAPP(u,hAPP(v,w)))* -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oimage(v,z,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),u,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(v,z,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))))*.
% 299.79/300.49 41147[0:SpL:24914.0,478.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(v),tc_Com_Opname,w),hAPP(c_in(v),v_x))))* hBOOL(hAPP(hAPP(c_in(v),v_x),x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,x,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x)))*.
% 299.79/300.49 41396[0:SpL:24914.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_in(v),w),v_x)),x)) hBOOL(hAPP(hAPP(c_in(v),w),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(v),w),tc_Com_Opname,y),u,tc_fun(v,tc_bool))))*.
% 299.79/300.49 41332[0:SpL:329.1,275.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(x),v),y))* hBOOL(hAPP(hAPP(c_in(z),x1),v))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,tc_fun(z,tc_bool))))*.
% 299.79/300.49 41331[0:SpL:328.1,275.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(x),u),y))* hBOOL(hAPP(hAPP(c_in(z),x1),v)) -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,tc_fun(z,tc_bool))))*.
% 299.79/300.49 41326[0:SpL:538.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),v),x1)))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),u,tc_fun(x,tc_bool))))*.
% 299.79/300.49 41642[0:SpL:105.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(w,v,x),y,u),z)))* c_Fun_Oinj__on(c_Set_Ovimage(w,v,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,u)* -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),z)).
% 299.79/300.49 41634[0:SpL:38.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(w,v,x),y,u),z)))* c_Fun_Oinj__on(c_Set_Ovimage(w,v,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,u)* -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),z)).
% 299.79/300.49 41633[0:SpL:321.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oimage(w,x,v),y,u),z)))* c_Fun_Oinj__on(c_Set_Oimage(w,x,v),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,u)* -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),z)).
% 299.79/300.49 41594[0:SpL:87.1,284.0] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),y)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,v)* -> hBOOL(hAPP(hAPP(c_in(x),c_HOL_Ouminus__class_Ouminus(w,u)),y)).
% 299.79/300.49 41560[0:SpL:15476.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),w,u),x)))* c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u)* -> hBOOL(hAPP(hAPP(c_in(w),v_x),x)).
% 299.79/300.49 41520[0:SpL:158.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,x,y,u,z),z,u),x1)))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,u)* -> hBOOL(hAPP(hAPP(c_in(y),w),hAPP(c_Set_Oimage(x,z,y),x1)))*.
% 299.79/300.49 41517[0:SpL:317.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oinsert(hAPP(v,x),u),hAPP(c_Set_Oimage(v,y,u),z))))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,u)* -> hBOOL(hAPP(hAPP(c_in(y),w),hAPP(c_Set_Oinsert(x,y),z)))*.
% 299.79/300.49 41717[0:SpL:24914.0,494.1] || hBOOL(hAPP(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_Com_Opname,u),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_x)),v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v_x),y),z),t_a)* c_Natural_Oevaln(y,w,x,x1)* -> hBOOL(hAPP(hAPP(z,v),x1))*.
% 299.79/300.49 41853[0:Res:8369.1,199.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool)),u,v,w))),y))* hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool)),z))*.
% 299.79/300.49 41851[0:Res:10930.1,199.0] || equal(hAPP(c_in(u),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Set_Oinsert(y,u),v_x),w,v,x))),v_Procs)** c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,u),v_x),z))*.
% 299.79/300.49 41850[7:Res:29397.1,199.0] || equal(hAPP(c_in(u),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Set_Oinsert(y,u),v_x),w,v,x))),v_x)** c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,u),v_x),z))*.
% 299.79/300.49 41866[0:Rew:586.0,41826.2] || hBOOL(hAPP(u,hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,y),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_COMBB(u,z,x1,x2),v),x,w,y)))))* c_Fun_Oinj__on(x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,y) -> hBOOL(hAPP(u,hAPP(v,x3)))*.
% 299.79/300.49 41867[0:Rew:585.0,41825.2] || hBOOL(hAPP(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_COMBC(u,y,z,x1),x2),w,v,x))),x2))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(hAPP(u,x3),x2))*.
% 299.79/300.49 41974[0:SpR:158.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(c_Set_Oimage(u,w,x),x1),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(u,w,x),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(v,y,w),z),x1,tc_fun(w,tc_bool))),tc_fun(x,tc_bool))*.
% 299.79/300.49 41971[0:SpR:317.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),y)),hAPP(c_Set_Oimage(u,x,w),z),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,x,w),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,x),y),z,tc_fun(x,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.49 41959[0:SpR:158.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,y,v,w,z),z,w),x1),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oimage(y,z,v),x1),tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.49 41956[0:SpR:317.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oinsert(hAPP(u,y),w),hAPP(c_Set_Oimage(u,v,w),z)),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,v),z),tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.49 42014[0:Res:37962.1,199.0] || hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x,y,z,x1),v,u,w)))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x,y,z,x1),x2))*.
% 299.79/300.49 42506[0:SpL:12944.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_Set_Oinsert(w,x),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),y,z)),x1,x2)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Set_Oimage(u,x1,x2),v),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(w,x),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),y,z)),x1,x2),v)).
% 299.79/300.49 42500[0:SpL:11473.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),y,z)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Set_Oimage(u,y,z),v),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),y,z),v)).
% 299.79/300.49 42496[0:SpL:23682.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,x)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,x))** -> equal(hAPP(c_Set_Oimage(u,w,x),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,x),v)).
% 299.79/300.49 42484[0:SpL:17045.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x,tc_fun(y,tc_bool)),z,x1)),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(c_Set_Oimage(u,z,x1),v),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x,tc_fun(y,tc_bool)),z,x1),v)).
% 299.79/300.49 42465[0:SpL:12944.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Set_Oinsert(w,x),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),y,z)),u,x1,x2)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(w,x),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),y,z)),x1,x2),v),hAPP(c_Set_Oimage(u,x1,x2),v)).
% 299.79/300.49 42459[0:SpL:11473.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u,y,z)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),y,z),v),hAPP(c_Set_Oimage(u,y,z),v)).
% 299.79/300.49 42455[0:SpL:23682.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,w,x)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,w,x))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,x),v),hAPP(c_Set_Oimage(u,w,x),v)).
% 299.79/300.49 42443[0:SpL:17045.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x,tc_fun(y,tc_bool)),u,z,x1)),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x,tc_fun(y,tc_bool)),z,x1),v),hAPP(c_Set_Oimage(u,z,x1),v)).
% 299.79/300.49 43088[0:SpR:10090.1,486.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool)))**.
% 299.79/300.49 43081[0:SpR:303.1,486.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,tc_fun(x,tc_bool)))**.
% 299.79/300.49 43065[0:SpR:11176.1,486.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),w),x))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(y,tc_bool)))**.
% 299.79/300.49 43061[0:SpR:11177.1,486.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v,tc_fun(x,tc_bool)))**.
% 299.79/300.49 43010[0:SpR:300.1,486.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,tc_fun(y,tc_bool)))**.
% 299.79/300.49 43005[0:SpR:3586.1,486.1] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v,u),w,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v,u),w,tc_fun(y,tc_bool)))**.
% 299.79/300.49 43004[7:SpR:27278.1,486.1] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(hAPP(c_in(w),v_x),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v,u),w,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(v,u),w,tc_fun(y,tc_bool)))**.
% 299.79/300.49 42973[0:SpR:9493.1,486.1] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(hAPP(c_in(v),u),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,t_a),v,tc_fun(x,tc_bool)))**.
% 299.79/300.49 42971[0:SpR:8498.1,486.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),u),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(z,v),w,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(z,v),w,tc_fun(y,tc_bool)))**.
% 299.79/300.49 43588[0:Rew:507.0,43538.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x))),y)),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),y)))**.
% 299.79/300.49 43590[0:Rew:507.0,43523.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,y),hAPP(c_Set_Oimage(u,v,w),v_x)))),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)))**.
% 299.79/300.49 43750[0:SpR:196.1,162.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x)),y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Ovimage(u,v,w),y)))**.
% 299.79/300.49 43735[0:SpR:196.1,162.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(u,v,w),y))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x)),y))**.
% 299.79/300.49 43819[0:Rew:162.0,43758.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Ovimage(u,v,w),v_x))),y)),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),y)))**.
% 299.79/300.49 43820[0:Rew:162.0,43743.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(u,v,w),tc_Com_Opname,y),hAPP(c_Set_Ovimage(u,v,w),v_x)))),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))**.
% 299.79/300.49 44135[0:SpR:8415.2,232.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(v_x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.49 44356[0:Res:31533.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))* equal(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,w,tc_Com_Opname,x),hAPP(w,v_x))),hAPP(v,u))* c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,y)* -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,w,tc_Com_Opname,x),hAPP(w,v_x)),u).
% 299.79/300.49 44355[0:Res:27443.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))* equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(w,x,y),w,tc_Com_Opname,z)),hAPP(v,u))* c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,x1)* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(w,x,y),w,tc_Com_Opname,z),u).
% 299.79/300.49 44354[0:Res:28312.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))* equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w)),hAPP(v,u))* c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,x)* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w),u).
% 299.79/300.49 44352[0:Res:27383.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))* equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,w,c_COMBK(w,x,y),tc_Com_Opname,z)),hAPP(v,u))* c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,x1)* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,w,c_COMBK(w,x,y),tc_Com_Opname,z),u).
% 299.79/300.49 44351[0:Res:28009.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))* equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w)),hAPP(v,u))* c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,x)* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),u).
% 299.79/300.49 44336[0:Res:23961.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_Procs)))* equal(hAPP(w,v_x),hAPP(w,v))* c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_Procs),u,x)* -> equal(v_x,v).
% 299.79/300.49 44333[0:Res:19441.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs))))* equal(hAPP(x,v_x),hAPP(x,u))* c_Fun_Oinj__on(x,hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),tc_Com_Opname,y)* -> equal(v_x,u).
% 299.79/300.49 44332[0:Res:19452.0,268.0] || hBOOL(hAPP(hAPP(c_in(t_a),u),hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))))* equal(hAPP(w,v_x),hAPP(w,u))* c_Fun_Oinj__on(w,hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),t_a,x)* -> equal(v_x,u).
% 299.79/300.49 44318[0:Res:9067.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(x,u),y))))* equal(hAPP(z,x),hAPP(z,v))* c_Fun_Oinj__on(z,hAPP(c_Set_Oinsert(w,u),hAPP(c_Set_Oinsert(x,u),y)),u,x1)* -> equal(x,v).
% 299.79/300.49 44311[0:Res:9071.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(w,u),tc_Com_Opname,tc_fun(u,tc_bool))))* equal(hAPP(x,w),hAPP(x,v))* c_Fun_Oinj__on(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(w,u),tc_Com_Opname,tc_fun(u,tc_bool)),u,y)* -> equal(w,v).
% 299.79/300.49 44305[0:Res:1157.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_COMBK(w,x,y),tc_Com_Opname,u),v_Procs)))* equal(hAPP(z,w),hAPP(z,v))* c_Fun_Oinj__on(z,hAPP(c_Set_Oimage(c_COMBK(w,x,y),tc_Com_Opname,u),v_Procs),u,x1)* -> equal(w,v).
% 299.79/300.49 44304[0:Res:254.1,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(u),x),hAPP(c_Set_Oinsert(y,u),w)))* equal(hAPP(z,v),hAPP(z,x))* c_Fun_Oinj__on(z,hAPP(c_Set_Oinsert(y,u),w),u,x1)* -> equal(v,x).
% 299.79/300.49 44275[0:SpL:8415.2,268.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,v)) hBOOL(hAPP(hAPP(c_in(u),w),v))* equal(hAPP(x,v_x),hAPP(x,w))* c_Fun_Oinj__on(x,v,u,y)* -> equal(v_x,w).
% 299.79/300.49 44394[0:SpR:8415.2,90.0] || equal(v_Procs,v_x) equal(c_COMBB(c_Set_Oimage(u,v,w),tc_fun(v,tc_bool),tc_fun(w,tc_bool),x),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v_x,x,tc_fun(v,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v_x,x,tc_fun(w,tc_bool)))**.
% 299.79/300.49 44448[0:SpR:8415.2,30.0] || equal(v_Procs,v_x) equal(c_COMBB(c_Set_Ovimage(u,v,w),tc_fun(w,tc_bool),tc_fun(v,tc_bool),x),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v_x,x,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v_x,x,tc_fun(v,tc_bool)))**.
% 299.79/300.49 44582[0:SpR:8415.2,240.2] class_Complete__Lattice_Ocomplete__lattice(u) || equal(v_Procs,v_x) equal(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** c_Finite__Set_Ofinite(w,v) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,v_x,v,u)),c_Finite__Set_Ofold(v_x,x,w,v,u))**.
% 299.79/300.49 45119[0:Res:326.2,430.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,y,tc_fun(w,tc_bool))* c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),z,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),z,tc_fun(w,tc_bool))*.
% 299.79/300.49 45023[0:SpR:542.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),tc_fun(w,tc_bool))*.
% 299.79/300.49 45135[0:SSi:45128.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,y,tc_fun(w,tc_bool))* c_lessequals(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),tc_fun(w,tc_bool))* -> c_lessequals(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),tc_fun(w,tc_bool))*.
% 299.79/300.49 45496[0:SpL:584.0,237.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(v,w,u),x,y,z),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u) -> equal(hAPP(v,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,u,w)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.79/300.49 45616[0:SpL:323.0,327.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.49 45586[0:SpR:323.0,329.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),v,w,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v,w,tc_fun(x,tc_bool))).
% 299.79/300.49 45581[0:SpR:323.0,328.1] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),u),v,w,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v,w,tc_fun(x,tc_bool))).
% 299.79/300.49 45555[0:SpR:323.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),y,tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),x1),w,x,tc_fun(u,tc_bool)),tc_bool)*.
% 299.79/300.49 45530[0:SpR:323.0,5875.0] || -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool))),x1,x2,x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))))*.
% 299.79/300.49 45848[0:SpL:104.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)))* hBOOL(hAPP(hAPP(c_in(w),y),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))))* -> hBOOL(hAPP(u,y))*.
% 299.79/300.49 46204[4:MRR:46110.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(w,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),x),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),x)))*.
% 299.79/300.49 46511[4:MRR:46428.2,6340.0] || equal(v_Procs,v_x) equal(hAPP(c_in(u),v),c_Set_Oinsert(v_x,tc_Com_Opname))** -> hBOOL(hAPP(w,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v_x),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v_x)))*.
% 299.79/300.49 46965[0:MRR:46926.0,208.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)).
% 299.79/300.49 47191[0:Res:364.1,242.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(w),v),u)) -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(y,w),x)),tc_fun(w,tc_bool))*.
% 299.79/300.49 47389[0:SpL:3229.1,485.1] || equal(u,c_in(v)) hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,w,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,w,v)),x))*.
% 299.79/300.49 47329[0:SpL:3229.1,485.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,y))* hBOOL(hAPP(hAPP(c_in(v),y),hAPP(u,v_x)))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,x,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,v)),w))*.
% 299.79/300.49 47323[0:SpL:3229.1,485.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) hBOOL(hAPP(w,x))* hBOOL(hAPP(hAPP(c_in(v),x),hAPP(hAPP(u,v_x),y)))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,w,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,w,v)),v_x))*.
% 299.79/300.49 47620[0:SpL:3229.1,484.1] || equal(u,c_in(v)) hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,w,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,w,v)),y))*.
% 299.79/300.49 47560[0:SpL:3229.1,484.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,y))* hBOOL(hAPP(hAPP(c_in(v),y),hAPP(u,v_x)))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,x,v)),v_x))*.
% 299.79/300.49 47554[0:SpL:3229.1,484.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) hBOOL(hAPP(w,x))* hBOOL(hAPP(hAPP(c_in(v),x),hAPP(hAPP(u,v_x),y)))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,w,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,w,v)),y))*.
% 299.79/300.49 47958[0:SpL:3229.1,490.1] || equal(u,c_in(v)) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,w,v)))* hBOOL(hAPP(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,w,v)),y))*.
% 299.79/300.49 47898[0:SpL:3229.1,490.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,x,v)))* hBOOL(hAPP(hAPP(c_in(v),y),hAPP(u,v_x)))* -> hBOOL(hAPP(x,y))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,v)),w))*.
% 299.79/300.49 47892[0:SpL:3229.1,490.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,w,v)))* hBOOL(hAPP(hAPP(c_in(v),y),hAPP(hAPP(u,v_x),x)))* -> hBOOL(hAPP(w,y))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,w,v)),v_x))*.
% 299.79/300.49 48070[0:SpL:3229.1,489.1] || equal(u,c_in(v)) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,w,v)))* hBOOL(hAPP(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,w,v)),y))*.
% 299.79/300.49 48010[0:SpL:3229.1,489.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,v)))* hBOOL(hAPP(hAPP(c_in(v),y),hAPP(u,v_x)))* -> hBOOL(hAPP(x,y))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,x,v)),v_x))*.
% 299.79/300.49 48004[0:SpL:3229.1,489.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,w,v)))* hBOOL(hAPP(hAPP(c_in(v),x),hAPP(hAPP(u,v_x),y)))* -> hBOOL(hAPP(w,x))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,w,v)),y))*.
% 299.79/300.49 48411[0:SpL:23912.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(c_Set_Oinsert(v,w),x),w,u) -> .
% 299.79/300.49 48372[0:SpL:351.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_COMBK(v,w,x),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(x1,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(c_COMBK(v,w,x),hAPP(c_Set_Oinsert(x1,y),z),y,u) -> .
% 299.79/300.49 48370[0:SpL:456.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Option_Othe(w),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(v,w),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Option_Othe(w),hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(v,w),x),y),x,u) -> .
% 299.79/300.49 48347[0:SpL:3229.1,224.0] || equal(u,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),hAPP(c_Set_Oimage(v,x,w),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v_x,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(v,hAPP(c_Set_Oinsert(v_x,x),y),x,w) -> .
% 299.79/300.49 48663[0:SpR:3229.1,197.1] || equal(u,c_Set_Oimage(v,w,x)) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(c_HOL_Ominus__class_Ominus(hAPP(u,v_x),hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),c_HOL_Ominus__class_Ominus(v_x,y,tc_fun(w,tc_bool))))*.
% 299.79/300.49 48648[0:SpR:3229.1,197.1] || equal(u,c_Set_Oimage(v,w,x)) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(v,w,x),y),hAPP(u,v_x),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),c_HOL_Ominus__class_Ominus(y,v_x,tc_fun(w,tc_bool))))*.
% 299.79/300.49 48686[0:SSi:48639.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,t_a) -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oimage(u,v,t_a),w),v_x),hAPP(hAPP(c_Set_Oimage(u,v,t_a),x),v_x),tc_bool),hAPP(hAPP(c_Set_Oimage(u,v,t_a),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool))),v_x))**.
% 299.79/300.49 48988[0:Res:8376.2,483.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_Procs)** -> hBOOL(hAPP(x,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.79/300.49 49194[0:Res:8376.2,239.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Oimage(v,w,u),x),v_Procs) c_lessequals(x,y,tc_fun(w,tc_bool)) c_Fun_Oinj__on(v,x,w,u) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(x,v,w,u),v_x)),y))*.
% 299.79/300.49 49295[0:SpL:584.0,488.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(c_COMBS(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y,z,x1),v))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)),x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,u,w)),v))*.
% 299.79/300.49 49364[0:SpR:49342.1,410.0] || hBOOL(hAPP(u,v_x)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,v),w),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,tc_fun(x,tc_bool))))*.
% 299.79/300.49 49642[0:Res:225.1,469.0] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,w),v),w,x) equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),u,hAPP(u,y),w,x)),hAPP(u,y))**.
% 299.79/300.49 49641[0:Res:225.1,464.0] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,w),v),w,x) equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),hAPP(u,y),u,w,x)),hAPP(u,y))**.
% 299.79/300.49 49707[0:Rew:49662.2,49475.2] || equal(u,v_Procs) c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(u,w),v))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(u,w),v),w,x).
% 299.79/300.49 49712[0:Rew:49662.2,49504.3] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) c_Fun_Oinj__on(u,v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),v_x),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(v_x,w),v))))* c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v_x,w),v),w,x).
% 299.79/300.49 49713[0:Rew:49662.2,49521.1] || c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),w,x),hAPP(c_Set_Oinsert(y,w),v))))* c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(y,w),v),w,x).
% 299.79/300.49 49714[0:Rew:49662.2,49522.1] || c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),w,x),hAPP(c_Set_Oinsert(y,w),v))))* c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(y,w),v),w,x).
% 299.79/300.49 50384[0:SpR:223.1,376.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,z,u,y),u,y),w),tc_fun(y,tc_bool))*.
% 299.79/300.49 51511[0:Res:429.0,195.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,w,y),v),hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,w,y),c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool))))**.
% 299.79/300.49 51627[0:MRR:51527.1,13385.1] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) c_Fun_Oinj__on(w,u,v,x)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(w,v,x),y),hAPP(c_Set_Oimage(w,v,x),z),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(w,v,x),c_HOL_Ominus__class_Ominus(y,z,tc_fun(v,tc_bool))))**.
% 299.79/300.49 51856[4:Res:40792.1,199.0] || c_lessequals(v_x,hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Set_Oinsert(y,z),u),w,v,x))),tc_bool)* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,z),u),x1))*.
% 299.79/300.49 52819[0:SpR:24019.2,486.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,u,tc_fun(w,tc_bool)))**.
% 299.79/300.49 53783[0:Res:7226.0,479.1] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(c_Option_Othe(x),y,w),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),z,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_Option_Othe(x),y,w),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),z)))*.
% 299.79/300.49 53782[0:Res:7226.0,478.1] || hBOOL(hAPP(u,v))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oimage(c_Option_Othe(y),z,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(c_Option_Othe(y),z,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))))*.
% 299.79/300.49 53800[0:SpR:53771.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Option_Othe(x),v,y)),z))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Option_Othe(x),u,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Option_Othe(x),u,tc_fun(x1,tc_bool)))**.
% 299.79/300.49 53831[0:SpR:53772.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(w),x,v,y)),z))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Option_Othe(w),u,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Option_Othe(w),u,tc_fun(x1,tc_bool)))**.
% 299.79/300.49 56120[0:SpR:30368.2,410.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,tc_fun(y,tc_bool))))*.
% 299.79/300.49 56561[0:SpR:30928.2,410.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,tc_fun(y,tc_bool))))*.
% 299.79/300.49 58685[0:SpL:354.2,15629.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,v,w,y) hBOOL(u) -> hBOOL(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z)))*.
% 299.79/300.49 59193[0:SpL:354.2,15857.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,v,w,y) hBOOL(u) -> hBOOL(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),x1)))*.
% 299.79/300.49 59937[0:SSi:59865.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool))) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.79/300.49 60461[0:SpR:5882.1,71.2] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) c_Fun_Oinj__on(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),w,v,x2) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v,x2),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.49 60460[0:SpR:5882.1,373.2] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) c_Fun_Oinj__on(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),w,v,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v,x2),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(u))**.
% 299.79/300.49 62187[0:Res:23754.0,479.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),v_Procs),w,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),v_Procs)),w)))*.
% 299.79/300.49 62186[0:Res:23754.0,478.1] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),v_Procs),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),v_Procs))))*.
% 299.79/300.49 64254[0:SpL:646.1,275.1] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),x)) hBOOL(hAPP(hAPP(c_in(y),z),v_x)) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,tc_fun(y,tc_bool))))*.
% 299.79/300.49 64247[0:SpR:131.0,646.1] || c_Fun_Oinj__on(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs,tc_Com_Opname,z) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))),v_x)**.
% 299.79/300.49 64246[0:SpR:158.0,646.1] || c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs,tc_Com_Opname,z) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))),v_x)**.
% 299.79/300.49 64219[0:SpR:523.1,646.1] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))),v_x)**.
% 299.79/300.49 64218[0:SpR:460.1,646.1] || class_Lattices_Olattice(t_b) c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_Procs,tc_Com_Opname,u) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),v_x)**.
% 299.79/300.49 64162[0:SpR:646.1,475.1] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),x)) -> equal(hAPP(c_Set_Oinsert(v_x,y),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,y),x)),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,y),x))**.
% 299.79/300.49 64161[0:SpR:646.1,71.2] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),x)) c_Fun_Oinj__on(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),x,w,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,y),v_x),hAPP(u,v_x))**.
% 299.79/300.49 64160[0:SpR:646.1,373.2] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),x)) c_Fun_Oinj__on(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),x,w,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,y),v_x),hAPP(u,v_x))**.
% 299.79/300.49 64422[0:SpL:645.1,275.1] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),x)) hBOOL(hAPP(hAPP(c_in(y),z),v_x)) -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,tc_fun(y,tc_bool))))*.
% 299.79/300.49 64414[0:SpR:131.0,645.1] || c_Fun_Oinj__on(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs,tc_Com_Opname,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x))),v_x)**.
% 299.79/300.49 64413[0:SpR:158.0,645.1] || c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),v_Procs,tc_Com_Opname,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x))),v_x)**.
% 299.79/300.49 64386[0:SpR:523.1,645.1] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))),v_x)**.
% 299.79/300.49 64385[0:SpR:460.1,645.1] || class_Lattices_Olattice(t_b) c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v_Procs,tc_Com_Opname,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),v_x)**.
% 299.79/300.49 64329[0:SpR:645.1,475.1] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),x)) -> equal(hAPP(c_Set_Oinsert(v_x,y),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,y),x)),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,y),x))**.
% 299.79/300.49 64328[0:SpR:645.1,71.2] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),x)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),x,w,y) -> equal(hAPP(c_Fun_Othe__inv__into(x,c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,y),v_x),hAPP(u,v_x))**.
% 299.79/300.49 64327[0:SpR:645.1,373.2] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),x)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),x,w,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,y),v_x),hAPP(u,v_x))**.
% 299.79/300.49 64482[0:Res:662.1,477.0] || hBOOL(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(y,tc_bool)),v)))* hBOOL(hAPP(hAPP(c_in(v),z),w))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(y,tc_bool)),z))*.
% 299.79/300.49 64481[0:Res:662.1,476.0] || hBOOL(hAPP(hAPP(u,v_x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(y,tc_bool)),v)))* hBOOL(hAPP(hAPP(c_in(v),z),x))* -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(y,tc_bool)),z))*.
% 299.79/300.49 64600[0:SpR:26782.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),y)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w,x),y)))*.
% 299.79/300.49 64599[0:SpR:26782.0,99.1] || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w,x),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.49 64598[0:SpR:26782.0,438.1] || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w,x),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.49 66776[0:SpL:1188.2,275.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(u))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.49 66707[0:SpR:1188.2,475.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,x),w))**.
% 299.79/300.49 67532[0:SpL:1189.2,275.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(u))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.49 67462[0:SpR:1189.2,475.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,x),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,x),w))**.
% 299.79/300.49 71100[0:Res:7568.0,242.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(w,hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),y))),tc_fun(u,tc_bool))*.
% 299.79/300.49 71310[0:Res:7538.0,242.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(w,hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(c_Set_Oinsert(y,u),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))),tc_fun(u,tc_bool))*.
% 299.79/300.49 72125[0:Res:7830.0,242.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(w,hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))),tc_fun(u,tc_bool))*.
% 299.79/300.49 74374[7:SpL:71835.1,490.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,v,u)))* hBOOL(hAPP(hAPP(c_in(u),x),hAPP(v_x,w)))* -> hBOOL(hAPP(v,x))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,v,u)),v_x))*.
% 299.79/300.49 74372[7:SpL:71835.1,489.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,v,u)))* hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,v,u)),x))*.
% 299.79/300.49 74371[7:SpL:71835.1,490.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,v,u)))* hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w)))* -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,v,u)),x))*.
% 299.79/300.49 74238[7:SpL:71835.1,485.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),w),hAPP(v_x,x)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,v,u)),v_x))*.
% 299.79/300.49 74237[7:SpL:71835.1,484.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),w),hAPP(v_x,x)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,v,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)),x))*.
% 299.79/300.49 74218[7:SpL:71835.1,224.0] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(u,w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v_x,w),x),w,v) -> .
% 299.79/300.49 74166[7:SpL:71835.1,489.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,v,u)))* hBOOL(hAPP(hAPP(c_in(u),w),hAPP(v_x,x)))* -> hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,v,u)),x))*.
% 299.79/300.49 74153[7:SpL:71835.1,485.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,v,u)),w))*.
% 299.79/300.49 74152[7:SpL:71835.1,484.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,v,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)),x))*.
% 299.79/300.49 73947[7:SpR:71835.1,620.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,w,tc_fun(u,tc_bool)),v),v_x,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),hAPP(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,tc_fun(u,tc_bool))))**.
% 299.79/300.49 73912[7:SpR:71835.1,197.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),v_x,tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,v_x,tc_fun(v,tc_bool))))*.
% 299.79/300.49 73707[7:SpR:71835.1,197.1] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(v_x,x,tc_fun(v,tc_bool))))*.
% 299.79/300.49 76172[0:SpL:9915.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Otop__class_Otop(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Set_Ovimage(z,x1,v),x2,x3,x4,x5),u,tc_fun(x,tc_bool))))*.
% 299.79/300.49 76159[0:SpR:9915.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x2),x4)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x3),hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3),x4)))*.
% 299.79/300.49 76158[0:SpR:9915.0,99.1] || c_Fun_Oinj__on(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,x3) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.79/300.49 76157[0:SpR:9915.0,438.1] || c_Fun_Oinj__on(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,x3) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))**.
% 299.79/300.49 76293[0:SpL:10469.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Set_Oimage(z,v,x1),x2,x3,x4,x5),u,tc_fun(x,tc_bool))))*.
% 299.79/300.49 76279[0:SpR:10469.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),x2,x3),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),x2),x4)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x3),hAPP(c_Set_Oimage(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),x2,x3),x4)))*.
% 299.79/300.49 76278[0:SpR:10469.0,99.1] || c_Fun_Oinj__on(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,x3) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),x2,x3),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.49 76277[0:SpR:10469.0,438.1] || c_Fun_Oinj__on(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,x3) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),x2,x3),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.79/300.49 76423[0:SpL:10470.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Obot__class_Obot(tc_bool))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Set_Ovimage(z,x1,v),x2,x3,x4,x5),u,tc_fun(x,tc_bool))))*.
% 299.79/300.49 76409[0:SpR:10470.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x2),x4)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x3),hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3),x4)))*.
% 299.79/300.49 76408[0:SpR:10470.0,99.1] || c_Fun_Oinj__on(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,x3) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.79/300.49 76407[0:SpR:10470.0,438.1] || c_Fun_Oinj__on(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,x3) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x3),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))**.
% 299.79/300.49 77902[0:Res:151.2,5892.0] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),v))* -> hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),w))* hBOOL(hAPP(c_COMBS(c_in(x),c_in(u),y,z,x1),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))))*.
% 299.79/300.49 77742[0:SpL:533.0,5892.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),x))* -> hBOOL(hAPP(c_COMBS(c_in(y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),z,x1,x2),x))*.
% 299.79/300.49 77726[0:SpL:536.1,5892.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))* -> hBOOL(hAPP(c_COMBS(c_in(y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))*.
% 299.79/300.49 77725[0:SpL:535.1,5892.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))* -> hBOOL(hAPP(c_COMBS(c_in(y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)))*.
% 299.79/300.49 78721[4:Res:78665.1,488.1] || equal(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),v_x)** hBOOL(hAPP(y,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,y,u)),w))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,y,u)),x))*.
% 299.79/300.49 79007[0:SpR:131.0,15630.1] || hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z)) -> hBOOL(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(z,x1),x2),x3,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),x1))))*.
% 299.79/300.49 79006[0:SpR:158.0,15630.1] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z)) -> hBOOL(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(z,x1),x2),x3,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),x1))))*.
% 299.79/300.49 79227[0:SpR:131.0,15858.1] || hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z)) -> hBOOL(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,hAPP(c_Set_Oinsert(z,x2),x3),c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),x2))))*.
% 299.79/300.49 79226[0:SpR:158.0,15858.1] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z)) -> hBOOL(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,hAPP(c_Set_Oinsert(z,x2),x3),c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),x2))))*.
% 299.79/300.49 80278[0:SpL:21268.0,280.1] || hBOOL(hAPP(hAPP(u,v),w)) hBOOL(hAPP(hAPP(c_in(x),v),y)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(x),v),hAPP(hAPP(c_in(x),v),y),z,x1),u,x,tc_fun(x2,tc_bool)),w))*.
% 299.79/300.49 80224[0:SpL:21268.0,513.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),z),x1))* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),x2,x3),x1)*.
% 299.79/300.49 80197[0:SpL:21268.0,529.0] || c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),v) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Com_Obody,hAPP(c_Com_Obody,x),z,x1))),y),v)*.
% 299.79/300.49 80139[0:SpL:21268.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(w,x),v,y)),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),hAPP(w,x)))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,w,u,tc_fun(x1,tc_bool))))*.
% 299.79/300.49 79839[0:SpR:317.0,21268.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(u,y),w),hAPP(c_Set_Oimage(u,v,w),z)),x,x1)),hAPP(c_Set_Oinsert(hAPP(u,y),w),hAPP(c_Set_Oimage(u,v,w),z)))**.
% 299.79/300.49 79661[0:SpR:21268.0,530.1] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Com_Obody,hAPP(c_Com_Obody,y),x,z))),x1),v)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,y))),x1),v).
% 299.79/300.49 81473[0:SpL:21894.0,280.1] || hBOOL(hAPP(hAPP(u,v),w)) hBOOL(hAPP(hAPP(c_in(x),v),y)) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_in(x),v),y),hAPP(c_in(x),v),z,x1),u,x,tc_fun(x2,tc_bool)),w))*.
% 299.79/300.49 81419[0:SpL:21894.0,513.0] || equal(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),z),x1))* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),x2,x3),x1)*.
% 299.79/300.49 81392[0:SpL:21894.0,529.0] || c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),v) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Com_Obody,x),c_Com_Obody,z,x1))),y),v)*.
% 299.79/300.49 81334[0:SpL:21894.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(w,x),w,v,y)),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),hAPP(w,x)))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,w,u,tc_fun(x1,tc_bool))))*.
% 299.79/300.49 81033[0:SpR:317.0,21894.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(hAPP(u,y),w),hAPP(c_Set_Oimage(u,v,w),z)),c_Set_Oimage(u,v,w),x,x1)),hAPP(c_Set_Oinsert(hAPP(u,y),w),hAPP(c_Set_Oimage(u,v,w),z)))**.
% 299.79/300.49 80855[0:SpR:21894.0,530.1] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Com_Obody,y),c_Com_Obody,x,z))),x1),v)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,y))),x1),v).
% 299.79/300.49 81868[0:SpR:532.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)),u)*.
% 299.79/300.49 81867[0:SpR:533.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),z,x1,x2),y),u)*.
% 299.79/300.49 81852[0:SpR:180.2,5879.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Oupper__semilattice(v) || c_Finite__Set_Ofinite(w,u) -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(y,u),w),u,u),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z,x1,x2),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,w,u,u)),v)*.
% 299.79/300.49 82340[0:SpR:532.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)),u)*.
% 299.79/300.49 82339[0:SpR:533.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),z,x1,x2),y),u)*.
% 299.79/300.49 82324[0:SpR:180.2,5880.1] class_Lattices_Oupper__semilattice(u) class_Lattices_Olattice(v) || c_Finite__Set_Ofinite(w,u) -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(y,u),w),u,u),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z,x1,x2),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,w,u,u)),v)*.
% 299.79/300.49 83120[0:SpL:5924.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(hAPP(z,v),x1)))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(z,c_COMBK(x1,x2,x3),x4,x5,x6),u,tc_fun(x,tc_bool))))*.
% 299.79/300.49 83057[0:SpR:5924.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,x3),hAPP(c_Set_Oinsert(x4,x2),x5)),hAPP(c_Set_Oinsert(hAPP(hAPP(u,x4),v),x3),hAPP(c_Set_Oimage(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,x3),x5)))*.
% 299.79/300.49 83056[0:SpR:5924.0,99.1] || c_Fun_Oinj__on(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,x3) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,x3),hAPP(hAPP(u,x4),v)),x4)**.
% 299.79/300.49 83055[0:SpR:5924.0,438.1] || c_Fun_Oinj__on(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,x3) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,x3),hAPP(hAPP(u,x4),v)),x4)**.
% 299.79/300.49 83439[0:SpL:5961.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(z,hAPP(x1,v))))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_COMBK(z,x2,x3),x1,x4,x5,x6),u,tc_fun(x,tc_bool))))*.
% 299.79/300.49 83382[0:SpR:5961.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2,x3),hAPP(c_Set_Oinsert(x4,x2),x5)),hAPP(c_Set_Oinsert(hAPP(u,hAPP(x,x4)),x3),hAPP(c_Set_Oimage(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2,x3),x5)))*.
% 299.79/300.49 83381[0:SpR:5961.0,99.1] || c_Fun_Oinj__on(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,x3) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2,x3),hAPP(u,hAPP(x,x4))),x4)**.
% 299.79/300.49 83380[0:SpR:5961.0,438.1] || c_Fun_Oinj__on(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,x3) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2,x3),hAPP(u,hAPP(x,x4))),x4)**.
% 299.79/300.49 83881[0:SpL:5899.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_COMBS(z,x1,x2,x3,x4),v)))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(z,x1,x5,x6,x7),u,tc_fun(x,tc_bool))))*.
% 299.79/300.49 88849[0:SpR:354.2,14196.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x1),hAPP(c_Set_Oinsert(u,x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),hAPP(c_Set_Oimage(x,w,y),u)))*.
% 299.79/300.49 89594[7:SpL:78590.1,406.0] || equal(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Set_Oinsert(v_x,t_a)) equal(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Set_Oinsert(w,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))))* -> equal(v_x,v) equal(v_x,w).
% 299.79/300.49 89480[7:SpR:78590.1,21894.0] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v),c_Set_Oinsert(v_x,t_a),u,w),c_Set_Oinsert(v_x,t_a))** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v),c_Set_Oinsert(v_x,t_a),u,w),hAPP(c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.49 89478[7:SpR:78590.1,21268.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v),u,w),c_Set_Oinsert(v_x,t_a))** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v),u,w),hAPP(c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.49 89380[7:SpR:78590.1,450.0] || equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oinsert(v_x,t_a),u,v,w),c_Set_Oinsert(v_x,t_a)) -> hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oinsert(v_x,t_a),u,v,w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Set_Oinsert(v_x,t_a),u,v,w)))* c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Set_Oinsert(v_x,t_a)),v),u),t_a).
% 299.79/300.49 89798[0:SpR:26183.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Fun_Ofun__upd(w,x,hAPP(c_Set_Oinsert(y,u),v),z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x1,x2,z),x,hAPP(c_Set_Oinsert(y,u),v),z,x2))*.
% 299.79/300.49 90385[4:SpL:78660.1,406.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x),v_x)** equal(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Set_Oinsert(w,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))))* -> equal(v_x,v) equal(v_x,w).
% 299.79/300.49 90271[4:SpR:78660.1,21894.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v),c_Set_Oinsert(v_x,t_a),u,w),v_x),v_x)** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v),c_Set_Oinsert(v_x,t_a),u,w),hAPP(c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.49 90269[4:SpR:78660.1,21268.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v),u,w),v_x),v_x)** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v),u,w),hAPP(c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.49 90170[4:SpR:78660.1,450.0] || equal(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oinsert(v_x,t_a),u,v,w),v_x),v_x) -> hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oinsert(v_x,t_a),u,v,w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Set_Oinsert(v_x,t_a),u,v,w)))* c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Set_Oinsert(v_x,t_a)),v),u),t_a).
% 299.79/300.49 90768[0:SpL:66.0,26480.0] || c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)).
% 299.79/300.49 92826[0:SpR:354.2,5876.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> c_lessequals(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),x1,x2,x3),hAPP(c_Set_Oimage(x,w,y),u)),tc_fun(z,tc_bool))*.
% 299.79/300.49 12680[0:Res:687.1,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_Com_Opname)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_Com_Opname)))*.
% 299.79/300.49 12679[0:Res:686.1,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_Com_Opname)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_Com_Opname)))*.
% 299.79/300.49 19359[0:SSi:19332.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool),tc_bool)* c_lessequals(v,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool),tc_bool)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v),w,tc_bool),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v)).
% 299.79/300.49 20851[0:SpR:317.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oimage(u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(z,v),x1),x),x2)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(hAPP(u,z),w),hAPP(c_Set_Oimage(u,v,w),x1)),y),hAPP(c_Set_Oimage(c_Set_Oimage(u,v,w),x,y),x2)))*.
% 299.79/300.49 20850[0:SpR:317.0,99.1] || c_Fun_Oinj__on(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(u,z),w),hAPP(c_Set_Oimage(u,v,w),x1))),hAPP(c_Set_Oinsert(z,v),x1))**.
% 299.79/300.49 20849[0:SpR:317.0,438.1] || c_Fun_Oinj__on(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(u,z),w),hAPP(c_Set_Oimage(u,v,w),x1))),hAPP(c_Set_Oinsert(z,v),x1))**.
% 299.79/300.49 21625[0:SpL:21267.0,298.1] class_Lattices_Oupper__semilattice(u) || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)) -> c_lessequals(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,w),u)*.
% 299.79/300.49 21401[0:SpR:21267.0,297.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,w),u)* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)).
% 299.79/300.49 22253[0:SpL:21893.0,298.1] class_Lattices_Oupper__semilattice(u) || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)) -> c_lessequals(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),u)*.
% 299.79/300.49 22027[0:SpR:21893.0,297.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),u)* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)).
% 299.79/300.49 22663[0:SpL:158.0,193.1] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(c_Fun_Ocomp(y,u,w,z,v),v,z),x),z),c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),x),w))* -> c_Fun_Oinj__on(y,hAPP(c_Set_Oimage(u,v,w),x),w,z)*.
% 299.79/300.49 22622[0:SpR:158.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oimage(u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(z,x1,v),x2),x),x3)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,z,v,w,x1),x1,w),x2),y),hAPP(c_Set_Oimage(c_Set_Oimage(u,v,w),x,y),x3)))*.
% 299.79/300.49 22621[0:SpR:158.0,99.1] || c_Fun_Oinj__on(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(u,v,w),x,y),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,z,v,w,x1),x1,w),x2)),hAPP(c_Set_Oimage(z,x1,v),x2))**.
% 299.79/300.49 22620[0:SpR:158.0,438.1] || c_Fun_Oinj__on(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(u,v,w),x,y),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,z,v,w,x1),x1,w),x2)),hAPP(c_Set_Oimage(z,x1,v),x2))**.
% 299.79/300.49 23003[0:SpR:131.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(z,w,x1),x2),x),x3)),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(c_Fun_Ocomp(z,u,w,x1,v),v,x1),x2),y),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,y),x3)))*.
% 299.79/300.49 23002[0:SpR:131.0,99.1] || c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Ovimage(c_Fun_Ocomp(z,u,w,x1,v),v,x1),x2)),hAPP(c_Set_Ovimage(z,w,x1),x2))**.
% 299.79/300.49 23001[0:SpR:131.0,438.1] || c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),x,y),hAPP(c_Set_Ovimage(c_Fun_Ocomp(z,u,w,x1,v),v,x1),x2)),hAPP(c_Set_Ovimage(z,w,x1),x2))**.
% 299.79/300.49 24910[0:SpL:21893.0,467.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> equal(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y))),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y))**.
% 299.79/300.49 24909[0:SpL:21267.0,467.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> equal(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y))**.
% 299.79/300.49 25137[0:Res:252.1,505.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x),t_a) c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(v,x,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w)),u),c_Suc(u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,x,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w)),u))*.
% 299.79/300.49 26221[0:SpR:21893.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,x))),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)))**.
% 299.79/300.49 26220[0:SpR:21267.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_Com_Opname,x))),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)))**.
% 299.79/300.49 26374[0:SpL:21893.0,85.0] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname,x),tc_fun(v,tc_bool))*.
% 299.79/300.49 26373[0:SpL:21267.0,85.0] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),tc_Com_Opname,x),tc_fun(v,tc_bool))*.
% 299.79/300.49 26519[0:SpR:21893.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),tc_Com_Opname,x),tc_fun(w,tc_bool))* -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),tc_fun(w,tc_bool)).
% 299.79/300.49 26518[0:SpR:21267.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),tc_Com_Opname,x),tc_fun(w,tc_bool))* -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),tc_fun(w,tc_bool)).
% 299.79/300.49 27162[0:SpR:9.0,450.0] || -> hBOOL(hAPP(hAPP(u,hAPP(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Fun_Ocomp(u,v,w,x,y),z,x1,x2))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Fun_Ocomp(u,v,w,x,y),z,x1,x2)))* c_Hoare__Mirabelle_Otriple__valid(x2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Fun_Ocomp(u,v,w,x,y)),x1),z),t_a).
% 299.79/300.49 27135[0:SpR:9493.1,450.0] || equal(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oinsert(v_x,t_a),u,v,w),v_x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oinsert(v_x,t_a),u,v,w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Set_Oinsert(v_x,t_a),u,v,w)))* c_Hoare__Mirabelle_Otriple__valid(w,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Set_Oinsert(v_x,t_a)),v),u),t_a).
% 299.79/300.49 27393[0:Res:171.2,470.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(x,c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),x),u),v,w,u)),x))*.
% 299.79/300.49 27392[0:Res:172.2,470.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),x),u),v,w,u)),x))*.
% 299.79/300.49 27453[0:Res:171.2,466.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),x),u),w,u)),x))*.
% 299.79/300.49 27452[0:Res:172.2,466.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),x),u),w,u)),x))*.
% 299.79/300.49 27644[0:SpR:15172.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),x,y),z,tc_fun(x1,tc_bool)),w,u,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),x,y),z,tc_fun(x1,tc_bool)),u,x2),c_Orderings_Obot__class_Obot(tc_bool)),v)*.
% 299.79/300.49 27631[0:SpR:336.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),w,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),u,y),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.79/300.49 27600[0:SpR:337.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),w,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),u,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),v)*.
% 299.79/300.49 27586[0:SpR:14526.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v)),w)) c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Option_Othe(v),x,tc_fun(y,tc_bool)),w,u,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_HOL_Ominus__class_Ominus(c_Option_Othe(v),x,tc_fun(y,tc_bool)),u,z),c_Orderings_Obot__class_Obot(tc_bool)),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v))**.
% 299.79/300.49 27797[0:SpR:15172.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),x,y),z,tc_fun(x1,tc_bool)),w,u,x2) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),x,y),z,tc_fun(x1,tc_bool)),u,x2),c_Orderings_Obot__class_Obot(tc_bool)),v)*.
% 299.79/300.49 27784[0:SpR:336.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),w,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),u,y),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.79/300.49 27753[0:SpR:337.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),w,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),u,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),v)*.
% 299.79/300.49 27739[0:SpR:14526.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v)),w)) c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Option_Othe(v),x,tc_fun(y,tc_bool)),w,u,z) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_HOL_Ominus__class_Ominus(c_Option_Othe(v),x,tc_fun(y,tc_bool)),u,z),c_Orderings_Obot__class_Obot(tc_bool)),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v))**.
% 299.79/300.49 27934[0:Res:468.0,156.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(x,v,y),z)),hAPP(c_Set_Oimage(x1,v,w),hAPP(c_Set_Ovimage(x,v,y),z))) hBOOL(hAPP(hAPP(c_in(y),hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Ovimage(x,v,y),z),u,x1,v,w))),z))*.
% 299.79/300.49 27923[0:Res:468.0,355.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),hAPP(c_Set_Oimage(y,v,w),hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))) equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),u,y,v,w),x)**.
% 299.79/300.49 28555[0:SpR:15172.0,118.0] || -> equal(c_Fun_Ocomp(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),c_Fun_Ofun__upd(y,z,x1,x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y,x3,x4,x2),z,c_Orderings_Obot__class_Obot(tc_bool),x2,x4))*.
% 299.79/300.49 28547[0:SpR:128.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Ovimage(u,v,w),c_Fun_Ofun__upd(x,y,c_HOL_Ouminus__class_Ouminus(z,tc_fun(w,tc_bool)),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Ovimage(u,v,w),x,x2,x3,x1),y,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),z),tc_fun(v,tc_bool)),x1,x3))*.
% 299.79/300.49 28511[0:SpR:337.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Fun_Ofun__upd(v,w,x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,z,x1,y),w,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),y,x1))*.
% 299.79/300.49 28505[0:SpR:544.1,118.0] class_Lattices_Olattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Fun_Ofun__upd(w,x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x1,x2,z),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),z,x2))*.
% 299.79/300.49 28504[0:SpR:543.1,118.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Fun_Ofun__upd(w,x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x1,x2,z),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),z,x2))*.
% 299.79/300.49 32355[0:SpL:328.1,477.0] || c_lessequals(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u),y,tc_fun(x,tc_bool))* hBOOL(y) hBOOL(hAPP(hAPP(c_in(u),z),v))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))*.
% 299.79/300.49 32535[0:SpL:328.1,476.0] || c_lessequals(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u),y,tc_fun(x,tc_bool))* hBOOL(y) hBOOL(hAPP(hAPP(c_in(u),z),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))*.
% 299.79/300.49 33020[0:SpR:12944.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(y,z),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x1,x2)),u,x),w)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(y,z),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x1,x2)),u,x),w))**.
% 299.79/300.49 32993[0:SpR:11473.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u,x),w)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u,x),w))**.
% 299.79/300.49 32982[0:SpR:329.1,475.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) hBOOL(hAPP(hAPP(c_in(x),v),y)) -> equal(hAPP(c_Set_Oinsert(v,z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,z),y)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,z),y))**.
% 299.79/300.49 32981[0:SpR:328.1,475.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(x),u),y))* -> equal(hAPP(c_Set_Oinsert(v,z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,z),y)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,z),y))**.
% 299.79/300.49 32978[0:SpR:538.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),y),z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u,z),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u,z),w))**.
% 299.79/300.49 32959[0:SpR:17045.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),z,tc_fun(x1,tc_bool)),u,x),w)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),z,tc_fun(x1,tc_bool)),u,x),w))**.
% 299.79/300.49 32895[0:SpR:158.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* -> equal(hAPP(c_Set_Oinsert(hAPP(z,v),x1),hAPP(c_Set_Oimage(c_Fun_Ocomp(z,w,u,x1,x),x,x1),y)),hAPP(c_Set_Oimage(c_Fun_Ocomp(z,w,u,x1,x),x,x1),y))**.
% 299.79/300.49 32859[0:SpR:475.1,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),w)),x1)) -> hBOOL(hAPP(hAPP(c_in(x2),hAPP(c_Set_Oimage(y,u,z),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(y,v),z),x,x2),x1)))*.
% 299.79/300.49 32855[0:SpR:475.1,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),w)),x1)) -> c_lessequals(hAPP(c_Set_Oimage(y,u,z),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oinsert(hAPP(y,v),z),x,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.79/300.49 33081[0:SpL:158.0,94.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),z,y,x) c_Fun_Oinj__on(x1,hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),z)),x,x2)* -> c_Fun_Oinj__on(c_Fun_Ocomp(x1,c_Fun_Ocomp(u,v,w,x,y),x,x2,y),z,y,x2)*.
% 299.79/300.49 33075[0:SpL:158.0,94.1] || c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(v,w,x),y),x,z) c_Fun_Oinj__on(x1,hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,x,z,w),w,z),y),z,x2)* -> c_Fun_Oinj__on(c_Fun_Ocomp(x1,u,z,x2,x),hAPP(c_Set_Oimage(v,w,x),y),x,x2)*.
% 299.79/300.49 33410[0:Res:151.2,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Ohoare__valids(w,c_HOL_Ominus__class_Ominus(v,x,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,y)),w))* c_Hoare__Mirabelle_Otriple__valid(y,u,t_a)*.
% 299.79/300.49 34524[0:Rew:523.1,34141.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),v_x)),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(v_x,v_x)))**.
% 299.79/300.49 34077[0:SpR:24914.0,188.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_COMBK(v,u,w),w,u),tc_Com_Opname,x),hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x))))* -> equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,w),w,u),v_x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))).
% 299.79/300.49 34631[0:SpR:55.1,338.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool)))))*.
% 299.79/300.49 34629[0:SpR:55.1,424.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_HOL_Ominus__class_Ominus(x,y,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),v),y)) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),y,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))*.
% 299.79/300.49 34628[0:SpR:55.1,56.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),v),x)) equal(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),x,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(y,x,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool)))**.
% 299.79/300.49 34624[0:SpR:55.1,584.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_COMBS(c_Set_Oinsert(v,u),x,y,z,x1),c_HOL_Ominus__class_Ominus(x2,w,tc_fun(u,tc_bool))),hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x2),w,tc_fun(u,tc_bool)),hAPP(x,c_HOL_Ominus__class_Ominus(x2,w,tc_fun(u,tc_bool)))))*.
% 299.79/300.49 34623[0:SpR:55.1,584.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_COMBS(x,c_Set_Oinsert(v,u),y,z,x1),c_HOL_Ominus__class_Ominus(x2,w,tc_fun(u,tc_bool))),hAPP(hAPP(x,c_HOL_Ominus__class_Ominus(x2,w,tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x2),w,tc_fun(u,tc_bool))))*.
% 299.79/300.49 34612[0:SpR:55.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(y,tc_bool))),z)) -> hBOOL(hAPP(hAPP(c_in(y),x1),x)) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x1,y),w),x,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oinsert(x1,y),v,u),u)*.
% 299.79/300.49 34606[0:SpR:55.1,339.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool))),y),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool))),y)))**.
% 299.79/300.49 34592[0:SpR:55.1,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool))),hAPP(c_Set_Ovimage(c_Set_Oinsert(v,u),x,z),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.49 34674[0:Rew:20386.1,34619.2] || c_Fun_Oinj__on(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> hBOOL(hAPP(hAPP(c_in(v),u),y)) equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(u,v),w,x),c_HOL_Ominus__class_Ominus(z,y,tc_fun(v,tc_bool))),c_HOL_Ominus__class_Ominus(z,y,tc_fun(v,tc_bool)))**.
% 299.79/300.49 34675[0:Rew:20386.1,34618.2] || c_Fun_Oinj__on(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> hBOOL(hAPP(hAPP(c_in(v),u),y)) equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(u,v),w,x),c_HOL_Ominus__class_Ominus(z,y,tc_fun(v,tc_bool))),c_HOL_Ominus__class_Ominus(z,y,tc_fun(v,tc_bool)))**.
% 299.79/300.49 35395[0:SpR:584.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_COMBS(x,y,z,x1,x2),v,tc_fun(x3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x3,tc_bool)),hAPP(hAPP(x,u),hAPP(y,u))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(x,y,z,x1,x2),v,tc_fun(x3,tc_bool))))*.
% 299.79/300.49 35394[0:SpR:586.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_COMBB(x,y,z,x1),x2),v,tc_fun(x3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x3,tc_bool)),hAPP(x,hAPP(x2,u))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_COMBB(x,y,z,x1),x2),v,tc_fun(x3,tc_bool))))*.
% 299.79/300.49 35393[0:SpR:585.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_COMBC(x,y,z,x1),x2),v,tc_fun(x3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x3,tc_bool)),hAPP(hAPP(x,u),x2)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_COMBC(x,y,z,x1),x2),v,tc_fun(x3,tc_bool))))*.
% 299.79/300.49 35390[0:SpR:11499.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),u),v),hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y)),u,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Set_Oinsert(w,x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y)),u,tc_fun(z,tc_bool))))*.
% 299.79/300.49 35386[0:SpR:336.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v,tc_fun(y,tc_bool))))*.
% 299.79/300.49 35334[0:SpR:14526.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),u),v),w),c_HOL_Ominus__class_Ominus(c_Option_Othe(u),x,tc_fun(y,tc_bool)),v,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(c_Option_Othe(u),x,tc_fun(y,tc_bool)),v,tc_fun(z,tc_bool))))*.
% 299.79/300.49 35322[0:SpR:331.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),v,tc_fun(y,tc_bool))))*.
% 299.79/300.49 35313[0:SpR:34428.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,w),u,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,w),u,tc_fun(x,tc_bool))))*.
% 299.79/300.49 35293[0:SpR:353.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),w),x),y),c_Set_Oinsert(z,v),x,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(z,v),w))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(z,v),x,tc_fun(x1,tc_bool))))*.
% 299.79/300.49 35272[0:SpR:338.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),y,u,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),y,u,tc_fun(z,tc_bool))))*.
% 299.79/300.49 35216[0:SpR:410.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,y,tc_fun(z,tc_bool))),x1)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x2,y),w),x,y,tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(x,x2)),v,u),u)*.
% 299.79/300.49 35198[0:SpR:410.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(w,z)),u,x1),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(z,x),v),w,x,tc_fun(y,tc_bool)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.79/300.49 35444[0:SSi:35230.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),y),z,x,tc_fun(u,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(z,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,z,x,tc_fun(u,tc_bool)))))*.
% 299.79/300.49 35445[0:SSi:35212.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),y,w,tc_fun(u,tc_bool))),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(y,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,w,tc_fun(u,tc_bool))),z)))*.
% 299.79/300.49 35486[0:SpR:113.0,151.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),z))) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),c_HOL_Ominus__class_Ominus(y,z,tc_fun(x,tc_bool)))))*.
% 299.79/300.49 35639[0:SpR:24914.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),hAPP(c_COMBB(y,w,tc_fun(z,tc_bool),v),u),v,tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,w),v_x),y,w,tc_fun(z,tc_bool)))**.
% 299.79/300.49 36519[0:SpL:89.0,372.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_COMBB(z,u,tc_fun(x1,tc_bool),x),w),x,tc_fun(x1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))** -> equal(hAPP(z,v),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))*.
% 299.79/300.49 36518[0:SpL:410.0,372.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(z,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,z,u,tc_fun(y,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))** -> equal(hAPP(z,v),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))*.
% 299.79/300.49 36968[0:SpL:89.0,375.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_COMBB(z,u,tc_fun(x1,tc_bool),x),w),x,tc_fun(x1,tc_bool)),x2,tc_fun(x1,tc_bool))* -> c_lessequals(hAPP(z,v),x2,tc_fun(x1,tc_bool))*.
% 299.79/300.49 36967[0:SpL:410.0,375.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(z,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,z,u,tc_fun(y,tc_bool))),x1,tc_fun(y,tc_bool))* -> c_lessequals(hAPP(z,v),x1,tc_fun(y,tc_bool))*.
% 299.79/300.49 37136[0:SpL:21893.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,u,x),v_x),c_Set_Oimage(w,u,x),tc_Com_Opname,y)))* c_lessequals(hAPP(c_Set_Oimage(w,u,x),v_x),z,tc_fun(x,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,v)),z))*.
% 299.79/300.49 37135[0:SpL:21267.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,u,x),hAPP(c_Set_Oimage(w,u,x),v_x),tc_Com_Opname,y)))* c_lessequals(hAPP(c_Set_Oimage(w,u,x),v_x),z,tc_fun(x,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,v)),z))*.
% 299.79/300.49 37446[0:SpR:205.1,415.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Fun_Ofun__upd(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),hAPP(c_Set_Oimage(u,v,w),x),x,y,z),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v))**.
% 299.79/300.49 38218[0:SpR:56.1,13.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(hAPP(c_Set_Oinsert(v,u),x),y,tc_fun(u,tc_bool))* c_lessequals(z,w,tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(y,z,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.49 38203[0:SpR:56.1,13.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(x,hAPP(c_Set_Oinsert(v,u),y),tc_fun(u,tc_bool))* c_lessequals(w,z,tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(x,z,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.49 38349[0:SSi:38313.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),w))* c_Finite__Set_Ofinite(w,tc_fun(u,tc_bool)) c_Finite__Set_Ofinite(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x,w,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),u)* -> c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),u)*.
% 299.79/300.49 38400[0:SpL:339.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oimage(u,v,w),z)) c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(x,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z)),v,w)* -> equal(hAPP(c_Set_Oinsert(x,v),y),z).
% 299.79/300.49 38396[0:SpL:338.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(y,v),z))) c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z)),v,w)* -> equal(x,hAPP(c_Set_Oinsert(y,v),z)).
% 299.79/300.49 38509[0:Rew:465.1,38480.4] || c_Finite__Set_Ofinite(u,v) c_lessequals(hAPP(c_Set_Oimage(w,v,v),u),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(c_Fun_Ofun__upd(w,x,y,v,v),u,v,v)* -> hBOOL(hAPP(hAPP(c_in(v),x),u)) equal(hAPP(c_Set_Oimage(w,v,v),u),u).
% 299.79/300.49 39021[0:MRR:39020.4,20734.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,v,w,w)* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x,w,w),u),w) c_lessequals(u,hAPP(c_Set_Oimage(x,w,w),u),tc_fun(w,tc_bool))* -> equal(hAPP(c_Set_Oimage(x,w,w),u),u).
% 299.79/300.49 41432[0:Res:171.2,275.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(v,w),u) hBOOL(hAPP(hAPP(c_in(x),w),y)) -> equal(hAPP(v,w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMin(hAPP(v,w),u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v,x,tc_fun(u,tc_bool))))*.
% 299.79/300.49 41431[0:Res:172.2,275.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(v,w),u) hBOOL(hAPP(hAPP(c_in(x),w),y)) -> equal(hAPP(v,w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMax(hAPP(v,w),u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v,x,tc_fun(u,tc_bool))))*.
% 299.79/300.49 41673[0:SpL:24914.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),w,u),x)))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u)* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_in(u),v_x)),x)).
% 299.79/300.49 41641[0:SpL:1196.1,284.0] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,v),x)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v)* -> hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Otop__class_Otop(u)),x)).
% 299.79/300.49 41636[0:SpL:3294.1,284.0] || equal(c_in(t_a),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(hAPP(u,v_x),w,v),x)))* c_Fun_Oinj__on(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v)* -> hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),x)).
% 299.79/300.49 41632[0:SpL:330.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,u),y)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u)* -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),y)).
% 299.79/300.49 41631[0:SpL:1195.1,284.0] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,v),x)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v)* -> hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Obot__class_Obot(u)),x)).
% 299.79/300.49 41625[0:SpL:584.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_COMBS(v,w,x,y,z),x1)),hAPP(c_Set_Oimage(hAPP(v,x1),x2,u),x3)))* c_Fun_Oinj__on(hAPP(v,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,u)* -> hBOOL(hAPP(hAPP(c_in(x2),hAPP(w,x1)),x3)).
% 299.79/300.49 41619[0:SpL:9935.1,284.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,v),y)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,v)* -> hBOOL(hAPP(hAPP(c_in(x),u),y))*.
% 299.79/300.49 41541[0:SpL:34427.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,v),w,u),x)))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u)* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),x)).
% 299.79/300.49 42257[0:SSi:42060.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)))**.
% 299.79/300.49 42687[0:SpR:161.0,340.2] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)) c_lessequals(c_HOL_Ominus__class_Ominus(y,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))*.
% 299.79/300.49 43104[0:SpR:27043.1,486.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_Procs,x),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_Procs,x),u,tc_fun(w,tc_bool)))**.
% 299.79/300.49 43102[0:SpR:10063.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,t_a),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_x,t_a),u,tc_fun(w,tc_bool)))**.
% 299.79/300.49 43083[0:SpR:105.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(z,y,v),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(z,y,v),u,tc_fun(x,tc_bool)))**.
% 299.79/300.49 43075[0:SpR:38.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(z,y,v),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(z,y,v),u,tc_fun(x,tc_bool)))**.
% 299.79/300.49 43074[0:SpR:321.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(z,v,y),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(z,v,y),u,tc_fun(x,tc_bool)))**.
% 299.79/300.49 43033[0:SpR:87.1,486.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ouminus__class_Ouminus(w,u)),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(y,tc_bool)))**.
% 299.79/300.49 43014[0:SpR:302.1,486.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(y,tc_bool)))**.
% 299.79/300.49 42999[0:SpR:15476.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(x,v_x),tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,tc_bool)),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_HOL_Ouminus__class_Ouminus(x,tc_fun(t_a,tc_bool)),u,tc_fun(w,tc_bool)))**.
% 299.79/300.49 42982[0:SpR:369.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(v,w),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(v,w),u,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(v,w),u,tc_fun(z,tc_bool)))**.
% 299.79/300.49 42981[0:SpR:2089.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_x,tc_Com_Opname),u,tc_fun(x,tc_bool)))**.
% 299.79/300.49 42897[0:SpR:486.1,415.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)),z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)))**.
% 299.79/300.49 43336[0:SpL:9493.1,406.0] || equal(hAPP(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(c_Set_Oinsert(u,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),hAPP(c_Set_Oinsert(v,t_a),hAPP(c_Set_Oinsert(w,t_a),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)))))* -> equal(v_x,v) equal(v_x,w).
% 299.79/300.49 43531[0:SpR:158.0,507.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,x,u,y),y,u),z)),hAPP(c_Set_Oimage(v,x,u),x1)),hAPP(c_Set_Oimage(v,x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(w,y,x),z)),x1)))*.
% 299.79/300.49 43516[0:SpR:158.0,507.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,y,w,u,z),z,u),x1)),hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(y,z,w),x1))))*.
% 299.79/300.49 43505[0:SpR:507.0,340.2] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Oimage(u,v,w),z),y,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z)),y,tc_fun(w,tc_bool))*.
% 299.79/300.49 43751[0:SpR:131.0,162.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,u),u,y),z)),hAPP(c_Set_Ovimage(w,u,x),x1)),hAPP(c_Set_Ovimage(w,u,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Ovimage(v,x,y),z)),x1)))*.
% 299.79/300.49 43736[0:SpR:131.0,162.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(y,v,w,z,u),u,z),x1)),hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Ovimage(y,w,z),x1))))*.
% 299.79/300.49 43727[0:SpR:162.0,340.2] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),y,tc_fun(v,tc_bool)) c_lessequals(hAPP(c_Set_Ovimage(u,v,w),z),y,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)),y,tc_fun(v,tc_bool))*.
% 299.79/300.49 43944[0:SpL:158.0,231.0] || c_lessequals(u,hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1),tc_fun(y,tc_bool))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> c_lessequals(hAPP(c_Set_Ovimage(v,x,y),u),hAPP(c_Set_Oimage(w,z,x),x1),tc_fun(x,tc_bool))*.
% 299.79/300.49 43941[0:SpL:317.0,231.0] || c_lessequals(u,hAPP(c_Set_Oinsert(hAPP(v,w),x),hAPP(c_Set_Oimage(v,y,x),z)),tc_fun(x,tc_bool))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,x) -> c_lessequals(hAPP(c_Set_Ovimage(v,y,x),u),hAPP(c_Set_Oinsert(w,y),z),tc_fun(y,tc_bool))*.
% 299.79/300.49 44065[0:SpL:158.0,358.0] || c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(c_Set_Oimage(u,w,x),x1),tc_fun(x,tc_bool))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_lessequals(hAPP(c_Set_Oimage(v,y,w),z),x1,tc_fun(w,tc_bool)).
% 299.79/300.49 44062[0:SpL:317.0,358.0] || c_lessequals(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),y)),hAPP(c_Set_Oimage(u,x,w),z),tc_fun(w,tc_bool))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w) -> c_lessequals(hAPP(c_Set_Oinsert(v,x),y),z,tc_fun(x,tc_bool)).
% 299.79/300.49 44050[0:SpL:158.0,358.0] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,y,v,w,z),z,w),x1),tc_fun(w,tc_bool))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(c_Set_Oimage(y,z,v),x1),tc_fun(v,tc_bool)).
% 299.79/300.49 44047[0:SpL:317.0,358.0] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oinsert(hAPP(u,y),w),hAPP(c_Set_Oimage(u,v,w),z)),tc_fun(w,tc_bool))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(x,hAPP(c_Set_Oinsert(y,v),z),tc_fun(v,tc_bool)).
% 299.79/300.49 44359[0:Res:1103.1,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,hAPP(c_in(u),x))))* equal(hAPP(y,x),hAPP(y,v))* c_Fun_Oinj__on(y,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,hAPP(c_in(u),x)),u,z)* -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(u),x),t_a) equal(x,v).
% 299.79/300.49 45094[0:SpR:339.0,326.2] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)) c_lessequals(y,z,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z),tc_fun(v,tc_bool))*.
% 299.79/300.49 45089[0:SpR:338.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Oinsert(x,w),y),z,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),z),tc_fun(w,tc_bool))*.
% 299.79/300.49 45053[0:SpR:8415.2,326.2] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(v_x,v,tc_fun(u,tc_bool)) c_lessequals(w,x,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(v_x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),tc_fun(u,tc_bool))*.
% 299.79/300.49 45029[0:SpR:339.0,326.2] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool)) c_lessequals(y,z,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)),tc_fun(w,tc_bool))*.
% 299.79/300.49 45024[0:SpR:338.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,hAPP(c_Set_Oinsert(y,w),z),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(c_Set_Oinsert(y,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),z)),tc_fun(w,tc_bool))*.
% 299.79/300.49 44994[0:SpR:8415.2,326.2] || equal(v_Procs,v_x) equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Set_Oinsert(v_x,tc_Com_Opname))** c_lessequals(w,v,tc_fun(u,tc_bool))* c_lessequals(x,v_x,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),v_x,tc_fun(u,tc_bool))*.
% 299.79/300.49 44988[0:SpR:8415.2,326.2] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_lessequals(v,v_x,tc_fun(u,tc_bool)) c_lessequals(w,x,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(v_x,x),tc_fun(u,tc_bool))*.
% 299.79/300.49 45332[0:SpL:8415.2,487.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,v,u)))* hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)))*.
% 299.79/300.49 45308[0:SpL:339.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oinsert(x,w),y),u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)))*.
% 299.79/300.49 45303[0:SpL:338.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oinsert(x,w),z),u,w)))*.
% 299.79/300.49 45267[0:SpL:8415.2,487.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),w),hAPP(v_x,x)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,v,u)))* hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)))*.
% 299.79/300.49 45490[0:SpL:8415.2,237.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u) -> equal(hAPP(v,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v_x,v,u,w)),v_x)**.
% 299.79/300.49 45652[0:Rew:39935.1,45556.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,z)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),x1),w,x,tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(u,tc_bool)))**.
% 299.79/300.49 46195[0:Rew:339.0,46160.1] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x)),u,t_a)),hAPP(c_Set_Oinsert(v,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x))))*.
% 299.79/300.49 46154[0:Res:15262.1,481.0] || equal(c_in(t_a),c_in(u)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w),v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w)))*.
% 299.79/300.49 46153[0:Res:3285.1,481.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),x),v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)),x)))*.
% 299.79/300.49 46152[0:Res:3317.1,481.0] || equal(c_in(u),c_in(v)) -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(v_x,u),x)),y),w,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(v_x,u),x)),y)))*.
% 299.79/300.49 46196[0:Rew:339.0,46148.1] || -> hBOOL(hAPP(u,v_Procs)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),x)),u,v)),hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_in(tc_Com_Opname),v_x)),x))))*.
% 299.79/300.49 46197[0:Rew:533.0,46125.1] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w)),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w))))*.
% 299.79/300.49 46205[0:Rew:104.0,46164.1] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),w,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),u,tc_Com_Opname)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),w,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))))*.
% 299.79/300.49 46478[0:Res:19451.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),hAPP(c_Set_Oinsert(w,t_a),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))),u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),hAPP(c_Set_Oinsert(w,t_a),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))))))*.
% 299.79/300.49 46472[0:Res:15262.1,480.0] || equal(c_in(t_a),c_in(u)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))))*.
% 299.79/300.49 46471[0:Res:3285.1,480.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),v,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs))))*.
% 299.79/300.49 46470[0:Res:3317.1,480.0] || equal(c_in(u),c_in(v)) -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(v_x,u),y)),w,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(v_x,u),y))))*.
% 299.79/300.49 46466[0:Res:19440.0,480.0] || -> hBOOL(hAPP(u,v_Procs)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),hAPP(c_in(tc_Com_Opname),v_x))),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),hAPP(c_in(tc_Com_Opname),v_x)))))*.
% 299.79/300.49 46443[0:Res:649.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs))))*.
% 299.79/300.49 46597[0:MRR:46576.0,418.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(u,v),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,x,tc_fun(w,tc_bool)),y)),c_Set_Oinsert(z,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(z,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,x),y),u,x,tc_fun(w,tc_bool))))*.
% 299.79/300.49 46932[0:Res:241.2,431.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool))* c_Fun_Oinj__on(y,x,u,z)* -> c_Fun_Oinj__on(y,c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),u,z)*.
% 299.79/300.49 47378[0:SpL:3294.1,485.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),w),c_Orderings_Obot__class_Obot(tc_bool)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,v,u)),v_x))*.
% 299.79/300.49 47373[0:SpL:584.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,y,z,x1),x2)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(x,x2),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x2,u,w)),x2))*.
% 299.79/300.49 47355[0:SpL:600.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)),y))*.
% 299.79/300.49 47947[0:SpL:3294.1,490.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v,u)))* hBOOL(hAPP(hAPP(c_in(u),w),c_Orderings_Obot__class_Obot(tc_bool)))* -> hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,v,u)),v_x))*.
% 299.79/300.49 47942[0:SpL:584.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(v,w),u,x)))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v,z,x1,x2),w)))* -> hBOOL(hAPP(u,y))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,u,x)),w))*.
% 299.79/300.49 47924[0:SpL:600.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),u,x)))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),w)))* -> hBOOL(hAPP(u,y))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,u,x)),w))*.
% 299.79/300.49 48363[0:SpL:10463.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(y,w),x),w,u) -> .
% 299.79/300.49 48362[0:SpL:9911.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(y,w),x),w,u) -> .
% 299.79/300.49 48789[0:Res:9246.0,619.0] || -> hBOOL(hAPP(u,v))* equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,x,tc_fun(y,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(x,tc_bool))),c_Set_Oinsert(z,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(z,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_HOL_Ouminus__class_Ouminus(u,tc_fun(x,tc_bool)),w,x,tc_fun(y,tc_bool))))**.
% 299.79/300.49 48757[0:SpL:3229.1,619.0] || equal(u,c_in(v))* hBOOL(hAPP(hAPP(u,v_x),w))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,v,tc_fun(y,tc_bool)),w),c_Set_Oinsert(z,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(z,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool))))**.
% 299.79/300.49 49313[0:Res:8376.2,488.1] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_Procs)** hBOOL(hAPP(x,v_x)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)),w))*.
% 299.79/300.49 49640[0:Res:225.1,467.0] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,w),v),w,x) equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),u,w,x),hAPP(u,y))),hAPP(u,y))**.
% 299.79/300.49 49671[0:Rew:49662.2,49473.2] || hBOOL(hAPP(u,v)) c_Fun_Oinj__on(c_Set_Oinsert(v,w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v,w),y,z),hAPP(c_Set_Oinsert(u,y),x))))* c_Fun_Oinj__on(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(u,y),x),y,z).
% 299.79/300.49 49695[0:Rew:49662.2,49574.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) c_Fun_Oinj__on(hAPP(u,v_x),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),v_x),hAPP(c_Set_Oimage(hAPP(u,v_x),w,x),hAPP(c_Set_Oinsert(v_x,w),v))))* c_Fun_Oinj__on(hAPP(u,v_x),hAPP(c_Set_Oinsert(v_x,w),v),w,x).
% 299.79/300.49 49703[0:Rew:49662.2,49585.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),v))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),v),w,x).
% 299.79/300.49 49723[0:Rew:49662.2,49628.2] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,w),v),w,x) equal(hAPP(c_Set_Oimage(c_COMBK(z,x1,x),x,x1),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(y,w),v))),hAPP(c_Set_Oinsert(z,x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))**.
% 299.79/300.49 49742[0:MRR:49636.1,114.1] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,w),v),w,x) equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),u,w,x),hAPP(u,y))),hAPP(u,y))**.
% 299.79/300.49 50494[0:SpL:223.1,377.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),z)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),z)*.
% 299.79/300.49 50464[0:SpR:223.1,19744.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,tc_Hoare__Mirabelle_Otriple(t_a)),u,tc_Hoare__Mirabelle_Otriple(t_a)),w),hAPP(c_Set_Oimage(x,u,tc_Hoare__Mirabelle_Otriple(t_a)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),t_a)*.
% 299.79/300.49 50390[0:SpR:223.1,378.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),y)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,z,u,y),u,y),w),y)*.
% 299.79/300.49 51111[0:MRR:51101.3,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(y),z),hAPP(c_Set_Oimage(x,u,y),w)))* equal(hAPP(c_Hilbert__Choice_Oinv__into(w,x,u,y),z),v)* -> equal(z,hAPP(x,v))*.
% 299.79/300.49 58600[0:Res:10771.1,199.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Set_Oinsert(y,u),z),w,v,x))),z))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(y,u),z),x1))*.
% 299.79/300.49 58762[0:SpL:486.1,15629.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,v)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,v)),z)))*.
% 299.79/300.49 58724[0:SpL:465.1,15629.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),x))* -> hBOOL(hAPP(hAPP(c_in(v),y),x))* hBOOL(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),x1)))*.
% 299.79/300.49 59270[0:SpL:486.1,15857.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,v)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,v)),x1)))*.
% 299.79/300.49 59232[0:SpL:465.1,15857.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),x))* -> hBOOL(hAPP(hAPP(c_in(v),y),x))* hBOOL(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),x2)))*.
% 299.79/300.49 60401[7:SpR:329.1,58968.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),v),tc_fun(x,tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),v)).
% 299.79/300.49 60398[7:SpR:339.0,58968.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_x) -> hBOOL(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x))))*.
% 299.79/300.49 60395[7:SpR:537.1,58968.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x))))*.
% 299.79/300.49 60394[7:SpR:534.1,58968.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x))))*.
% 299.79/300.49 60462[0:SpR:5882.1,475.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),y,z,x1,x2),v,x),w)),hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),y,z,x1,x2),v,x),w))**.
% 299.79/300.49 60514[0:SpR:329.1,58969.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),v),tc_fun(x,tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),v)).
% 299.79/300.49 60511[0:SpR:339.0,58969.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x))))*.
% 299.79/300.49 60508[0:SpR:537.1,58969.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x))))*.
% 299.79/300.49 60507[0:SpR:534.1,58969.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x))))*.
% 299.79/300.49 60587[7:SpR:329.1,59476.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),w),tc_fun(x,tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),v_x) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),w)).
% 299.79/300.49 60584[7:SpR:339.0,59476.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_x) -> hBOOL(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),y))))*.
% 299.79/300.49 60581[7:SpR:537.1,59476.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y))))*.
% 299.79/300.49 60580[7:SpR:534.1,59476.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y))))*.
% 299.79/300.49 60660[0:SpR:329.1,59477.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),w),tc_fun(x,tc_bool))* equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),v_Procs) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),w)).
% 299.79/300.49 60657[0:SpR:339.0,59477.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_Procs) -> hBOOL(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),y))))*.
% 299.79/300.49 60654[0:SpR:537.1,59477.1] class_Lattices_Olattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y))))*.
% 299.79/300.49 60653[0:SpR:534.1,59477.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y))))*.
% 299.79/300.49 60845[0:SpR:329.1,59017.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),v),tc_fun(x,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),v)).
% 299.79/300.49 60842[0:SpR:339.0,59017.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x)),t_a)* hBOOL(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x)),y))))*.
% 299.79/300.49 60839[0:SpR:537.1,59017.1] class_Lattices_Olattice(u) || -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),t_a)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y))))*.
% 299.79/300.49 60838[0:SpR:534.1,59017.1] class_Lattices_Oupper__semilattice(u) || -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),t_a)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y))))*.
% 299.79/300.49 60918[0:SpR:329.1,59525.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),w),tc_fun(x,tc_bool))* -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),t_a)* hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),w)).
% 299.79/300.49 60915[0:SpR:339.0,59525.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x)),t_a)* hBOOL(hAPP(c_Set_Oinsert(w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,v),x)),z))))*.
% 299.79/300.49 60912[0:SpR:537.1,59525.1] class_Lattices_Olattice(u) || -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),t_a)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),z))))*.
% 299.79/300.49 60911[0:SpR:534.1,59525.1] class_Lattices_Oupper__semilattice(u) || -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),t_a)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),z))))*.
% 299.79/300.49 61784[0:SpR:11167.1,475.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(x,y),c_Set_Oinsert(v_x,tc_Com_Opname)),u,w),v)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(x,y),c_Set_Oinsert(v_x,tc_Com_Opname)),u,w),v))**.
% 299.79/300.49 64227[0:SpR:104.0,646.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),tc_Com_Opname,w),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))),v_x)**.
% 299.79/300.49 64150[0:SpR:646.1,410.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(u,v_x),w),x),c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,tc_fun(y,tc_bool))))*.
% 299.79/300.49 64394[0:SpR:104.0,645.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),tc_Com_Opname,w),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))),v_x)**.
% 299.79/300.49 64312[0:SpR:645.1,410.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(u,v_x),w),x),c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,tc_fun(y,tc_bool))))*.
% 299.79/300.49 66689[0:SpR:1188.2,410.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(u),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.49 67444[0:SpR:1189.2,410.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(u),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.49 74115[7:SpL:71835.1,619.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,v)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,u,tc_fun(x,tc_bool)),v),c_Set_Oinsert(y,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,u,tc_fun(x,tc_bool))))**.
% 299.79/300.49 75763[7:SpL:71883.1,224.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v_x,v,u),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v_x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))))* c_Fun_Oinj__on(v_x,hAPP(c_Set_Oinsert(v_x,v),w),v,u) -> .
% 299.79/300.49 77806[0:SpL:338.0,5892.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))* -> hBOOL(hAPP(c_COMBS(c_in(y),c_Set_Oinsert(w,u),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))*.
% 299.79/300.49 78615[0:Res:59525.1,5986.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_COMBS(c_in(v),w,x,y,z),t_a)* hBOOL(hAPP(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_in(v),w,x,y,z),x2)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_COMBS(c_in(v),w,x,y,z),x2)))*.
% 299.79/300.49 78614[0:Res:59017.1,5986.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_COMBS(c_in(v),w,x,y,z),t_a)* hBOOL(hAPP(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_COMBS(c_in(v),w,x,y,z),x1)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x2,c_COMBS(c_in(v),w,x,y,z),x1)))*.
% 299.79/300.49 78611[7:Res:58968.1,5986.0] || equal(c_COMBS(c_in(u),v,w,x,y),v_x) -> hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_COMBS(c_in(u),v,w,x,y),z)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_COMBS(c_in(u),v,w,x,y),z)))*.
% 299.79/300.49 78610[0:Res:58969.1,5986.0] || equal(c_COMBS(c_in(u),v,w,x,y),v_Procs) -> hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_COMBS(c_in(u),v,w,x,y),z)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_COMBS(c_in(u),v,w,x,y),z)))*.
% 299.79/300.49 78609[7:Res:59476.1,5986.0] || equal(c_COMBS(c_in(u),v,w,x,y),v_x) -> hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_COMBS(c_in(u),v,w,x,y),x1)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_COMBS(c_in(u),v,w,x,y),x1)))*.
% 299.79/300.49 78608[0:Res:59477.1,5986.0] || equal(c_COMBS(c_in(u),v,w,x,y),v_Procs) -> hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_COMBS(c_in(u),v,w,x,y),x1)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_COMBS(c_in(u),v,w,x,y),x1)))*.
% 299.79/300.49 80204[0:SpL:21268.0,356.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oimage(c_COMBK(x,y,u),u,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),z,x1)),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.49 80008[0:SpL:21268.0,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x)),w))* c_Hoare__Mirabelle_Otriple__valid(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),y,z),t_a)*.
% 299.79/300.49 79972[0:SpR:55.1,21268.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(v,u),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool)),x,z)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool)))**.
% 299.79/300.49 79898[0:SpR:536.1,21268.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)),w,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)))**.
% 299.79/300.49 79897[0:SpR:535.1,21268.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)),w,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)))**.
% 299.79/300.49 79848[0:SpR:205.1,21268.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),y,x,z)),y)**.
% 299.79/300.49 79696[0:SpR:21268.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y),w,z)))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y))).
% 299.79/300.49 79687[0:SpR:21268.0,536.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),x,z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)))**.
% 299.79/300.49 79686[0:SpR:21268.0,535.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),x,z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)))**.
% 299.79/300.49 80419[0:Rew:537.1,79582.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),w,y)),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z)))**.
% 299.79/300.49 80420[0:Rew:534.1,79581.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),w,y)),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z)))**.
% 299.79/300.49 79568[0:SpR:21268.0,410.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(w,y),hAPP(c_Set_Oinsert(w,y),z),x,x1),v,y,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,y),z),v,y,tc_fun(u,tc_bool)))**.
% 299.79/300.49 79557[0:SpR:21268.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(w,x),v,y)),z))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(w,x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,w,u,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,w,u,tc_fun(x1,tc_bool)))**.
% 299.79/300.49 79444[0:SpR:21268.0,5890.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),x1),u,x2),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),x1),tc_fun(v,tc_bool))*.
% 299.79/300.49 79378[0:SpR:21268.0,9493.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v),u,w),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(v_x,t_a),v),u,w),hAPP(c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.49 79366[0:SpR:21268.0,8498.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),hAPP(c_Set_Oinsert(v,w),x)).
% 299.79/300.49 79356[0:SpR:21268.0,463.1] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Com_Obody,hAPP(c_Com_Obody,v),u,w)),x,y,z) -> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v)),x,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Com_Obody,hAPP(c_Com_Obody,v),u,w),y,x,z),z)*.
% 299.79/300.49 80471[0:Rew:221.1,79624.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),y),x,z),w,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(v,w),y,w,u))**.
% 299.79/300.49 81399[0:SpL:21894.0,356.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oimage(c_COMBK(x,y,u),u,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),z,x1)),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))**.
% 299.79/300.49 81203[0:SpL:21894.0,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,x)),w))* c_Hoare__Mirabelle_Otriple__valid(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),c_in(tc_Hoare__Mirabelle_Otriple(t_a)),y,z),t_a)*.
% 299.79/300.49 81166[0:SpR:55.1,21894.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool)),c_Set_Oinsert(v,u),x,z)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool)))**.
% 299.79/300.49 81092[0:SpR:536.1,21894.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)))**.
% 299.79/300.49 81091[0:SpR:535.1,21894.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)))**.
% 299.79/300.49 81042[0:SpR:205.1,21894.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,z)),y)**.
% 299.79/300.49 80890[0:SpR:21894.0,511.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w,z)))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y))).
% 299.79/300.49 80881[0:SpR:21894.0,536.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)))**.
% 299.79/300.49 80880[0:SpR:21894.0,535.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y)))**.
% 299.79/300.49 81614[0:Rew:537.1,80775.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,y)),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z)))**.
% 299.79/300.49 81615[0:Rew:534.1,80774.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,y)),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z)))**.
% 299.79/300.49 80761[0:SpR:21894.0,410.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(w,y),z),c_Set_Oinsert(w,y),x,x1),v,y,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,y),z),v,y,tc_fun(u,tc_bool)))**.
% 299.79/300.49 80750[0:SpR:21894.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(w,x),w,v,y)),z))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(w,x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,w,u,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,w,u,tc_fun(x1,tc_bool)))**.
% 299.79/300.49 80637[0:SpR:21894.0,5890.0] || -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),x1),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),u,x2),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),x1),tc_fun(v,tc_bool))*.
% 299.79/300.49 80571[0:SpR:21894.0,9493.1] || equal(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v),c_Set_Oinsert(v_x,t_a),u,w),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v_x,t_a),v),c_Set_Oinsert(v_x,t_a),u,w),hAPP(c_Set_Oinsert(v_x,t_a),v)).
% 299.79/300.49 80559[0:SpR:21894.0,8498.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),hAPP(c_Set_Oinsert(v,w),x)).
% 299.79/300.49 80549[0:SpR:21894.0,463.1] || c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Com_Obody,v),c_Com_Obody,u,w)),x,y,z) -> c_Natural_Oevaln(hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v)),x,c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Com_Obody,v),c_Com_Obody,u,w),y,x,z),z)*.
% 299.79/300.49 81666[0:Rew:221.1,80818.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),y),c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),x,z),w,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(v,w),y,w,u))**.
% 299.79/300.49 81871[0:SpR:161.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,tc_fun(v,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(w,y,tc_fun(v,tc_bool))),z,x1,x2),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),u)*.
% 299.79/300.49 81870[0:SpR:162.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),y)),x1,x2,x3),hAPP(c_Set_Ovimage(v,w,x),z)),u)*.
% 299.79/300.49 81869[0:SpR:507.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y)),x1,x2,x3),hAPP(c_Set_Oimage(v,w,x),z)),u)*.
% 299.79/300.49 82343[0:SpR:161.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,tc_fun(v,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(w,y,tc_fun(v,tc_bool))),z,x1,x2),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),u)*.
% 299.79/300.49 82342[0:SpR:162.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),y)),x1,x2,x3),hAPP(c_Set_Ovimage(v,w,x),z)),u)*.
% 299.79/300.49 82341[0:SpR:507.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y)),x1,x2,x3),hAPP(c_Set_Oimage(v,w,x),z)),u)*.
% 299.79/300.49 83888[0:SpL:5899.0,477.0] || hBOOL(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),x2),c_COMBS(u,v,x3,x4,x5),z)))* hBOOL(hAPP(hAPP(c_in(z),x6),x1))* -> hBOOL(hAPP(c_COMBS(u,v,x3,x4,x5),x6))*.
% 299.79/300.49 83887[0:SpL:5899.0,476.0] || hBOOL(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),x2),c_COMBS(u,v,x3,x4,x5),z)))* hBOOL(hAPP(hAPP(c_in(z),x6),x2))* -> hBOOL(hAPP(c_COMBS(u,v,x3,x4,x5),x6))*.
% 299.79/300.49 83751[0:SpR:5899.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_COMBS(x,y,z,x1,x2),v),x3),hAPP(c_Set_Oimage(c_COMBS(x,y,x4,x5,x6),u,x3),w)),hAPP(c_Set_Oimage(c_COMBS(x,y,x4,x5,x6),u,x3),w))**.
% 299.79/300.49 85088[0:SpL:644.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oimage(c_COMBK(y,z,tc_Com_Opname),tc_Com_Opname,z),u,tc_fun(w,tc_bool))))*.
% 299.79/300.49 85064[0:SpR:644.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),c_Fun_Ofun__upd(w,x,v_Procs,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oimage(c_COMBK(u,v,tc_Com_Opname),tc_Com_Opname,v),w,z,x1,y),x,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),y,x1))*.
% 299.79/300.49 85046[0:SpR:644.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(w,x,tc_Com_Opname),tc_Com_Opname,x),v,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oimage(c_COMBK(w,x,tc_Com_Opname),tc_Com_Opname,x),u,y),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_Procs)**.
% 299.79/300.49 85045[0:SpR:644.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(w,x,tc_Com_Opname),tc_Com_Opname,x),v,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oimage(c_COMBK(w,x,tc_Com_Opname),tc_Com_Opname,x),u,y),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_Procs)**.
% 299.79/300.49 85162[0:SpL:223.1,85001.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),u,y),u,y),w),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))* -> .
% 299.79/300.49 86999[0:SpR:32817.1,197.1] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))* c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.49 87101[0:Rew:321.0,86968.2] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(w),v),u)) -> equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,w,z),w,z),u),hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))**.
% 299.79/300.49 87201[0:SpL:197.1,32820.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(y,x,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))* -> equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.79/300.49 88551[0:Res:241.2,8306.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),c_HOL_Ominus__class_Ominus(x,y,tc_fun(u,tc_bool))),tc_fun(u,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))*.
% 299.79/300.49 88918[0:SpR:532.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),z)))*.
% 299.79/300.49 88917[0:SpR:533.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),z))*.
% 299.79/300.49 88902[0:SpR:180.2,14196.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y),hAPP(c_Set_Oinsert(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),z,hAPP(c_Set_Oinsert(w,u),v),u,u),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),z,v,u,u)))*.
% 299.79/300.49 89922[0:SpL:26183.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y))* hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(c_Set_Oinsert(v,w),x)))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u,tc_fun(z,tc_bool))))*.
% 299.79/300.49 92428[0:Rew:24914.0,92351.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),v_x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),tc_fun(v,tc_bool))* -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),hAPP(c_Set_Oinsert(u,v),v_x)).
% 299.79/300.49 92895[0:SpR:532.0,5876.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)),tc_fun(y,tc_bool))*.
% 299.79/300.49 92894[0:SpR:533.0,5876.0] || -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),z,x1,x2),x),tc_fun(y,tc_bool))*.
% 299.79/300.49 92879[0:SpR:180.2,5876.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z,x1,x2),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u)),tc_fun(y,tc_bool))*.
% 299.79/300.49 93241[0:SpL:5878.1,275.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(z,c_Orderings_Obot__class_Obot(u)))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),z,x1,x2,x3),v,tc_fun(x,tc_bool))))*.
% 299.79/300.49 93222[0:SpR:5878.1,118.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Fun_Ocomp(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),c_Fun_Ofun__upd(z,x1,c_Orderings_Obot__class_Obot(u),x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),v,w,x,y),z,x3,x4,x2),x1,hAPP(v,c_Orderings_Obot__class_Obot(u)),x2,x4))*.
% 299.79/300.49 94153[0:Res:14364.3,202.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Set_Oimage(w,u,u),c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)))))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_Finite__Set_Ofinite(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),u) -> c_Fun_Oinj__on(w,c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),u,u).
% 299.79/300.49 94283[0:Res:14491.3,375.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,y,tc_fun(u,tc_bool))))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) hBOOL(hAPP(hAPP(c_in(y),z),w))* -> c_lessequals(hAPP(x,z),c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.49 94282[0:Res:14491.3,471.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Set_Oimage(w,x,u),y)))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) hBOOL(hAPP(hAPP(c_in(x),z),y))* -> hBOOL(hAPP(hAPP(c_in(u),hAPP(w,z)),c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool))))*.
% 299.79/300.49 94344[0:MRR:94256.3,24483.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> c_lessequals(w,hAPP(c_Set_Oinsert(x,u),c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool))),tc_fun(u,tc_bool)).
% 299.79/300.49 20973[0:SpR:600.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(y,v,tc_fun(u,tc_bool)),w),z)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),z)))*.
% 299.79/300.49 20963[0:SpR:181.1,317.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z),hAPP(c_Set_Oinsert(w,y),x1)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),z),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z),x1)))*.
% 299.79/300.49 20895[0:SpR:317.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(u,v),w),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,z,w),x1),x),x2)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,z,w),hAPP(c_Set_Oinsert(v,z),x1)),y),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(u,v),w),x,y),x2)))*.
% 299.79/300.49 20894[0:SpR:317.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(hAPP(u,v),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(hAPP(u,v),w),x,y),hAPP(c_Set_Oimage(u,z,w),hAPP(c_Set_Oinsert(v,z),x1))),hAPP(c_Set_Oimage(u,z,w),x1))**.
% 299.79/300.49 20893[0:SpR:317.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(hAPP(u,v),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(hAPP(u,v),w),x,y),hAPP(c_Set_Oimage(u,z,w),hAPP(c_Set_Oinsert(v,z),x1))),hAPP(c_Set_Oimage(u,z,w),x1))**.
% 299.79/300.49 22611[0:SpR:158.0,97.1] || c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(v,w,x),y),x,z) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(v,w,x),y),u,x,z),z,x),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,x,z,w),w,z),y)),hAPP(c_Set_Oimage(v,w,x),y))**.
% 299.79/300.49 26134[0:SpR:338.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z),w),x1)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),hAPP(c_Set_Oinsert(u,v),z)),x),hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),w,x),x1)))*.
% 299.79/300.49 27562[0:SpR:130.1,373.2] class_HOL_Ominus(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(x,y,tc_fun(t_a,u)),w,v,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_HOL_Ominus__class_Ominus(x,y,tc_fun(t_a,u)),v,z),c_HOL_Ominus__class_Ominus(hAPP(x,v_x),hAPP(y,v_x),u)),v_x)**.
% 299.79/300.49 27550[0:SpR:353.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) c_Fun_Oinj__on(c_Set_Oinsert(z,w),y,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,c_Set_Oinsert(z,w),u,x1),hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(z,w),x))),hAPP(c_Set_Oinsert(v,w),x))**.
% 299.79/300.49 27715[0:SpR:130.1,71.2] class_HOL_Ominus(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(x,y,tc_fun(t_a,u)),w,v,z) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_HOL_Ominus__class_Ominus(x,y,tc_fun(t_a,u)),v,z),c_HOL_Ominus__class_Ominus(hAPP(x,v_x),hAPP(y,v_x),u)),v_x)**.
% 299.79/300.49 27702[0:SpR:353.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) c_Fun_Oinj__on(c_Set_Oinsert(z,w),y,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(y,c_Set_Oinsert(z,w),u,x1),hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(z,w),x))),hAPP(c_Set_Oinsert(v,w),x))**.
% 299.79/300.49 28159[0:SpR:465.1,21893.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,u,y),v_x),c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),tc_Com_Opname,z)),hAPP(c_Set_Oimage(w,u,y),v_x))**.
% 299.79/300.49 28154[0:SpR:465.1,21267.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),hAPP(c_Set_Oimage(w,u,y),v_x),tc_Com_Opname,z)),hAPP(c_Set_Oimage(w,u,y),v_x))**.
% 299.79/300.49 28561[0:SpR:64.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(u,v),w,x1,x2,z),x,hAPP(c_Set_Oinsert(u,v),y),z,x2))*.
% 299.79/300.49 28472[0:SpR:130.1,118.0] class_HOL_Ominus(u) || -> equal(c_Fun_Ocomp(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),c_Fun_Ofun__upd(x,y,v_x,z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x,x1,x2,z),y,c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u),z,x2))*.
% 299.79/300.49 28460[0:SpR:196.1,118.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Fun_Ocomp(c_Set_Ovimage(u,v,w),c_Fun_Ofun__upd(x,y,hAPP(c_Set_Oimage(u,v,w),z),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Ovimage(u,v,w),x,x2,x3,x1),y,z,x1,x3))*.
% 299.79/300.49 29301[0:SSi:29067.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_HOL_Ominus__class_Ominus(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_fun(u,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))**.
% 299.79/300.49 31099[0:SpR:28771.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),c_Fun_Ofun__upd(v,w,v_Procs,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v,y,z,x),w,v_Procs,x,z))*.
% 299.79/300.49 31078[0:SpR:28771.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),tc_Com_Opname),v,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),tc_Com_Opname),u,x),v_Procs),v_Procs)**.
% 299.79/300.49 31077[0:SpR:28771.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),tc_Com_Opname),v,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),tc_Com_Opname),u,x),v_Procs),v_Procs)**.
% 299.79/300.49 31185[0:SpR:28926.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),c_Fun_Ofun__upd(v,w,v_Procs,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v,y,z,x),w,v_Procs,x,z))*.
% 299.79/300.49 31164[0:SpR:28926.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w),tc_Com_Opname),v,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w),tc_Com_Opname),u,x),v_Procs),v_Procs)**.
% 299.79/300.49 31163[0:SpR:28926.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w),tc_Com_Opname),v,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w),tc_Com_Opname),u,x),v_Procs),v_Procs)**.
% 299.79/300.49 31402[0:SpL:9.0,449.0] || hBOOL(hAPP(hAPP(u,hAPP(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(w,c_Fun_Ocomp(u,v,x,y,z),x1,x2))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(w,c_Fun_Ocomp(u,v,x,y,z),x1,x2)))* -> c_Hoare__Mirabelle_Otriple__valid(x2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),w),x1),c_Fun_Ocomp(u,v,x,y,z)),t_a).
% 299.79/300.49 31546[0:Res:171.2,473.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),x),u))),x))*.
% 299.79/300.49 31545[0:Res:172.2,473.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),x),u))),x))*.
% 299.79/300.49 31748[0:SpL:465.1,389.0] || equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),z),hAPP(c_Set_Oimage(u,x,y),x1))* c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y)* -> hBOOL(hAPP(hAPP(c_in(x),v),x1))* equal(z,x1).
% 299.79/300.49 32064[0:Res:151.2,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v))* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(x,c_HOL_Ominus__class_Ominus(v,w,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)))),c_HOL_Ominus__class_Ominus(v,w,tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))))* c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.79/300.49 33032[0:SpR:28334.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,x,hAPP(x,v_x),tc_Com_Opname,y),tc_Com_Opname),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,x,hAPP(x,v_x),tc_Com_Opname,y),tc_Com_Opname),u,w),v))**.
% 299.79/300.49 33030[0:SpR:28031.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(x,v_x),x,tc_Com_Opname,y),tc_Com_Opname),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(x,v_x),x,tc_Com_Opname,y),tc_Com_Opname),u,w),v))**.
% 299.79/300.49 32893[0:SpR:317.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* -> equal(hAPP(c_Set_Oinsert(hAPP(y,v),z),hAPP(c_Set_Oinsert(hAPP(y,w),z),hAPP(c_Set_Oimage(y,u,z),x))),hAPP(c_Set_Oinsert(hAPP(y,w),z),hAPP(c_Set_Oimage(y,u,z),x)))**.
% 299.79/300.49 33241[0:SpR:32668.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),c_Fun_Ofun__upd(w,x,v_Procs,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),w,z,x1,y),x,v_Procs,y,x1))*.
% 299.79/300.49 33219[0:SpR:32668.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,w,tc_Com_Opname,x),hAPP(w,v_x)),tc_Com_Opname),v,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,w,tc_Com_Opname,x),hAPP(w,v_x)),tc_Com_Opname),u,y),v_Procs),v_Procs)**.
% 299.79/300.49 33218[0:SpR:32668.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,w,tc_Com_Opname,x),hAPP(w,v_x)),tc_Com_Opname),v,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,w,tc_Com_Opname,x),hAPP(w,v_x)),tc_Com_Opname),u,y),v_Procs),v_Procs)**.
% 299.79/300.49 33396[0:SpL:21893.0,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname,w),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,x)),v))* c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.79/300.49 33395[0:SpL:21267.0,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Ohoare__valids(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x),tc_Com_Opname,w),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,x)),v))* c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.79/300.49 33798[0:Res:248.4,437.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(tc_fun(u,tc_bool),tc_bool))* c_Finite__Set_Ofinite(c_Finite__Set_Olinorder__class_OMin(w,tc_fun(u,tc_bool)),u)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,tc_bool),tc_bool))) c_Finite__Set_Ofinite(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),u)*.
% 299.79/300.49 33878[0:Res:247.4,437.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(tc_fun(u,tc_bool),tc_bool))* c_Finite__Set_Ofinite(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),u)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,tc_bool),tc_bool))) c_Finite__Set_Ofinite(c_Finite__Set_Olinorder__class_OMax(w,tc_fun(u,tc_bool)),u)*.
% 299.79/300.49 34397[0:SpL:24914.0,85.0] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),tc_fun(v,tc_bool))*.
% 299.79/300.49 34369[0:SpL:24914.0,279.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(hAPP(c_Set_Oinsert(v,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,w),hAPP(hAPP(c_in(u),v),v_x))),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,w),hAPP(hAPP(c_in(u),v),v_x)))**.
% 299.79/300.49 34306[0:SpL:24914.0,469.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x)),w,u)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x)))**.
% 299.79/300.49 34305[0:SpL:24914.0,464.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x)),v,w,u)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x)))**.
% 299.79/300.49 34184[0:SpR:24914.0,10931.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,w),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),v_x)),t_a) hBOOL(hAPP(hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),v_x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,w),hAPP(c_Set_Oinsert(v,tc_Hoare__Mirabelle_Otriple(t_a)),v_x)))))*.
% 299.79/300.49 34139[0:SpR:24914.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x)),tc_fun(w,tc_bool))* -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),tc_fun(w,tc_bool)).
% 299.79/300.49 34131[0:SpR:24914.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)))),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)))**.
% 299.79/300.49 34601[0:SpR:55.1,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) -> hBOOL(hAPP(hAPP(c_in(x),z),w)) hBOOL(hAPP(hAPP(c_in(x1),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(z,x),v),w,tc_fun(x,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(z,x),u,x1),y)))*.
% 299.79/300.49 34597[0:SpR:55.1,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) -> hBOOL(hAPP(hAPP(c_in(x),z),w)) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(z,x),v),w,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(z,x),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.49 35057[0:SpR:28755.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),c_Fun_Ofun__upd(y,z,v_Procs,x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),y,x2,x3,x1),z,v_Procs,x1,x3))*.
% 299.79/300.49 35035[0:SpR:28755.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,w,c_COMBK(w,x,y),tc_Com_Opname,z),tc_Com_Opname),v,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,w,c_COMBK(w,x,y),tc_Com_Opname,z),tc_Com_Opname),u,x1),v_Procs),v_Procs)**.
% 299.79/300.49 35034[0:SpR:28755.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,w,c_COMBK(w,x,y),tc_Com_Opname,z),tc_Com_Opname),v,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,w,c_COMBK(w,x,y),tc_Com_Opname,z),tc_Com_Opname),u,x1),v_Procs),v_Procs)**.
% 299.79/300.49 35146[0:SpR:28910.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),c_Fun_Ofun__upd(y,z,v_Procs,x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),y,x2,x3,x1),z,v_Procs,x1,x3))*.
% 299.79/300.49 35124[0:SpR:28910.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(w,x,y),w,tc_Com_Opname,z),tc_Com_Opname),v,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(w,x,y),w,tc_Com_Opname,z),tc_Com_Opname),u,x1),v_Procs),v_Procs)**.
% 299.79/300.49 35123[0:SpR:28910.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(w,x,y),w,tc_Com_Opname,z),tc_Com_Opname),v,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(w,x,y),w,tc_Com_Opname,z),tc_Com_Opname),u,x1),v_Procs),v_Procs)**.
% 299.79/300.49 35398[0:SpR:12944.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(x,y),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),z,x1)),v,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(x,y),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),z,x1)),v,tc_fun(x2,tc_bool))))*.
% 299.79/300.49 35370[0:SpR:11473.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),v,tc_fun(z,tc_bool))))*.
% 299.79/300.49 35359[0:SpR:329.1,410.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,tc_fun(z,tc_bool))))*.
% 299.79/300.49 35358[0:SpR:328.1,410.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,tc_fun(z,tc_bool))))*.
% 299.79/300.49 35355[0:SpR:538.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),v,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),v,tc_fun(z,tc_bool))))*.
% 299.79/300.49 35336[0:SpR:17045.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y,tc_fun(z,tc_bool)),v,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y,tc_fun(z,tc_bool)),v,tc_fun(x1,tc_bool))))*.
% 299.79/300.49 35251[0:SpR:410.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),x,y,z,x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,v,x3,tc_fun(u,tc_bool))),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x3),x2),v,x3,tc_fun(u,tc_bool)),hAPP(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,v,x3,tc_fun(u,tc_bool)))))*.
% 299.79/300.49 35250[0:SpR:410.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(w,x)),y,z,x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,w,x3,tc_fun(v,tc_bool))),hAPP(hAPP(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,w,x3,tc_fun(v,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,x3),x2),w,x3,tc_fun(v,tc_bool))))*.
% 299.79/300.49 35203[0:SpR:410.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),z)) -> hBOOL(hAPP(hAPP(c_in(x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x2,x),v),w,x,tc_fun(y,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(w,x2)),u,x1),z)))*.
% 299.79/300.49 35199[0:SpR:410.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),z)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x1,x),v),w,x,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(w,x1)),u,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.79/300.49 35446[0:SSi:35232.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),v,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),v,tc_fun(x,tc_bool)))))*.
% 299.79/300.49 35520[0:SpR:131.0,113.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),z)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x1),tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),c_HOL_Ominus__class_Ominus(z,x1,tc_fun(y,tc_bool))))**.
% 299.79/300.49 35505[0:SpR:131.0,113.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x1)),tc_fun(y,tc_bool)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_HOL_Ominus__class_Ominus(z,x1,tc_fun(x,tc_bool))))**.
% 299.79/300.49 35653[0:Rew:586.0,35612.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_COMBB(x,y,tc_fun(z,tc_bool),v),x1),v,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(x,hAPP(x1,u))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x1,v,y),w),x,y,tc_fun(z,tc_bool))))*.
% 299.79/300.49 36205[0:SSi:36146.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y))))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x))) hBOOL(hAPP(hAPP(c_in(u),v),y)).
% 299.79/300.49 36206[0:SSi:36144.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y))))* -> hBOOL(hAPP(hAPP(c_in(u),v),x)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y))).
% 299.79/300.49 36738[0:SpR:67.0,35.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(v,c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(v,c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,w),u),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),u)**.
% 299.79/300.49 36727[0:SpR:67.0,151.2] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(u),v),y)) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,u),y),tc_fun(u,tc_bool))))*.
% 299.79/300.49 36881[0:SpR:35.2,66.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(v,x,tc_fun(w,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(y,w),c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))**.
% 299.79/300.49 36851[0:SpR:66.0,151.2] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(y,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(y,u),x),tc_fun(u,tc_bool))))*.
% 299.79/300.49 37133[0:SpL:24914.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,u,x),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,u,x),v_x))))* c_lessequals(hAPP(c_Set_Oimage(w,u,x),v_x),z,tc_fun(x,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(w,v)),z))*.
% 299.79/300.49 37481[0:SpR:97.1,205.1] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(c_Fun_Othe__inv__into(v,u,w,x),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Fun_Othe__inv__into(v,u,w,x),x,w),w,x),v),hAPP(c_Set_Oimage(u,w,x),v))**.
% 299.79/300.49 37476[0:SpR:205.1,584.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_COMBS(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,y,z,x1),hAPP(c_Set_Oimage(u,v,w),x2)),hAPP(x2,hAPP(x,hAPP(c_Set_Oimage(u,v,w),x2))))*.
% 299.79/300.49 37475[0:SpR:205.1,584.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_COMBS(x,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),y,z,x1),hAPP(c_Set_Oimage(u,v,w),x2)),hAPP(hAPP(x,hAPP(c_Set_Oimage(u,v,w),x2)),x2))*.
% 299.79/300.49 37462[0:SpR:205.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oimage(v,w,x),z)),x1)) -> c_lessequals(z,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,x),x,w),y,u),u)*.
% 299.79/300.49 37451[0:SpR:205.1,176.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),hAPP(c_Set_Ovimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,z),hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.79/300.49 38035[0:MRR:38003.2,418.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* c_lessequals(x,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))* -> equal(hAPP(c_Set_Oinsert(v,u),x),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))*.
% 299.79/300.49 38305[0:SpR:21893.0,201.3] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,x),w,u,u),u)*.
% 299.79/300.49 38304[0:SpR:21267.0,201.3] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),tc_Com_Opname,x),w,u,u),u)*.
% 299.79/300.49 38350[0:SSi:38306.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),w)) c_Finite__Set_Ofinite(w,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),y),hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x,w,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),y),tc_bool)*.
% 299.79/300.49 38975[0:SpR:354.2,196.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v,x,w,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,w)* -> equal(hAPP(c_Set_Ovimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),u),hAPP(c_Set_Oimage(x,w,y),u))**.
% 299.79/300.49 39237[0:SpR:533.0,584.0] || -> equal(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x1),hAPP(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),x1)))))*.
% 299.79/300.49 40905[0:Res:153.1,479.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* hBOOL(hAPP(y,w))* -> hBOOL(hAPP(hAPP(c_in(z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Ovimage(v,z,u),x),x1,y,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Ovimage(v,z,u),x)),x1)))*.
% 299.79/300.49 40904[0:Res:545.1,479.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,hAPP(y,v)))* -> hBOOL(hAPP(hAPP(c_in(z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(y,u,z),w),x1,x,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,u,z),w)),x1)))*.
% 299.79/300.49 41186[0:Res:153.1,478.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* hBOOL(hAPP(y,w))* -> hBOOL(hAPP(hAPP(c_in(z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,hAPP(c_Set_Ovimage(v,z,u),x),y,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),hAPP(c_Set_Ovimage(v,z,u),x))))*.
% 299.79/300.49 41185[0:Res:545.1,478.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,hAPP(y,v)))* -> hBOOL(hAPP(hAPP(c_in(z),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,hAPP(c_Set_Oimage(y,u,z),w),x,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),hAPP(c_Set_Oimage(y,u,z),w))))*.
% 299.79/300.49 41261[0:SpL:353.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y))* hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x2,w),x))))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(x2,w),u,tc_fun(z,tc_bool))))*.
% 299.79/300.49 41650[0:SpL:9.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,x))),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,y,z,x1),x2,u),x3)))* c_Fun_Oinj__on(c_Fun_Ocomp(v,w,y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,u)* -> hBOOL(hAPP(hAPP(c_in(x2),x),x3)).
% 299.79/300.49 41629[0:SpL:11695.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),y,u),z)))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,u)* -> hBOOL(hAPP(hAPP(c_in(y),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),x)),z)).
% 299.79/300.49 41593[0:SpL:88.1,284.0] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),x,v),y)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,v)* -> hBOOL(hAPP(hAPP(c_in(x),w),y)).
% 299.79/300.49 41572[0:SpL:299.2,284.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* hBOOL(hAPP(hAPP(c_in(x),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,x),z)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,x)* -> hBOOL(hAPP(hAPP(c_in(y),v),z))*.
% 299.79/300.49 41697[0:Rew:9.0,41528.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,x))),hAPP(c_Set_Oimage(v,y,u),hAPP(c_Set_Oimage(w,z,y),x1))))* c_Fun_Oinj__on(c_Fun_Ocomp(v,w,y,u,z),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,u)* -> hBOOL(hAPP(hAPP(c_in(z),x),x1)).
% 299.79/300.49 41839[0:Res:34.1,199.0] || hBOOL(hAPP(u,hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,y),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Set_Ovimage(v,z,x1),u),x,w,y)))))* c_Fun_Oinj__on(x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,y) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(v,z,x1),u),x2))*.
% 299.79/300.49 41797[0:SpL:299.2,199.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w,v,x)),y,u)* hBOOL(y) c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z))*.
% 299.79/300.49 41947[0:SpR:56.1,82.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,u,y),hAPP(c_Set_Oinsert(v,u),z)),hAPP(c_Set_Oimage(x,u,y),w),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(z,w,tc_fun(u,tc_bool))),tc_fun(y,tc_bool))*.
% 299.79/300.49 42258[0:SSi:42165.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) c_Finite__Set_Ofinite(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(x,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v)* -> c_Finite__Set_Ofinite(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v).
% 299.79/300.49 42507[0:SpL:15172.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),y,tc_fun(z,tc_bool)),x1,x2)),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(c_Set_Oimage(u,x1,x2),v),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),y,tc_fun(z,tc_bool)),x1,x2),v)).
% 299.79/300.49 42487[0:SpL:337.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,y)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** -> equal(hAPP(c_Set_Oimage(u,x,y),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,y),v)).
% 299.79/300.49 42466[0:SpL:15172.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),y,tc_fun(z,tc_bool)),u,x1,x2)),c_Orderings_Obot__class_Obot(tc_bool))** -> equal(hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),w,x),y,tc_fun(z,tc_bool)),x1,x2),v),hAPP(c_Set_Oimage(u,x1,x2),v)).
% 299.79/300.49 42446[0:SpL:337.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u,x,y)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,y),v),hAPP(c_Set_Oimage(u,x,y),v)).
% 299.79/300.49 43082[0:SpR:1196.1,486.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,tc_fun(x,tc_bool)))**.
% 299.79/300.49 43077[0:SpR:3294.1,486.1] || equal(c_in(t_a),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(u,v_x),v,tc_fun(x,tc_bool)))**.
% 299.79/300.49 43073[0:SpR:330.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),u,tc_fun(x,tc_bool)))**.
% 299.79/300.49 43072[0:SpR:1195.1,486.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(x,tc_bool)))**.
% 299.79/300.49 43066[0:SpR:584.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_COMBS(z,v,x1,x2,x3),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(z,w),u,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(z,w),u,tc_fun(y,tc_bool)))**.
% 299.79/300.49 43064[0:SpR:9936.1,486.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),w),x))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,tc_fun(y,tc_bool)))**.
% 299.79/300.49 43060[0:SpR:9935.1,486.1] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),u),w))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),y),v,tc_fun(x,tc_bool)))**.
% 299.79/300.49 42980[0:SpR:34427.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,x),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,x),u,tc_fun(w,tc_bool)))**.
% 299.79/300.49 43876[0:Res:38131.1,199.0] || hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z)),v,u,w)))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z)),x1))*.
% 299.79/300.49 44170[0:SpR:128.0,232.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(x,v,y),c_HOL_Ouminus__class_Ouminus(z,tc_fun(y,tc_bool)))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(x,v,y),z)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.49 44133[0:SpR:158.0,232.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(x,y,v),z),tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.49 44130[0:SpR:317.0,232.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(x,v),y),tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(hAPP(u,x),w),hAPP(c_Set_Oimage(u,v,w),y)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.49 44335[0:Res:19748.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))))* equal(hAPP(w,v_x),hAPP(w,u))* c_Fun_Oinj__on(w,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),tc_Com_Opname,x)* -> equal(v_x,u).
% 299.79/300.49 45351[0:Res:168.0,487.1] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),x))))* -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),x),t_a) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,u,tc_Hoare__Mirabelle_Otriple(t_a))))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,tc_Hoare__Mirabelle_Otriple(t_a))))*.
% 299.79/300.49 45337[0:SpL:21893.0,487.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(v),v_x),c_in(v),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,v)))*.
% 299.79/300.49 45336[0:SpL:21267.0,487.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(v),hAPP(c_in(v),v_x),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,v)))*.
% 299.79/300.49 45464[0:Res:45357.1,479.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),x,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname)),x)))*.
% 299.79/300.49 45463[0:Res:45357.1,478.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname))))*.
% 299.79/300.49 45625[0:SpL:323.0,85.0] || c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,v,tc_fun(z,tc_bool)),tc_fun(z,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,v,tc_fun(z,tc_bool)),tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.79/300.49 45587[0:SpR:323.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool)),tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,w,x,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))* -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),z),w,x,tc_fun(y,tc_bool)),tc_fun(y,tc_bool)).
% 299.79/300.49 45576[0:SpR:323.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(y,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,w,x,tc_fun(u,tc_bool)))),hAPP(c_Set_Oinsert(y,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),z),w,x,tc_fun(u,tc_bool))))**.
% 299.79/300.49 45559[0:SpR:323.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),y,z),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(u,tc_bool)),y),x2)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),x1),w,x,tc_fun(u,tc_bool))))*.
% 299.79/300.49 45533[0:SpR:323.0,9569.0] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))),tc_bool)*.
% 299.79/300.49 45532[0:SpR:323.0,9568.0] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool)))),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))),tc_bool)*.
% 299.79/300.49 45874[0:SpL:8415.2,482.2] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,v,u)))* hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,v,u)))* hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(v,v_x)).
% 299.79/300.49 45849[0:SpL:339.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,w),x),u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,u,w)))* hBOOL(hAPP(hAPP(c_in(w),z),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y))))* -> hBOOL(hAPP(u,z))*.
% 299.79/300.49 45844[0:SpL:338.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(x,w),y),u,w)))* hBOOL(hAPP(hAPP(c_in(w),z),hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y))))* -> hBOOL(hAPP(u,z))*.
% 299.79/300.49 45808[0:SpL:8415.2,482.2] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,v,u)))* hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,v,u)))* hBOOL(hAPP(hAPP(c_in(u),x),hAPP(v_x,w)))* -> hBOOL(hAPP(v,x))*.
% 299.79/300.49 46175[0:Res:171.2,481.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(w,c_Finite__Set_Olinorder__class_OMin(v,u))) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))*.
% 299.79/300.49 46174[0:Res:172.2,481.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(w,c_Finite__Set_Olinorder__class_OMax(v,u))) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))*.
% 299.79/300.49 46113[0:SpL:584.0,481.0] || hBOOL(hAPP(c_COMBS(c_in(u),v,w,x,y),z))* -> hBOOL(hAPP(x1,z)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,z)),x2),x1,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,z)),x2)))*.
% 299.79/300.49 46493[0:Res:171.2,480.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(w,c_Finite__Set_Olinorder__class_OMin(v,u))) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v)))*.
% 299.79/300.49 46492[0:Res:172.2,480.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(v,u) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(w,c_Finite__Set_Olinorder__class_OMax(v,u))) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v)))*.
% 299.79/300.49 46431[0:SpL:584.0,480.0] || hBOOL(hAPP(c_COMBS(c_in(u),v,w,x,y),z))* -> hBOOL(hAPP(x1,z)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x2),hAPP(v,z)),x1,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x2),hAPP(v,z))))*.
% 299.79/300.49 46567[0:SpR:617.1,362.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oimage(w,x,tc_fun(u,tc_bool)),y))) -> equal(y,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) c_lessequals(hAPP(c_Set_Oinsert(z,u),v),hAPP(c_Set_Oinsert(z,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,x,tc_fun(u,tc_bool))),tc_fun(u,tc_bool))*.
% 299.79/300.49 46594[0:Rew:617.1,46584.2] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(c_Set_Oinsert(x,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ofun__upd(z,v,x1,u,tc_fun(y,tc_bool)),u,tc_fun(y,tc_bool))),hAPP(c_Set_Oinsert(x,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,z,u,tc_fun(y,tc_bool))))**.
% 299.79/300.49 46829[0:SSi:46775.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(tc_Com_Opname,tc_bool)),u),v))* c_Finite__Set_Ofinite(v,tc_fun(tc_Com_Opname,tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),u),w),v_Procs)** -> hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w,v,tc_fun(tc_Com_Opname,tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.79/300.49 46944[0:Res:241.2,357.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oimage(x,y,u),z)),tc_fun(u,tc_bool))* c_Finite__Set_Ofinite(z,y) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),u)*.
% 299.79/300.49 47592[0:SpL:104.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)),y))*.
% 299.79/300.49 48042[0:SpL:104.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,u,w)),y))*.
% 299.79/300.49 48426[0:SpL:23840.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),x),w,u) -> .
% 299.79/300.49 48410[0:SpL:23682.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oinsert(v,w),x),w,u) -> .
% 299.79/300.49 48316[0:SpL:8385.1,224.0] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(u,w),x),w,v) -> .
% 299.79/300.49 48827[0:Res:468.0,619.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(y,v,w),x))* equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(z,v,tc_fun(x1,tc_bool)),x),c_Set_Oinsert(x2,x1),tc_fun(x1,tc_bool),tc_fun(x1,tc_bool)),hAPP(c_Set_Oinsert(x2,x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,z,v,tc_fun(x1,tc_bool))))**.
% 299.79/300.49 48966[0:SpL:3229.1,483.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))* -> hBOOL(hAPP(y,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,y,v)),w))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,y,v)),x))*.
% 299.79/300.49 48906[0:SpL:3229.1,483.0] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(hAPP(c_in(v),x),hAPP(u,v_x)))* -> hBOOL(hAPP(y,x))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,y,v)),w))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,y,v)),v_x))*.
% 299.79/300.49 48900[0:SpL:3229.1,483.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_in(v),w),hAPP(hAPP(u,v_x),x)))* -> hBOOL(hAPP(y,w))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,y,v)),v_x))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,y,v)),x))*.
% 299.79/300.49 49171[0:SpL:3229.1,239.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(w,x,v),y)))* c_lessequals(y,z,tc_fun(x,tc_bool)) c_Fun_Oinj__on(w,y,x,v) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Fun_Othe__inv__into(y,w,x,v),v_x)),z))*.
% 299.79/300.49 49162[0:SpL:3229.1,239.0] || equal(u,c_Set_Oimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(u,v_x)))* c_lessequals(v_x,z,tc_fun(w,tc_bool)) c_Fun_Oinj__on(v,v_x,w,x) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(v_x,v,w,x),y)),z))*.
% 299.79/300.49 49685[0:Rew:49662.2,49512.2] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),hAPP(c_Set_Oinsert(v,x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Set_Oinsert(v,x),w),x,y).
% 299.79/300.49 49702[0:Rew:49662.2,49594.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),v))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),v),w,x).
% 299.79/300.49 49705[0:Rew:49662.2,49480.2] || equal(c_in(tc_Com_Opname),c_in(u)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,u),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),w,x),hAPP(c_Set_Oinsert(v_Procs,w),v))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,u),hAPP(c_Set_Oinsert(v_Procs,w),v),w,x).
% 299.79/300.49 49719[0:Rew:49662.2,49645.3] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(y,hAPP(u,z)),x1)) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(z,w),v),w,x) hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(z,w),v)),y,x,tc_fun(x2,tc_bool)),x1))*.
% 299.79/300.49 49729[0:Rew:49662.2,49569.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v,w) -> hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,w),hAPP(c_Set_Oinsert(x,v),u))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oinsert(x,v),u),v,w).
% 299.79/300.49 49927[2:SpR:497.0,4250.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))).
% 299.79/300.49 49916[0:SpR:497.0,3282.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))).
% 299.79/300.49 49915[7:SpR:497.0,27207.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_x)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))).
% 299.79/300.49 50151[0:SpR:3229.1,620.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(y,x,tc_fun(v,tc_bool)),w),hAPP(u,v_x),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),hAPP(hAPP(u,v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,x,tc_fun(v,tc_bool))))**.
% 299.79/300.49 50426[0:SpR:223.1,15367.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),tc_fun(z,tc_bool)),z)*.
% 299.79/300.49 50394[0:SpR:223.1,9566.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),z),hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,x1,u,y),u,y),w),z),tc_bool)*.
% 299.79/300.49 51112[0:MRR:51100.2,474.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))))* equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x),y)* -> equal(x,hAPP(u,y))*.
% 299.79/300.49 51787[4:Res:40244.1,199.0] || c_lessequals(v_x,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x,y,z,x1),v,u,w)),tc_bool)* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x,y,z,x1),x2))*.
% 299.79/300.49 52463[0:Res:229.0,228.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSemi(c_Com_Ocom_OSKIP,x)),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.79/300.49 52478[0:Res:37898.1,199.0] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,y,z,x1),w,v,x))))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u,y,z,x1),x2))*.
% 299.79/300.49 53359[0:Res:31543.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))* equal(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),v_x)),hAPP(v,u))* c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,x)* -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),v_x),u).
% 299.79/300.49 53446[0:SpR:33303.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(v_Procs,v),x)),hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v,w),x)))*.
% 299.79/300.49 53445[0:SpR:33303.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v,w),v_Procs),v_Procs)**.
% 299.79/300.49 53444[0:SpR:33303.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v,w),v_Procs),v_Procs)**.
% 299.79/300.49 53797[0:SpR:53771.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Option_Othe(x),v,y)),z))* c_Fun_Oinj__on(c_Option_Othe(x),z,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(z,c_Option_Othe(x),u,x1),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Option_Othe(x),v,y))*.
% 299.79/300.49 53796[0:SpR:53771.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Option_Othe(x),v,y)),z))* c_Fun_Oinj__on(c_Option_Othe(x),z,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,c_Option_Othe(x),u,x1),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,c_Option_Othe(x),v,y))*.
% 299.79/300.49 53828[0:SpR:53772.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(w),x,v,y)),z))* c_Fun_Oinj__on(c_Option_Othe(w),z,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(z,c_Option_Othe(w),u,x1),x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(w),x,v,y))*.
% 299.79/300.49 53827[0:SpR:53772.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(w),x,v,y)),z))* c_Fun_Oinj__on(c_Option_Othe(w),z,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,c_Option_Othe(w),u,x1),x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Option_Othe(w),x,v,y))*.
% 299.79/300.49 54115[0:SpR:52997.1,486.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_Procs,x),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(v_Procs,x),u,tc_fun(w,tc_bool)))**.
% 299.79/300.49 59129[0:Rew:339.0,58752.1] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))* -> hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),y))))*.
% 299.79/300.49 59130[0:Rew:537.1,58742.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y))))*.
% 299.79/300.49 59131[0:Rew:534.1,58741.2] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y))))*.
% 299.79/300.49 58687[0:SpL:205.1,15629.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(x)* -> hBOOL(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),y)))*.
% 299.79/300.49 59639[0:Rew:339.0,59260.1] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))* -> hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),z))))*.
% 299.79/300.49 59640[0:Rew:537.1,59250.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),z))))*.
% 299.79/300.49 59641[0:Rew:534.1,59249.2] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),z))))*.
% 299.79/300.49 59195[0:SpL:205.1,15857.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(x)* -> hBOOL(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),z)))*.
% 299.79/300.49 60447[0:SpR:5882.1,410.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),v),w),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v,tc_fun(x2,tc_bool))))*.
% 299.79/300.49 61770[0:SpR:11167.1,410.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),hAPP(c_Set_Oinsert(w,x),c_Set_Oinsert(v_x,tc_Com_Opname)),u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Set_Oinsert(w,x),c_Set_Oinsert(v_x,tc_Com_Opname)),u,tc_fun(y,tc_bool))))*.
% 299.79/300.49 62161[0:Res:23754.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs)))* equal(hAPP(w,v_x),hAPP(w,v))* c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v_Procs),u,x)* -> equal(v_x,v).
% 299.79/300.49 64215[0:SpR:465.1,646.1] || c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_Procs,tc_Com_Opname,z) -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),tc_Com_Opname,z),hAPP(c_Set_Oimage(u,x,y),v_x)),v_x)**.
% 299.79/300.49 64382[0:SpR:465.1,645.1] || c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_Procs,tc_Com_Opname,z) -> hBOOL(hAPP(hAPP(c_in(x),v),v_x)) equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),tc_Com_Opname,z),hAPP(c_Set_Oimage(u,x,y),v_x)),v_x)**.
% 299.79/300.49 64602[0:SpR:26782.0,118.0] || -> equal(c_Fun_Ocomp(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),c_Fun_Ofun__upd(w,x,c_Orderings_Obot__class_Obot(tc_bool),y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w,z,x1,y),x,c_Orderings_Obot__class_Obot(tc_bool),y,x1))*.
% 299.79/300.49 64695[0:Res:27986.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))* equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x)),hAPP(v,u))* c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,y)* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x),u).
% 299.79/300.49 64715[0:Res:27987.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))* equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x)),hAPP(v,u))* c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,y)* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x),u).
% 299.79/300.49 64735[0:Res:28288.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))* equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x)),hAPP(v,u))* c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,y)* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x),u).
% 299.79/300.49 64755[0:Res:28289.0,268.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs))* equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,x)),hAPP(v,u))* c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,y)* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,x),u).
% 299.79/300.49 64837[0:SpR:28747.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),hAPP(c_Set_Oinsert(v_Procs,x),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),y)))*.
% 299.79/300.49 64836[0:SpR:28747.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),v_Procs),v_Procs)**.
% 299.79/300.49 64835[0:SpR:28747.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),v_Procs),v_Procs)**.
% 299.79/300.49 64957[0:SpR:28748.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),hAPP(c_Set_Oinsert(v_Procs,x),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),y)))*.
% 299.79/300.49 64956[0:SpR:28748.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),v_Procs),v_Procs)**.
% 299.79/300.49 64955[0:SpR:28748.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,x),v_Procs),v_Procs)**.
% 299.79/300.49 65077[0:SpR:28902.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),hAPP(c_Set_Oinsert(v_Procs,x),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),y)))*.
% 299.79/300.49 65076[0:SpR:28902.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),v_Procs),v_Procs)**.
% 299.79/300.49 65075[0:SpR:28902.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),v_Procs),v_Procs)**.
% 299.79/300.49 65197[0:SpR:28903.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),y)),hAPP(c_Set_Oinsert(v_Procs,x),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),y)))*.
% 299.79/300.49 65196[0:SpR:28903.0,99.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),v_Procs),v_Procs)**.
% 299.79/300.49 65195[0:SpR:28903.0,438.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,x),v_Procs),v_Procs)**.
% 299.79/300.49 68248[0:SpR:1250.3,221.1] class_Lattices_Oboolean__algebra(u) class_OrderedGroup_Ogroup__add(u) class_Complete__Lattice_Ocomplete__lattice(u) || equal(c_Orderings_Otop__class_Otop(u),c_HOL_Ozero__class_Ozero(u)) -> equal(c_List_Ofoldl(c_COMBC(hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),v),w),v,u,u),c_HOL_Ozero__class_Ozero(u),x,u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_List_Oset(x,v),w,v,u))**.
% 299.79/300.49 71775[7:SpL:71455.1,224.0] || equal(u,v_x) hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(u,w),x),w,v) -> .
% 299.79/300.49 74349[7:SpL:71835.1,239.0] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) c_lessequals(v_x,y,tc_fun(v,tc_bool)) c_Fun_Oinj__on(u,v_x,v,w) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Fun_Othe__inv__into(v_x,u,v,w),x)),y))*.
% 299.79/300.49 74214[7:SpL:71835.1,483.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(v_x,w)))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,x,u)),v_x))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.79/300.49 74134[7:SpL:71835.1,239.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x))) c_lessequals(x,y,tc_fun(w,tc_bool)) c_Fun_Oinj__on(v,x,w,u) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(x,v,w,u),v_x)),y))*.
% 299.79/300.49 74130[7:SpL:71835.1,483.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))* -> hBOOL(hAPP(x,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.79/300.49 76161[0:SpR:9915.0,118.0] || -> equal(c_Fun_Ocomp(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_Fun_Ofun__upd(x2,x3,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x4,x5),x5,x6,x4),c_Fun_Ofun__upd(c_Fun_Ocomp(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x5,x6,x4),x3,c_Orderings_Otop__class_Otop(tc_bool),x4,x6))*.
% 299.79/300.49 76281[0:SpR:10469.0,118.0] || -> equal(c_Fun_Ocomp(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),c_Fun_Ofun__upd(x2,x3,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),x4,x5),x5,x6,x4),c_Fun_Ofun__upd(c_Fun_Ocomp(c_COMBS(c_Set_Oimage(u,v,w),x,y,z,x1),x2,x5,x6,x4),x3,c_Orderings_Obot__class_Obot(tc_bool),x4,x6))*.
% 299.79/300.49 76411[0:SpR:10470.0,118.0] || -> equal(c_Fun_Ocomp(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),c_Fun_Ofun__upd(x2,x3,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x4,x5),x5,x6,x4),c_Fun_Ofun__upd(c_Fun_Ocomp(c_COMBS(c_Set_Ovimage(u,v,w),x,y,z,x1),x2,x5,x6,x4),x3,c_Orderings_Obot__class_Obot(tc_bool),x4,x6))*.
% 299.79/300.49 76781[7:SpR:223.1,71682.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),v_x)** -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,z,u,y),u,y),w),v_x))*.
% 299.79/300.49 77353[0:Res:2399.2,325.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_fun(u,tc_bool)) c_lessequals(v,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.49 77352[0:Res:2399.2,324.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_fun(u,tc_bool)) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.79/300.49 77801[0:SpL:55.1,5892.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(v),u),x)) hBOOL(hAPP(c_COMBS(c_in(y),c_Set_Oinsert(u,v),z,x1,x2),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool))))*.
% 299.79/300.49 79032[0:Res:15630.1,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) -> c_Hoare__Mirabelle_Ohoare__valids(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,w),x),y,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w),z,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,w),x),y,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w),z),u,t_a)*.
% 299.79/300.49 79017[0:Res:15630.1,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,hAPP(c_in(u),v),x),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,hAPP(c_in(u),v),x),u),v,u)*.
% 299.79/300.49 79016[0:Res:15630.1,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,hAPP(c_in(u),v),x),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,x),y),z,hAPP(c_in(u),v),x),u),u)*.
% 299.79/300.49 78972[0:SpR:445.1,15630.1] || hBOOL(hAPP(c_Fun_Ofun__upd(u,v,w,x,y),z)) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(z,x1),x2),x3,c_Fun_Ofun__upd(u,v,w,x,y),x1),v) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(z,x1),x2),x3,c_Fun_Ofun__upd(u,v,w,x,y),x1)))*.
% 299.79/300.49 79252[0:Res:15858.1,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) -> c_Hoare__Mirabelle_Ohoare__valids(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oinsert(v,x),y),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x),z,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,hAPP(c_Set_Oinsert(v,x),y),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x),z),u,t_a)*.
% 299.79/300.49 79237[0:Res:15858.1,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(w,y),z),hAPP(c_in(u),v),y),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(w,y),z),hAPP(c_in(u),v),y),u),v,u)*.
% 299.79/300.49 79236[0:Res:15858.1,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(w,y),z),hAPP(c_in(u),v),y),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(w,y),z),hAPP(c_in(u),v),y),u),u)*.
% 299.79/300.49 79192[0:SpR:445.1,15858.1] || hBOOL(hAPP(c_Fun_Ofun__upd(u,v,w,x,y),z)) -> equal(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,hAPP(c_Set_Oinsert(z,x2),x3),c_Fun_Ofun__upd(u,v,w,x,y),x2),v) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,hAPP(c_Set_Oinsert(z,x2),x3),c_Fun_Ofun__upd(u,v,w,x,y),x2)))*.
% 299.79/300.49 80268[0:SpL:21268.0,5988.0] || c_Finite__Set_Ofinite(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),u) -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),x1,x2),u)*.
% 299.79/300.49 80215[0:SpL:21268.0,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) c_Hoare__Mirabelle_Ohoare__valids(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),x,y),t_a)* c_Hoare__Mirabelle_Otriple__valid(z,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,z),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(z,u,t_a)*.
% 299.79/300.49 80120[0:SpL:21268.0,57.1] class_OrderedGroup_Olordered__ab__group__add(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),u)),c_HOL_Ozero__class_Ozero(u))** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.49 80095[0:SpL:21268.0,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_in(w),hAPP(c_in(w),x),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),z))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,x1,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x1)))*.
% 299.79/300.49 80094[0:SpL:21268.0,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_in(w),hAPP(c_in(w),x),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),z))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,z,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),z)))*.
% 299.79/300.49 80060[0:SpL:21268.0,494.1] || hBOOL(hAPP(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),u,w),x),y))* c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),x1),x2),t_a)* c_Natural_Oevaln(x1,y,z,x3)* -> hBOOL(hAPP(hAPP(x2,x),x3))*.
% 299.79/300.49 79623[0:SpR:21268.0,23789.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w),x,y),tc_bool)*.
% 299.79/300.49 79618[0:SpR:21268.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oimage(x,u,y),hAPP(c_Set_Oimage(x,u,y),z),w,x1)))* -> equal(hAPP(c_Set_Oinsert(hAPP(x,v),y),hAPP(c_Set_Oimage(x,u,y),z)),hAPP(c_Set_Oimage(x,u,y),z)).
% 299.79/300.49 79613[0:SpR:21268.0,181.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,x),x,u),hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y),w,z)))* equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))).
% 299.79/300.49 80442[0:Rew:162.0,79795.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),z),y,x1))),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)))**.
% 299.79/300.49 80443[0:Rew:507.0,79792.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),z),y,x1))),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z)))**.
% 299.79/300.49 80444[0:Rew:507.0,79660.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),y),x,z)),x1)),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x1)))**.
% 299.79/300.49 80445[0:Rew:162.0,79644.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),y),x,z)),x1)),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),x1)))**.
% 299.79/300.49 81463[0:SpL:21894.0,5988.0] || c_Finite__Set_Ofinite(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),u) -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),z),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x,y),x1,x2),u)*.
% 299.79/300.49 81410[0:SpL:21894.0,455.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) c_Hoare__Mirabelle_Ohoare__valids(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x,y),t_a)* c_Hoare__Mirabelle_Otriple__valid(z,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,z),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(z,u,t_a)*.
% 299.79/300.49 81315[0:SpL:21894.0,57.1] class_OrderedGroup_Olordered__ab__group__add(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_HOL_Ouminus__class_Ouminus(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(u),w,x),u)),c_HOL_Ozero__class_Ozero(u))** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Lattices_Oupper__semilattice__class_Osup(u),w,x),c_HOL_Ozero__class_Ozero(u)).
% 299.79/300.49 81290[0:SpL:21894.0,479.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(w),x),c_in(w),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),z))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,x1,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x1)))*.
% 299.79/300.49 81289[0:SpL:21894.0,478.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(w),x),c_in(w),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),z))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,z,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),z)))*.
% 299.79/300.49 81255[0:SpL:21894.0,494.1] || hBOOL(hAPP(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),c_Hoare__Mirabelle_Otriple_Otriple(t_a),u,w),x),y))* c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),x1),x2),t_a)* c_Natural_Oevaln(x1,y,z,x3)* -> hBOOL(hAPP(hAPP(x2,x),x3))*.
% 299.79/300.49 80817[0:SpR:21894.0,23789.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),w),c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,tc_fun(v,tc_bool)),x,y),tc_bool)*.
% 299.79/300.49 80812[0:SpR:21894.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(x,u,y),z),c_Set_Oimage(x,u,y),w,x1)))* -> equal(hAPP(c_Set_Oinsert(hAPP(x,v),y),hAPP(c_Set_Oimage(x,u,y),z)),hAPP(c_Set_Oimage(x,u,y),z)).
% 299.79/300.49 80807[0:SpR:21894.0,181.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y),c_Set_Ovimage(c_COMBK(v,u,x),x,u),w,z)))* equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))).
% 299.79/300.49 81637[0:Rew:162.0,80989.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),z),c_Set_Ovimage(u,v,w),y,x1))),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)))**.
% 299.79/300.49 81638[0:Rew:507.0,80986.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(u,v,w),z),c_Set_Oimage(u,v,w),y,x1))),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z)))**.
% 299.79/300.49 81639[0:Rew:507.0,80854.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(u,v,w),y),c_Set_Oimage(u,v,w),x,z)),x1)),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x1)))**.
% 299.79/300.49 81640[0:Rew:162.0,80838.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),y),c_Set_Ovimage(u,v,w),x,z)),x1)),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),x1)))**.
% 299.79/300.49 83059[0:SpR:5924.0,118.0] || -> equal(c_Fun_Ocomp(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),c_Fun_Ofun__upd(x2,x3,x4,x5,x6),x6,x7,x5),c_Fun_Ofun__upd(c_Fun_Ocomp(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,x6,x7,x5),x3,hAPP(hAPP(u,x4),v),x5,x7))*.
% 299.79/300.49 83041[0:SpR:5924.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_COMBS(x,c_COMBK(y,z,x1),x2,x3,x4),w,u,x5) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_COMBS(x,c_COMBK(y,z,x1),x2,x3,x4),u,x5),hAPP(hAPP(x,v),y)),v)**.
% 299.79/300.49 83040[0:SpR:5924.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_COMBS(x,c_COMBK(y,z,x1),x2,x3,x4),w,u,x5) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_COMBS(x,c_COMBK(y,z,x1),x2,x3,x4),u,x5),hAPP(hAPP(x,v),y)),v)**.
% 299.79/300.49 83167[0:Rew:5924.0,83125.2] || hBOOL(hAPP(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_COMBS(u,c_COMBK(y,z,x1),x2,x3,x4),w,v,x))),y))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(hAPP(u,x5),y))*.
% 299.79/300.49 83384[0:SpR:5961.0,118.0] || -> equal(c_Fun_Ocomp(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),c_Fun_Ofun__upd(x2,x3,x4,x5,x6),x6,x7,x5),c_Fun_Ofun__upd(c_Fun_Ocomp(c_COMBS(c_COMBK(u,v,w),x,y,z,x1),x2,x6,x7,x5),x3,hAPP(u,hAPP(x,x4)),x5,x7))*.
% 299.79/300.49 83368[0:SpR:5961.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_COMBS(c_COMBK(x,y,z),x1,x2,x3,x4),w,u,x5) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_COMBS(c_COMBK(x,y,z),x1,x2,x3,x4),u,x5),hAPP(x,hAPP(x1,v))),v)**.
% 299.79/300.49 83367[0:SpR:5961.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_COMBS(c_COMBK(x,y,z),x1,x2,x3,x4),w,u,x5) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_COMBS(c_COMBK(x,y,z),x1,x2,x3,x4),u,x5),hAPP(x,hAPP(x1,v))),v)**.
% 299.79/300.49 83477[0:Rew:5961.0,83444.2] || hBOOL(hAPP(u,hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,y),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_COMBS(c_COMBK(u,z,x1),v,x2,x3,x4),x,w,y)))))* c_Fun_Oinj__on(x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,y) -> hBOOL(hAPP(u,hAPP(v,x5)))*.
% 299.79/300.49 83665[0:SpR:5899.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_COMBS(x,y,z,x1,x2),v,tc_fun(x3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x3,tc_bool)),hAPP(c_COMBS(x,y,x4,x5,x6),u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(x,y,z,x1,x2),v,tc_fun(x3,tc_bool))))*.
% 299.79/300.49 86460[0:SpL:86109.1,224.0] || equal(u,v_Procs) hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(u,w),x),w,v) -> .
% 299.79/300.49 86589[0:SpR:21893.0,19823.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v_x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_Com_Opname,x)))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v_x)).
% 299.79/300.49 86587[0:SpR:21267.0,19823.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v_x),tc_Com_Opname,x)))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v_x)).
% 299.79/300.49 86886[0:SpR:223.1,86345.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,z,u,y),u,y),w),v_x))*.
% 299.79/300.49 88926[0:SpR:486.1,14196.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),z,x1),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool))))*.
% 299.79/300.49 88921[0:SpR:161.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),x,y),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z),w,tc_fun(u,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),c_HOL_Ominus__class_Ominus(z,w,tc_fun(u,tc_bool))))*.
% 299.79/300.49 88920[0:SpR:162.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),y,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x1)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))),hAPP(c_Set_Ovimage(v,u,w),x1)))*.
% 299.79/300.49 88919[0:SpR:507.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),y,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x1)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))),hAPP(c_Set_Oimage(v,w,u),x1)))*.
% 299.79/300.49 89773[0:SpR:26183.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),x),z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u,z),y)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u,z),y))**.
% 299.79/300.49 92898[0:SpR:161.0,5876.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool))),z,x1,x2),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))),tc_fun(y,tc_bool))*.
% 299.79/300.49 92897[0:SpR:162.0,5876.0] || -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x)),x1,x2,x3),hAPP(c_Set_Ovimage(u,v,w),y)),tc_fun(z,tc_bool))*.
% 299.79/300.49 92896[0:SpR:507.0,5876.0] || -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x)),x1,x2,x3),hAPP(c_Set_Oimage(u,v,w),y)),tc_fun(z,tc_bool))*.
% 299.79/300.49 93203[0:SpR:5878.1,71.2] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) c_Fun_Oinj__on(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),w,v,x2) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v,x2),hAPP(x,c_Orderings_Obot__class_Obot(u))),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.49 93202[0:SpR:5878.1,373.2] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) c_Fun_Oinj__on(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),w,v,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v,x2),hAPP(x,c_Orderings_Obot__class_Obot(u))),c_Orderings_Obot__class_Obot(u))**.
% 299.79/300.49 19657[0:Res:176.0,496.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(u,hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),w),hAPP(c_Set_Oinsert(hAPP(v,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))))),hAPP(c_Set_Ovimage(v,tc_Hoare__Mirabelle_Otriple(t_a),w),hAPP(c_Set_Oinsert(hAPP(v,x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))))* c_Hoare__Mirabelle_Otriple__valid(u,x,t_a).
% 299.79/300.49 19992[0:SpR:64.0,584.0] || -> equal(hAPP(c_COMBS(c_Set_Oinsert(u,v),w,x,y,z),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),hAPP(hAPP(c_Set_Oinsert(u,v),x1),hAPP(w,c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))))*.
% 299.79/300.49 19991[0:SpR:64.0,584.0] || -> equal(hAPP(c_COMBS(u,c_Set_Oinsert(v,w),x,y,z),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))),hAPP(hAPP(u,c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))),hAPP(c_Set_Oinsert(v,w),x1)))*.
% 299.79/300.49 20962[0:SpR:188.1,317.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z),hAPP(c_Set_Oinsert(w,y),x1)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),z),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z),x1)))*.
% 299.79/300.49 21642[0:SpL:21267.0,447.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),v_x),w) c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v,w)* -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v).
% 299.79/300.49 21384[0:SpR:21267.0,98.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v,w)* -> equal(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v),c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),v_x),w)).
% 299.79/300.49 21747[0:Rew:104.0,21542.0] || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_Com_Opname,w),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))**.
% 299.79/300.49 22270[0:SpL:21893.0,447.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),v_x),w) c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v,w)* -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v).
% 299.79/300.49 22010[0:SpR:21893.0,98.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v,w)* -> equal(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v),c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),v_x),w)).
% 299.79/300.49 22376[0:Rew:104.0,22169.0] || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),tc_Com_Opname,w),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))**.
% 299.79/300.49 24787[0:SpR:614.2,317.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,y),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u),x),x1)),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,y),x1)))*.
% 299.79/300.49 24786[0:SpR:614.2,99.1] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u))**.
% 299.79/300.49 24785[0:SpR:614.2,438.1] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u))**.
% 299.79/300.49 26398[0:Res:47.2,85.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))*.
% 299.79/300.49 26961[0:Res:424.2,208.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* c_lessequals(y,hAPP(c_Set_Oinsert(w,u),x),tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),w),hAPP(c_Set_Oinsert(v,u),y)))* c_lessequals(hAPP(c_Set_Oinsert(v,u),y),x,tc_fun(u,tc_bool))*.
% 299.79/300.49 26960[0:Res:424.2,85.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x))) c_lessequals(y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),y),w,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))*.
% 299.79/300.49 27178[0:SpR:329.1,450.0] || c_lessequals(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x),tc_fun(u,tc_bool))* -> hBOOL(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x)) c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool))),w),v),t_a).
% 299.79/300.49 27177[0:SpR:328.1,450.0] || c_lessequals(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x),tc_fun(u,tc_bool))* -> hBOOL(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v,w,x)) c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool))),w),v),t_a).
% 299.79/300.49 27156[0:SpR:11177.1,450.0] || equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x),c_Orderings_Otop__class_Otop(tc_bool)) -> hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x)))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u)),w),v),t_a).
% 299.79/300.49 28465[0:SpR:131.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Ovimage(u,v,w),c_Fun_Ofun__upd(x,y,hAPP(c_Set_Ovimage(z,w,x1),x2),x3,x4),x4,x5,x3),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Ovimage(u,v,w),x,x4,x5,x3),y,hAPP(c_Set_Ovimage(c_Fun_Ocomp(z,u,w,x1,v),v,x1),x2),x3,x5))*.
% 299.79/300.49 28464[0:SpR:158.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oimage(u,v,w),c_Fun_Ofun__upd(x,y,hAPP(c_Set_Oimage(z,x1,v),x2),x3,x4),x4,x5,x3),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oimage(u,v,w),x,x4,x5,x3),y,hAPP(c_Set_Oimage(c_Fun_Ocomp(u,z,v,w,x1),x1,w),x2),x3,x5))*.
% 299.79/300.49 28459[0:SpR:317.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oimage(u,v,w),c_Fun_Ofun__upd(x,y,hAPP(c_Set_Oinsert(z,v),x1),x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oimage(u,v,w),x,x3,x4,x2),y,hAPP(c_Set_Oinsert(hAPP(u,z),w),hAPP(c_Set_Oimage(u,v,w),x1)),x2,x4))*.
% 299.79/300.49 32138[0:SpR:21893.0,340.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),tc_Com_Opname,x),v,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v_x),v,tc_fun(w,tc_bool)).
% 299.79/300.49 32137[0:SpR:21267.0,340.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v_x),tc_Com_Opname,x),v,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v_x),v,tc_fun(w,tc_bool)).
% 299.79/300.49 32511[0:SpL:21893.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),u,v)))* hBOOL(hAPP(hAPP(c_in(v),x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname,y)))* -> hBOOL(hAPP(u,x))*.
% 299.79/300.49 32510[0:SpL:21267.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),u,v)))* hBOOL(hAPP(hAPP(c_in(v),x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),tc_Com_Opname,y)))* -> hBOOL(hAPP(u,x))*.
% 299.79/300.49 33021[0:SpR:15172.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),y,z),x1,tc_fun(x2,tc_bool)),u,x),w)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),y,z),x1,tc_fun(x2,tc_bool)),u,x),w))**.
% 299.79/300.49 33013[0:SpR:128.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),x)) -> equal(hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(y,z,w),v),tc_fun(z,tc_bool)),x1),hAPP(c_Set_Oimage(c_Set_Ovimage(y,z,w),u,x1),x)),hAPP(c_Set_Oimage(c_Set_Ovimage(y,z,w),u,x1),x))**.
% 299.79/300.49 32977[0:SpR:337.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),u,y),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),u,y),w))**.
% 299.79/300.49 32965[0:SpR:544.1,475.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,z),y)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,z),y))**.
% 299.79/300.49 32964[0:SpR:543.1,475.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,z),y)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,z),y))**.
% 299.79/300.49 33079[0:SpL:465.1,94.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),z,x,y) c_Fun_Oinj__on(x1,hAPP(c_Set_Oimage(u,x,y),z),y,x2) -> hBOOL(hAPP(hAPP(c_in(x),v),z)) c_Fun_Oinj__on(c_Fun_Ocomp(x1,c_Fun_Ofun__upd(u,v,w,x,y),y,x2,x),z,x,x2)*.
% 299.79/300.49 33426[0:Res:450.0,453.0] || c_Hoare__Mirabelle_Ohoare__valids(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v,w,x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(tc_Hoare__Mirabelle_Otriple(t_a))),w),v),t_a)* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(u,y)),u))* c_Hoare__Mirabelle_Otriple__valid(y,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v,w,x),t_a)*.
% 299.79/300.49 33793[0:Res:248.4,18625.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(tc_fun(u,tc_bool),tc_bool)) -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,tc_bool),tc_bool))) c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),x),hAPP(c_Finite__Set_Olinorder__class_OMin(w,tc_fun(u,tc_bool)),x),tc_bool)*.
% 299.79/300.49 33873[0:Res:247.4,18625.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(tc_fun(u,tc_bool),tc_bool)) -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,tc_bool),tc_bool))) c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMax(w,tc_fun(u,tc_bool)),x),hAPP(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),x),tc_bool)*.
% 299.79/300.49 34374[0:SpL:24914.0,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname,w),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(v,x)),v))* c_Hoare__Mirabelle_Otriple__valid(x,u,t_a)*.
% 299.79/300.49 34341[0:SpL:24914.0,298.1] class_Lattices_Oupper__semilattice(u) || equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)) -> c_lessequals(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),u)*.
% 299.79/300.49 34304[0:SpL:24914.0,467.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) -> equal(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x)))),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x)))**.
% 299.79/300.49 34224[0:SpR:465.1,24914.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_x)) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),tc_Com_Opname,z),hAPP(c_Set_Oimage(w,u,y),v_x))),hAPP(c_Set_Oimage(w,u,y),v_x))**.
% 299.79/300.49 34053[0:SpR:24914.0,297.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),u)* -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)).
% 299.79/300.49 35413[0:SpR:28334.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,hAPP(w,v_x),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,w,hAPP(w,v_x),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool))))*.
% 299.79/300.49 35410[0:SpR:28031.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(w,v_x),w,tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(w,v_x),w,tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool))))*.
% 299.79/300.49 35268[0:SpR:475.1,410.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,hAPP(z,v))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(z,u,x1),w),y,x1,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(z,u,x1),w),y,x1,tc_fun(x,tc_bool)))**.
% 299.79/300.49 36728[0:SpR:67.0,55.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),w,tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,u),w),tc_fun(u,tc_bool))))**.
% 299.79/300.49 36880[0:SpR:113.0,66.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))),hAPP(c_Set_Oinsert(z,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(u,v,w),x),hAPP(c_Set_Oinsert(z,v),hAPP(c_Set_Ovimage(u,v,w),y)),tc_fun(v,tc_bool)))*.
% 299.79/300.49 37489[0:SpR:158.0,205.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,x) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Fun_Ocomp(u,v,w,x,y),y,x),x,y),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),z))),z)**.
% 299.79/300.49 37460[0:SpR:205.1,545.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),z)) -> hBOOL(hAPP(hAPP(c_in(x1),y),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,x1),z)))*.
% 299.79/300.49 37456[0:SpR:205.1,362.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),z)) -> c_lessequals(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.79/300.49 37442[0:SpR:205.1,89.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_COMBB(y,v,tc_fun(z,tc_bool),w),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w)),w,tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,tc_fun(z,tc_bool)))**.
% 299.79/300.49 37682[0:SpR:198.1,23.0] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,x) -> equal(c_Fun_Ocomp(c_Fun_Ocomp(c_Fun_Ocomp(z,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Fun_Ocomp(u,v,w,x,y),y,x),y,x1,x),u,x,x1,w),v,w,x1,y),z)**.
% 299.79/300.49 38226[0:Res:13.2,402.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,y,tc_fun(w,tc_bool)) c_lessequals(c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool))).
% 299.79/300.49 38220[0:SpR:35.2,13.2] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(v,x,tc_fun(w,tc_bool))* c_lessequals(v,y,tc_fun(w,tc_bool))* c_lessequals(z,c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> c_lessequals(u,c_HOL_Ominus__class_Ominus(y,z,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.49 38205[0:SpR:35.2,13.2] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(v,x,tc_fun(w,tc_bool))* c_lessequals(y,v,tc_fun(w,tc_bool))* c_lessequals(c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),z,tc_fun(w,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(y,z,tc_fun(w,tc_bool)),u,tc_fun(w,tc_bool))*.
% 299.79/300.49 38298[0:SpR:24914.0,201.3] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),v_x)),w,u,u),u)*.
% 299.79/300.49 38351[0:SSi:38310.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),w))* c_Finite__Set_Ofinite(w,tc_fun(u,tc_bool)) hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),y))* -> hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x,w,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),y))*.
% 299.79/300.49 38395[0:SpL:542.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(c_Set_Oimage(u,v,w),x))** c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y),v,w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y),x).
% 299.79/300.49 38634[0:SpL:317.0,184.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(hAPP(w,x),u),hAPP(c_Set_Oimage(w,y,u),z))))* c_Fun_Oinj__on(w,hAPP(c_Set_Oinsert(x,y),z),y,u) -> equal(hAPP(w,hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oinsert(x,y),z),w,y,u),v)),v)**.
% 299.79/300.49 39013[0:SpL:354.2,469.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(w),z),u)) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,x,w,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(hAPP(c_Set_Oimage(x,w,y),u),c_Hilbert__Choice_Oinv__into(v,x,w,y),z,y,w)),z)**.
% 299.79/300.49 39012[0:SpL:354.2,464.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(w),z),u)) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,x,w,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(hAPP(c_Set_Oimage(x,w,y),u),z,c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w)),z)**.
% 299.79/300.49 38983[0:SpR:317.0,354.2] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),x,tc_fun(v,tc_bool)) c_Fun_Oinj__on(y,x,v,z) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(x,y,v,z),z,v),hAPP(c_Set_Oinsert(hAPP(y,u),z),hAPP(c_Set_Oimage(y,v,z),w))),hAPP(c_Set_Oinsert(u,v),w))**.
% 299.79/300.49 38982[0:SpR:393.1,354.2] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(c_COMBK(x,y,w),v,w,y) -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,c_COMBK(x,y,w),w,y),y,w),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),u)*.
% 299.79/300.49 38981[0:SpR:354.2,317.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),hAPP(c_Set_Oinsert(z,y),hAPP(c_Set_Oimage(x,w,y),u))),hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v,x,w,y),z),w),u))**.
% 299.79/300.49 38979[0:SpR:354.2,584.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(hAPP(c_COMBS(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x1,x2,x3),hAPP(c_Set_Oimage(x,w,y),u)),hAPP(u,hAPP(z,hAPP(c_Set_Oimage(x,w,y),u))))*.
% 299.79/300.49 38978[0:SpR:354.2,584.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(hAPP(c_COMBS(z,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),x1,x2,x3),hAPP(c_Set_Oimage(x,w,y),u)),hAPP(hAPP(z,hAPP(c_Set_Oimage(x,w,y),u)),u))*.
% 299.79/300.49 38965[0:SpR:354.2,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_lessequals(v,w,tc_fun(x,tc_bool)) c_Fun_Oinj__on(y,w,x,z) hBOOL(hAPP(hAPP(c_in(x1),hAPP(c_Set_Oimage(y,x,z),v)),x2)) -> c_lessequals(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(w,y,x,z),z,x),x1,u),u)*.
% 299.79/300.49 38954[0:SpR:354.2,176.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oimage(x,w,y),u)),hAPP(c_Set_Ovimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x1),hAPP(c_Set_Oinsert(u,x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.79/300.49 41277[0:SpL:130.1,275.1] class_HOL_Ominus(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) hBOOL(hAPP(hAPP(c_in(x),y),c_HOL_Ominus__class_Ominus(hAPP(z,v_x),hAPP(x1,v_x),u))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(z,x1,tc_fun(t_a,u)),v,tc_fun(x,tc_bool))))*.
% 299.79/300.49 41559[0:SpL:25.1,284.0] class_HOL_Ouminus(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u)),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u)),x,v),y)))* c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,v)* -> hBOOL(hAPP(hAPP(c_in(x),v_x),y)).
% 299.79/300.49 41539[0:SpL:653.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,v),v,tc_Com_Opname),w,u),x)))* c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,v),v,tc_Com_Opname),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u)* -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),x)).
% 299.79/300.49 41536[0:SpL:445.1,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(v,x,y,z,x1),x2,u),x3)))* c_Fun_Oinj__on(c_Fun_Ofun__upd(v,x,y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,u)* -> equal(w,x) hBOOL(hAPP(hAPP(c_in(x2),w),x3)).
% 299.79/300.49 41730[0:SpL:21893.0,494.1] || hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v_x),y),t_a)* c_Natural_Oevaln(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v_x),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),tc_Com_Opname,z),w,x,x1)* -> hBOOL(hAPP(hAPP(y,v),x1))*.
% 299.79/300.49 41729[0:SpL:21267.0,494.1] || hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v_x),y),t_a)* c_Natural_Oevaln(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v_x),tc_Com_Opname,z),w,x,x1)* -> hBOOL(hAPP(hAPP(y,v),x1))*.
% 299.79/300.49 41984[0:SpR:21893.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),v_x),hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,y),x,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.49 41983[0:SpR:21267.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),v_x),hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,y),x,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.49 41969[0:SpR:21893.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),v_x),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,y),tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.49 41968[0:SpR:21267.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),v_x),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,y),tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.49 42260[0:SSi:42178.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,hAPP(c_Set_Oinsert(y,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),w,v)))* hBOOL(hAPP(hAPP(c_in(v),z),y))* -> hBOOL(hAPP(w,z))*.
% 299.79/300.49 42261[0:SSi:42120.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),x),hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(y,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),x),tc_bool)*.
% 299.79/300.49 42473[0:SpL:300.1,315.0] class_Lattices_Obounded__lattice(u) || equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,y)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,y))** -> equal(hAPP(c_Set_Oimage(v,x,y),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,y),w)).
% 299.79/300.49 42432[0:SpL:300.1,315.0] class_Lattices_Obounded__lattice(u) || equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,x,y)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,x,y))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,y),w),hAPP(c_Set_Oimage(v,x,y),w)).
% 299.79/300.49 42738[0:SpL:161.0,516.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),y,tc_fun(u,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool)))) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(x,y,tc_fun(u,tc_bool)))).
% 299.79/300.49 43091[0:SpR:9.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,hAPP(z,v))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ocomp(y,z,x1,x2,x3),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ocomp(y,z,x1,x2,x3),u,tc_fun(x,tc_bool)))**.
% 299.79/300.49 43070[0:SpR:11695.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),v)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(y,z),c_Option_Othe(v)),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(y,z),c_Option_Othe(v)),u,tc_fun(x,tc_bool)))**.
% 299.79/300.49 43032[0:SpR:88.1,486.1] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),v,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),v,tc_fun(y,tc_bool)))**.
% 299.79/300.49 43022[0:SpR:540.1,486.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,tc_fun(y,tc_bool)))**.
% 299.79/300.49 43021[0:SpR:539.1,486.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,tc_fun(y,tc_bool)))**.
% 299.79/300.49 43020[0:SpR:297.2,486.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) hBOOL(hAPP(hAPP(c_in(x),w),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,tc_fun(z,tc_bool)))**.
% 299.79/300.49 43017[0:SpR:2098.1,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(x,v,t_a) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,v),tc_Hoare__Mirabelle_Otriple(t_a)),u,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,v),tc_Hoare__Mirabelle_Otriple(t_a)),u,tc_fun(y,tc_bool)))**.
% 299.79/300.49 43011[0:SpR:299.2,486.1] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u)* hBOOL(hAPP(hAPP(c_in(x),v),y))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,tc_fun(z,tc_bool)))**.
% 299.79/300.49 43557[0:SpL:507.0,516.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),z))).
% 299.79/300.49 43779[0:SpL:162.0,516.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))))* -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y))) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),z))).
% 299.79/300.49 44676[0:SSi:44621.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v,u,tc_fun(tc_Com_Opname,tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v,hAPP(c_Set_Oinsert(w,tc_fun(tc_Com_Opname,tc_bool)),u),tc_fun(tc_Com_Opname,tc_bool),tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.79/300.49 45335[0:SpL:24914.0,487.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(v),tc_Com_Opname,w),hAPP(c_in(v),v_x))))* hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,v)))*.
% 299.79/300.49 45893[0:Res:168.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,tc_Hoare__Mirabelle_Otriple(t_a))))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,u,tc_Hoare__Mirabelle_Otriple(t_a))))* -> c_Hoare__Mirabelle_Ohoare__valids(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w),t_a) hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w))))*.
% 299.79/300.49 45879[0:SpL:21893.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)))* hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(w),v_x),c_in(w),tc_Com_Opname,y)))*.
% 299.79/300.49 45878[0:SpL:21267.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)))* hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(w),hAPP(c_in(w),v_x),tc_Com_Opname,y)))*.
% 299.79/300.49 46165[0:Res:23961.0,481.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_Procs)),w),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_Procs)),w)))*.
% 299.79/300.49 46200[0:Rew:339.0,46162.1,339.0,46162.1] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x))),u,tc_Com_Opname)),hAPP(c_Set_Oinsert(v,tc_Com_Opname),hAPP(c_Set_Oinsert(w,tc_Com_Opname),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),x)))))*.
% 299.79/300.49 46201[0:Rew:339.0,46161.1] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w)),u,t_a)),hAPP(c_Set_Oinsert(v,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w))))*.
% 299.79/300.49 46202[0:Rew:339.0,46147.1,339.0,46147.1] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))),u,w)),hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)))))*.
% 299.79/300.49 46140[0:Res:9071.0,481.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,tc_fun(w,tc_bool))),x),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,tc_fun(w,tc_bool))),x)))*.
% 299.79/300.49 46134[0:Res:1157.0,481.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_COMBK(v,x,y),tc_Com_Opname,w),v_Procs)),z),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_COMBK(v,x,y),tc_Com_Opname,w),v_Procs)),z)))*.
% 299.79/300.49 46203[0:Rew:339.0,46133.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(y,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z)),x,u)),hAPP(c_Set_Oinsert(y,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z))))*.
% 299.79/300.49 46104[0:SpL:8415.2,481.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))*.
% 299.79/300.49 46483[0:Res:23961.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_Procs)),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_Procs))))*.
% 299.79/300.49 46480[0:Res:19441.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs))),u,tc_Com_Opname)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v),hAPP(c_Set_Oinsert(w,tc_Com_Opname),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)))))*.
% 299.79/300.49 46479[0:Res:19452.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(t_a),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))),u,t_a)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),hAPP(c_Set_Oinsert(w,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))))))*.
% 299.79/300.49 46465[0:Res:9067.0,480.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(y,w),hAPP(c_Set_Oinsert(v,w),z))),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(y,w),hAPP(c_Set_Oinsert(v,w),z)))))*.
% 299.79/300.49 46458[0:Res:9071.0,480.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,tc_fun(w,tc_bool))),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,tc_fun(w,tc_bool)))))*.
% 299.79/300.49 46452[0:Res:1157.0,480.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(c_COMBK(v,y,z),tc_Com_Opname,w),v_Procs)),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(c_COMBK(v,y,z),tc_Com_Opname,w),v_Procs))))*.
% 299.79/300.49 46451[0:Res:254.1,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(c_Set_Oinsert(z,u),w)),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(c_Set_Oinsert(z,u),w))))*.
% 299.79/300.49 46422[0:SpL:8415.2,480.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,v)) -> hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v)))*.
% 299.79/300.49 46787[0:Res:247.4,44639.0] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) || c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) c_lessequals(v,u,tc_fun(tc_fun(tc_Com_Opname,tc_bool),tc_bool))* equal(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_Com_Opname,tc_bool),tc_bool))) hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMax(u,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.79/300.49 46786[0:Res:248.4,44639.0] class_Orderings_Olinorder(tc_fun(tc_Com_Opname,tc_bool)) || c_Finite__Set_Ofinite(u,tc_fun(tc_Com_Opname,tc_bool)) c_lessequals(v,u,tc_fun(tc_fun(tc_Com_Opname,tc_bool),tc_bool))* equal(c_Finite__Set_Olinorder__class_OMin(u,tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(tc_Com_Opname,tc_bool),tc_bool))) hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(tc_Com_Opname,tc_bool)),v_x))*.
% 299.79/300.49 46931[0:Res:241.2,430.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool))* c_lessequals(x,y,tc_fun(u,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool))*.
% 299.79/300.49 46927[0:SpR:66.0,241.2] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)))) c_lessequals(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),y),tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool))*.
% 299.79/300.49 46957[0:SSi:46946.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool))* c_lessequals(y,c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> c_lessequals(y,x,tc_fun(u,tc_bool))*.
% 299.79/300.49 47200[0:Res:13.2,242.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)) hBOOL(hAPP(hAPP(c_in(w),y),u)) -> c_lessequals(u,hAPP(c_Set_Oinsert(y,w),c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool))),tc_fun(w,tc_bool))*.
% 299.79/300.49 47184[0:SpL:66.0,242.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)))) c_lessequals(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),y),tc_fun(u,tc_bool)).
% 299.79/300.49 47269[0:SSi:47220.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(w),v),u)) -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),tc_fun(w,tc_bool))*.
% 299.79/300.49 47270[0:SSi:47217.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(w),v),u)) -> c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),x)),tc_fun(w,tc_bool))*.
% 299.79/300.49 47604[0:SpL:584.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,y,z,x1),x2)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x2,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(x,x2),u,w)),hAPP(x,x2)))*.
% 299.79/300.49 48054[0:SpL:584.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y,z,x1,x2),v)))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(y,v),u,w)),hAPP(y,v)))*.
% 299.79/300.49 48435[0:SpL:9925.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),x),w,u) -> .
% 299.79/300.49 48415[0:SpL:24020.1,224.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(hAPP(u,v_x),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(u,v_x),hAPP(c_Set_Oinsert(v_x,w),x),w,v) -> .
% 299.79/300.49 48407[0:SpL:9924.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v,u),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oinsert(x,v),w),v,u) -> .
% 299.79/300.49 48353[0:SpL:525.1,224.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Set_Oinsert(w,x),y),x,v) -> .
% 299.79/300.49 48314[0:SpL:2097.1,224.0] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v,x),y,w),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(u,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v,x),hAPP(c_Set_Oinsert(u,y),z),y,w) -> .
% 299.79/300.49 48805[0:Res:15262.1,619.0] || equal(c_in(t_a),c_in(u)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),c_Set_Oinsert(x,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v,u,tc_fun(w,tc_bool))))**.
% 299.79/300.49 48804[0:Res:3285.1,619.0] || equal(c_in(tc_Com_Opname),c_in(u)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),c_Set_Oinsert(y,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(y,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs),v,u,tc_fun(w,tc_bool))))**.
% 299.79/300.49 48803[0:Res:3317.1,619.0] || equal(c_in(u),c_in(v)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,v,tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(v_x,u),y)),c_Set_Oinsert(z,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(z,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),y),w,v,tc_fun(x,tc_bool))))**.
% 299.79/300.49 48776[0:Res:649.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,tc_Com_Opname,tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs)),c_Set_Oinsert(x,v),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(x,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),w),v_Procs),u,tc_Com_Opname,tc_fun(v,tc_bool))))**.
% 299.79/300.49 48775[0:Res:650.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,tc_Com_Opname,tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w)),c_Set_Oinsert(x,v),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(x,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),v_Procs),w),u,tc_Com_Opname,tc_fun(v,tc_bool))))**.
% 299.79/300.49 49067[0:SpR:49017.1,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> hBOOL(hAPP(w,v_x)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,w,tc_Com_Opname),tc_Com_Opname),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,w,tc_Com_Opname),tc_Com_Opname),u,tc_fun(x,tc_bool)))**.
% 299.79/300.49 49291[0:SpL:3229.1,488.1] || equal(u,c_in(v)) hBOOL(hAPP(w,v_x)) hBOOL(hAPP(hAPP(u,v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,w,v)),x))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,w,v)),y))*.
% 299.79/300.49 49231[0:SpL:3229.1,488.1] || equal(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))* hBOOL(hAPP(x,y))* hBOOL(hAPP(hAPP(c_in(v),y),hAPP(u,v_x)))* -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,v)),w))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,x,v)),v_x))*.
% 299.79/300.49 49225[0:SpL:3229.1,488.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))) hBOOL(hAPP(w,x))* hBOOL(hAPP(hAPP(c_in(v),x),hAPP(hAPP(u,v_x),y)))* -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,w,v)),v_x))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,w,v)),y))*.
% 299.79/300.49 49662[0:Rew:20916.0,49632.2] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,w),v),w,x) equal(hAPP(c_Set_Oimage(u,w,x),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(y,w),v)))**.
% 299.79/300.49 49670[0:Rew:49662.2,49474.2] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) c_Fun_Oinj__on(c_Set_Oinsert(w,v),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),u),hAPP(c_Set_Oimage(c_Set_Oinsert(w,v),y,z),hAPP(c_Set_Oinsert(u,y),x))))* c_Fun_Oinj__on(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(u,y),x),y,z).
% 299.79/300.49 49686[7:Rew:49662.2,49507.2] || equal(hAPP(c_in(u),v),v_x) c_Fun_Oinj__on(c_Set_Oinsert(v,u),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),x,y),hAPP(c_Set_Oinsert(v_x,x),w))))* c_Fun_Oinj__on(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v_x,x),w),x,y).
% 299.79/300.49 49687[0:Rew:49662.2,49508.2] || equal(hAPP(c_in(u),v),v_Procs) c_Fun_Oinj__on(c_Set_Oinsert(v,u),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),x,y),hAPP(c_Set_Oinsert(v_x,x),w))))* c_Fun_Oinj__on(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v_x,x),w),x,y).
% 299.79/300.49 49694[0:Rew:49662.2,49586.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) c_Fun_Oinj__on(hAPP(u,v_x),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),v_x),hAPP(c_Set_Oimage(hAPP(u,v_x),w,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),v))))* c_Fun_Oinj__on(hAPP(u,v_x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),v),w,x).
% 299.79/300.49 49706[0:Rew:49662.2,49476.2] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,x),hAPP(c_Set_Oinsert(u,w),v))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(u,w),v),w,x).
% 299.79/300.49 49710[0:Rew:49662.2,49499.2] class_Orderings_Otop(u) || c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),w,x),hAPP(c_Set_Oinsert(v_x,w),v))))* c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),hAPP(c_Set_Oinsert(v_x,w),v),w,x).
% 299.79/300.49 49711[0:Rew:49662.2,49500.2] class_Orderings_Obot(u) || c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),w,x),hAPP(c_Set_Oinsert(v_x,w),v))))* c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),hAPP(c_Set_Oinsert(v_x,w),v),w,x).
% 299.79/300.49 49728[0:Rew:49662.2,49566.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),u,v,w) -> hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v,w),hAPP(c_Set_Oinsert(x,v),u))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oinsert(x,v),u),v,w).
% 299.79/300.49 50173[7:MRR:50161.2,27297.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,u,v,tc_fun(w,tc_bool))))*.
% 299.79/300.49 50454[0:SpR:223.1,317.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oimage(x,u,y),hAPP(c_Set_Oinsert(z,u),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,hAPP(x,z),u,y),u,y),w))*.
% 299.79/300.49 50393[0:SpR:223.1,212.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),z))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,x1,u,y),u,y),w),z))*.
% 299.79/300.49 51432[0:Rew:585.0,51431.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_in(t_a),v_x),u)),hAPP(hAPP(c_Set_Oinsert(w,t_a),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_x)),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.49 53042[0:SpR:23955.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)),w))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(x,tc_bool)))**.
% 299.79/300.49 53174[0:SpR:23958.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)),w))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,tc_fun(x,tc_bool)))**.
% 299.79/300.49 54728[0:SpR:13749.2,486.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,tc_fun(x,tc_bool)))**.
% 299.79/300.49 55202[0:SpR:14043.2,486.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),v,tc_fun(x,tc_bool)))**.
% 299.79/300.49 60437[7:Res:58968.1,496.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w)))* c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.49 60550[0:Res:58969.1,496.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Procs) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w)))* c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.49 60623[7:Res:59476.1,496.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x)))* c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.49 60696[0:Res:59477.1,496.0] || equal(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_Procs) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x)))* c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.79/300.49 60881[0:Res:59017.1,496.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v),t_a)* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v),x))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v),x)))* c_Hoare__Mirabelle_Otriple__valid(w,v,t_a).
% 299.79/300.49 60954[0:Res:59525.1,496.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v),t_a)* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v),y))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v),y)))* c_Hoare__Mirabelle_Otriple__valid(w,v,t_a).
% 299.79/300.49 62446[0:SSi:62235.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,y,tc_fun(w,tc_bool)) equal(c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool))) -> c_lessequals(c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.79/300.49 64228[0:SpR:339.0,646.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),tc_Com_Opname,x),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),v_x)**.
% 299.79/300.49 64223[0:SpR:537.1,646.1] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),v_x)**.
% 299.79/300.49 64222[0:SpR:534.1,646.1] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),v_x)**.
% 299.79/300.49 64395[0:SpR:339.0,645.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),tc_Com_Opname,x),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),v_x)**.
% 299.79/300.49 64390[0:SpR:537.1,645.1] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),v_x)**.
% 299.79/300.49 64389[0:SpR:534.1,645.1] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))),v_x)**.
% 299.79/300.49 64588[0:SpR:26782.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,tc_fun(x,tc_bool)),v,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,tc_fun(x,tc_bool)),u,y),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.49 64587[0:SpR:26782.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,tc_fun(x,tc_bool)),v,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,tc_fun(x,tc_bool)),u,y),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.79/300.49 66220[0:SpL:65404.1,224.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Set_Oinsert(w,x),y),x,v) -> .
% 299.79/300.49 74236[7:SpL:71835.1,488.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),w),hAPP(v_x,x)))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,v,u)),v_x))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)),x))*.
% 299.79/300.49 74151[7:SpL:71835.1,488.1] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,v,u)),w))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)),x))*.
% 299.79/300.49 75623[0:SSi:75471.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(w,hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))),tc_fun(u,tc_bool))*.
% 299.79/300.49 76091[0:SSi:75925.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(w,hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),y))),tc_fun(u,tc_bool))*.
% 299.79/300.49 77333[0:SpR:128.0,2399.2] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || -> c_lessequals(hAPP(c_Set_Ovimage(v,u,w),x),hAPP(c_Set_Ovimage(v,u,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),tc_fun(u,tc_bool))* c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x),tc_fun(u,tc_bool)).
% 299.79/300.49 77476[7:SpL:71894.1,224.0] || equal(c_Set_Oinsert(v_x,t_a),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v_x,v,u),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))))* c_Fun_Oinj__on(v_x,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),v),w),v,u) -> .
% 299.79/300.49 77750[0:SpL:410.0,5892.0] || hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),x,v,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool))))* -> hBOOL(hAPP(c_COMBS(c_in(z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,u)),x1,x2,x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,v,tc_fun(y,tc_bool))))*.
% 299.79/300.49 77672[0:SpL:205.1,5892.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(x,hAPP(c_Set_Oimage(u,v,w),x)))* -> hBOOL(hAPP(c_COMBS(c_in(y),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),z,x1,x2),hAPP(c_Set_Oimage(u,v,w),x)))*.
% 299.79/300.49 79057[0:Rew:339.0,78991.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) -> hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(x,y),z),x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),y))))*.
% 299.79/300.49 79058[0:Rew:537.1,78988.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(x,y),z),x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y))))*.
% 299.79/300.49 79059[0:Rew:534.1,78987.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(x,y),z),x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y))))*.
% 299.79/300.49 79277[0:Rew:339.0,79211.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) -> hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(x,z),x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),z))))*.
% 299.79/300.49 79278[0:Rew:537.1,79208.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(x,z),x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),z))))*.
% 299.79/300.49 79279[0:Rew:534.1,79207.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(x,z),x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),z))))*.
% 299.79/300.49 80431[0:Rew:523.1,79721.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),x),w,y),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(x,v_x)))**.
% 299.79/300.49 79614[0:SpR:21268.0,188.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Ovimage(c_COMBK(v,u,x),x,u),hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y),w,z)))* -> equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))).
% 299.79/300.49 79392[0:SpR:21268.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),u,z),hAPP(c_COMBB(x1,x,tc_fun(x2,tc_bool),w),v),w,tc_fun(x2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,x),y),x1,x,tc_fun(x2,tc_bool)))**.
% 299.79/300.49 81626[0:Rew:523.1,80915.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w,y),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(x,v_x)))**.
% 299.79/300.49 80808[0:SpR:21894.0,188.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y),c_Set_Ovimage(c_COMBK(v,u,x),x,u),w,z)))* -> equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))).
% 299.79/300.49 80585[0:SpR:21894.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),u,z),hAPP(c_COMBB(x1,x,tc_fun(x2,tc_bool),w),v),w,tc_fun(x2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,x),y),x1,x,tc_fun(x2,tc_bool)))**.
% 299.79/300.49 85047[0:SpR:644.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),y),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(w,x,tc_Com_Opname),tc_Com_Opname,x),u,y),v)),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(w,x,tc_Com_Opname),tc_Com_Opname,x),u,y),v))**.
% 299.79/300.49 86586[0:SpR:24914.0,19823.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),tc_Com_Opname,x),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v_x))))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v_x)).
% 299.79/300.49 89754[0:SpR:26183.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),w),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,tc_fun(z,tc_bool))))*.
% 299.79/300.49 92392[0:Res:84.1,5022.0] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),w,tc_fun(v,tc_bool)),x,tc_fun(v,tc_bool))* -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)).
% 299.79/300.49 92796[0:SpR:21894.0,5876.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u,x,y,z),x1),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u,x,y,z),v,x2)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u,x,y,z),x1),tc_fun(w,tc_bool))*.
% 299.79/300.49 92794[0:SpR:21268.0,5876.0] || -> c_lessequals(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u,x,y,z),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u,x,y,z),x1),v,x2)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u,x,y,z),x1),tc_fun(w,tc_bool))*.
% 299.79/300.49 93204[0:SpR:5878.1,475.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(x,c_Orderings_Obot__class_Obot(u)),y),hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,z,x1,x2),v,y),w)),hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,z,x1,x2),v,y),w))**.
% 299.79/300.49 19994[0:SpR:64.0,10931.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),t_a) hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),v),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)))))*.
% 299.79/300.49 20863[0:SpR:317.0,246.2] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,y)),hAPP(c_Set_Oimage(u,v,w),x)))* equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(y,v),x)),w),c_Suc(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),x),w)))**.
% 299.79/300.49 23362[0:SpR:460.1,21893.0] || class_Lattices_Olattice(t_b) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))**.
% 299.79/300.49 23359[0:SpR:460.1,21267.0] || class_Lattices_Olattice(t_b) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),tc_Com_Opname,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))**.
% 299.79/300.49 23493[0:SpR:523.1,21893.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_Com_Opname,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)))**.
% 299.79/300.49 23490[0:SpR:523.1,21267.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),tc_Com_Opname,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)))**.
% 299.79/300.49 24155[0:SpR:542.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),w),z)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),z)))*.
% 299.79/300.49 27195[0:Res:450.0,496.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(tc_Hoare__Mirabelle_Otriple(t_a))),v),w),t_a) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(x,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),w,v,u))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),w,v,u)))* c_Hoare__Mirabelle_Otriple__valid(x,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),w,v,u),t_a).
% 299.79/300.49 27164[0:SpR:586.0,450.0] || -> hBOOL(hAPP(hAPP(u,hAPP(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_COMBB(u,w,x,y),v),z,x1,x2))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_COMBB(u,w,x,y),v),z,x1,x2)))* c_Hoare__Mirabelle_Otriple__valid(x2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_COMBB(u,w,x,y),v)),x1),z),t_a).
% 299.79/300.49 27163[0:SpR:585.0,450.0] || -> hBOOL(hAPP(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_COMBC(u,v,w,x),y),z,x1,x2)),y),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_COMBC(u,v,w,x),y),z,x1,x2)))* c_Hoare__Mirabelle_Otriple__valid(x2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_COMBC(u,v,w,x),y)),x1),z),t_a).
% 299.79/300.49 27152[0:SpR:328.1,450.0] || c_lessequals(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y),v,tc_fun(u,tc_bool))* -> hBOOL(hAPP(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y))) c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v)),x),w),t_a)*.
% 299.79/300.49 27584[0:SpR:181.1,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(x,y,z),z,y),w,u,x1) -> hBOOL(hAPP(hAPP(c_in(y),x),v))* equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Ovimage(c_COMBK(x,y,z),z,y),u,x1),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),v)*.
% 299.79/300.49 27533[0:SpR:373.2,317.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x1),hAPP(c_Set_Oinsert(hAPP(x,v),z),x2)),hAPP(c_Set_Oinsert(v,x1),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x1),x2)))*.
% 299.79/300.49 27532[0:SpR:373.2,99.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(w,x,u,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x1),v),hAPP(x,v))**.
% 299.79/300.49 27531[0:SpR:373.2,438.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(w,x,u,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x1),v),hAPP(x,v))**.
% 299.79/300.49 27737[0:SpR:181.1,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(x,y,z),z,y),w,u,x1) -> hBOOL(hAPP(hAPP(c_in(y),x),v))* equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Ovimage(c_COMBK(x,y,z),z,y),u,x1),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),v)*.
% 299.79/300.49 27685[0:SpR:71.2,317.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(w,x,u,y),z,x1),hAPP(c_Set_Oinsert(hAPP(x,v),z),x2)),hAPP(c_Set_Oinsert(v,x1),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(w,x,u,y),z,x1),x2)))*.
% 299.79/300.49 27684[0:SpR:71.2,99.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) c_Fun_Oinj__on(c_Fun_Othe__inv__into(w,x,u,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Fun_Othe__inv__into(w,x,u,y),z,x1),v),hAPP(x,v))**.
% 299.79/300.49 27683[0:SpR:71.2,438.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) c_Fun_Oinj__on(c_Fun_Othe__inv__into(w,x,u,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Fun_Othe__inv__into(w,x,u,y),z,x1),v),hAPP(x,v))**.
% 299.79/300.49 27936[0:Res:468.0,470.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(c_Set_Oimage(x1,v,w),hAPP(c_Set_Oimage(x,y,v),z))) hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__XimageE__1__1(z,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(x,y,v),z),u,x1,v,w),x,y,v)),z))*.
% 299.79/300.49 27935[0:Res:468.0,466.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(c_Set_Oimage(x1,v,w),hAPP(c_Set_Oimage(x,y,v),z))) hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(z,x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(x,y,v),z),u,x1,v,w),y,v)),z))*.
% 299.79/300.49 28560[0:SpR:338.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(u,v),c_Fun_Ofun__upd(w,x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(u,v),w,x2,x3,x1),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),hAPP(c_Set_Oinsert(u,v),z)),x1,x3))*.
% 299.79/300.49 28556[0:SpR:317.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(hAPP(u,v),w),c_Fun_Ofun__upd(x,y,hAPP(c_Set_Oimage(u,z,w),x1),x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(hAPP(u,v),w),x,x3,x4,x2),y,hAPP(c_Set_Oimage(u,z,w),hAPP(c_Set_Oinsert(v,z),x1)),x2,x4))*.
% 299.79/300.49 28508[0:SpR:600.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Fun_Ofun__upd(w,x,c_HOL_Ominus__class_Ominus(y,v,tc_fun(u,tc_bool)),z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x1,x2,z),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v),z,x2))*.
% 299.79/300.49 28494[0:SpR:181.1,118.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_Fun_Ocomp(c_Set_Ovimage(c_COMBK(v,u,x),x,u),c_Fun_Ofun__upd(y,z,w,x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,x2,x3,x1),z,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),x1,x3))*.
% 299.79/300.49 28629[0:SpR:317.0,177.1] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(v,x,u),y))) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(v,x,u),hAPP(c_Set_Oinsert(w,x),y)),hAPP(c_Set_Oinsert(hAPP(v,w),u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,x,u),y))**.
% 299.79/300.49 30102[0:SpR:536.1,317.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z),w),x1)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z)),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),x1)))*.
% 299.79/300.49 30658[0:SpR:535.1,317.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z),w),x1)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z)),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x),x1)))*.
% 299.79/300.49 31418[0:SpL:329.1,449.0] || c_lessequals(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x),tc_fun(v,tc_bool))* hBOOL(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x)) -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),w),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))),t_a).
% 299.79/300.49 31417[0:SpL:328.1,449.0] || c_lessequals(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x),tc_fun(v,tc_bool))* hBOOL(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x)) -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),w),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool))),t_a).
% 299.79/300.49 31396[0:SpL:11177.1,449.0] || equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x)))* -> c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v)),t_a).
% 299.79/300.49 32334[0:SpL:8385.1,477.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,tc_Com_Opname),u),v_Procs) hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,tc_Com_Opname),u))* hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),x)).
% 299.79/300.49 32514[0:SpL:8385.1,476.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,tc_Com_Opname),u),v_Procs) hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,tc_Com_Opname),u))* hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),x)).
% 299.79/300.49 33033[0:SpR:28926.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,x),tc_Com_Opname),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,x),tc_Com_Opname),u,w),v))**.
% 299.79/300.49 33031[0:SpR:28771.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,x),tc_Com_Opname),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,x),tc_Com_Opname),u,w),v))**.
% 299.79/300.49 33028[0:SpR:64.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool))),y))* -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(w,x),v),z),hAPP(c_Set_Oimage(c_Set_Oinsert(w,x),u,z),y)),hAPP(c_Set_Oimage(c_Set_Oinsert(w,x),u,z),y))**.
% 299.79/300.49 32931[0:SpR:130.1,475.1] class_HOL_Ominus(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(hAPP(x,v_x),hAPP(y,v_x),u),z),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(x,y,tc_fun(t_a,u)),v,z),w)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(x,y,tc_fun(t_a,u)),v,z),w))**.
% 299.79/300.49 32919[0:SpR:196.1,475.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),z)) -> equal(hAPP(c_Set_Oinsert(y,x1),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,x1),z)),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),x,x1),z))**.
% 299.79/300.49 33220[0:SpR:32668.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,x,tc_Com_Opname,y),hAPP(x,v_x)),tc_Com_Opname),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,x,tc_Com_Opname,y),hAPP(x,v_x)),tc_Com_Opname),u,w),v))**.
% 299.79/300.49 33797[0:Res:248.4,436.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(tc_fun(u,tc_bool),tc_bool))* hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),x))* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,tc_bool),tc_bool))) hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMin(w,tc_fun(u,tc_bool)),x))*.
% 299.79/300.49 33877[0:Res:247.4,436.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(tc_fun(u,tc_bool),tc_bool))* hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMax(w,tc_fun(u,tc_bool)),x))* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,tc_bool),tc_bool))) hBOOL(hAPP(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),x))*.
% 299.79/300.49 34398[0:SpL:24914.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),u,v)))* hBOOL(hAPP(hAPP(c_in(v),x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x))))* -> hBOOL(hAPP(u,x))*.
% 299.79/300.49 34137[0:SpR:24914.0,340.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v_x)),v,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v_x),v,tc_fun(w,tc_bool)).
% 299.79/300.49 34528[0:Rew:104.0,34235.0] || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),tc_Com_Opname,w),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))**.
% 299.79/300.49 35036[0:SpR:28755.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,x,c_COMBK(x,y,z),tc_Com_Opname,x1),tc_Com_Opname),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,x,c_COMBK(x,y,z),tc_Com_Opname,x1),tc_Com_Opname),u,w),v))**.
% 299.79/300.49 35125[0:SpR:28910.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(x,y,z),x,tc_Com_Opname,x1),tc_Com_Opname),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(x,y,z),x,tc_Com_Opname,x1),tc_Com_Opname),u,w),v))**.
% 299.79/300.49 35419[0:SpR:24914.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),v),w),c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),tc_Com_Opname,x),v,tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),tc_Com_Opname,x),v,tc_fun(u,tc_bool))))**.
% 299.79/300.49 35399[0:SpR:15172.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),x,y),z,tc_fun(x1,tc_bool)),v,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),x,y),z,tc_fun(x1,tc_bool)),v,tc_fun(x2,tc_bool))))*.
% 299.79/300.49 35391[0:SpR:128.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)),w),x),c_Set_Ovimage(y,z,v),w,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(y,z,v),u),tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Ovimage(y,z,v),w,tc_fun(x1,tc_bool))))*.
% 299.79/300.49 35354[0:SpR:337.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),v,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),v,tc_fun(y,tc_bool))))*.
% 299.92/300.49 35342[0:SpR:544.1,410.0] class_Lattices_Olattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,tc_fun(z,tc_bool))))*.
% 299.92/300.49 35341[0:SpR:543.1,410.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,tc_fun(z,tc_bool))))*.
% 299.92/300.49 35266[0:SpR:55.1,410.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),y,u,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),y,u,tc_fun(z,tc_bool))))*.
% 299.92/300.49 37496[0:SpL:205.1,471.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oimage(u,v,w),y)))* c_lessequals(y,z,tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x)),z))*.
% 299.92/300.49 37472[0:SpR:205.1,196.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v)* -> equal(hAPP(c_Set_Ovimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x),hAPP(c_Set_Oimage(u,v,w),x))**.
% 299.92/300.49 38219[0:SpR:113.0,13.2] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),y,tc_fun(v,tc_bool)) c_lessequals(z,hAPP(c_Set_Ovimage(u,v,w),x1),tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(x,x1,tc_fun(w,tc_bool))),c_HOL_Ominus__class_Ominus(y,z,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.92/300.49 38204[0:SpR:113.0,13.2] || c_lessequals(u,hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Ovimage(v,w,x),z),x1,tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,x1,tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),c_HOL_Ominus__class_Ominus(y,z,tc_fun(x,tc_bool))),tc_fun(w,tc_bool))*.
% 299.92/300.49 38483[0:SpL:158.0,385.1] || c_Finite__Set_Ofinite(u,v) c_lessequals(hAPP(c_Set_Oimage(w,x,v),hAPP(c_Set_Oimage(y,v,x),u)),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(c_Fun_Ocomp(w,y,x,v,v),u,v,v) -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(w,y,x,v,v),v,v),u),u)**.
% 299.92/300.49 38667[0:Res:168.0,184.0] || c_Fun_Oinj__on(u,v,w,tc_Hoare__Mirabelle_Otriple(t_a)) -> c_Hoare__Mirabelle_Ohoare__valids(x,hAPP(c_Set_Oimage(u,w,tc_Hoare__Mirabelle_Otriple(t_a)),v),t_a) equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(v,u,w,tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,hAPP(c_Set_Oimage(u,w,tc_Hoare__Mirabelle_Otriple(t_a)),v)))),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,hAPP(c_Set_Oimage(u,w,tc_Hoare__Mirabelle_Otriple(t_a)),v)))**.
% 299.92/300.49 38636[0:SpL:158.0,184.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Fun_Ocomp(w,x,y,u,z),z,u),x1)))* c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(x,z,y),x1),y,u) -> equal(hAPP(w,hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,z,y),x1),w,y,u),v)),v)**.
% 299.92/300.49 39011[0:SpL:354.2,467.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(w),z),u)) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,x,w,y),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,w,y),u),c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z)),z)**.
% 299.92/300.49 38993[0:SpR:158.0,354.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(c_Fun_Ocomp(x,y,z,x1,w),v,w,x1) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,c_Fun_Ocomp(x,y,z,x1,w),w,x1),x1,w),hAPP(c_Set_Oimage(x,z,x1),hAPP(c_Set_Oimage(y,w,z),u))),u)**.
% 299.92/300.49 38985[0:SpR:158.0,354.2] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool)) c_Fun_Oinj__on(z,y,w,x1) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(y,z,w,x1),x1,w),hAPP(c_Set_Oimage(c_Fun_Ocomp(z,u,w,x1,v),v,x1),x)),hAPP(c_Set_Oimage(u,v,w),x))**.
% 299.92/300.49 38963[0:SpR:354.2,545.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oimage(x,w,y),u)),x1)) -> hBOOL(hAPP(hAPP(c_in(x2),u),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x2),x1)))*.
% 299.92/300.49 38959[0:SpR:354.2,362.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oimage(x,w,y),u)),x1)) -> c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.92/300.49 38944[0:SpR:354.2,89.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,w,y),u),hAPP(c_COMBB(z,w,tc_fun(x1,tc_bool),y),c_Hilbert__Choice_Oinv__into(v,x,w,y)),y,tc_fun(x1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,z,w,tc_fun(x1,tc_bool)))**.
% 299.92/300.49 39019[0:MRR:39007.3,20734.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(w),z),u)) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,x,w,y),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,w,y),u),c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z)),z)**.
% 299.92/300.49 39186[0:SpR:533.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),x1),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1)),v,u),u)*.
% 299.92/300.49 39168[0:SpR:533.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),u,z),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.92/300.49 39914[0:Rew:533.0,39775.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y))))*.
% 299.92/300.49 39612[0:SpR:532.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),z)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),v,u),u)*.
% 299.92/300.49 39594[0:SpR:532.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),u,z),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.92/300.49 39932[0:Rew:24251.1,39616.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),z))**.
% 299.92/300.49 40946[0:Res:687.1,479.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,hAPP(c_in(u),v),tc_Com_Opname),y,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,hAPP(c_in(u),v),tc_Com_Opname)),y)))*.
% 299.92/300.49 40945[0:Res:686.1,479.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,hAPP(c_in(u),v),tc_Com_Opname),y,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,hAPP(c_in(u),v),tc_Com_Opname)),y)))*.
% 299.92/300.49 40964[0:Rew:533.0,40896.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y),z,x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),z))))*.
% 299.92/300.49 40965[0:Rew:533.0,40895.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w),z,x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z))))*.
% 299.92/300.49 41227[0:Res:687.1,478.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,v_Procs,hAPP(c_in(u),v),tc_Com_Opname),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,v_Procs,hAPP(c_in(u),v),tc_Com_Opname))))*.
% 299.92/300.49 41226[0:Res:686.1,478.1] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,y,hAPP(c_in(u),v),tc_Com_Opname),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,y,hAPP(c_in(u),v),tc_Com_Opname))))*.
% 299.92/300.49 41177[0:Res:510.1,478.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z))))*.
% 299.92/300.49 41176[0:Res:511.1,478.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),w),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),w))))*.
% 299.92/300.49 41433[0:Res:468.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oimage(x,y,z),hAPP(x1,v)),hAPP(c_Set_Oimage(x2,y,z),hAPP(x1,v))) hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(x1,v),x,x2,y,z)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x1,u,tc_fun(y,tc_bool))))*.
% 299.92/300.49 41365[0:SpL:128.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),x))* hBOOL(hAPP(hAPP(c_in(y),z),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(x1,x2,w),v),tc_fun(x2,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Ovimage(x1,x2,w),u,tc_fun(y,tc_bool))))*.
% 299.92/300.49 41312[0:SpL:544.1,275.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y))* hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(z,tc_bool))))*.
% 299.92/300.49 41311[0:SpL:543.1,275.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y))* hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(z,tc_bool))))*.
% 299.92/300.49 41301[0:SpL:181.1,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(x1),x2),v))* hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(c_COMBK(x2,x1,z),z,x1),u,tc_fun(x,tc_bool))))*.
% 299.92/300.49 41653[0:SpL:584.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(v,w),hAPP(x,w))),hAPP(c_Set_Oimage(c_COMBS(v,x,y,z,x1),x2,u),x3)))* c_Fun_Oinj__on(c_COMBS(v,x,y,z,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,u)* -> hBOOL(hAPP(hAPP(c_in(x2),w),x3)).
% 299.92/300.49 41652[0:SpL:586.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,x))),hAPP(c_Set_Oimage(hAPP(c_COMBB(v,y,z,x1),w),x2,u),x3)))* c_Fun_Oinj__on(hAPP(c_COMBB(v,y,z,x1),w),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,u)* -> hBOOL(hAPP(hAPP(c_in(x2),x),x3)).
% 299.92/300.49 41651[0:SpL:585.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(v,w),x)),hAPP(c_Set_Oimage(hAPP(c_COMBC(v,y,z,x1),x),x2,u),x3)))* c_Fun_Oinj__on(hAPP(c_COMBC(v,y,z,x1),x),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,u)* -> hBOOL(hAPP(hAPP(c_in(x2),w),x3)).
% 299.92/300.49 41648[0:SpL:11499.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),y,u),z)))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,u)* -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(tc_bool)),z)).
% 299.92/300.49 41588[0:SpL:14526.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Option_Othe(v),w,tc_fun(x,tc_bool)),y,u),z)))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Option_Othe(v),w,tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,u)* -> hBOOL(hAPP(hAPP(c_in(y),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v)),z)).
% 299.92/300.49 41567[0:SpL:34428.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),w,u),x)))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u)* -> hBOOL(hAPP(hAPP(c_in(w),v_x),x)).
% 299.92/300.49 41518[0:SpL:97.1,284.0] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(v,u,w,x),y)),v))* c_Fun_Oinj__on(c_Fun_Othe__inv__into(v,u,w,x),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w)* -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(u,w,x),v)))*.
% 299.92/300.49 41727[0:SpL:24914.0,494.1] || hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v_x),y),t_a)* c_Natural_Oevaln(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),tc_Com_Opname,z),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),v_x)),w,x,x1)* -> hBOOL(hAPP(hAPP(y,v),x1))*.
% 299.92/300.49 41847[0:Res:517.1,199.0] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),z),w,v,x))))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),z),x1))*.
% 299.92/300.49 41844[0:Res:518.1,199.0] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),u),w,v,x))))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),u),x1))*.
% 299.92/300.49 41981[0:SpR:24914.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),v_x),hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,y),hAPP(c_Set_Oimage(u,v,w),v_x)),x,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.92/300.49 41972[0:SpR:97.1,82.0] || c_Fun_Oinj__on(u,v,w,x) -> c_lessequals(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,w,x),v),y,tc_fun(x,tc_bool))),tc_fun(w,tc_bool))*.
% 299.92/300.49 41970[0:SpR:393.1,82.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),hAPP(c_Set_Oimage(c_COMBK(w,x,v),v,x),y),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(c_COMBK(w,x,v),v,x),c_HOL_Ominus__class_Ominus(u,y,tc_fun(v,tc_bool))),tc_fun(x,tc_bool))*.
% 299.92/300.49 41966[0:SpR:24914.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),v_x),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,y),hAPP(c_Set_Oimage(u,v,w),v_x)),tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.92/300.49 41957[0:SpR:97.1,82.0] || c_Fun_Oinj__on(u,v,w,x) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y),v,tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oimage(u,w,x),v),tc_fun(x,tc_bool))),tc_fun(w,tc_bool))*.
% 299.92/300.49 41955[0:SpR:393.1,82.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_COMBK(w,x,v),v,x),y),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(c_COMBK(w,x,v),v,x),c_HOL_Ominus__class_Ominus(y,u,tc_fun(v,tc_bool))),tc_fun(x,tc_bool))*.
% 299.92/300.49 41952[0:SpR:393.1,82.0] || -> equal(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_COMBK(x,y,w),w,y),u),hAPP(c_Set_Oimage(c_COMBK(x,y,w),w,y),v),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool))*.
% 299.92/300.49 41949[0:SpR:35.2,82.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(v,x,tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(y,w,z),v),hAPP(c_Set_Oimage(y,w,z),c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool))),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,w,z),u),tc_fun(z,tc_bool))*.
% 299.92/300.49 42085[0:SpR:180.2,361.2] class_Lattices_Oupper__semilattice(u) class_Complete__Lattice_Ocomplete__lattice(v) || c_Finite__Set_Ofinite(w,u) hBOOL(hAPP(hAPP(c_in(x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),y,w,u,u)),z)) -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),y,hAPP(c_Set_Oinsert(x1,u),w),u,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x,v),v)*.
% 299.92/300.49 42067[0:SpR:180.2,176.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> hBOOL(hAPP(hAPP(c_in(w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),w,z),hAPP(c_Set_Oinsert(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(y,u),v),u,u),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.92/300.49 42259[0:Obv:42097.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(hAPP(c_in(u),w),x)) c_Finite__Set_Ofinite(x,u) -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),y,hAPP(c_Set_Oinsert(w,u),v),u,u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),y,v,u,u),x,u,u),u)*.
% 299.92/300.49 42262[0:SSi:42119.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),x)) -> hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(y,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),x))*.
% 299.92/300.49 42494[0:SpL:9935.1,315.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,y),tc_bool)* equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,y)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Set_Oimage(v,x,y),u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,y),u)).
% 299.92/300.49 42453[0:SpL:9935.1,315.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x,y),tc_bool)* equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x,y)),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),x,y),u),hAPP(c_Set_Oimage(w,x,y),u)).
% 299.92/300.49 42633[0:SpR:161.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),w,tc_fun(u,tc_bool)),y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))))**.
% 299.92/300.49 43068[0:SpR:14216.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(y,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(y,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),u,tc_fun(x,tc_bool)))**.
% 299.92/300.49 42998[0:SpR:25.1,486.1] class_HOL_Ouminus(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(y,v_x),u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ouminus__class_Ouminus(y,tc_fun(t_a,u)),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ouminus__class_Ouminus(y,tc_fun(t_a,u)),v,tc_fun(x,tc_bool)))**.
% 299.92/300.49 42978[0:SpR:653.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,x),x,tc_Com_Opname),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,x),x,tc_Com_Opname),u,tc_fun(w,tc_bool)))**.
% 299.92/300.49 42975[0:SpR:445.1,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(v,x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(z,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ofun__upd(z,x,x1,x2,x3),u,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ofun__upd(z,x,x1,x2,x3),u,tc_fun(y,tc_bool)))**.
% 299.92/300.49 43450[0:SpR:507.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),hAPP(c_Set_Oimage(v,w,u),y),hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)))**.
% 299.92/300.49 43672[0:SpR:162.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),hAPP(c_Set_Ovimage(v,u,w),y),hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)))**.
% 299.92/300.49 44317[0:Res:153.1,268.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* hBOOL(hAPP(hAPP(c_in(y),z),hAPP(c_Set_Ovimage(v,y,u),x)))* equal(hAPP(x1,w),hAPP(x1,z))* c_Fun_Oinj__on(x1,hAPP(c_Set_Ovimage(v,y,u),x),y,x2)* -> equal(w,z).
% 299.92/300.49 44301[0:Res:474.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))* equal(hAPP(y,hAPP(w,z)),hAPP(y,v))* c_Fun_Oinj__on(y,hAPP(c_Set_Oimage(w,x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),u,x1)* -> equal(hAPP(w,z),v).
% 299.92/300.49 45102[0:SpR:410.0,326.2] || c_lessequals(hAPP(u,v),w,tc_fun(x,tc_bool)) c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,u,z,tc_fun(x,tc_bool)),x1,tc_fun(x,tc_bool)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,z),y),u,z,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),x1),tc_fun(x,tc_bool))*.
% 299.92/300.49 45037[0:SpR:410.0,326.2] || c_lessequals(u,hAPP(v,w),tc_fun(x,tc_bool)) c_lessequals(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,v,x1,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x1),z),v,x1,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.92/300.49 45316[0:SpL:410.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,y),z),x1,y,tc_fun(w,tc_bool))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(x1,x),u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x1,y,tc_fun(w,tc_bool)),u,w)))*.
% 299.92/300.49 45445[0:Res:45357.1,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname)))* equal(hAPP(x,v),hAPP(x,w))* c_Fun_Oinj__on(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),u,y)* -> equal(v,w).
% 299.92/300.49 45584[0:SpR:323.0,340.2] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),y,tc_fun(x,tc_bool)) c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,v,w,tc_fun(x,tc_bool)),y,tc_fun(x,tc_bool)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),z),v,w,tc_fun(x,tc_bool)),y,tc_fun(x,tc_bool))*.
% 299.92/300.49 45649[0:SSi:45606.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_COMBK(x,tc_fun(w,tc_bool),v),v,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),y),c_COMBK(x,tc_fun(w,tc_bool),v),v,tc_fun(w,tc_bool)))*.
% 299.92/300.49 45651[0:SSi:45650.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_COMBK(x,tc_fun(w,tc_bool),v),v,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),u),c_COMBK(x,tc_fun(w,tc_bool),v),v,tc_fun(w,tc_bool)))*.
% 299.92/300.49 45877[0:SpL:24914.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)))* hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x)))* -> hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(w),tc_Com_Opname,y),hAPP(c_in(w),v_x))))*.
% 299.92/300.49 46189[0:Res:1103.1,481.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a) hBOOL(hAPP(x,w)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(v),w))),y),x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(v),w))),y)))*.
% 299.92/300.49 46109[0:SpL:21893.0,481.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,x)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)))*.
% 299.92/300.49 46108[0:SpL:21267.0,481.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,x)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)))*.
% 299.92/300.49 46507[0:Res:1103.1,480.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a) hBOOL(hAPP(x,w)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(v),w))),x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(v),w)))))*.
% 299.92/300.49 46427[0:SpL:21893.0,480.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,x)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v)))*.
% 299.92/300.49 46426[0:SpL:21267.0,480.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,x)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v)))*.
% 299.92/300.49 46936[0:Res:241.2,390.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oimage(x,y,u),z)),tc_fun(u,tc_bool)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(z,x,y,u),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),u,y)*.
% 299.92/300.49 47387[0:SpL:8415.2,485.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,v,u)),w))*.
% 299.92/300.49 47357[0:SpL:338.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oinsert(x,w),z),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)),y))*.
% 299.92/300.49 47321[0:SpL:8415.2,485.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),w),hAPP(v_x,x)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,v,u)),v_x))*.
% 299.92/300.49 47618[0:SpL:8415.2,484.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,v,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)),x))*.
% 299.92/300.49 47609[0:SpL:3294.1,484.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),w),c_Orderings_Obot__class_Obot(tc_bool)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,v,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v,u)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))))*.
% 299.92/300.49 47593[0:SpL:339.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oinsert(x,w),y),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)),z))*.
% 299.92/300.49 47552[0:SpL:8415.2,484.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),w),hAPP(v_x,x)))* -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,v,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)),x))*.
% 299.92/300.49 47956[0:SpL:8415.2,490.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,v,u)))* hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),w)))* -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,v,u)),x))*.
% 299.92/300.49 47926[0:SpL:338.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,w),x),u,w)))* hBOOL(hAPP(hAPP(c_in(w),y),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x))))* -> hBOOL(hAPP(u,y))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(z,u,w)),z))*.
% 299.92/300.49 47890[0:SpL:8415.2,490.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,v,u)))* hBOOL(hAPP(hAPP(c_in(u),x),hAPP(v_x,w)))* -> hBOOL(hAPP(v,x))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,v,u)),v_x))*.
% 299.92/300.49 48068[0:SpL:8415.2,489.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,v,u)))* hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(v,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,v,u)),x))*.
% 299.92/300.49 48059[0:SpL:3294.1,489.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,v,u)))* hBOOL(hAPP(hAPP(c_in(u),w),c_Orderings_Obot__class_Obot(tc_bool)))* -> hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v,u)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))))*.
% 299.92/300.49 48043[0:SpL:339.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(v,w),x),u,w)))* hBOOL(hAPP(hAPP(c_in(w),y),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z))))* -> hBOOL(hAPP(u,y))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(z,u,w)),z))*.
% 299.92/300.49 48002[0:SpL:8415.2,489.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,v,u)))* hBOOL(hAPP(hAPP(c_in(u),w),hAPP(v_x,x)))* -> hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,v,u)),x))*.
% 299.92/300.49 48360[0:SpL:414.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,x,v,y,z),x1,u),c_HOL_Ominus__class_Ominus(x2,hAPP(c_Set_Oinsert(x,x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),tc_fun(x1,tc_bool)))))* c_Fun_Oinj__on(c_Fun_Ofun__upd(w,x,v,y,z),hAPP(c_Set_Oinsert(x,x1),x2),x1,u) -> .
% 299.92/300.49 48351[0:SpL:524.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(c_Set_Oinsert(v,x),y),x,u) -> .
% 299.92/300.49 48345[0:SpL:8415.2,224.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),u) hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(u,w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(v_x,w),x),w,v) -> .
% 299.92/300.49 48341[0:SpL:365.1,224.0] class_Orderings_Obot(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Oimage(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Orderings_Obot__class_Obot(tc_fun(t_a,u)),hAPP(c_Set_Oinsert(v_x,w),x),w,v) -> .
% 299.92/300.49 48340[0:SpL:397.1,224.0] class_Orderings_Otop(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Orderings_Otop__class_Otop(tc_fun(t_a,u)),hAPP(c_Set_Oinsert(v_x,w),x),w,v) -> .
% 299.92/300.49 48321[0:SpL:3744.1,224.0] || equal(c_in(tc_Com_Opname),c_in(u)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,u),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,u),hAPP(c_Set_Oinsert(v_Procs,w),x),w,v) -> .
% 299.92/300.49 48661[0:SpR:8415.2,197.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_HOL_Ominus__class_Ominus(v_x,hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(v_x,x,tc_fun(v,tc_bool))))*.
% 299.92/300.49 48646[0:SpR:8415.2,197.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),v_x,tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,v_x,tc_fun(v,tc_bool))))*.
% 299.92/300.49 48790[0:Res:149.1,619.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,u,tc_fun(y,tc_bool)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))),c_Set_Oinsert(z,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(z,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),x,u,tc_fun(y,tc_bool))))**.
% 299.92/300.49 48764[0:SpL:584.0,619.0] || hBOOL(hAPP(c_COMBS(c_in(u),v,w,x,y),z))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x1,u,tc_fun(x2,tc_bool)),hAPP(v,z)),c_Set_Oinsert(x3,x2),tc_fun(x2,tc_bool),tc_fun(x2,tc_bool)),hAPP(c_Set_Oinsert(x3,x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(v,z),x1,u,tc_fun(x2,tc_bool))))**.
% 299.92/300.49 49390[0:SpR:49342.1,486.1] || hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,tc_fun(x,tc_bool)))**.
% 299.92/300.49 49677[0:Rew:49662.2,49568.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),x,y),hAPP(c_Set_Oinsert(u,x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(c_Set_Oinsert(u,x),w),x,y).
% 299.92/300.49 49683[0:Rew:49662.2,49578.2] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),x),w),x,y).
% 299.92/300.49 49692[0:Rew:49662.2,49595.2] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) c_Fun_Oinj__on(hAPP(u,v_x),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(u,v_x),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),v))))* c_Fun_Oinj__on(hAPP(u,v_x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),v),w,x).
% 299.92/300.49 49700[0:Rew:49662.2,49572.2] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,x),hAPP(c_Set_Oinsert(y,w),v))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(c_Set_Oinsert(y,w),v),w,x).
% 299.92/300.49 49709[0:Rew:49662.2,49611.2] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),w,x),hAPP(c_Set_Oinsert(v_x,w),v))))* c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),hAPP(c_Set_Oinsert(v_x,w),v),w,x).
% 299.92/300.49 49726[0:Rew:49662.2,49648.1] || c_Fun_Oinj__on(u,v,w,tc_Hoare__Mirabelle_Otriple(t_a)) c_Hoare__Mirabelle_Ohoare__valids(x,hAPP(c_Set_Oimage(u,w,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(y,w),v)),t_a)* c_Hoare__Mirabelle_Otriple__valid(z,v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(x,z),t_a)* -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,w),v),w,tc_Hoare__Mirabelle_Otriple(t_a)) c_Hoare__Mirabelle_Otriple__valid(z,hAPP(u,y),t_a)*.
% 299.92/300.49 50029[0:SpL:497.0,3483.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Com_Ocom_OBODY)** equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),c_Com_Ocom_OSKIP) -> .
% 299.92/300.49 50068[0:Rew:585.0,50024.1] || c_lessequals(hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v),tc_fun(t_a,tc_bool))* -> equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.92/300.49 50069[0:Rew:585.0,50023.1] || c_lessequals(hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v),tc_fun(t_a,tc_bool))* -> equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),u)),hAPP(hAPP(c_in(t_a),v_x),v)).
% 299.92/300.49 50149[0:SpR:8415.2,620.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,w,tc_fun(u,tc_bool)),v),v_x,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),hAPP(v_x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,tc_fun(u,tc_bool))))**.
% 299.92/300.49 50388[0:SpR:223.1,7539.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(z,y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,x1,u,y),u,y),w)),tc_fun(y,tc_bool))*.
% 299.92/300.49 50779[2:SpR:622.0,4250.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))).
% 299.92/300.49 50768[0:SpR:622.0,3282.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))).
% 299.92/300.49 50767[7:SpR:622.0,27207.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))).
% 299.92/300.49 53039[0:SpR:23955.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)),w))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,x),v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v))*.
% 299.92/300.49 53038[0:SpR:23955.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)),w))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,x),v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v))*.
% 299.92/300.50 53171[0:SpR:23958.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)),w))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,x),v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v))*.
% 299.92/300.50 53170[0:SpR:23958.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)),w))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),u,x),v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v))*.
% 299.92/300.50 53448[0:SpR:33303.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),c_Fun_Ofun__upd(v,w,v_Procs,x,y),y,z,x),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),v_x),tc_Com_Opname),v,y,z,x),w,v_Procs,x,z))*.
% 299.92/300.50 53425[0:SpR:33303.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),v_x),tc_Com_Opname),v,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),v_x),tc_Com_Opname),u,x),v_Procs),v_Procs)**.
% 299.92/300.50 53424[0:SpR:33303.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),v_x),tc_Com_Opname),v,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),v_x),tc_Com_Opname),u,x),v_Procs),v_Procs)**.
% 299.92/300.50 56206[0:SpR:30368.2,486.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(y,tc_bool)))**.
% 299.92/300.50 56648[0:SpR:30928.2,486.1] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,tc_fun(y,tc_bool)))**.
% 299.92/300.50 62445[0:Obv:62309.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,w,u,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)) -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,w,u,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),u)*.
% 299.92/300.50 62751[0:Obv:62644.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,w,u,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),u)* -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,w,u,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)).
% 299.92/300.50 64255[0:SpL:646.1,284.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),x,w),y)))* c_Fun_Oinj__on(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w)* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(u,v_x)),y)).
% 299.92/300.50 64423[0:SpL:645.1,284.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),x,w),y)))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w)* -> hBOOL(hAPP(hAPP(c_in(x),hAPP(u,v_x)),y)).
% 299.92/300.50 64479[0:Res:662.1,199.0] || hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(y,tc_bool)),w,v,x))))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,u,tc_Com_Opname,tc_fun(y,tc_bool)),z))*.
% 299.92/300.50 64589[0:SpR:26782.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),x,tc_fun(y,tc_bool)),u,w),v)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),x,tc_fun(y,tc_bool)),u,w),v))**.
% 299.92/300.50 64839[0:SpR:28747.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),c_Fun_Ofun__upd(w,x,v_Procs,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,z,x1,y),x,v_Procs,y,x1))*.
% 299.92/300.50 64815[0:SpR:28747.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),v,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),u,y),v_Procs),v_Procs)**.
% 299.92/300.50 64814[0:SpR:28747.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),v,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),u,y),v_Procs),v_Procs)**.
% 299.92/300.50 64959[0:SpR:28748.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),c_Fun_Ofun__upd(w,x,v_Procs,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),tc_Com_Opname,v),tc_Com_Opname),w,z,x1,y),x,v_Procs,y,x1))*.
% 299.92/300.50 64935[0:SpR:28748.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),v,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),u,y),v_Procs),v_Procs)**.
% 299.92/300.50 64934[0:SpR:28748.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),v,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),u,y),v_Procs),v_Procs)**.
% 299.92/300.50 65079[0:SpR:28902.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),c_Fun_Ofun__upd(w,x,v_Procs,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,z,x1,y),x,v_Procs,y,x1))*.
% 299.92/300.50 65055[0:SpR:28902.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x),tc_Com_Opname),v,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x),tc_Com_Opname),u,y),v_Procs),v_Procs)**.
% 299.92/300.50 65054[0:SpR:28902.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x),tc_Com_Opname),v,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x),tc_Com_Opname),u,y),v_Procs),v_Procs)**.
% 299.92/300.50 65199[0:SpR:28903.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),c_Fun_Ofun__upd(w,x,v_Procs,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,v),tc_Com_Opname),w,z,x1,y),x,v_Procs,y,x1))*.
% 299.92/300.50 65175[0:SpR:28903.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,x),tc_Com_Opname),v,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,x),tc_Com_Opname),u,y),v_Procs),v_Procs)**.
% 299.92/300.50 65174[0:SpR:28903.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,x),tc_Com_Opname),v,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,x),tc_Com_Opname),u,y),v_Procs),v_Procs)**.
% 299.92/300.50 66783[0:SpL:1188.2,284.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),w,v),x)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v)* -> hBOOL(hAPP(hAPP(c_in(w),c_HOL_Ozero__class_Ozero(u)),x)).
% 299.92/300.50 67539[0:SpL:1189.2,284.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),w,v),x)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v)* -> hBOOL(hAPP(hAPP(c_in(w),c_HOL_Ozero__class_Ozero(u)),x)).
% 299.92/300.50 76150[0:SpR:9915.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),x),hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(y,z,v),x1,x2,x3,x4),u,x),w)),hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(y,z,v),x1,x2,x3,x4),u,x),w))**.
% 299.92/300.50 76270[0:SpR:10469.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x),hAPP(c_Set_Oimage(c_COMBS(c_Set_Oimage(y,v,z),x1,x2,x3,x4),u,x),w)),hAPP(c_Set_Oimage(c_COMBS(c_Set_Oimage(y,v,z),x1,x2,x3,x4),u,x),w))**.
% 299.92/300.50 76400[0:SpR:10470.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> equal(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x),hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(y,z,v),x1,x2,x3,x4),u,x),w)),hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(y,z,v),x1,x2,x3,x4),u,x),w))**.
% 299.92/300.50 77670[0:SpL:354.2,5892.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(u,hAPP(c_Set_Oimage(x,w,y),u)))* -> hBOOL(hAPP(c_COMBS(c_in(z),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),x1,x2,x3),hAPP(c_Set_Oimage(x,w,y),u)))*.
% 299.92/300.50 79040[0:Res:15630.1,5986.0] || hBOOL(hAPP(c_COMBS(c_in(u),v,w,x,y),z)) -> hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(z,x1),x2),x3,c_COMBS(c_in(u),v,w,x,y),x1)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(z,x1),x2),x3,c_COMBS(c_in(u),v,w,x,y),x1)))*.
% 299.92/300.50 78994[0:SpR:329.1,15630.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,w),x),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),u),w),tc_fun(z,tc_bool))* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),u),v)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,w),x),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),u),w)).
% 299.92/300.50 79260[0:Res:15858.1,5986.0] || hBOOL(hAPP(c_COMBS(c_in(u),v,w,x,y),z)) -> hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,hAPP(c_Set_Oinsert(z,x2),x3),c_COMBS(c_in(u),v,w,x,y),x2)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,hAPP(c_Set_Oinsert(z,x2),x3),c_COMBS(c_in(u),v,w,x,y),x2)))*.
% 299.92/300.50 79214[0:SpR:329.1,15858.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(w,x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),u),x),tc_fun(z,tc_bool))* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),u),w)) -> hBOOL(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v,hAPP(c_Set_Oinsert(w,x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),u),x)).
% 299.92/300.50 80244[0:SpL:21268.0,85.0] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,z),tc_fun(v,tc_bool))*.
% 299.92/300.50 80171[0:SpL:21268.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oimage(x,u,y),hAPP(c_Set_Oimage(x,u,y),z),w,x1)))* c_lessequals(hAPP(c_Set_Oimage(x,u,y),z),x2,tc_fun(y,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(y),hAPP(x,v)),x2))*.
% 299.92/300.50 79994[0:SpR:223.1,21268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(x,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oinsert(x,y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x1,v,x,u,y),u,y),w),z,x2)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x1,v,x,u,y),u,y),w))**.
% 299.92/300.50 79908[0:SpR:338.0,21268.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)),w,z)),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)))**.
% 299.92/300.50 79723[0:SpR:21268.0,11177.1] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),u,x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),u,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)).
% 299.92/300.50 79717[0:SpR:21268.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),x,z),tc_fun(w,tc_bool))* -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),tc_fun(w,tc_bool)).
% 299.92/300.50 79705[0:SpR:21268.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),x,z))),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)))**.
% 299.92/300.50 79554[0:SpR:21268.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(w,x),v,y)),z))* c_Fun_Oinj__on(w,z,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(z,w,u,x1),hAPP(w,x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(w,x),v,y))*.
% 299.92/300.50 79553[0:SpR:21268.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(w,x),v,y)),z))* c_Fun_Oinj__on(w,z,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,w,u,x1),hAPP(w,x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,hAPP(w,x),v,y))*.
% 299.92/300.50 81439[0:SpL:21894.0,85.0] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,w,tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y,z),tc_fun(v,tc_bool))*.
% 299.92/300.50 81366[0:SpL:21894.0,471.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(x,u,y),z),c_Set_Oimage(x,u,y),w,x1)))* c_lessequals(hAPP(c_Set_Oimage(x,u,y),z),x2,tc_fun(y,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(y),hAPP(x,v)),x2))*.
% 299.92/300.50 81188[0:SpR:223.1,21894.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(x,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x1,v,x,u,y),u,y),w),c_Set_Oinsert(x,y),z,x2)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x1,v,x,u,y),u,y),w))**.
% 299.92/300.50 81102[0:SpR:338.0,21894.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,z)),hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)))**.
% 299.92/300.50 80917[0:SpR:21894.0,11177.1] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w)).
% 299.92/300.50 80911[0:SpR:21894.0,84.1] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,z),tc_fun(w,tc_bool))* -> c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),tc_fun(w,tc_bool)).
% 299.92/300.50 80899[0:SpR:21894.0,338.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,z))),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)))**.
% 299.92/300.50 80747[0:SpR:21894.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(w,x),w,v,y)),z))* c_Fun_Oinj__on(w,z,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(z,w,u,x1),hAPP(w,x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(w,x),w,v,y))*.
% 299.92/300.50 80746[0:SpR:21894.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(w,x),w,v,y)),z))* c_Fun_Oinj__on(w,z,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,w,u,x1),hAPP(w,x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(w,x),w,v,y))*.
% 299.92/300.50 81872[0:SpR:323.0,5879.1] class_Lattices_Oupper__semilattice(u) || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,v,tc_fun(z,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,v,tc_fun(z,tc_bool))),x1,x2,x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,tc_fun(z,tc_bool))),u)*.
% 299.92/300.50 82216[7:SpL:78597.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Set_Oinsert(v_x,v)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(c_Set_Oinsert(v_x,v),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(c_Set_Oinsert(v_x,v),w),x),w,u) -> .
% 299.92/300.50 82344[0:SpR:323.0,5880.1] class_Lattices_Olattice(u) || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,v,tc_fun(z,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,v,tc_fun(z,tc_bool))),x1,x2,x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,tc_fun(z,tc_bool))),u)*.
% 299.92/300.50 83042[0:SpR:5924.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(x,v),y),z),hAPP(c_Set_Oimage(c_COMBS(x,c_COMBK(y,x1,x2),x3,x4,x5),u,z),w)),hAPP(c_Set_Oimage(c_COMBS(x,c_COMBK(y,x1,x2),x3,x4,x5),u,z),w))**.
% 299.92/300.50 83369[0:SpR:5961.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(x,hAPP(y,v)),z),hAPP(c_Set_Oimage(c_COMBS(c_COMBK(x,x1,x2),y,x3,x4,x5),u,z),w)),hAPP(c_Set_Oimage(c_COMBS(c_COMBK(x,x1,x2),y,x3,x4,x5),u,z),w))**.
% 299.92/300.50 83779[0:SpR:5899.0,450.0] || -> hBOOL(hAPP(hAPP(c_COMBS(u,v,w,x,y),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_COMBS(u,v,z,x1,x2),x3,x4,x5)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_COMBS(u,v,z,x1,x2),x3,x4,x5)))* c_Hoare__Mirabelle_Otriple__valid(x5,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBS(u,v,z,x1,x2)),x4),x3),t_a).
% 299.92/300.50 85026[0:SpR:644.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),c_Set_Oimage(c_COMBK(w,x,tc_Com_Opname),tc_Com_Opname,x),u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oimage(c_COMBK(w,x,tc_Com_Opname),tc_Com_Opname,x),u,tc_fun(y,tc_bool))))*.
% 299.92/300.50 85866[0:Rew:339.0,85847.1,533.0,85847.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(v,w),y)),z,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)))))*.
% 299.92/300.50 85846[0:Res:9066.0,478.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),hAPP(c_Set_Oinsert(v,w),z)),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),hAPP(c_Set_Oinsert(v,w),z)))))*.
% 299.92/300.50 86477[0:SpL:86109.1,477.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u),v_Procs) hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u))* hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),x)).
% 299.92/300.50 86476[0:SpL:86109.1,476.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u),v_Procs) hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u))* hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),x)).
% 299.92/300.50 86598[0:Res:19823.1,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(y,u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool)),v)))* hBOOL(hAPP(hAPP(c_in(v),x1),w))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(y,u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool)),x1))*.
% 299.92/300.50 86597[0:Res:19823.1,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(y,u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool)),v)))* hBOOL(hAPP(hAPP(c_in(v),x1),x))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(y,u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool)),x1))*.
% 299.92/300.50 88332[0:Res:7227.0,479.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(c_COMBK(v,x,y),z,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),x1,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_COMBK(v,x,y),z,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))),x1)))*.
% 299.92/300.50 88331[0:Res:7227.0,478.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oimage(c_COMBK(v,y,z),x1,w),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(c_COMBK(v,y,z),x1,w),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))))))*.
% 299.92/300.50 89549[7:SpL:78590.1,224.0] || equal(c_Set_Oinsert(v_x,t_a),u) hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(u,w),x),w,v) -> .
% 299.92/300.50 89772[0:SpR:26183.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y,u,z) -> equal(hAPP(c_Fun_Othe__inv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u,z),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Oinsert(v,w),x))**.
% 299.92/300.50 89771[0:SpR:26183.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y,u,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u,z),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Oinsert(v,w),x))**.
% 299.92/300.50 89963[0:Rew:89962.0,77441.3] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* c_lessequals(v,hAPP(c_Set_Oinsert(w,u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),tc_fun(u,tc_bool))*.
% 299.92/300.50 90340[4:SpL:78660.1,224.0] || equal(hAPP(u,v_x),v_x) hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(u,w),x),w,v) -> .
% 299.92/300.50 93187[0:SpR:5878.1,410.0] class_Lattices_Obounded__lattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),v),w),c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),hAPP(x,c_Orderings_Obot__class_Obot(u))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),x,y,z,x1),v,tc_fun(x2,tc_bool))))*.
% 299.92/300.50 94149[0:Res:14364.3,231.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Set_Oimage(w,x,u),y))) c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u) -> c_lessequals(hAPP(c_Set_Ovimage(w,x,u),c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool))),y,tc_fun(x,tc_bool))*.
% 299.92/300.50 20286[0:SpR:438.1,438.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y),z),hAPP(u,z))**.
% 299.92/300.50 20446[0:SpR:438.1,99.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y),z),hAPP(u,z))**.
% 299.92/300.50 20429[0:SpR:99.1,99.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y),z),hAPP(u,z))**.
% 299.92/300.50 20428[0:SpR:99.1,438.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y),z),hAPP(u,z))**.
% 299.92/300.50 20936[0:SpR:99.1,317.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(u,z),x),x1)),hAPP(c_Set_Oinsert(z,y),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y),x1)))*.
% 299.92/300.50 20935[0:SpR:438.1,317.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y),hAPP(c_Set_Oinsert(hAPP(u,z),x),x1)),hAPP(c_Set_Oinsert(z,y),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y),x1)))*.
% 299.92/300.50 21672[0:SpL:21267.0,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(c_Set_Oinsert(u,v),w),v_x),tc_Com_Opname,x)))* equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(c_Set_Oinsert(u,v),w),v_x),tc_Com_Opname,x),u).
% 299.92/300.50 21385[0:SpR:21267.0,96.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v,w) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),w,v)*.
% 299.92/300.50 22300[0:SpL:21893.0,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),v_x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),w),v_x),hAPP(c_Set_Oinsert(u,v),w),tc_Com_Opname,x)))* equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Set_Oinsert(u,v),w),v_x),hAPP(c_Set_Oinsert(u,v),w),tc_Com_Opname,x),u).
% 299.92/300.50 22011[0:SpR:21893.0,96.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v,w) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),w,v)*.
% 299.92/300.50 22414[0:SpR:97.1,317.0] || c_Fun_Oinj__on(u,v,w,x) -> equal(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,w,x),v),y),x1)),hAPP(c_Set_Oinsert(v,z),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,z),x1)))*.
% 299.92/300.50 22413[0:SpR:97.1,99.1] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,z) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,z),v),hAPP(c_Set_Oimage(u,w,x),v))**.
% 299.92/300.50 22412[0:SpR:97.1,438.1] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,z),v),hAPP(c_Set_Oimage(u,w,x),v))**.
% 299.92/300.50 22597[0:SpR:158.0,21893.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),tc_Com_Opname,z))),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x))**.
% 299.92/300.50 22596[0:SpR:158.0,21267.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x),tc_Com_Opname,z))),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x))**.
% 299.92/300.50 22550[0:SpR:158.0,21893.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))**.
% 299.92/300.50 22547[0:SpR:158.0,21267.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_Com_Opname,z)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))**.
% 299.92/300.50 22979[0:SpR:131.0,21893.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_x),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),tc_Com_Opname,z))),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_x))**.
% 299.92/300.50 22978[0:SpR:131.0,21267.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_x),tc_Com_Opname,z))),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_x))**.
% 299.92/300.50 22936[0:SpR:131.0,21893.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z)),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)))**.
% 299.92/300.50 22933[0:SpR:131.0,21267.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)),tc_Com_Opname,z)),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)))**.
% 299.92/300.50 24335[0:SpR:393.1,317.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(w,x,v),v,x),y,z),hAPP(c_Set_Oinsert(u,y),x1)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),z),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(w,x,v),v,x),y,z),x1)))*.
% 299.92/300.50 24334[0:SpR:393.1,99.1] || c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(z,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(c_COMBK(u,v,w),w,v),x,y),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),z)*.
% 299.92/300.50 24333[0:SpR:393.1,438.1] || c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(z,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(c_COMBK(u,v,w),w,v),x,y),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),z)*.
% 299.92/300.50 25813[0:SpL:21893.0,273.0] || equal(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x))* -> equal(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),tc_Com_Opname,w))*.
% 299.92/300.50 25812[0:SpL:21267.0,273.0] || equal(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x))* -> equal(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),tc_Com_Opname,w))*.
% 299.92/300.50 26113[0:SpR:338.0,2098.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w),t_a) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),hAPP(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w)),tc_Hoare__Mirabelle_Otriple(t_a)),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w))**.
% 299.92/300.50 26064[0:SpR:338.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(y,u),z),w),x1)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(y,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z)),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),x1)))*.
% 299.92/300.50 26423[0:SSi:26412.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)) c_lessequals(y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),y),w,tc_fun(v,tc_bool)),x,tc_fun(v,tc_bool))*.
% 299.92/300.50 27636[0:SpR:128.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),x)) c_Fun_Oinj__on(c_Set_Ovimage(y,z,w),x,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,c_Set_Ovimage(y,z,w),u,x1),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(y,z,w),v),tc_fun(z,tc_bool))),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)))**.
% 299.92/300.50 27583[0:SpR:188.1,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),w),y))* c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v,u,z),z,u),y,x,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,c_Set_Ovimage(c_COMBK(v,u,z),z,u),x,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),w)*.
% 299.92/300.50 27789[0:SpR:128.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),x)) c_Fun_Oinj__on(c_Set_Ovimage(y,z,w),x,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(x,c_Set_Ovimage(y,z,w),u,x1),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(y,z,w),v),tc_fun(z,tc_bool))),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)))**.
% 299.92/300.50 27736[0:SpR:188.1,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),w),y))* c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v,u,z),z,u),y,x,x1) -> equal(hAPP(c_Fun_Othe__inv__into(y,c_Set_Ovimage(c_COMBK(v,u,z),z,u),x,x1),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),w)*.
% 299.92/300.50 28205[0:SpR:465.1,1103.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z))))* c_Hoare__Mirabelle_Ohoare__valids(w,c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),t_a) hBOOL(hAPP(c_Set_Oimage(x,u,z),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z))))*.
% 299.92/300.50 28506[0:SpR:614.2,118.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Fun_Ofun__upd(x,y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,x2,x3,x1),y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u),x1,x3))*.
% 299.92/300.50 28493[0:SpR:188.1,118.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Fun_Ocomp(c_Set_Ovimage(c_COMBK(v,u,x),x,u),c_Fun_Ofun__upd(y,z,w,x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,x2,x3,x1),z,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x1,x3))*.
% 299.92/300.50 31404[0:SpL:586.0,449.0] || hBOOL(hAPP(hAPP(u,hAPP(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(w,hAPP(c_COMBB(u,x,y,z),v),x1,x2))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(w,hAPP(c_COMBB(u,x,y,z),v),x1,x2)))* -> c_Hoare__Mirabelle_Otriple__valid(x2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),w),x1),hAPP(c_COMBB(u,x,y,z),v)),t_a).
% 299.92/300.50 31403[0:SpL:585.0,449.0] || hBOOL(hAPP(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,hAPP(c_COMBC(u,w,x,y),z),x1,x2)),z),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,hAPP(c_COMBC(u,w,x,y),z),x1,x2)))* -> c_Hoare__Mirabelle_Otriple__valid(x2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),x1),hAPP(c_COMBC(u,w,x,y),z)),t_a).
% 299.92/300.50 31547[0:Res:468.0,473.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(c_Set_Oimage(x1,v,w),hAPP(c_Set_Oimage(x,y,v),z))) hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Hilbert__Choice_Oinv__into(z,x,y,v),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(x,y,v),z),u,x1,v,w))),z))*.
% 299.92/300.50 32332[0:SpL:2097.1,477.0] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(x,y),u),x))* hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(x,y),u)) hBOOL(hAPP(hAPP(c_in(u),z),v))* -> hBOOL(hAPP(c_Set_Oinsert(x,y),z))*.
% 299.92/300.50 32512[0:SpL:2097.1,476.0] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(x,y),u),x))* hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(x,y),u)) hBOOL(hAPP(hAPP(c_in(u),z),w))* -> hBOOL(hAPP(c_Set_Oinsert(x,y),z))*.
% 299.92/300.50 32779[0:SpR:35.2,35.2] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(v,x,tc_fun(w,tc_bool))* c_lessequals(c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),y,tc_fun(w,tc_bool))* c_lessequals(y,v,tc_fun(w,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(y,u,tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool))).
% 299.92/300.50 32924[0:SpR:131.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),z)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,x1,w,x,x2),x2,x),y),x3),hAPP(c_Set_Oimage(c_Set_Ovimage(x1,x2,w),u,x3),z)),hAPP(c_Set_Oimage(c_Set_Ovimage(x1,x2,w),u,x3),z))**.
% 299.92/300.50 32923[0:SpR:158.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(c_Fun_Ocomp(x1,v,x,x2,w),w,x2),y),x3),hAPP(c_Set_Oimage(c_Set_Oimage(x1,x,x2),u,x3),z)),hAPP(c_Set_Oimage(c_Set_Oimage(x1,x,x2),u,x3),z))**.
% 299.92/300.50 32918[0:SpR:317.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(hAPP(z,v),x1),hAPP(c_Set_Oimage(z,w,x1),x)),x2),hAPP(c_Set_Oimage(c_Set_Oimage(z,w,x1),u,x2),y)),hAPP(c_Set_Oimage(c_Set_Oimage(z,w,x1),u,x2),y))**.
% 299.92/300.50 34363[0:SpL:24914.0,447.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),v_x),w) c_Fun_Oinj__on(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v,w)* -> c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v).
% 299.92/300.50 34228[0:SpR:523.1,24914.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)))**.
% 299.92/300.50 34227[0:SpR:460.1,24914.0] || class_Lattices_Olattice(t_b) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),tc_Com_Opname,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))**.
% 299.92/300.50 34029[0:SpR:24914.0,98.1] || c_Fun_Oinj__on(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v,w)* -> equal(c_Finite__Set_Ocard(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v),c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),v_x),w)).
% 299.92/300.50 34620[0:SpR:55.1,317.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),x,y),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(z,w,tc_fun(u,tc_bool)),x),x1)),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),z),w,tc_fun(u,tc_bool)),y),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),x,y),x1)))*.
% 299.92/300.50 35416[0:SpR:32668.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,w,tc_Com_Opname,x),hAPP(w,v_x)),tc_Com_Opname),u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,w,tc_Com_Opname,x),hAPP(w,v_x)),tc_Com_Opname),u,tc_fun(y,tc_bool))))*.
% 299.92/300.50 35415[0:SpR:28910.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(w,x,y),w,tc_Com_Opname,z),tc_Com_Opname),u,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(w,x,y),w,tc_Com_Opname,z),tc_Com_Opname),u,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 35414[0:SpR:28926.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w),tc_Com_Opname),u,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,w),tc_Com_Opname),u,tc_fun(x,tc_bool))))*.
% 299.92/300.50 35412[0:SpR:28755.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,w,c_COMBK(w,x,y),tc_Com_Opname,z),tc_Com_Opname),u,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,w,c_COMBK(w,x,y),tc_Com_Opname,z),tc_Com_Opname),u,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 35411[0:SpR:28771.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),tc_Com_Opname),u,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),tc_Com_Opname),u,tc_fun(x,tc_bool))))*.
% 299.92/300.50 35408[0:SpR:64.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),x),y),c_Set_Oinsert(v,w),x,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(v,w),u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(v,w),x,tc_fun(z,tc_bool))))*.
% 299.92/300.50 35307[0:SpR:130.1,410.0] class_HOL_Ominus(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,v),w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(t_a,u)),v,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(x,v_x),hAPP(y,v_x),u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(x,y,tc_fun(t_a,u)),v,tc_fun(z,tc_bool))))*.
% 299.92/300.50 35295[0:SpR:196.1,410.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),x),y),z),c_Set_Ovimage(u,v,w),y,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Ovimage(u,v,w),y,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 36172[0:SpL:21893.0,516.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))) -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),tc_Com_Opname,x)))*.
% 299.92/300.50 36171[0:SpL:21267.0,516.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))) -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x),tc_Com_Opname,x)))*.
% 299.92/300.50 37177[0:Res:49.2,471.1] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(hAPP(c_Set_Oimage(v,w,u),x),c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) hBOOL(hAPP(hAPP(c_in(w),y),x)) -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,y)),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(v,w,u),x),tc_fun(u,tc_bool))))*.
% 299.92/300.50 37507[0:SpL:205.1,469.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(v),x),y)) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(hAPP(c_Set_Oimage(u,v,w),y),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,w,v)),x)**.
% 299.92/300.50 37506[0:SpL:205.1,464.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(v),x),y)) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(hAPP(c_Set_Oimage(u,v,w),y),x,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v)),x)**.
% 299.92/300.50 37504[0:SpL:205.1,470.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(v),x),y)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(hAPP(c_Set_Oimage(u,v,w),y),x,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v)),hAPP(c_Set_Oimage(u,v,w),y)))*.
% 299.92/300.50 37503[0:SpL:205.1,466.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(v),x),y)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(hAPP(c_Set_Oimage(u,v,w),y),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,w,v)),hAPP(c_Set_Oimage(u,v,w),y)))*.
% 299.92/300.50 37486[0:SpR:465.1,205.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> hBOOL(hAPP(hAPP(c_in(x),v),z)) equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Fun_Ofun__upd(u,v,w,x,y),x,y),y,x),hAPP(c_Set_Oimage(u,x,y),z)),z)**.
% 299.92/300.50 37478[0:SpR:205.1,317.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oimage(u,v,w),y))),hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x),v),y))**.
% 299.92/300.50 38222[0:SpR:66.0,13.2] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)) c_lessequals(y,hAPP(c_Set_Oinsert(z,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(z,w),v),tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.92/300.50 38207[0:SpR:66.0,13.2] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)) c_lessequals(hAPP(c_Set_Oinsert(y,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),z,tc_fun(x,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,z,tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(y,x),w),tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.92/300.50 38352[0:SSi:38308.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),w))* c_Finite__Set_Ofinite(w,tc_fun(u,tc_bool)) c_Fun_Oinj__on(x,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y,w,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),u,z)* -> c_Fun_Oinj__on(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),u,z)*.
% 299.92/300.50 38353[0:SSi:38273.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),w)) c_Finite__Set_Ofinite(w,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),v),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(x,v,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.92/300.50 39001[0:SpL:354.2,471.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(y),z),hAPP(c_Set_Oimage(x,w,y),u)))* c_lessequals(u,x1,tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(v,x,w,y),z)),x1))*.
% 299.92/300.50 39247[0:SpR:533.0,1103.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),t_a) hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))))))*.
% 299.92/300.50 39173[0:SpR:533.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),x1),v))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1)),u,x),w)))*.
% 299.92/300.50 39169[0:SpR:533.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.92/300.50 39163[0:SpR:533.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))**.
% 299.92/300.50 39599[0:SpR:532.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),x))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),u,z),y)))*.
% 299.92/300.50 39595[0:SpR:532.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.92/300.50 41321[0:SpL:600.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y))* hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),w)))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),u,tc_fun(z,tc_bool))))*.
% 299.92/300.50 41300[0:SpL:188.1,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),w),y))* hBOOL(hAPP(hAPP(c_in(z),x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Ovimage(c_COMBK(v,u,x2),x2,u),x,tc_fun(z,tc_bool))))*.
% 299.92/300.50 41263[0:SpL:196.1,275.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),y))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Ovimage(u,v,w),x,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 41615[0:SpL:328.1,284.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(x),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y,x),z)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,x)* -> hBOOL(hAPP(hAPP(c_in(y),u),z))*.
% 299.92/300.50 41814[0:SpL:328.1,199.0] || c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),v,u,w)),y,tc_fun(x,tc_bool))* hBOOL(y) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))*.
% 299.92/300.50 41982[0:SpR:158.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x1),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),c_HOL_Ominus__class_Ominus(z,x1,tc_fun(y,tc_bool))),tc_fun(w,tc_bool))*.
% 299.92/300.50 41967[0:SpR:158.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x1)),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_HOL_Ominus__class_Ominus(z,x1,tc_fun(y,tc_bool))),tc_fun(x,tc_bool))*.
% 299.92/300.50 41954[0:SpR:158.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),x1),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),c_HOL_Ominus__class_Ominus(z,x1,tc_fun(y,tc_bool)))),tc_fun(x,tc_bool))*.
% 299.92/300.50 41948[0:SpR:113.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(x,v,y),z)),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(x,v,y),x1)),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(x,v,y),c_HOL_Ominus__class_Ominus(z,x1,tc_fun(y,tc_bool)))),tc_fun(w,tc_bool))*.
% 299.92/300.50 42147[0:SpR:180.2,584.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z,x1),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x2,v,u,u)),hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x2,hAPP(c_Set_Oinsert(w,u),v),u,u),hAPP(x,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x2,v,u,u))))*.
% 299.92/300.50 42146[0:SpR:180.2,584.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(hAPP(c_COMBS(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y,z,x1),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x2,v,u,u)),hAPP(hAPP(w,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x2,v,u,u)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x2,hAPP(c_Set_Oinsert(x,u),v),u,u)))*.
% 299.92/300.50 42072[0:SpR:180.2,545.1] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(hAPP(c_in(w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u)),y)) -> hBOOL(hAPP(hAPP(c_in(z),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(x1,u),v),u,u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),w,z),y)))*.
% 299.92/300.50 42068[0:SpR:180.2,362.1] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(hAPP(c_in(w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u)),y)) -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(z,u),v),u,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.92/300.50 42264[0:Rew:42263.3,42089.3] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),z,v,u,u)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),z,v,u,u))**.
% 299.92/300.50 42474[0:SpL:299.2,315.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y,z),x,u)* equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y,z)),x)** -> equal(hAPP(c_Set_Oimage(w,y,z),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y,z),v)).
% 299.92/300.50 42469[0:SpL:8385.1,315.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,tc_Com_Opname),w,x),v_Procs) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,tc_Com_Opname),w,x)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,tc_Com_Opname),w,x))** -> equal(hAPP(c_Set_Oimage(v,w,x),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),w,x),u)).
% 299.92/300.50 42433[0:SpL:299.2,315.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z),w,u)* equal(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z)),w)** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,z),v),hAPP(c_Set_Oimage(x,y,z),v)).
% 299.92/300.50 42428[0:SpL:8385.1,315.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,tc_Com_Opname),v,w,x),v_Procs) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,tc_Com_Opname),v,w,x)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,tc_Com_Opname),v,w,x))** -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),w,x),u),hAPP(c_Set_Oimage(v,w,x),u)).
% 299.92/300.50 42692[0:SpR:161.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),x,y,z,x1),c_HOL_Ominus__class_Ominus(x2,w,tc_fun(u,tc_bool))),hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x2),w,tc_fun(u,tc_bool)),hAPP(x,c_HOL_Ominus__class_Ominus(x2,w,tc_fun(u,tc_bool)))))*.
% 299.92/300.50 42691[0:SpR:161.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool))),y,z,x1),c_HOL_Ominus__class_Ominus(x2,x,tc_fun(v,tc_bool))),hAPP(hAPP(u,c_HOL_Ominus__class_Ominus(x2,x,tc_fun(v,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x2),x,tc_fun(v,tc_bool))))*.
% 299.92/300.50 42680[0:SpR:161.0,532.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),w,tc_fun(u,tc_bool))))**.
% 299.92/300.50 42674[0:SpR:161.0,533.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool))),y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),w,tc_fun(u,tc_bool))),y))**.
% 299.92/300.50 42656[0:SpR:161.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(y,tc_bool))),z)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),x1),w),x,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_HOL_Ominus__class_Ominus(x1,x,tc_fun(y,tc_bool))),v,u),u)*.
% 299.92/300.50 42638[0:SpR:161.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(y,w,tc_fun(x,tc_bool))),u,z),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),v),w,tc_fun(x,tc_bool)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))))*.
% 299.92/300.50 43094[0:SpR:584.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(y,v),hAPP(z,v))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(y,z,x1,x2,x3),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(y,z,x1,x2,x3),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 43093[0:SpR:586.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,hAPP(z,v))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_COMBB(y,x1,x2,x3),z),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_COMBB(y,x1,x2,x3),z),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 43092[0:SpR:585.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(y,v),z)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_COMBC(y,x1,x2,x3),z),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_COMBC(y,x1,x2,x3),z),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 43089[0:SpR:11499.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z)),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Set_Oinsert(x,y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),z)),u,tc_fun(w,tc_bool)))**.
% 299.92/300.50 43085[0:SpR:336.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 43027[0:SpR:14526.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(c_Option_Othe(v),y,tc_fun(z,tc_bool)),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(c_Option_Othe(v),y,tc_fun(z,tc_bool)),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 43015[0:SpR:331.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 43006[0:SpR:34428.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,x),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,x),u,tc_fun(w,tc_bool)))**.
% 299.92/300.50 42984[0:SpR:353.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x1,w),x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(x1,w),u,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(x1,w),u,tc_fun(z,tc_bool)))**.
% 299.92/300.50 42951[0:SpR:486.1,532.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool))))**.
% 299.92/300.50 42941[0:SpR:486.1,533.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool))),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool))),z))**.
% 299.92/300.50 42921[0:SpR:486.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) hBOOL(hAPP(hAPP(c_in(y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,z,v,tc_fun(x1,tc_bool))),x2)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,z,v,tc_fun(x1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(z,w)),y,u),u)*.
% 299.92/300.50 42902[0:SpR:486.1,176.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool))),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x,x1),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.92/300.50 43529[0:SpR:97.1,507.0] || c_Fun_Oinj__on(u,v,w,x) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(u,w,x),v)),y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y)))**.
% 299.92/300.50 43591[0:Rew:538.0,43514.1] || c_Fun_Oinj__on(u,v,w,x) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(u,w,x),v))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y)))**.
% 299.92/300.50 43511[0:SpR:507.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),y,z,x1,x2),hAPP(c_Set_Oimage(v,w,u),x3)),hAPP(hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x3)),hAPP(y,hAPP(c_Set_Oimage(v,w,u),x3))))*.
% 299.92/300.50 43510[0:SpR:507.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(w,x,v),y)),z,x1,x2),hAPP(c_Set_Oimage(w,x,v),x3)),hAPP(hAPP(u,hAPP(c_Set_Oimage(w,x,v),x3)),hAPP(c_Set_Oimage(w,x,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),x3))))*.
% 299.92/300.50 43498[0:SpR:507.0,532.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(c_Set_Oimage(v,w,u),z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z))))**.
% 299.92/300.50 43492[0:SpR:507.0,533.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),y)),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y))),z))**.
% 299.92/300.50 43474[0:SpR:507.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Set_Oimage(w,x,y),z)),x1)) -> c_lessequals(hAPP(c_Set_Oimage(w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x2),z)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(w,x,y),x2)),v,u),u)*.
% 299.92/300.50 43455[0:SpR:507.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),z)),u,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),y)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.92/300.50 43733[0:SpR:162.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),y,z,x1,x2),hAPP(c_Set_Ovimage(v,u,w),x3)),hAPP(hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x3)),hAPP(y,hAPP(c_Set_Ovimage(v,u,w),x3))))*.
% 299.92/300.50 43732[0:SpR:162.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(w,v,x),y)),z,x1,x2),hAPP(c_Set_Ovimage(w,v,x),x3)),hAPP(hAPP(u,hAPP(c_Set_Ovimage(w,v,x),x3)),hAPP(c_Set_Ovimage(w,v,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),x3))))*.
% 299.92/300.50 43720[0:SpR:162.0,532.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(c_Set_Ovimage(v,u,w),z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z))))**.
% 299.92/300.50 43714[0:SpR:162.0,533.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),y)),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y))),z))**.
% 299.92/300.50 43696[0:SpR:162.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Set_Ovimage(w,x,y),z)),x1)) -> c_lessequals(hAPP(c_Set_Ovimage(w,x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),x2),z)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Ovimage(w,x,y),x2)),v,u),u)*.
% 299.92/300.50 43677[0:SpR:162.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),z)),u,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),y)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.92/300.50 43942[0:SpL:97.1,231.0] || c_Fun_Oinj__on(u,v,w,x) c_lessequals(y,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(c_Fun_Othe__inv__into(v,u,w,x),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w) -> c_lessequals(hAPP(c_Set_Ovimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y),hAPP(c_Set_Oimage(u,w,x),v),tc_fun(x,tc_bool))*.
% 299.92/300.50 44063[0:SpL:97.1,358.0] || c_Fun_Oinj__on(u,v,w,x) c_lessequals(v,hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y),tc_fun(w,tc_bool))* c_Fun_Oinj__on(c_Fun_Othe__inv__into(v,u,w,x),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w)* -> c_lessequals(hAPP(c_Set_Oimage(u,w,x),v),y,tc_fun(x,tc_bool)).
% 299.92/300.50 44048[0:SpL:97.1,358.0] || c_Fun_Oinj__on(u,v,w,x) c_lessequals(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y),v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(c_Fun_Othe__inv__into(v,u,w,x),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w)* -> c_lessequals(y,hAPP(c_Set_Oimage(u,w,x),v),tc_fun(x,tc_bool)).
% 299.92/300.50 44388[0:SpR:90.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,hAPP(c_COMBB(hAPP(c_COMBB(c_Set_Oimage(v,w,x),tc_fun(w,tc_bool),tc_fun(x,tc_bool),y),z),y,tc_fun(x,tc_bool),x1),x2),x1,tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x2,x1,y),u),z,y,tc_fun(w,tc_bool))))**.
% 299.92/300.50 44442[0:SpR:30.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,hAPP(c_COMBB(hAPP(c_COMBB(c_Set_Ovimage(v,w,x),tc_fun(x,tc_bool),tc_fun(w,tc_bool),y),z),y,tc_fun(w,tc_bool),x1),x2),x1,tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x2,x1,y),u),z,y,tc_fun(x,tc_bool))))**.
% 299.92/300.50 45858[0:SpL:410.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(v,w),u,x)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,v,z,tc_fun(x,tc_bool)),u,x)))* hBOOL(hAPP(hAPP(c_in(x),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,z),y),v,z,tc_fun(x,tc_bool))))* -> hBOOL(hAPP(u,x1))*.
% 299.92/300.50 46176[0:Res:468.0,481.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(y,v,w),x)) hBOOL(hAPP(z,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(x,u,y,v,w)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),x1),z,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),x1)))*.
% 299.92/300.50 46130[0:Res:474.0,481.0] || -> hBOOL(hAPP(u,hAPP(v,w)))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,y,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),z),u,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,y,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),z)))*.
% 299.92/300.50 46107[0:SpL:24914.0,481.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,x),hAPP(c_in(u),v_x))))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)))*.
% 299.92/300.50 46494[0:Res:468.0,480.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(y,v,w),x)) hBOOL(hAPP(z,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(x,u,y,v,w)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),x),z,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),x)))*.
% 299.92/300.50 46448[0:Res:474.0,480.0] || -> hBOOL(hAPP(u,hAPP(v,w)))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(v,z,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))),u,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(v,z,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))))*.
% 299.92/300.50 46425[0:SpL:24914.0,480.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,x),hAPP(c_in(u),v_x))))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),v)))*.
% 299.92/300.50 47392[0:SpL:21893.0,485.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(v),v_x),c_in(v),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)),x))*.
% 299.92/300.50 47391[0:SpL:21267.0,485.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(v),hAPP(c_in(v),v_x),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)),x))*.
% 299.92/300.50 47623[0:SpL:21893.0,484.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(v),v_x),c_in(v),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,v)),y))*.
% 299.92/300.50 47622[0:SpL:21267.0,484.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(v),hAPP(c_in(v),v_x),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,v)),y))*.
% 299.92/300.50 47961[0:SpL:21893.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(w),v_x),c_in(w),tc_Com_Opname,y)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)),x))*.
% 299.92/300.50 47960[0:SpL:21267.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(w),hAPP(c_in(w),v_x),tc_Com_Opname,y)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)),x))*.
% 299.92/300.50 48073[0:SpL:21893.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(w),v_x),c_in(w),tc_Com_Opname,y)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)),x))*.
% 299.92/300.50 48072[0:SpL:21267.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(w),hAPP(c_in(w),v_x),tc_Com_Opname,y)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)),x))*.
% 299.92/300.50 48427[0:SpL:23902.1,224.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(c_Set_Oimage(hAPP(u,v_x),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(u,v_x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),w),x),w,v) -> .
% 299.92/300.50 48419[0:SpL:301.1,224.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),x),y),x,v) -> .
% 299.92/300.50 48413[0:SpL:11176.1,224.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(c_Set_Oinsert(y,w),x),w,v) -> .
% 299.92/300.50 48409[0:SpL:11177.1,224.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,v),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(u,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(c_Set_Oinsert(u,x),y),x,v) -> .
% 299.92/300.50 48354[0:SpL:300.1,224.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,v),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Oinsert(w,x),y),x,v) -> .
% 299.92/300.50 48349[0:SpL:3586.1,224.0] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),x,w),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v_x,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v_x,x),y),x,w) -> .
% 299.92/300.50 48348[7:SpL:27278.1,224.0] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v,u),x,w),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v_x,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v_x,x),y),x,w) -> .
% 299.92/300.50 48317[0:SpL:9493.1,224.0] || equal(hAPP(u,v_x),c_Orderings_Otop__class_Otop(tc_bool)) hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(u,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(u,w),x),w,v) -> .
% 299.92/300.50 48315[0:SpL:8498.1,224.0] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),u),hAPP(c_Set_Oimage(c_Set_Oinsert(x,v),y,w),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(u,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(u,y),z),y,w) -> .
% 299.92/300.50 48791[0:Res:9071.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(x,v),tc_Com_Opname,tc_fun(v,tc_bool))),c_Set_Oinsert(y,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(y,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(x,v),tc_Com_Opname,tc_fun(v,tc_bool)),u,v,tc_fun(w,tc_bool))))**.
% 299.92/300.50 48781[0:Res:474.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(x,y,v),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),c_Set_Oinsert(z,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(z,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,y,v),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u,v,tc_fun(w,tc_bool))))**.
% 299.92/300.50 48755[0:SpL:8415.2,619.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,v)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,u,tc_fun(x,tc_bool)),v),c_Set_Oinsert(y,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,u,tc_fun(x,tc_bool))))**.
% 299.92/300.50 48950[0:SpL:584.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w,x,y,z),x1)))* -> hBOOL(hAPP(x2,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x1,x2,u)),x1)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(w,x1),x2,u)),hAPP(w,x1)))*.
% 299.92/300.50 49189[0:Res:168.0,239.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,u,w,tc_Hoare__Mirabelle_Otriple(t_a)) -> c_Hoare__Mirabelle_Ohoare__valids(y,hAPP(c_Set_Oimage(x,w,tc_Hoare__Mirabelle_Otriple(t_a)),u),t_a) hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(u,x,w,tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(y,hAPP(c_Set_Oimage(x,w,tc_Hoare__Mirabelle_Otriple(t_a)),u)))),v))*.
% 299.92/300.50 49664[0:Rew:49662.2,49519.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),z,x1,x2) -> hBOOL(hAPP(hAPP(c_in(x2),w),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x1,x2),hAPP(c_Set_Oinsert(v,x1),z))))* c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),hAPP(c_Set_Oinsert(v,x1),z),x1,x2).
% 299.92/300.50 49674[0:Rew:49662.2,49591.1] || c_Fun_Oinj__on(c_Set_Oinsert(u,v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),x,y),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),w))))* c_Fun_Oinj__on(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),w),x,y).
% 299.92/300.50 49676[0:Rew:49662.2,49510.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,y),hAPP(c_Set_Oinsert(v,x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(v,x),w),x,y).
% 299.92/300.50 49682[0:Rew:49662.2,49588.2] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),w),x,y).
% 299.92/300.50 49684[0:Rew:49662.2,49511.3] class_Lattices_Obounded__lattice(u) class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),hAPP(c_Set_Oinsert(v,x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Set_Oinsert(v,x),w),x,y).
% 299.92/300.50 49699[0:Rew:49662.2,49513.2] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,x),hAPP(c_Set_Oinsert(y,w),v))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Oinsert(y,w),v),w,x).
% 299.92/300.50 49704[0:Rew:49662.2,49482.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,u),w,x),hAPP(c_Set_Oinsert(hAPP(c_in(tc_Com_Opname),v_x),w),v))))* c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,u),hAPP(c_Set_Oinsert(hAPP(c_in(tc_Com_Opname),v_x),w),v),w,x).
% 299.92/300.50 49731[0:Rew:49662.2,49593.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),u,v,w) -> hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),v),u))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),v),u),v,w).
% 299.92/300.50 50035[0:SpL:497.0,16286.0] || equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_Procs)** -> .
% 299.92/300.50 50034[7:SpL:497.0,31868.0] || equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),c_Orderings_Obot__class_Obot(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_x)** -> .
% 299.92/300.50 50008[0:SpR:3229.1,497.0] || equal(u,c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(u,v_x)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v_x),v)))**.
% 299.92/300.50 50002[0:SpR:3229.1,497.0] || equal(u,c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(u,v_x)),v_x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),v_x)))**.
% 299.92/300.50 49962[0:SpR:497.0,3229.1] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)))* -> equal(hAPP(u,v_x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)))*.
% 299.92/300.50 49958[4:SpR:497.0,38042.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),w,t_a)*.
% 299.92/300.50 49948[0:SpR:497.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_Com_Opname,w)))*.
% 299.92/300.50 49942[0:SpR:497.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_Com_Opname,w)))*.
% 299.92/300.50 49935[4:SpR:497.0,37987.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),w))*.
% 299.92/300.50 49925[0:SpR:497.0,3283.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),v_Procs)).
% 299.92/300.50 49918[0:SpR:497.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_Com_Opname,w),v_Procs),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))))*.
% 299.92/300.50 50508[0:SpL:223.1,7600.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,x1,u,y),u,y),w)),y)* -> c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(z,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),y)*.
% 299.92/300.50 50505[0:SpL:223.1,360.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),w),x1,x2)* -> c_Fun_Oinj__on(x,hAPP(c_Set_Oimage(y,u,x1),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),x1,x2)*.
% 299.92/300.50 50499[7:SpL:223.1,27282.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),v_x)** -> hBOOL(hAPP(hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),v_x))* equal(y,v_x).
% 299.92/300.50 50496[0:SpL:223.1,4382.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),v_Procs)** -> hBOOL(hAPP(hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),v_x))* equal(y,v_x).
% 299.92/300.50 50453[0:SpR:223.1,37394.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_Set_Oimage(x,u,t_a),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),v_x))* -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,t_a),u,t_a),w),tc_Com_Opname,tc_bool))*.
% 299.92/300.50 50398[0:SpR:223.1,19436.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(x,u,tc_Com_Opname),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),v_Procs)** -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v_x),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,tc_Com_Opname),u,tc_Com_Opname),w)))*.
% 299.92/300.50 50397[0:SpR:223.1,7460.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(v_Procs,hAPP(c_Set_Oimage(x,u,tc_Com_Opname),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),tc_fun(tc_Com_Opname,tc_bool))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,tc_Com_Opname),u,tc_Com_Opname),w),v_x))*.
% 299.92/300.50 50387[0:SpR:223.1,36802.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(t_a,tc_bool)))** -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,z,u,y),u,y),w),v_x))*.
% 299.92/300.50 50386[4:SpR:223.1,42029.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x))** -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,z,u,y),u,y),w),v_x))*.
% 299.92/300.50 51188[0:SpR:223.1,26873.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,z,u,y),u,y),w),tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))**.
% 299.92/300.50 51299[0:SpR:223.1,51231.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Set_Oimage(x,u,t_a),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),v_x),hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,t_a),u,t_a),w),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.92/300.50 51502[0:SpL:223.1,33513.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),y)* equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,z,u,y),u,y),w),y),c_HOL_Ozero__class_Ozero(tc_nat))** -> .
% 299.92/300.50 51706[0:Res:13385.1,233.2] || equal(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))) c_Finite__Set_Ofinite(w,x) c_Finite__Set_Ofinite(u,v) c_lessequals(hAPP(c_Set_Oimage(y,v,x),u),w,tc_fun(x,tc_bool))* c_Fun_Oinj__on(z,w,x,v)* c_Fun_Oinj__on(y,u,v,x) -> equal(c_Finite__Set_Ocard(w,x),c_Finite__Set_Ocard(u,v)).
% 299.92/300.50 51831[4:SpR:223.1,40792.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(v_x,hAPP(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),z),tc_bool)* -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,x1,u,y),u,y),w),z))*.
% 299.92/300.50 52846[0:SpL:24019.2,224.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v_x,v,u),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v_x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))))* c_Fun_Oinj__on(v_x,hAPP(c_Set_Oinsert(v_x,v),w),v,u) -> .
% 299.92/300.50 53756[0:Res:7226.0,481.0] || -> hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_Option_Othe(x),y,w),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),z),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_Option_Othe(x),y,w),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))),z)))*.
% 299.92/300.50 53755[0:Res:7226.0,480.0] || -> hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(c_Option_Othe(y),z,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(c_Option_Othe(y),z,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))))*.
% 299.92/300.50 58202[0:SpL:497.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool),w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)))* -> .
% 299.92/300.50 58757[0:SpL:161.0,15629.0] || hBOOL(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool))),y)))*.
% 299.92/300.50 58756[0:SpL:162.0,15629.0] || hBOOL(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x)),z)))*.
% 299.92/300.50 58755[0:SpL:507.0,15629.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x)),z)))*.
% 299.92/300.50 59265[0:SpL:161.0,15857.0] || hBOOL(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool))),z)))*.
% 299.92/300.50 59264[0:SpL:162.0,15857.0] || hBOOL(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x)),x1)))*.
% 299.92/300.50 59263[0:SpL:507.0,15857.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x)),x1)))*.
% 299.92/300.50 60483[0:SpL:5882.1,284.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1,v),x2)))* c_Fun_Oinj__on(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x1,v)* -> hBOOL(hAPP(hAPP(c_in(x1),c_Orderings_Otop__class_Otop(u)),x2)).
% 299.92/300.50 61809[0:SpL:11167.1,284.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,tc_Com_Opname)),x,u),y)))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,tc_Com_Opname)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u)* -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),y)).
% 299.92/300.50 62160[0:Res:23754.0,481.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),v_Procs)),w),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),v_Procs)),w)))*.
% 299.92/300.50 62159[0:Res:23754.0,480.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),v_Procs)),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),v_Procs))))*.
% 299.92/300.50 64164[0:SpR:646.1,486.1] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),w,tc_fun(y,tc_bool)))**.
% 299.92/300.50 64331[0:SpR:645.1,486.1] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v_x)),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),w,tc_fun(y,tc_bool)))**.
% 299.92/300.50 64579[0:SpR:26782.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),u),v),c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,tc_fun(x,tc_bool)),u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,tc_fun(x,tc_bool)),u,tc_fun(y,tc_bool))))*.
% 299.92/300.50 66709[0:SpR:1188.2,486.1] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,tc_fun(x,tc_bool)))**.
% 299.92/300.50 67464[0:SpR:1189.2,486.1] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ozero__class_Ozero(u)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),v,tc_fun(x,tc_bool)))**.
% 299.92/300.50 71410[7:SpL:497.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_x)** -> .
% 299.92/300.50 71822[7:SpL:71455.1,315.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,t_a),w,x),v_x) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,t_a),w,x)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,t_a),w,x))** -> equal(hAPP(c_Set_Oimage(v,w,x),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,x),u)).
% 299.92/300.50 71794[7:SpL:71455.1,315.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,t_a),v,w,x),v_x) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,t_a),v,w,x)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,t_a),v,w,x))** -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,x),u),hAPP(c_Set_Oimage(v,w,x),u)).
% 299.92/300.50 73748[7:SpR:71835.1,497.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),v_x).
% 299.92/300.50 74528[7:Rew:538.0,73616.1] || equal(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),c_Set_Oinsert(v_x,t_a)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v_x),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),v_x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v_x)))**.
% 299.92/300.50 74869[7:SpR:497.0,72297.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),v_x)).
% 299.92/300.50 76149[0:SpR:9915.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_COMBS(c_Set_Ovimage(x,y,v),z,x1,x2,x3),w,u,x4) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_COMBS(c_Set_Ovimage(x,y,v),z,x1,x2,x3),u,x4),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.92/300.50 76148[0:SpR:9915.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_COMBS(c_Set_Ovimage(x,y,v),z,x1,x2,x3),w,u,x4) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_COMBS(c_Set_Ovimage(x,y,v),z,x1,x2,x3),u,x4),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))**.
% 299.92/300.50 76140[0:SpR:9915.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v),w),c_COMBS(c_Set_Ovimage(x,y,u),z,x1,x2,x3),v,tc_fun(x4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x4,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Set_Ovimage(x,y,u),z,x1,x2,x3),v,tc_fun(x4,tc_bool))))*.
% 299.92/300.50 76269[0:SpR:10469.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_COMBS(c_Set_Oimage(x,v,y),z,x1,x2,x3),w,u,x4) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_COMBS(c_Set_Oimage(x,v,y),z,x1,x2,x3),u,x4),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.92/300.50 76268[0:SpR:10469.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_COMBS(c_Set_Oimage(x,v,y),z,x1,x2,x3),w,u,x4) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_COMBS(c_Set_Oimage(x,v,y),z,x1,x2,x3),u,x4),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.92/300.50 76260[0:SpR:10469.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),w),c_COMBS(c_Set_Oimage(x,u,y),z,x1,x2,x3),v,tc_fun(x4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x4,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Set_Oimage(x,u,y),z,x1,x2,x3),v,tc_fun(x4,tc_bool))))*.
% 299.92/300.50 76399[0:SpR:10470.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_COMBS(c_Set_Ovimage(x,y,v),z,x1,x2,x3),w,u,x4) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_COMBS(c_Set_Ovimage(x,y,v),z,x1,x2,x3),u,x4),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.92/300.50 76398[0:SpR:10470.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) c_Fun_Oinj__on(c_COMBS(c_Set_Ovimage(x,y,v),z,x1,x2,x3),w,u,x4) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_COMBS(c_Set_Ovimage(x,y,v),z,x1,x2,x3),u,x4),c_Orderings_Obot__class_Obot(tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))**.
% 299.92/300.50 76390[0:SpR:10470.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v),w),c_COMBS(c_Set_Ovimage(x,y,u),z,x1,x2,x3),v,tc_fun(x4,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x4,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Set_Ovimage(x,y,u),z,x1,x2,x3),v,tc_fun(x4,tc_bool))))*.
% 299.92/300.50 80214[0:SpL:21268.0,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) c_Hoare__Mirabelle_Ohoare__valids(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),x,y),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,z)),w))* c_Hoare__Mirabelle_Otriple__valid(z,u,t_a)*.
% 299.92/300.50 80101[0:SpL:21268.0,487.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_in(w),hAPP(c_in(w),x),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x1)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x1,u,w)))*.
% 299.92/300.50 79899[0:SpR:180.2,21268.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),y,hAPP(c_Set_Oinsert(w,u),v),u,u),x,z)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),y,hAPP(c_Set_Oinsert(w,u),v),u,u))**.
% 299.92/300.50 79883[0:SpR:465.1,21268.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),hAPP(c_Set_Oimage(x,u,z),w),x1,x2)),hAPP(c_Set_Oimage(x,u,z),w))**.
% 299.92/300.50 79681[0:SpR:21268.0,201.3] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),y,z),w,u,u),u)*.
% 299.92/300.50 79387[0:SpR:21268.0,393.1] || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(c_COMBK(v,w,x),x,w),hAPP(c_Set_Oimage(c_COMBK(v,w,x),x,w),y),u,z),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))** equal(hAPP(c_Set_Oimage(c_COMBK(v,w,x),x,w),y),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))).
% 299.92/300.50 81409[0:SpL:21894.0,453.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) c_Hoare__Mirabelle_Ohoare__valids(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x,y),t_a)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(w,z)),w))* c_Hoare__Mirabelle_Otriple__valid(z,u,t_a)*.
% 299.92/300.50 81296[0:SpL:21894.0,487.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(w),x),c_in(w),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x1)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x1,u,w)))*.
% 299.92/300.50 81093[0:SpR:180.2,21894.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),y,hAPP(c_Set_Oinsert(w,u),v),u,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,z)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),y,hAPP(c_Set_Oinsert(w,u),v),u,u))**.
% 299.92/300.50 81077[0:SpR:465.1,21894.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(x,u,z),w),c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1,x2)),hAPP(c_Set_Oimage(x,u,z),w))**.
% 299.92/300.50 80875[0:SpR:21894.0,201.3] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(w,u) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,z),w,u,u),u)*.
% 299.92/300.50 80580[0:SpR:21894.0,393.1] || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(c_COMBK(v,w,x),x,w),y),c_Set_Oimage(c_COMBK(v,w,x),x,w),u,z),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))** equal(hAPP(c_Set_Oimage(c_COMBK(v,w,x),x,w),y),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))).
% 299.92/300.50 82958[0:SpR:5924.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_COMBS(x,c_COMBK(y,z,x1),x2,x3,x4),v,tc_fun(x5,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x5,tc_bool)),hAPP(hAPP(x,u),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(x,c_COMBK(y,z,x1),x2,x3,x4),v,tc_fun(x5,tc_bool))))*.
% 299.92/300.50 83241[7:SpR:497.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),w,x),v_x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))))*.
% 299.92/300.50 83296[0:SpR:5961.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_COMBS(c_COMBK(x,y,z),x1,x2,x3,x4),v,tc_fun(x5,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x5,tc_bool)),hAPP(x,hAPP(x1,u))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_COMBK(x,y,z),x1,x2,x3,x4),v,tc_fun(x5,tc_bool))))*.
% 299.92/300.50 83886[0:SpL:5899.0,199.0] || hBOOL(hAPP(c_COMBS(u,v,w,x,y),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,z,x2),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_COMBS(u,v,x3,x4,x5),x1,z,x2))))* c_Fun_Oinj__on(x1,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x2) -> hBOOL(hAPP(c_COMBS(u,v,x3,x4,x5),x6))*.
% 299.92/300.50 83884[0:SpL:5899.0,449.0] || hBOOL(hAPP(hAPP(c_COMBS(u,v,w,x,y),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(z,c_COMBS(u,v,x1,x2,x3),x4,x5)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(z,c_COMBS(u,v,x1,x2,x3),x4,x5)))* -> c_Hoare__Mirabelle_Otriple__valid(x5,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),z),x4),c_COMBS(u,v,x1,x2,x3)),t_a).
% 299.92/300.50 83882[0:SpL:5899.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_COMBS(v,w,x,y,z),x1)),hAPP(c_Set_Oimage(c_COMBS(v,w,x2,x3,x4),x5,u),x6)))* c_Fun_Oinj__on(c_COMBS(v,w,x2,x3,x4),c_Orderings_Otop__class_Otop(tc_fun(x5,tc_bool)),x5,u)* -> hBOOL(hAPP(hAPP(c_in(x5),x1),x6)).
% 299.92/300.50 86058[0:SpL:497.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_Procs)** -> .
% 299.92/300.50 86510[0:SpL:86109.1,315.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,t_a),w,x),v_Procs) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,t_a),w,x)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,t_a),w,x))** -> equal(hAPP(c_Set_Oimage(v,w,x),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,x),u)).
% 299.92/300.50 86479[0:SpL:86109.1,315.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,t_a),v,w,x),v_Procs) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,t_a),v,w,x)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,t_a),v,w,x))** -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,x),u),hAPP(c_Set_Oimage(v,w,x),u)).
% 299.92/300.50 86590[0:SpR:21894.0,19823.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),y),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),v,z)))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),y)).
% 299.92/300.50 86588[0:SpR:21268.0,19823.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),y),v,z)))* -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),y)).
% 299.92/300.50 88922[0:SpR:323.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),y,z),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),x1),w,x,tc_fun(u,tc_bool)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(u,tc_bool))))*.
% 299.92/300.50 91370[0:Rew:91288.1,91223.2,91288.1,91223.1] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),x),y),x,v) -> .
% 299.92/300.50 92359[0:SpL:338.0,5022.0] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),tc_fun(u,tc_bool))* -> equal(hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)).
% 299.92/300.50 92429[0:Rew:21894.0,92384.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(u,v),x,y),tc_fun(v,tc_bool))* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),c_Set_Oinsert(u,v),x,y),hAPP(c_Set_Oinsert(u,v),w)).
% 299.92/300.50 92430[0:Rew:21268.0,92382.1] || c_lessequals(hAPP(c_Set_Oinsert(u,v),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),w),x,y),tc_fun(v,tc_bool))* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),w),x,y),hAPP(c_Set_Oinsert(u,v),w)).
% 299.92/300.50 92579[0:SpR:61.1,5227.1] || c_Finite__Set_Ofinite(u,v) c_Natural_Oevaln(hAPP(c_Com_Ocom_OBODY,w),x,c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(y,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),z)* -> equal(c_Suc(c_Natural_Osko__Natural__Xevaln__elim__cases__6__1(w,c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(y,v),u),v),x,z)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(y,v),u),v)).
% 299.92/300.50 92899[0:SpR:323.0,5876.0] || -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool))),x1,x2,x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))),tc_fun(z,tc_bool))*.
% 299.92/300.50 21279[0:Res:171.2,469.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),x),u),w,u)),c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),x),u))**.
% 299.92/300.50 21278[0:Res:172.2,469.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(x,v,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),x),u),w,u)),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),x),u))**.
% 299.92/300.50 21645[0:SpL:21267.0,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,w),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,w),u),v,u)*.
% 299.92/300.50 21644[0:SpL:21267.0,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,w),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,w),u),u)*.
% 299.92/300.50 21905[0:Res:171.2,464.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(x,c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),x),u),v,w,u)),c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),x),u))**.
% 299.92/300.50 21904[0:Res:172.2,464.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(x,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),x),u),v,w,u)),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),x),u))**.
% 299.92/300.50 22273[0:SpL:21893.0,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,w),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,w),u),v,u)*.
% 299.92/300.50 22272[0:SpL:21893.0,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,w),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,w),u),u)*.
% 299.92/300.50 22580[0:SpR:158.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x2)),x1),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),x3)))*.
% 299.92/300.50 22579[0:SpR:158.0,99.1] || c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x2))),x2)**.
% 299.92/300.50 22578[0:SpR:158.0,438.1] || c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x2))),x2)**.
% 299.92/300.50 22966[0:SpR:131.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x2)),x1),hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),x3)))*.
% 299.92/300.50 22965[0:SpR:131.0,99.1] || c_Fun_Oinj__on(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x2))),x2)**.
% 299.92/300.50 22964[0:SpR:131.0,438.1] || c_Fun_Oinj__on(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x2))),x2)**.
% 299.92/300.50 23388[0:SpR:460.1,317.0] || class_Lattices_Olattice(t_b) -> equal(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,v),hAPP(c_Set_Oinsert(v_x,u),w)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),v),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,v),w)))*.
% 299.92/300.50 23387[0:SpR:460.1,99.1] || class_Lattices_Olattice(t_b) c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),v_x)**.
% 299.92/300.50 23386[0:SpR:460.1,438.1] || class_Lattices_Olattice(t_b) c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),v_x)**.
% 299.92/300.50 23519[0:SpR:523.1,317.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x,y),hAPP(c_Set_Oinsert(v_x,x),z)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),y),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x,y),z)))*.
% 299.92/300.50 23518[0:SpR:523.1,99.1] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))),v_x)**.
% 299.92/300.50 23517[0:SpR:523.1,438.1] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))),v_x)**.
% 299.92/300.50 25526[0:Rew:25273.0,25344.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),c_Set_Oimage(hAPP(c_COMBB(u,w,x,y),v),y,x),tc_Com_Opname,z)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))**.
% 299.92/300.50 25527[0:Rew:25273.0,25341.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(hAPP(c_COMBB(u,w,x,y),v),y,x),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)),tc_Com_Opname,z)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))**.
% 299.92/300.50 25528[0:Rew:25273.0,25394.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x),c_Set_Oimage(hAPP(c_COMBB(u,v,w,y),x),y,w),tc_Com_Opname,z))),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x))**.
% 299.92/300.50 25529[0:Rew:25273.0,25393.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(hAPP(c_COMBB(u,v,w,y),x),y,w),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x),tc_Com_Opname,z))),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x))**.
% 299.92/300.50 26695[0:SpR:317.0,244.2] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(v,x,u),y)))* equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(v,x,u),y),u),c_HOL_Ozero__class_Ozero(tc_nat)) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(v,x,u),hAPP(c_Set_Oinsert(w,x),y)),u),c_Suc(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(v,x,u),y),u)))**.
% 299.92/300.50 27144[0:SpR:297.2,450.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y),u) -> hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y)))* c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),x),w),t_a).
% 299.92/300.50 27141[0:SpR:331.0,450.0] || -> hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,w,x),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,w,x)))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))),w),v),t_a).
% 299.92/300.50 27594[0:SpR:544.1,373.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,v,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))**.
% 299.92/300.50 27593[0:SpR:543.1,373.2] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,v,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))**.
% 299.92/300.50 27747[0:SpR:544.1,71.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,v,z) -> equal(hAPP(c_Fun_Othe__inv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))**.
% 299.92/300.50 27746[0:SpR:543.1,71.2] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,v,z) -> equal(hAPP(c_Fun_Othe__inv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))**.
% 299.92/300.50 28242[0:SpL:465.1,19641.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),z)))* -> hBOOL(hAPP(hAPP(c_in(v),x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),z)))* c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),z,t_a).
% 299.92/300.50 28509[0:SpR:542.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Fun_Ofun__upd(w,x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x1,x2,z),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),z,x2))*.
% 299.92/300.50 28467[0:SpR:71.2,118.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(c_Fun_Ocomp(c_Fun_Othe__inv__into(w,x,u,y),c_Fun_Ofun__upd(z,x1,hAPP(x,v),x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Fun_Othe__inv__into(w,x,u,y),z,x3,x4,x2),x1,v,x2,x4))*.
% 299.92/300.50 28466[0:SpR:373.2,118.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(w,x,u,y),c_Fun_Ofun__upd(z,x1,hAPP(x,v),x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x3,x4,x2),x1,v,x2,x4))*.
% 299.92/300.50 28633[0:SpR:338.0,177.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x))) equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(v,u),x)),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x))**.
% 299.92/300.50 30104[0:SpR:536.1,118.0] class_Lattices_Olattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Fun_Ofun__upd(w,x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x2,x3,x1),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z)),x1,x3))*.
% 299.92/300.50 30660[0:SpR:535.1,118.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_Fun_Ofun__upd(w,x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x2,x3,x1),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z)),x1,x3))*.
% 299.92/300.50 32346[0:SpL:181.1,477.0] || hBOOL(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(v),w),x))* -> hBOOL(hAPP(hAPP(c_in(y),z),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),x1),c_Set_Ovimage(c_COMBK(z,y,u),u,y),v)))* hBOOL(hAPP(c_Set_Ovimage(c_COMBK(z,y,u),u,y),w))*.
% 299.92/300.50 32526[0:SpL:181.1,476.0] || hBOOL(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(v),w),x))* -> hBOOL(hAPP(hAPP(c_in(y),z),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),x),c_Set_Ovimage(c_COMBK(z,y,u),u,y),v)))* hBOOL(hAPP(c_Set_Ovimage(c_COMBK(z,y,u),u,y),w))*.
% 299.92/300.50 32796[0:SpR:177.1,35.2] || c_lessequals(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w,tc_fun(v,tc_bool))* c_lessequals(w,hAPP(c_Set_Oinsert(u,v),x),tc_fun(v,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(v),u),x)) equal(c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))).
% 299.92/300.50 32774[0:SpR:35.2,117.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* c_lessequals(c_HOL_Ominus__class_Ominus(v,c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),w,tc_fun(x,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(v,c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),u).
% 299.92/300.50 33027[0:SpR:338.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(z,v),x)),x1),hAPP(c_Set_Oimage(c_Set_Oinsert(z,v),u,x1),y)),hAPP(c_Set_Oimage(c_Set_Oinsert(z,v),u,x1),y))**.
% 299.92/300.50 33022[0:SpR:317.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(x1,w),y)),x2),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(v,x1),x),u,x2),z)),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(v,x1),x),u,x2),z))**.
% 299.92/300.50 32974[0:SpR:600.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),w),z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),u,z),y)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),u,z),y))**.
% 299.92/300.50 32954[0:SpR:181.1,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),y),v))* equal(hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)),x1),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(y,x,z),z,x),u,x1),w)),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(y,x,z),z,x),u,x1),w))**.
% 299.92/300.50 32877[0:SpR:475.1,317.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(x,v),y),z,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,u,y),w),z),x2)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,u,y),w),x1),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(x,v),y),z,x1),x2)))*.
% 299.92/300.50 32876[0:SpR:475.1,99.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Set_Oinsert(hAPP(x,v),y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oinsert(hAPP(x,v),y),z,x1),hAPP(c_Set_Oimage(x,u,y),w)),hAPP(c_Set_Oimage(x,u,y),w))**.
% 299.92/300.50 32875[0:SpR:475.1,438.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Set_Oinsert(hAPP(x,v),y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oinsert(hAPP(x,v),y),z,x1),hAPP(c_Set_Oimage(x,u,y),w)),hAPP(c_Set_Oimage(x,u,y),w))**.
% 299.92/300.50 33524[0:Rew:26884.1,33508.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),x),u)* -> equal(c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),u)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,u),x),u))**.
% 299.92/300.50 33799[0:Res:248.4,251.1] class_Orderings_Olinorder(tc_fun(u,v)) class_HOL_Oord(v) || c_Finite__Set_Ofinite(w,tc_fun(u,v)) c_lessequals(x,w,tc_fun(tc_fun(u,v),tc_bool)) -> equal(x,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,v),tc_bool))) c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMin(w,tc_fun(u,v)),y),hAPP(c_Finite__Set_Olinorder__class_OMin(x,tc_fun(u,v)),y),v)*.
% 299.92/300.50 33795[0:Res:248.4,431.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(tc_fun(u,tc_bool),tc_bool))* c_Fun_Oinj__on(x,c_Finite__Set_Olinorder__class_OMin(w,tc_fun(u,tc_bool)),u,y)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,tc_bool),tc_bool))) c_Fun_Oinj__on(x,c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),u,y)*.
% 299.92/300.50 33879[0:Res:247.4,251.1] class_Orderings_Olinorder(tc_fun(u,v)) class_HOL_Oord(v) || c_Finite__Set_Ofinite(w,tc_fun(u,v)) c_lessequals(x,w,tc_fun(tc_fun(u,v),tc_bool)) -> equal(x,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,v),tc_bool))) c_lessequals(hAPP(c_Finite__Set_Olinorder__class_OMax(x,tc_fun(u,v)),y),hAPP(c_Finite__Set_Olinorder__class_OMax(w,tc_fun(u,v)),y),v)*.
% 299.92/300.50 33875[0:Res:247.4,431.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(tc_fun(u,tc_bool),tc_bool))* c_Fun_Oinj__on(x,c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),u,y)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,tc_bool),tc_bool))) c_Fun_Oinj__on(x,c_Finite__Set_Olinorder__class_OMax(w,tc_fun(u,tc_bool)),u,y)*.
% 299.92/300.50 34352[0:SpL:24914.0,273.0] || equal(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x))* -> equal(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),tc_Com_Opname,w),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x)))*.
% 299.92/300.50 34254[0:SpR:131.0,24914.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)))),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),v_x)))**.
% 299.92/300.50 34253[0:SpR:158.0,24914.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),tc_Com_Opname,z),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),v_x)))**.
% 299.92/300.50 34171[0:SpR:24914.0,131.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),tc_Com_Opname,z),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_x)))),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),v_x))**.
% 299.92/300.50 34169[0:SpR:24914.0,158.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),tc_Com_Opname,z),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x)))),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),v_x))**.
% 299.92/300.50 34648[0:SpR:35.2,55.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(v,x,tc_fun(w,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(w),y),c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)))) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(y,w),v),c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(y,w),u))**.
% 299.92/300.50 35300[0:SpR:131.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(u,v,w),x),y),z),c_Set_Ovimage(x1,x2,v),y,tc_fun(x3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x3,tc_bool)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,x1,v,w,x2),x2,w),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Ovimage(x1,x2,v),y,tc_fun(x3,tc_bool))))*.
% 299.92/300.50 35299[0:SpR:158.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),x),y),z),c_Set_Oimage(x1,w,x2),y,tc_fun(x3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x3,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ocomp(x1,u,w,x2,v),v,x2),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(x1,w,x2),y,tc_fun(x3,tc_bool))))*.
% 299.92/300.50 35294[0:SpR:317.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),w),x),y),c_Set_Oimage(z,v,x1),x,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),hAPP(c_Set_Oinsert(hAPP(z,u),x1),hAPP(c_Set_Oimage(z,v,x1),w))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oimage(z,v,x1),x,tc_fun(x2,tc_bool))))*.
% 299.92/300.50 35491[0:SpR:113.0,35.2] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),y,tc_fun(v,tc_bool)) c_lessequals(y,hAPP(c_Set_Ovimage(u,v,w),z),tc_fun(v,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Ovimage(u,v,w),c_HOL_Ominus__class_Ominus(z,x,tc_fun(w,tc_bool))),tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x))**.
% 299.92/300.50 35629[0:SpR:21893.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBB(u,v,tc_fun(w,tc_bool),x),v_x),c_COMBB(u,v,tc_fun(w,tc_bool),x),tc_Com_Opname,y),x,v),z),u,v,tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_COMBB(u,v,tc_fun(w,tc_bool),x),v_x),x,tc_fun(w,tc_bool)))**.
% 299.92/300.50 35628[0:SpR:21267.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBB(u,v,tc_fun(w,tc_bool),x),hAPP(c_COMBB(u,v,tc_fun(w,tc_bool),x),v_x),tc_Com_Opname,y),x,v),z),u,v,tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_COMBB(u,v,tc_fun(w,tc_bool),x),v_x),x,tc_fun(w,tc_bool)))**.
% 299.92/300.50 36166[0:SpL:24914.0,516.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))) -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.92/300.50 37007[0:Res:49.2,375.1] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool)),c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) hBOOL(hAPP(hAPP(c_in(x),y),v)) -> c_lessequals(hAPP(w,y),c_HOL_Ouminus__class_Ouminus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.92/300.50 37505[0:SpL:205.1,467.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(v),x),y)) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,v,w),y),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x)),x)**.
% 299.92/300.50 37502[0:SpL:205.1,473.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(v),x),y)) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,v,w),y),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x)),hAPP(c_Set_Oimage(u,v,w),y)))*.
% 299.92/300.50 37493[0:SpL:205.1,202.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,v) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,v),w),v) c_lessequals(hAPP(c_Set_Oimage(u,v,v),w),w,tc_fun(v,tc_bool))* -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,v),hAPP(c_Set_Oimage(u,v,v),w),v,v)*.
% 299.92/300.50 38354[0:SSi:38278.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w)) c_Finite__Set_Ofinite(w,tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x,w,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.92/300.50 38676[0:Rew:9.0,38644.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1))))* c_Fun_Oinj__on(c_Fun_Ocomp(w,y,x,u,z),x1,z,u) -> equal(hAPP(w,hAPP(y,hAPP(c_Fun_Othe__inv__into(x1,c_Fun_Ocomp(w,y,x,u,z),z,u),v))),v)**.
% 299.92/300.50 39010[0:SpL:354.2,470.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(w),z),u)) -> hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__XimageE__1__1(hAPP(c_Set_Oimage(x,w,y),u),z,c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w)),hAPP(c_Set_Oimage(x,w,y),u)))*.
% 299.92/300.50 39009[0:SpL:354.2,466.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(w),z),u)) -> hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(hAPP(c_Set_Oimage(x,w,y),u),c_Hilbert__Choice_Oinv__into(v,x,w,y),z,y,w)),hAPP(c_Set_Oimage(x,w,y),u)))*.
% 299.92/300.50 39006[0:SpL:354.2,389.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,v,w,y) equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z),u)* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v,x,w,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,w)* -> equal(z,hAPP(c_Set_Oimage(x,w,y),u))*.
% 299.92/300.50 38990[0:SpR:465.1,354.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(c_Fun_Ofun__upd(x,y,z,w,x1),v,w,x1) -> hBOOL(hAPP(hAPP(c_in(w),y),u)) equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,c_Fun_Ofun__upd(x,y,z,w,x1),w,x1),x1,w),hAPP(c_Set_Oimage(x,w,x1),u)),u)**.
% 299.92/300.50 39353[0:SpL:533.0,19641.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x))))* -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,t_a).
% 299.92/300.50 39670[0:SpR:532.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x1),x2)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x2)),hAPP(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x1),x2))))*.
% 299.92/300.50 39669[0:SpR:532.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),x2)),hAPP(hAPP(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),x2)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x2))))*.
% 299.92/300.50 39940[0:Rew:39937.1,35220.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),x,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,v,x1,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,v,x1,tc_fun(u,tc_bool)))**.
% 299.92/300.50 41375[0:SpL:317.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(x3,w),y))))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oinsert(hAPP(v,x3),x),u,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 41371[0:SpL:131.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Ovimage(z,x1,x2),hAPP(c_Set_Ovimage(x3,x2,x4),v))))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(c_Fun_Ocomp(x3,z,x2,x4,x1),x1,x4),u,tc_fun(x,tc_bool))))*.
% 299.92/300.50 41370[0:SpL:158.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(z,x1,x2),hAPP(c_Set_Oimage(x3,x4,x1),v))))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_Fun_Ocomp(z,x3,x1,x2,x4),x4,x2),u,tc_fun(x,tc_bool))))*.
% 299.92/300.50 41327[0:SpL:104.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(z,v,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_HOL_Ouminus__class_Ouminus(z,tc_fun(x1,tc_bool))),u,tc_fun(x,tc_bool))))*.
% 299.92/300.50 41270[0:SpL:131.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,x3,w,x,x4),x4,x),y)))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Ovimage(x3,x4,w),u,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 41268[0:SpL:158.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),hAPP(c_Set_Oimage(c_Fun_Ocomp(x3,v,x,x4,w),w,x4),y)))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(x3,x,x4),u,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 41266[0:SpL:97.1,275.1] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oimage(u,w,x),v)),z)) hBOOL(hAPP(hAPP(c_in(x1),x2),v)) -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 41265[0:SpL:99.1,275.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),y))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 41264[0:SpL:438.1,275.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),y))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 41262[0:SpL:317.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y))* hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(c_Set_Oinsert(hAPP(x2,v),x3),hAPP(c_Set_Oimage(x2,w,x3),x))))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oimage(x2,w,x3),u,tc_fun(z,tc_bool))))*.
% 299.92/300.50 41951[0:SpR:66.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(z,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(z,v),y),tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.92/300.50 42265[0:SSi:42174.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) c_Fun_Oinj__on(w,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,hAPP(c_Set_Oinsert(y,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v,z)* -> c_Fun_Oinj__on(w,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v,z).
% 299.92/300.50 42266[0:SSi:42083.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) c_Finite__Set_Ofinite(w,v) c_Finite__Set_Ofinite(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v) -> c_Finite__Set_Ofinite(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,hAPP(c_Set_Oinsert(w,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v)*.
% 299.92/300.50 42467[0:SpL:2097.1,315.0] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(w,x),y,z),w))* equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(w,x),y,z)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(w,x),y,z))** -> equal(hAPP(c_Set_Oimage(v,y,z),u),hAPP(c_Set_Oimage(c_Set_Oinsert(w,x),y,z),u)).
% 299.92/300.50 42426[0:SpL:2097.1,315.0] || hBOOL(hAPP(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v,w),x,y,z),v))* equal(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v,w),x,y,z)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v,w),x,y,z))** -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v,w),y,z),u),hAPP(c_Set_Oimage(x,y,z),u)).
% 299.92/300.50 42643[0:SpR:161.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) -> hBOOL(hAPP(hAPP(c_in(z),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),v),w,tc_fun(x,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(x1,w,tc_fun(x,tc_bool))),u,z),y)))*.
% 299.92/300.50 42639[0:SpR:161.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),v),w,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(z,w,tc_fun(x,tc_bool))),u,tc_fun(x1,tc_bool)),tc_fun(x1,tc_bool))*.
% 299.92/300.50 43097[0:SpR:12944.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(y,z),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x1,x2)),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(y,z),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x1,x2)),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 43069[0:SpR:11473.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Set_Oinsert(y,z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 43057[0:SpR:329.1,486.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) hBOOL(hAPP(hAPP(c_in(x),v),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,tc_fun(z,tc_bool)))**.
% 299.92/300.50 43056[0:SpR:328.1,486.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(x),u),y))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,tc_fun(z,tc_bool)))**.
% 299.92/300.50 43050[0:SpR:538.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),z)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 43029[0:SpR:17045.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),z,tc_fun(x1,tc_bool)),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)),z,tc_fun(x1,tc_bool)),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 42964[0:SpR:486.1,584.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),z,x1,x2,x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool))),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)),hAPP(z,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)))))*.
% 299.92/300.50 42963[0:SpR:486.1,584.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_COMBS(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(z,v)),x1,x2,x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,z,u,tc_fun(y,tc_bool))),hAPP(hAPP(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,z,u,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,z,u,tc_fun(y,tc_bool))))*.
% 299.92/300.50 42949[0:SpR:486.1,533.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u,tc_fun(x,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 42907[0:SpR:486.1,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool))),x1)) -> hBOOL(hAPP(hAPP(c_in(x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x,x2),x1)))*.
% 299.92/300.50 42903[0:SpR:486.1,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool))),x1)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.92/300.50 43539[0:SpR:158.0,507.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z))),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,x,w,u,y),y,u),x1)),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,x,w,u,y),y,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1)))**.
% 299.92/300.50 43524[0:SpR:158.0,507.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,x,u,y),y,u),z)),hAPP(c_Set_Oimage(v,x,u),hAPP(c_Set_Oimage(w,y,x),x1))),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,x,u,y),y,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1)))**.
% 299.92/300.50 43460[0:SpR:507.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) -> hBOOL(hAPP(hAPP(c_in(x1),hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x2),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),x2)),u,x1),z)))*.
% 299.92/300.50 43456[0:SpR:507.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) -> c_lessequals(hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),x1)),u,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.92/300.50 43761[0:SpR:131.0,162.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Ovimage(x,w,y),z))),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,v,w,y,u),u,y),x1)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,v,w,y,u),u,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1)))**.
% 299.92/300.50 43746[0:SpR:131.0,162.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,u),u,y),z)),hAPP(c_Set_Ovimage(w,u,x),hAPP(c_Set_Ovimage(v,x,y),x1))),hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,u),u,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1)))**.
% 299.92/300.50 43682[0:SpR:162.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),z)) -> hBOOL(hAPP(hAPP(c_in(x1),hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x2),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),x2)),u,x1),z)))*.
% 299.92/300.50 43678[0:SpR:162.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),z)) -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),x1)),u,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.92/300.50 43952[0:SpL:158.0,231.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,z,w),x1)),tc_fun(x,tc_bool))* c_Fun_Oinj__on(c_Fun_Ocomp(v,y,w,x,z),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x) -> c_lessequals(hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,y,w,x,z),z,x),u),x1,tc_fun(z,tc_bool))*.
% 299.92/300.50 44073[0:SpL:158.0,358.0] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x1),tc_fun(w,tc_bool))* c_Fun_Oinj__on(c_Fun_Ocomp(u,x,v,w,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,w) -> c_lessequals(z,x1,tc_fun(y,tc_bool)).
% 299.92/300.50 44058[0:SpL:158.0,358.0] || c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x1)),tc_fun(x,tc_bool))* c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,x) -> c_lessequals(z,x1,tc_fun(y,tc_bool)).
% 299.92/300.50 44131[0:SpR:97.1,232.1] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(c_Fun_Othe__inv__into(v,u,w,x),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w) -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,w,x),v),tc_fun(x,tc_bool))),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.92/300.50 44358[0:Res:687.1,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,hAPP(c_in(u),v),tc_Com_Opname)))* equal(hAPP(y,v),hAPP(y,w))* c_Fun_Oinj__on(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,hAPP(c_in(u),v),tc_Com_Opname),u,z)* -> equal(v,w).
% 299.92/300.50 44357[0:Res:686.1,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,hAPP(c_in(u),v),tc_Com_Opname)))* equal(hAPP(y,v),hAPP(y,w))* c_Fun_Oinj__on(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,hAPP(c_in(u),v),tc_Com_Opname),u,z)* -> equal(v,w).
% 299.92/300.50 44316[0:Res:545.1,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(z,u,x),w)))* equal(hAPP(x1,hAPP(z,v)),hAPP(x1,y))* c_Fun_Oinj__on(x1,hAPP(c_Set_Oimage(z,u,x),w),x,x2)* -> equal(hAPP(z,v),y).
% 299.92/300.50 44308[0:Res:510.1,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)))* equal(hAPP(z,v),hAPP(z,x))* c_Fun_Oinj__on(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y),u,x1)* -> equal(v,x).
% 299.92/300.50 44307[0:Res:511.1,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w)))* equal(hAPP(z,v),hAPP(z,x))* c_Fun_Oinj__on(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),w),u,x1)* -> equal(v,x).
% 299.92/300.50 44794[0:Res:27441.0,593.0] || c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w))),t_a)*.
% 299.92/300.50 44791[0:Res:27381.0,593.0] || c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w))),t_a)*.
% 299.92/300.50 45622[0:SpL:323.0,516.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),z,w,tc_fun(u,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,z,w,tc_fun(u,tc_bool)))) hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,z,w,tc_fun(u,tc_bool)))).
% 299.92/300.50 47406[0:Res:168.0,485.1] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),x))))* -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),x),t_a) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,tc_Hoare__Mirabelle_Otriple(t_a))))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,u,tc_Hoare__Mirabelle_Otriple(t_a))),w))*.
% 299.92/300.50 47390[0:SpL:24914.0,485.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(v),tc_Com_Opname,w),hAPP(c_in(v),v_x))))* hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)),x))*.
% 299.92/300.50 47361[0:SpL:104.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),u,w)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))))*.
% 299.92/300.50 47637[0:Res:168.0,484.1] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),x))))* -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),x),t_a) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,u,tc_Hoare__Mirabelle_Otriple(t_a))))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,tc_Hoare__Mirabelle_Otriple(t_a))),x))*.
% 299.92/300.50 47621[0:SpL:24914.0,484.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(v),tc_Com_Opname,w),hAPP(c_in(v),v_x))))* hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,v)),y))*.
% 299.92/300.50 47586[0:SpL:600.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),u,w)),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))))*.
% 299.92/300.50 47975[0:Res:168.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,tc_Hoare__Mirabelle_Otriple(t_a))))* -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),x),v),t_a) hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),x),v))))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,tc_Hoare__Mirabelle_Otriple(t_a))),x))*.
% 299.92/300.50 47959[0:SpL:24914.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v)))* -> hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(w),tc_Com_Opname,y),hAPP(c_in(w),v_x))))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)),x))*.
% 299.92/300.50 47930[0:SpL:104.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(y,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ouminus__class_Ouminus(y,tc_fun(w,tc_bool)),u,w)),c_HOL_Ouminus__class_Ouminus(y,tc_fun(w,tc_bool))))*.
% 299.92/300.50 48087[0:Res:168.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,tc_Hoare__Mirabelle_Otriple(t_a))))* -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),x),t_a) hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),x))))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,tc_Hoare__Mirabelle_Otriple(t_a))),x))*.
% 299.92/300.50 48071[0:SpL:24914.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x)))* -> hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(w),tc_Com_Opname,y),hAPP(c_in(w),v_x))))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)),x))*.
% 299.92/300.50 48036[0:SpL:600.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v)))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ominus__class_Ominus(y,v,tc_fun(w,tc_bool)),u,w)),c_HOL_Ominus__class_Ominus(y,v,tc_fun(w,tc_bool))))*.
% 299.92/300.50 48452[0:SpL:27043.1,224.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,v),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,v),hAPP(c_Set_Oinsert(v_x,w),x),w,u) -> .
% 299.92/300.50 48436[0:SpL:10090.1,224.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(u,v_x),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(u,v_x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),w),x),w,v) -> .
% 299.92/300.50 48429[0:SpL:303.1,224.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),y),x,v) -> .
% 299.92/300.50 48358[0:SpL:302.1,224.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oinsert(y,w),x),w,v) -> .
% 299.92/300.50 48343[0:SpL:15476.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,tc_bool)),hAPP(c_Set_Oinsert(v_x,w),x),w,u) -> .
% 299.92/300.50 48659[0:SpR:158.0,197.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z),hAPP(c_Set_Oimage(u,v,w),x1),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,y,v),z),x1,tc_fun(v,tc_bool))))*.
% 299.92/300.50 48656[0:SpR:317.0,197.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(hAPP(u,x),w),hAPP(c_Set_Oimage(u,v,w),y)),hAPP(c_Set_Oimage(u,v,w),z),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,v),y),z,tc_fun(v,tc_bool))))*.
% 299.92/300.50 48644[0:SpR:158.0,197.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,y,v,w,z),z,w),x1),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oimage(y,z,v),x1),tc_fun(v,tc_bool))))*.
% 299.92/300.50 48641[0:SpR:317.0,197.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oinsert(hAPP(u,y),w),hAPP(c_Set_Oimage(u,v,w),z)),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,v),z),tc_fun(v,tc_bool))))*.
% 299.92/300.50 48840[0:Res:1103.1,619.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,v,tc_fun(y,tc_bool)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(v),w))),c_Set_Oinsert(z,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(z,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(c_in(v),w)),x,v,tc_fun(y,tc_bool))))**.
% 299.92/300.50 48964[0:SpL:8415.2,483.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))* -> hBOOL(hAPP(x,v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.92/300.50 48955[0:SpL:3294.1,483.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) hBOOL(hAPP(hAPP(c_in(u),v),c_Orderings_Obot__class_Obot(tc_bool)))* -> hBOOL(hAPP(w,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,w,u)),v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),w,u)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))))*.
% 299.92/300.50 48898[0:SpL:8415.2,483.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v),hAPP(v_x,w)))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_x,x,u)),v_x))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.92/300.50 49169[0:SpL:8415.2,239.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),x))) c_lessequals(x,y,tc_fun(w,tc_bool)) c_Fun_Oinj__on(v,x,w,u) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(x,v,w,u),v_x)),y))*.
% 299.92/300.50 49160[0:SpL:8415.2,239.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(w),x),v_x)) c_lessequals(v_x,y,tc_fun(v,tc_bool)) c_Fun_Oinj__on(u,v_x,v,w) -> hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Fun_Othe__inv__into(v_x,u,v,w),x)),y))*.
% 299.92/300.50 49275[0:SpL:584.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,y,z,x1),x2)))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x2,u,w)),x2)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(x,x2),u,w)),hAPP(x,x2)))*.
% 299.92/300.50 49678[0:Rew:49662.2,49567.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),x,y),hAPP(c_Set_Oinsert(u,x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),hAPP(c_Set_Oinsert(u,x),w),x,y).
% 299.92/300.50 49690[0:Rew:49662.2,49621.1] || c_Fun_Oinj__on(u,v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(u,v_x)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,y),w),v))))* c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,y),w),v),w,x).
% 299.92/300.50 49691[0:Rew:49662.2,49622.1] || c_Fun_Oinj__on(u,v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(u,v_x)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,y),w),v))))* c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,y),w),v),w,x).
% 299.92/300.50 49698[0:Rew:49662.2,49517.2] class_Lattices_Obounded__lattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,x),hAPP(c_Set_Oinsert(y,w),v))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oinsert(y,w),v),w,x).
% 299.92/300.50 49701[0:Rew:49662.2,49571.2] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,x),hAPP(c_Set_Oinsert(y,w),v))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(c_Set_Oinsert(y,w),v),w,x).
% 299.92/300.50 49708[0:Rew:49662.2,49502.1] || c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),w,x),hAPP(c_Set_Oinsert(v_x,w),v))))* c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(u,tc_fun(t_a,tc_bool)),hAPP(c_Set_Oinsert(v_x,w),v),w,x).
% 299.92/300.50 49727[0:Rew:49662.2,49583.1] || c_Fun_Oinj__on(hAPP(c_in(t_a),v_x),u,v,w) -> hBOOL(hAPP(hAPP(c_in(w),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_in(t_a),v_x),v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v),u))))* c_Fun_Oinj__on(hAPP(c_in(t_a),v_x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v),u),v,w).
% 299.92/300.50 50030[0:SpL:497.0,3506.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(w,x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)))* -> .
% 299.92/300.50 49975[0:SpR:497.0,9566.0] || -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v))),v_x),tc_bool)*.
% 299.92/300.50 49954[0:SpR:497.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_Com_Opname,w),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)))))*.
% 299.92/300.50 49929[0:SpR:497.0,24020.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),v_x),v_x).
% 299.92/300.50 50504[0:SpL:223.1,442.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,tc_Hoare__Mirabelle_Otriple(x1)),u,tc_Hoare__Mirabelle_Otriple(x1)),w),x1)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oimage(y,u,tc_Hoare__Mirabelle_Otriple(x1)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),x1)*.
% 299.92/300.50 50495[0:SpL:223.1,371.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),x1))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),x1))* equal(y,x1).
% 299.92/300.50 50407[0:SpR:223.1,9566.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),hAPP(hAPP(c_Set_Oinsert(x1,x2),c_Set_Oinsert(y,z)),hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),tc_bool)*.
% 299.92/300.50 50405[0:SpR:223.1,415.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Fun_Ofun__upd(c_Set_Oinsert(x,y),hAPP(c_Set_Oimage(z,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,x,u,y),u,y),w),x1,x2),c_Set_Oinsert(x,y))**.
% 299.92/300.50 50853[0:SpL:622.0,3483.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),c_Com_Ocom_OSKIP) -> .
% 299.92/300.50 51754[0:MRR:51753.1,20737.2] || c_Fun_Oinj__on(u,v,w,x) c_Finite__Set_Ofinite(y,w) c_lessequals(v,y,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Oimage(z,w,x),y),hAPP(c_Set_Oimage(u,w,x),v),tc_fun(x,tc_bool))* c_Fun_Oinj__on(z,y,w,x) -> equal(c_Finite__Set_Ocard(v,w),c_Finite__Set_Ocard(y,w)).
% 299.92/300.50 53426[0:SpR:33303.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,x),v_x),tc_Com_Opname),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,x),v_x),tc_Com_Opname),u,w),v))**.
% 299.92/300.50 58575[0:SpR:223.1,10771.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(z,u,x),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,x1,u,x),u,x),w),y))*.
% 299.92/300.50 60445[7:Res:58968.1,519.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)))*.
% 299.92/300.50 60464[0:SpR:5882.1,486.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),y,z,x1,x2),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),y,z,x1,x2),v,tc_fun(x,tc_bool)))**.
% 299.92/300.50 60558[0:Res:58969.1,519.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_Procs) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)))*.
% 299.92/300.50 60631[7:Res:59476.1,519.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),y)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),y)))*.
% 299.92/300.50 60704[0:Res:59477.1,519.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_Procs) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),y)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),y)))*.
% 299.92/300.50 60889[0:Res:59017.1,519.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),t_a)* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y)))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y)))*.
% 299.92/300.50 60962[0:Res:59525.1,519.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),t_a)* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),z)))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),z)))*.
% 299.92/300.50 61786[0:SpR:11167.1,486.1] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Set_Oinsert(x,y),c_Set_Oinsert(v_x,tc_Com_Opname)),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Set_Oinsert(x,y),c_Set_Oinsert(v_x,tc_Com_Opname)),u,tc_fun(w,tc_bool)))**.
% 299.92/300.50 64816[0:SpR:28747.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),tc_Com_Opname,y),tc_Com_Opname),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),tc_Com_Opname,y),tc_Com_Opname),u,w),v))**.
% 299.92/300.50 64936[0:SpR:28748.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),tc_Com_Opname,y),tc_Com_Opname),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),tc_Com_Opname,y),tc_Com_Opname),u,w),v))**.
% 299.92/300.50 65056[0:SpR:28902.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,y),tc_Com_Opname),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,y),tc_Com_Opname),u,w),v))**.
% 299.92/300.50 65176[0:SpR:28903.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,y),tc_Com_Opname),u,w),v)),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,y),tc_Com_Opname),u,w),v))**.
% 299.92/300.50 77178[7:SpL:497.0,74788.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_x)** equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),w)* -> hBOOL(w)*.
% 299.92/300.50 77746[0:SpL:161.0,5892.0] || hBOOL(hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))))* -> hBOOL(hAPP(c_COMBS(c_in(y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool))),z,x1,x2),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))))*.
% 299.92/300.50 77745[0:SpL:162.0,5892.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),hAPP(c_Set_Ovimage(u,v,w),y)))* -> hBOOL(hAPP(c_COMBS(c_in(z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x)),x1,x2,x3),hAPP(c_Set_Ovimage(u,v,w),y)))*.
% 299.92/300.50 77744[0:SpL:507.0,5892.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(c_Set_Oimage(u,v,w),y)))* -> hBOOL(hAPP(c_COMBS(c_in(z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x)),x1,x2,x3),hAPP(c_Set_Oimage(u,v,w),y)))*.
% 299.92/300.50 77727[0:SpL:180.2,5892.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(x,u),v),u,u),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u)))* -> hBOOL(hAPP(c_COMBS(c_in(y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z,x1,x2),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u)))*.
% 299.92/300.50 79030[0:Res:15630.1,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,x),y),z,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(v,x),y),z,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x)))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a).
% 299.92/300.50 79250[0:Res:15858.1,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(v,y),z),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),y))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Oinsert(v,y),z),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),y)))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a).
% 299.92/300.50 80308[0:SpL:21268.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)))* hBOOL(hAPP(hAPP(c_in(w),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(w),hAPP(c_in(w),y),z,x1)))*.
% 299.92/300.50 80281[0:SpL:21268.0,494.1] || hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),z),t_a)* c_Natural_Oevaln(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),x1,x2),w,x,x3)* -> hBOOL(hAPP(hAPP(z,v),x3))*.
% 299.92/300.50 80245[0:SpL:21268.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,v)))* hBOOL(hAPP(hAPP(c_in(v),y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),z,x1)))* -> hBOOL(hAPP(u,y))*.
% 299.92/300.50 80208[0:SpL:21268.0,279.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),x,y)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),x,y))**.
% 299.92/300.50 80088[0:SpL:21268.0,469.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(y,w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1),x,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1))**.
% 299.92/300.50 80087[0:SpL:21268.0,464.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1),w,x,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1))**.
% 299.92/300.50 79923[0:SpR:486.1,21268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)),z,x1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 79922[0:SpR:410.0,21268.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,y),z),v,y,tc_fun(u,tc_bool)),x,x1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,y),z),v,y,tc_fun(u,tc_bool)))**.
% 299.92/300.50 79811[0:SpR:21268.0,10931.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x),v,y),t_a) hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x),v,y))))*.
% 299.92/300.50 79790[0:SpR:21268.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),y),z,x1),tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.92/300.50 79713[0:SpR:21268.0,340.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),x,z),v,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),v,tc_fun(w,tc_bool)).
% 299.92/300.50 79656[0:SpR:21268.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),x),z,x1),y,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.92/300.50 80447[0:Rew:104.0,79912.0] || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v,y),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)))**.
% 299.92/300.50 81503[0:SpL:21894.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)))* hBOOL(hAPP(hAPP(c_in(w),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(w),y),c_in(w),z,x1)))*.
% 299.92/300.50 81476[0:SpL:21894.0,494.1] || hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),z),t_a)* c_Natural_Oevaln(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),x1,x2),w,x,x3)* -> hBOOL(hAPP(hAPP(z,v),x3))*.
% 299.92/300.50 81440[0:SpL:21894.0,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,v)))* hBOOL(hAPP(hAPP(c_in(v),y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),z,x1)))* -> hBOOL(hAPP(u,y))*.
% 299.92/300.50 81403[0:SpL:21894.0,279.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(v,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),x,y)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),x,y))**.
% 299.92/300.50 81283[0:SpL:21894.0,469.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(y,w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1),x,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1))**.
% 299.92/300.50 81282[0:SpL:21894.0,464.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> equal(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(y,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1),w,x,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1))**.
% 299.92/300.50 81117[0:SpR:486.1,21894.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),z,x1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 81116[0:SpR:410.0,21894.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,y),z),v,y,tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),x,x1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,y),z),v,y,tc_fun(u,tc_bool)))**.
% 299.92/300.50 81005[0:SpR:21894.0,10931.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x),c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),v,y),t_a) hBOOL(hAPP(hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),x),c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(t_a)),v,y))))*.
% 299.92/300.50 80984[0:SpR:21894.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(u,v,w),y),c_Set_Oimage(u,v,w),z,x1),tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.92/300.50 80907[0:SpR:21894.0,340.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,z),v,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),v,tc_fun(w,tc_bool)).
% 299.92/300.50 80850[0:SpR:21894.0,82.0] || -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x),c_Set_Oimage(u,v,w),z,x1),y,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.92/300.50 81642[0:Rew:104.0,81106.0] || -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(x,tc_bool))),v,y),tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)))**.
% 299.92/300.50 83753[0:SpR:5899.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_COMBS(y,z,x1,x2,x3),v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(y,z,x4,x5,x6),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(y,z,x4,x5,x6),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 84192[7:SpL:497.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool),v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_x)** -> .
% 299.92/300.50 85100[0:SpL:644.0,239.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* c_lessequals(v_Procs,x,tc_fun(tc_Com_Opname,tc_bool)) c_Fun_Oinj__on(c_COMBK(w,u,tc_Com_Opname),v_Procs,tc_Com_Opname,u) -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Fun_Othe__inv__into(v_Procs,c_COMBK(w,u,tc_Com_Opname),tc_Com_Opname,u),v)),x))*.
% 299.92/300.50 85821[0:Res:9066.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(x,u),y))))* equal(hAPP(z,x),hAPP(z,v))* c_Fun_Oinj__on(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(x,u),y)),u,x1)* -> equal(x,v).
% 299.92/300.50 86737[4:SpL:497.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool),v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_Procs)** -> .
% 299.92/300.50 88304[0:Res:7227.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_COMBK(w,x,y),z,u),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))))* equal(hAPP(x1,w),hAPP(x1,v))* c_Fun_Oinj__on(x1,hAPP(c_Set_Oimage(c_COMBK(w,x,y),z,u),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),u,x2)* -> equal(w,v).
% 299.92/300.50 88644[7:SpL:497.0,88086.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(w,hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool))* -> .
% 299.92/300.50 89566[7:SpL:78590.1,477.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u),c_Set_Oinsert(v_x,t_a)) hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u))* hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),x)).
% 299.92/300.50 89565[7:SpL:78590.1,476.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u),c_Set_Oinsert(v_x,t_a)) hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u))* hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),x)).
% 299.92/300.50 90357[4:SpL:78660.1,477.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u),v_x),v_x)** hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u)) hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),x)).
% 299.92/300.50 90356[4:SpL:78660.1,476.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u),v_x),v_x)** hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u)) hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),x)).
% 299.92/300.50 90770[0:SpL:197.1,26480.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)).
% 299.92/300.50 94156[0:Res:14364.3,441.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) -> equal(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))).
% 299.92/300.50 20976[0:SpR:104.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w,x),hAPP(c_Set_Oinsert(y,w),z)),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,y,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w,x),z)))*.
% 299.92/300.50 24474[0:Res:47.2,208.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool))))* c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),w),tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))*.
% 299.92/300.50 24926[0:Res:171.2,467.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),x),u))),c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),x),u))**.
% 299.92/300.50 24925[0:Res:172.2,467.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(x,v,w,u),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),x),u))),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),x),u))**.
% 299.92/300.50 27552[0:SpR:196.1,373.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),z))* c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),z,x,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,c_Set_Ovimage(u,v,w),x,x1),y),hAPP(c_Set_Oimage(u,v,w),y))**.
% 299.92/300.50 27551[0:SpR:317.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) c_Fun_Oinj__on(c_Set_Oimage(z,w,x1),y,u,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,c_Set_Oimage(z,w,x1),u,x2),hAPP(c_Set_Oinsert(hAPP(z,v),x1),hAPP(c_Set_Oimage(z,w,x1),x))),hAPP(c_Set_Oinsert(v,w),x))**.
% 299.92/300.50 27541[0:SpR:393.1,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(x,y,z),z,y),w,u,x1) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))) equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oimage(c_COMBK(x,y,z),z,y),u,x1),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),v)*.
% 299.92/300.50 27704[0:SpR:196.1,71.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),z))* c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),z,x,x1) -> equal(hAPP(c_Fun_Othe__inv__into(z,c_Set_Ovimage(u,v,w),x,x1),y),hAPP(c_Set_Oimage(u,v,w),y))**.
% 299.92/300.50 27703[0:SpR:317.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) c_Fun_Oinj__on(c_Set_Oimage(z,w,x1),y,u,x2) -> equal(hAPP(c_Fun_Othe__inv__into(y,c_Set_Oimage(z,w,x1),u,x2),hAPP(c_Set_Oinsert(hAPP(z,v),x1),hAPP(c_Set_Oimage(z,w,x1),x))),hAPP(c_Set_Oinsert(v,w),x))**.
% 299.92/300.50 27693[0:SpR:393.1,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(x,y,z),z,y),w,u,x1) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))) equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oimage(c_COMBK(x,y,z),z,y),u,x1),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),v)*.
% 299.92/300.50 28510[0:SpR:338.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Fun_Ofun__upd(w,x,hAPP(c_Set_Oinsert(y,u),z),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x2,x3,x1),x,hAPP(c_Set_Oinsert(y,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z)),x1,x3))*.
% 299.92/300.50 28463[0:SpR:97.1,118.0] || c_Fun_Oinj__on(u,v,w,x) -> equal(c_Fun_Ocomp(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),c_Fun_Ofun__upd(y,z,hAPP(c_Set_Oimage(u,w,x),v),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,x2,x3,x1),z,v,x1,x3))*.
% 299.92/300.50 28462[0:SpR:99.1,118.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Fun_Ocomp(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Fun_Ofun__upd(x,y,hAPP(u,z),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,x2,x3,x1),y,z,x1,x3))*.
% 299.92/300.50 28461[0:SpR:438.1,118.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Fun_Ofun__upd(x,y,hAPP(u,z),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,x2,x3,x1),y,z,x1,x3))*.
% 299.92/300.50 28449[0:SpR:393.1,118.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(c_Fun_Ocomp(c_Set_Oimage(c_COMBK(w,x,v),v,x),c_Fun_Ofun__upd(y,z,u,x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oimage(c_COMBK(w,x,v),v,x),y,x2,x3,x1),z,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),x1,x3))*.
% 299.92/300.50 28636[0:SpR:21893.0,177.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,u),v_x),c_Set_Oinsert(v,u),tc_Com_Opname,w)))* equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),v_x),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,u),v_x),c_Set_Oinsert(v,u),tc_Com_Opname,w))*.
% 299.92/300.50 28635[0:SpR:21267.0,177.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v,u),v_x),tc_Com_Opname,w)))* equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),v_x),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v,u),v_x),tc_Com_Opname,w))*.
% 299.92/300.50 31381[0:SpL:297.2,449.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),u) hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y)))* -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v)),t_a).
% 299.92/300.50 32345[0:SpL:188.1,477.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),c_Set_Ovimage(c_COMBK(v,u,z),z,u),w)))* hBOOL(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),x1),x))* -> hBOOL(hAPP(c_Set_Ovimage(c_COMBK(v,u,z),z,u),x1))*.
% 299.92/300.50 32335[0:SpL:9493.1,477.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u)) hBOOL(hAPP(hAPP(c_in(u),x),v))* -> hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),x)).
% 299.92/300.50 32333[0:SpL:8498.1,477.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(x,y),u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))) hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(x,y),u))* hBOOL(hAPP(hAPP(c_in(u),z),v))* -> hBOOL(hAPP(c_Set_Oinsert(x,y),z))*.
% 299.92/300.50 32525[0:SpL:188.1,476.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),c_Set_Ovimage(c_COMBK(v,u,z),z,u),w)))* hBOOL(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),x1),y))* -> hBOOL(hAPP(c_Set_Ovimage(c_COMBK(v,u,z),z,u),x1))*.
% 299.92/300.50 32515[0:SpL:9493.1,476.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(v_x,t_a),u)) hBOOL(hAPP(hAPP(c_in(u),x),w))* -> hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),x)).
% 299.92/300.50 32513[0:SpL:8498.1,476.0] || equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(x,y),u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))) hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Set_Oinsert(x,y),u))* hBOOL(hAPP(hAPP(c_in(u),z),w))* -> hBOOL(hAPP(c_Set_Oinsert(x,y),z))*.
% 299.92/300.50 32768[0:SpR:35.2,56.1] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool))* c_lessequals(hAPP(c_Set_Oinsert(v,w),x),y,tc_fun(w,tc_bool))* hBOOL(hAPP(hAPP(c_in(w),v),c_HOL_Ominus__class_Ominus(y,u,tc_fun(w,tc_bool))))* -> equal(c_HOL_Ominus__class_Ominus(x,c_HOL_Ominus__class_Ominus(y,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),u)**.
% 299.92/300.50 32972[0:SpR:614.2,475.1] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),z)) -> equal(hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u),x1),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,x1),z)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,x1),z))**.
% 299.92/300.50 32953[0:SpR:188.1,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),w),y))* -> equal(hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,z),z,u),x,x1),y)),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,z),z,u),x,x1),y))**.
% 299.92/300.50 34403[0:SpL:24914.0,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),v_x)) -> hBOOL(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),w),tc_Com_Opname,x),hAPP(hAPP(c_Set_Oinsert(u,v),w),v_x))))* equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Set_Oinsert(u,v),w),tc_Com_Opname,x),hAPP(hAPP(c_Set_Oinsert(u,v),w),v_x)),u).
% 299.92/300.50 34030[0:SpR:24914.0,96.1] || c_Fun_Oinj__on(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v,w) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),w,v)*.
% 299.92/300.50 34647[0:SpR:177.1,55.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),x),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,u),hAPP(c_Set_Oinsert(v,u),w)),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(x,u),w))**.
% 299.92/300.50 34622[0:SpR:55.1,118.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_Fun_Ocomp(c_Set_Oinsert(v,u),c_Fun_Ofun__upd(x,y,c_HOL_Ominus__class_Ominus(z,w,tc_fun(u,tc_bool)),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(v,u),x,x2,x3,x1),y,c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),z),w,tc_fun(u,tc_bool)),x1,x3))*.
% 299.92/300.50 35407[0:SpR:338.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),y),c_Set_Oinsert(z,u),x,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(z,u),w))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(z,u),x,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 35401[0:SpR:317.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),x),y),z),c_Set_Oinsert(hAPP(u,x1),w),y,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x1,v),x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oinsert(hAPP(u,x1),w),y,tc_fun(x2,tc_bool))))*.
% 299.92/300.50 35351[0:SpR:600.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,tc_fun(z,tc_bool))))*.
% 299.92/300.50 35331[0:SpR:181.1,410.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),y),c_Set_Ovimage(c_COMBK(v,u,z),z,u),x,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Ovimage(c_COMBK(v,u,z),z,u),x,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 35487[0:SpR:113.0,55.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),y))) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Ovimage(w,u,x),z)),hAPP(c_Set_Ovimage(w,u,x),y),tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Ovimage(w,u,x),c_HOL_Ominus__class_Ominus(z,y,tc_fun(x,tc_bool)))))**.
% 299.92/300.50 35627[0:SpR:24914.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBB(u,v,tc_fun(w,tc_bool),x),tc_Com_Opname,y),hAPP(c_COMBB(u,v,tc_fun(w,tc_bool),x),v_x)),x,v),z),u,v,tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_COMBB(u,v,tc_fun(w,tc_bool),x),v_x),x,tc_fun(w,tc_bool)))**.
% 299.92/300.50 36192[0:Res:168.0,516.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w),t_a) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w))),v))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w))),w))*.
% 299.92/300.50 37492[0:SpL:205.1,193.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),x),w),c_Finite__Set_Ocard(x,v)) -> c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Set_Oimage(u,v,w),x),w,v)*.
% 299.92/300.50 37453[0:SpR:205.1,96.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Set_Oimage(u,v,w),x),w,v) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,v,w),x),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,v,w)*.
% 299.92/300.50 38009[0:Res:20152.0,441.0] || -> equal(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(c_HOL_Ominus__class_Ominus(u,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.92/300.50 38355[0:SSi:38307.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),w))* c_Finite__Set_Ofinite(w,tc_fun(u,tc_bool)) c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x,w,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),y,tc_fun(u,tc_bool))*.
% 299.92/300.50 38652[0:SpL:21893.0,184.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) c_Fun_Oinj__on(v,x,w,u) -> equal(hAPP(v,hAPP(c_Fun_Othe__inv__into(x,v,w,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y))),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y))**.
% 299.92/300.50 38651[0:SpL:21267.0,184.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) c_Fun_Oinj__on(v,x,w,u) -> equal(hAPP(v,hAPP(c_Fun_Othe__inv__into(x,v,w,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y))**.
% 299.92/300.50 39008[0:SpL:354.2,473.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(w),z),u)) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,w,y),u),c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z)),hAPP(c_Set_Oimage(x,w,y),u)))*.
% 299.92/300.50 39396[0:Rew:533.0,39308.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w)),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),x)))**.
% 299.92/300.50 39397[0:Rew:533.0,39307.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_Com_Opname,w)),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),x)))**.
% 299.92/300.50 39792[0:SpR:21893.0,532.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)))**.
% 299.92/300.50 39791[0:SpR:21267.0,532.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_Com_Opname,x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)))**.
% 299.92/300.50 40900[0:Res:151.2,479.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_in(u),v),y))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool)),z,x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool))),z)))*.
% 299.92/300.50 41181[0:Res:151.2,478.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(x,v))* -> hBOOL(hAPP(hAPP(c_in(u),v),y))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool)),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool)))))*.
% 299.92/300.50 41322[0:SpL:542.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y))* hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,tc_fun(z,tc_bool))))*.
% 299.92/300.50 41319[0:SpL:614.2,275.1] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 41308[0:SpL:523.1,275.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(z,v_x)),hAPP(x1,v_x)))) -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),z),x1),v,tc_fun(x,tc_bool))))*.
% 299.92/300.50 41307[0:SpL:460.1,275.1] || class_Lattices_Olattice(t_b) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,tc_fun(w,tc_bool))))*.
% 299.92/300.50 41251[0:SpL:393.1,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oinsert(z,x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))) -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool)))* hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_COMBK(z,x1,x2),x2,x1),u,tc_fun(x,tc_bool))))*.
% 299.92/300.50 41649[0:SpL:128.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(v,w,x),z,u),x1)))* c_Fun_Oinj__on(c_Set_Ovimage(v,w,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,u)* -> hBOOL(hAPP(hAPP(c_in(z),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))),x1)).
% 299.92/300.50 41525[0:SpL:465.1,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Fun_Ofun__upd(v,w,x,y,u),z)),hAPP(c_Set_Oimage(v,y,u),x1)))* c_Fun_Oinj__on(c_Fun_Ofun__upd(v,w,x,y,u),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,u)* -> hBOOL(hAPP(hAPP(c_in(y),w),x1)) hBOOL(hAPP(hAPP(c_in(y),z),x1)).
% 299.92/300.50 41741[0:SpL:21893.0,494.1] || hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),v_x),t_a)* c_Natural_Oevaln(y,w,x,z)* -> hBOOL(hAPP(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),v_x),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),tc_Com_Opname,x1),v),z))*.
% 299.92/300.50 41740[0:SpL:21267.0,494.1] || hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),v_x),t_a)* c_Natural_Oevaln(y,w,x,z)* -> hBOOL(hAPP(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),v_x),tc_Com_Opname,x1),v),z))*.
% 299.92/300.50 41979[0:SpR:465.1,82.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,u,y),w),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,z,u,y),u,y),x1),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,z,u,y),u,y),c_HOL_Ominus__class_Ominus(w,x1,tc_fun(u,tc_bool))),tc_fun(y,tc_bool))*.
% 299.92/300.50 41964[0:SpR:465.1,82.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1),hAPP(c_Set_Oimage(x,u,z),w),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),c_HOL_Ominus__class_Ominus(x1,w,tc_fun(u,tc_bool))),tc_fun(z,tc_bool))*.
% 299.92/300.50 42501[0:SpL:9.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Fun_Ocomp(w,x,y,z,x1),x2,x3)),hAPP(w,hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Fun_Ocomp(w,x,y,z,x1),x2,x3))))* -> equal(hAPP(c_Set_Oimage(u,x2,x3),v),hAPP(c_Set_Oimage(c_Fun_Ocomp(w,x,y,z,x1),x2,x3),v)).
% 299.92/300.50 42460[0:SpL:9.0,315.0] || equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,c_Fun_Ocomp(u,v,x,y,z),x1,x2,x3))),hAPP(x1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,c_Fun_Ocomp(u,v,x,y,z),x1,x2,x3)))* -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,x,y,z),x2,x3),w),hAPP(c_Set_Oimage(x1,x2,x3),w)).
% 299.92/300.50 43108[0:SpR:28334.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,x,hAPP(x,v_x),tc_Com_Opname,y),tc_Com_Opname),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,x,hAPP(x,v_x),tc_Com_Opname,y),tc_Com_Opname),u,tc_fun(w,tc_bool)))**.
% 299.92/300.50 43105[0:SpR:28031.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(x,v_x),x,tc_Com_Opname,y),tc_Com_Opname),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(x,v_x),x,tc_Com_Opname,y),tc_Com_Opname),u,tc_fun(w,tc_bool)))**.
% 299.92/300.50 44177[0:SpR:158.0,232.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,x) -> c_lessequals(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),c_HOL_Ouminus__class_Ouminus(z,tc_fun(y,tc_bool)))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.92/300.50 44141[0:SpR:158.0,232.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,x) -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_HOL_Ouminus__class_Ouminus(z,tc_fun(y,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),z)),tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.92/300.50 44347[0:Res:468.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,y,z,u,x1)),hAPP(x,v))* c_Fun_Oinj__on(x,w,u,x2)* -> equal(hAPP(c_Set_Oimage(y,u,x1),w),hAPP(c_Set_Oimage(z,u,x1),w)) equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,y,z,u,x1),v).
% 299.92/300.50 45096[0:SpR:532.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),z,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),z),tc_fun(w,tc_bool))*.
% 299.92/300.50 45095[0:SpR:533.0,326.2] || c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,tc_fun(u,tc_bool)) c_lessequals(y,z,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),z),tc_fun(u,tc_bool))*.
% 299.92/300.50 45031[0:SpR:532.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),z)),tc_fun(w,tc_bool))*.
% 299.92/300.50 45030[0:SpR:533.0,326.2] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool)) c_lessequals(y,z,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z)),tc_fun(v,tc_bool))*.
% 299.92/300.50 45310[0:SpL:532.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z),u,w)))*.
% 299.92/300.50 45309[0:SpL:533.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)))*.
% 299.92/300.50 45486[0:Rew:533.0,45426.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname))))*.
% 299.92/300.50 45602[0:SpR:89.0,323.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_COMBB(w,x,tc_fun(u,tc_bool),y),z),y,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(z,y,x),v)),x1),w,x,tc_fun(u,tc_bool)))*.
% 299.92/300.50 45595[0:SpR:89.0,323.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_COMBB(w,x,tc_fun(u,tc_bool),z),x1),z,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),hAPP(c_Set_Oimage(x1,z,x),y)),w,x,tc_fun(u,tc_bool)))*.
% 299.92/300.50 46009[0:Rew:533.0,45941.1] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname))))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))).
% 299.92/300.50 46188[0:Res:45357.1,481.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname)),x),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname)),x)))*.
% 299.92/300.50 46146[0:Res:153.1,481.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* -> hBOOL(hAPP(y,w))* hBOOL(hAPP(hAPP(c_in(z),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Ovimage(v,z,u),x)),x1),y,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Ovimage(v,z,u),x)),x1)))*.
% 299.92/300.50 46145[0:Res:545.1,481.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,hAPP(y,v)))* hBOOL(hAPP(hAPP(c_in(z),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,u,z),w)),x1),x,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,u,z),w)),x1)))*.
% 299.92/300.50 46506[0:Res:45357.1,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname)),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname))))*.
% 299.92/300.50 46464[0:Res:153.1,480.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* -> hBOOL(hAPP(y,w))* hBOOL(hAPP(hAPP(c_in(z),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),hAPP(c_Set_Ovimage(v,z,u),x)),y,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),hAPP(c_Set_Ovimage(v,z,u),x))))*.
% 299.92/300.50 46463[0:Res:545.1,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,hAPP(y,v)))* hBOOL(hAPP(hAPP(c_in(z),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),hAPP(c_Set_Oimage(y,u,z),w)),x,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),hAPP(c_Set_Oimage(y,u,z),w))))*.
% 299.92/300.50 46587[0:SpR:158.0,617.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,x,tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(z,v,x),u)),c_Set_Oinsert(x1,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(x1,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Fun_Ocomp(w,z,x,tc_fun(y,tc_bool),v),v,tc_fun(y,tc_bool))))*.
% 299.92/300.50 48434[0:SpL:9987.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w),x),w,u) -> .
% 299.92/300.50 48432[0:SpL:2095.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(w,v),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(w,v),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),y),x,u) -> .
% 299.92/300.50 48424[0:SpL:2935.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_in(t_a),v_x),v,u),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_in(t_a),v_x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v),w),v,u) -> .
% 299.92/300.50 48412[0:SpL:9936.1,224.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),hAPP(c_Set_Oinsert(y,w),x),w,v) -> .
% 299.92/300.50 48408[0:SpL:9935.1,224.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,v),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(u,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(c_Set_Oinsert(u,x),y),x,v) -> .
% 299.92/300.50 48323[0:SpL:2093.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(tc_Com_Opname),v_x)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,v),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(hAPP(c_in(tc_Com_Opname),v_x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,v),hAPP(c_Set_Oinsert(hAPP(c_in(tc_Com_Opname),v_x),w),x),w,u) -> .
% 299.92/300.50 48815[0:Res:19748.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,tc_Com_Opname,tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool))),c_Set_Oinsert(x,v),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(x,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),tc_fun(tc_Com_Opname,tc_bool)),u,tc_Com_Opname,tc_fun(v,tc_bool))))**.
% 299.92/300.50 48796[0:Res:545.1,619.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,y,tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(x1,u,y),w)),c_Set_Oinsert(x2,z),tc_fun(z,tc_bool),tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(x2,z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x1,u,y),w),x,y,tc_fun(z,tc_bool))))**.
% 299.92/300.50 48969[0:SpL:21893.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.92/300.50 48968[0:SpL:21267.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.92/300.50 49174[0:SpL:21893.0,239.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) c_lessequals(x,y,tc_fun(w,tc_bool)) c_Fun_Oinj__on(v,x,w,u) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(x,v,w,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,z))),y))*.
% 299.92/300.50 49173[0:SpL:21267.0,239.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) c_lessequals(x,y,tc_fun(w,tc_bool)) c_Fun_Oinj__on(v,x,w,u) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(x,v,w,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,z))),y))*.
% 299.92/300.50 49197[0:MRR:49156.3,96.1] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(w),y),v)) c_lessequals(hAPP(c_Set_Oimage(u,w,x),v),z,tc_fun(x,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,w,x),v),c_Fun_Othe__inv__into(v,u,w,x),x,w),y)),z))*.
% 299.92/300.50 49289[0:SpL:8415.2,488.1] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v,v_x)) hBOOL(hAPP(v_x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,v,u)),w))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)),x))*.
% 299.92/300.50 49280[0:SpL:3294.1,488.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),w),c_Orderings_Obot__class_Obot(tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,v,u)),v_x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),v,u)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))))*.
% 299.92/300.50 49223[0:SpL:8415.2,488.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(v,w))* hBOOL(hAPP(hAPP(c_in(u),w),hAPP(v_x,x)))* -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_x,v,u)),v_x))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,v,u)),x))*.
% 299.92/300.50 49469[0:SpR:66.0,225.1] || c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(u,z)),hAPP(c_Set_Oimage(u,x,y),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(z,x),w),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(z,x),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),x,y).
% 299.92/300.50 49668[0:Rew:49662.2,49514.3] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,z),hAPP(c_Set_Oinsert(v,y),x))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Set_Oinsert(v,y),x),y,z).
% 299.92/300.50 49669[0:Rew:49662.2,49523.3] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,z),hAPP(c_Set_Oinsert(w,y),x))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Set_Oinsert(w,y),x),y,z).
% 299.92/300.50 49675[0:Rew:49662.2,49573.1] || c_Fun_Oinj__on(hAPP(u,v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(c_COMBS(u,z,x1,x2,x3),v)),hAPP(c_Set_Oimage(hAPP(u,v),x,y),hAPP(c_Set_Oinsert(hAPP(z,v),x),w))))* c_Fun_Oinj__on(hAPP(u,v),hAPP(c_Set_Oinsert(hAPP(z,v),x),w),x,y).
% 299.92/300.50 49679[0:Rew:49662.2,49524.2] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),hAPP(c_Set_Oinsert(z,x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Set_Oinsert(z,x),w),x,y).
% 299.92/300.50 49680[0:Rew:49662.2,49525.2] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),hAPP(c_Set_Oinsert(z,x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Set_Oinsert(z,x),w),x,y).
% 299.92/300.50 49681[0:Rew:49662.2,49536.2] class_Lattices_Oboolean__algebra(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(v,u),x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(v,u),x),w),x,y).
% 299.92/300.50 49725[0:Rew:49662.2,49647.1] || c_Fun_Oinj__on(u,v,w,tc_Hoare__Mirabelle_Otriple(t_a)) c_Hoare__Mirabelle_Ohoare__valids(x,hAPP(c_Set_Oimage(u,w,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(y,w),v)),t_a)* -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,w),v),w,tc_Hoare__Mirabelle_Otriple(t_a)) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__1(x,z)),x))* c_Hoare__Mirabelle_Otriple__valid(z,hAPP(u,y),t_a)*.
% 299.92/300.50 49763[0:Rew:49662.2,49631.4,49662.2,49631.2] class_Orderings_Olinorder(u) || c_Fun_Oinj__on(v,w,x,u) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,x,u),hAPP(c_Set_Oinsert(y,x),w)),u) -> c_Fun_Oinj__on(v,hAPP(c_Set_Oinsert(y,x),w),x,u) c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,x,u),hAPP(c_Set_Oinsert(y,x),w)),u),hAPP(v,y),u)*.
% 299.92/300.50 49764[0:Rew:49662.2,49630.4,49662.2,49630.2] class_Orderings_Olinorder(u) || c_Fun_Oinj__on(v,w,x,u) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,x,u),hAPP(c_Set_Oinsert(y,x),w)),u) -> c_Fun_Oinj__on(v,hAPP(c_Set_Oinsert(y,x),w),x,u) c_lessequals(hAPP(v,y),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,x,u),hAPP(c_Set_Oinsert(y,x),w)),u),u)*.
% 299.92/300.50 50028[0:SpL:497.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_Procs)** -> .
% 299.92/300.50 50027[7:SpL:497.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_x)** -> .
% 299.92/300.50 50026[0:SpL:497.0,3929.0] || hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.92/300.50 49988[0:SpR:497.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),w,tc_fun(x,tc_bool)),v_x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool)*.
% 299.92/300.50 49959[0:SpR:497.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),tc_Com_Opname,u),u)*.
% 299.92/300.50 49957[4:SpR:497.0,38236.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_Com_Opname,tc_bool)).
% 299.92/300.50 49952[0:SpR:497.0,23902.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.92/300.50 50072[0:Rew:497.0,50011.0] || -> equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v_x),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_Com_Opname,u)),v)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v_x),v)))**.
% 299.92/300.50 50073[0:Rew:497.0,50010.0] || -> equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v_x),tc_Com_Opname,u)),v)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v_x),v)))**.
% 299.92/300.50 50074[0:Rew:497.0,50005.0] || -> equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v_x),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_Com_Opname,v))),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v_x)))**.
% 299.92/300.50 50075[0:Rew:497.0,50004.0] || -> equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v_x),tc_Com_Opname,v))),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v_x)))**.
% 299.92/300.50 50177[0:MRR:50156.0,418.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(u,v),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,x,tc_fun(w,tc_bool)),y)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,x),y),u,x,tc_fun(w,tc_bool))))*.
% 299.92/300.50 50498[0:SpL:223.1,363.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),x1,tc_fun(z,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),x1,tc_fun(z,tc_bool))*.
% 299.92/300.50 50440[0:SpR:223.1,9567.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Set_Oinsert(x,y),z,tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(x2,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x2,v,x,u,y),u,y),w),tc_bool)*.
% 299.92/300.50 50415[0:SpR:223.1,364.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(x,hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),tc_fun(z,tc_bool))* -> c_lessequals(x,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,x1,u,z),u,z),w),tc_fun(z,tc_bool))*.
% 299.92/300.50 50406[0:SpR:223.1,5875.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(c_COMBS(c_Set_Oinsert(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),x1),c_Set_Oinsert(y,z),x2,x3,x4),hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))))*.
% 299.92/300.50 50859[0:SpL:622.0,16286.0] || equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.92/300.50 50858[7:SpL:622.0,31868.0] || equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.92/300.50 50814[0:SpR:622.0,3229.1] || equal(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* -> equal(hAPP(u,v_x),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool))))*.
% 299.92/300.50 50810[4:SpR:622.0,38042.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),w,t_a)*.
% 299.92/300.50 50800[0:SpR:622.0,28032.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,w)))*.
% 299.92/300.50 50794[0:SpR:622.0,28335.0] || -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),tc_Com_Opname,w)))*.
% 299.92/300.50 50787[4:SpR:622.0,37987.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),w))*.
% 299.92/300.50 50777[0:SpR:622.0,3283.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),v_Procs)).
% 299.92/300.50 50770[0:SpR:622.0,1158.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,w),v_Procs),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))))*.
% 299.92/300.50 53398[0:SpR:33303.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),v_x),tc_Com_Opname),u,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,w),v_x),tc_Com_Opname),u,tc_fun(x,tc_bool))))*.
% 299.92/300.50 54185[0:SpL:52997.1,224.0] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),c_in(tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,v),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,v),hAPP(c_Set_Oinsert(v_x,w),x),w,u) -> .
% 299.92/300.50 58172[0:SpL:622.0,58055.0] || equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),tc_bool),w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* -> .
% 299.92/300.50 58477[0:SpL:497.0,58248.0] || equal(c_COMBK(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),w,x),c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_fun(t_a,tc_bool)))* -> .
% 299.92/300.50 63991[0:SpR:223.1,647.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,u,tc_Com_Opname),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),v_Procs,tc_fun(tc_Com_Opname,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,tc_Com_Opname),u,tc_Com_Opname),w),v_Procs,tc_fun(tc_Com_Opname,tc_bool)))**.
% 299.92/300.50 64100[0:SpR:223.1,679.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_Set_Oimage(x,u,tc_Com_Opname),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),v_Procs,tc_fun(tc_Com_Opname,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,tc_Com_Opname),u,tc_Com_Opname),w),v_Procs,tc_fun(tc_Com_Opname,tc_bool)).
% 299.92/300.50 64787[0:SpR:28747.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool))))*.
% 299.92/300.50 64907[0:SpR:28748.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool))))*.
% 299.92/300.50 65027[0:SpR:28902.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool))))*.
% 299.92/300.50 65147[0:SpR:28903.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_Procs,u),v),c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(y,tc_bool))))*.
% 299.92/300.50 71266[0:SpR:223.1,7538.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,x1,u,y),u,y),w)),tc_fun(y,tc_bool))*.
% 299.92/300.50 71380[7:SpL:622.0,71221.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),tc_bool)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.92/300.50 73478[7:SpR:71835.1,622.0] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,t_a))** -> equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),v_x).
% 299.92/300.50 74839[7:SpR:622.0,72297.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),v_x)).
% 299.92/300.50 77743[0:SpL:532.0,5892.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))* -> hBOOL(hAPP(c_COMBS(c_in(y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z,x1,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x)))*.
% 299.92/300.50 80151[0:SpL:21268.0,298.1] class_Lattices_Oupper__semilattice(u) || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),v,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)) -> c_lessequals(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),v,y),u)*.
% 299.92/300.50 80086[0:SpL:21268.0,467.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> equal(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1))**.
% 299.92/300.50 80064[0:SpL:21268.0,481.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_in(u),hAPP(c_in(u),v),y,z)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x1),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x1)))*.
% 299.92/300.50 80063[0:SpL:21268.0,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_in(u),hAPP(c_in(u),v),y,z)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x1),w),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x1),w)))*.
% 299.92/300.50 79889[0:SpR:523.1,21268.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),x,y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)))**.
% 299.92/300.50 79888[0:SpR:460.1,21268.0] || class_Lattices_Olattice(t_b) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))**.
% 299.92/300.50 79578[0:SpR:21268.0,297.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),w,y),u)* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),w,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)).
% 299.92/300.50 81346[0:SpL:21894.0,298.1] class_Lattices_Oupper__semilattice(u) || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)) -> c_lessequals(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,y),u)*.
% 299.92/300.50 81281[0:SpL:21894.0,467.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> equal(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1))),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1))**.
% 299.92/300.50 81259[0:SpL:21894.0,481.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),c_in(u),y,z)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x1),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x1)))*.
% 299.92/300.50 81258[0:SpL:21894.0,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),c_in(u),y,z)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x1),w),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x1),w)))*.
% 299.92/300.50 81083[0:SpR:523.1,21894.0] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x,y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)))**.
% 299.92/300.50 81082[0:SpR:460.1,21894.0] || class_Lattices_Olattice(t_b) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)))**.
% 299.92/300.50 80771[0:SpR:21894.0,297.2] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,y),u)* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x)).
% 299.92/300.50 83212[7:SpR:622.0,78357.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),w,x),v_x),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))))*.
% 299.92/300.50 84910[4:SpL:533.0,78744.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x))),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,t_a).
% 299.92/300.50 84902[4:SpL:465.1,78744.0] || equal(hAPP(c_Set_Oimage(u,v,w),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),z)),v_x)** -> hBOOL(hAPP(hAPP(c_in(v),x),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),z)))* c_Hoare__Mirabelle_Ohoare__valids(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),z,t_a).
% 299.92/300.50 85089[0:SpL:644.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(v,w,tc_Com_Opname),tc_Com_Opname,w),x,u),y)))* c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(v,w,tc_Com_Opname),tc_Com_Opname,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u)* -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),y)).
% 299.92/300.50 85531[4:SpL:78507.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,v),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,v),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w),x),w,u) -> .
% 299.92/300.50 86029[0:SpL:622.0,86011.0] || hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),tc_bool)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.92/300.50 87313[7:SpR:497.0,71492.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))),w))*.
% 299.92/300.50 87461[7:SpR:497.0,71493.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))),w,t_a)*.
% 299.92/300.50 87591[7:SpR:497.0,71679.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))))*.
% 299.92/300.50 89602[7:SpL:78590.1,315.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,t_a),w,x),c_Set_Oinsert(v_x,t_a)) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,t_a),w,x)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,t_a),w,x))** -> equal(hAPP(c_Set_Oimage(v,w,x),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,x),u)).
% 299.92/300.50 89568[7:SpL:78590.1,315.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,t_a),v,w,x),c_Set_Oinsert(v_x,t_a)) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,t_a),v,w,x)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,t_a),v,w,x))** -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,x),u),hAPP(c_Set_Oimage(v,w,x),u)).
% 299.92/300.50 89775[0:SpR:26183.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(v,w),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),u,tc_fun(z,tc_bool)))**.
% 299.92/300.50 90393[4:SpL:78660.1,315.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,t_a),w,x),v_x),v_x)** equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,t_a),w,x)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,t_a),w,x))** -> equal(hAPP(c_Set_Oimage(v,w,x),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,x),u)).
% 299.92/300.50 90359[4:SpL:78660.1,315.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,t_a),v,w,x),v_x),v_x)** equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,t_a),v,w,x)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,t_a),v,w,x))** -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,x),u),hAPP(c_Set_Oimage(v,w,x),u)).
% 299.92/300.50 91995[0:SpL:79073.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(v_Procs,w),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_Procs,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),y),x,u) -> .
% 299.92/300.50 92157[7:SpL:79101.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_in(v),v_x)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,w),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(hAPP(c_in(v),v_x),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,w),hAPP(c_Set_Oinsert(hAPP(c_in(v),v_x),x),y),x,u) -> .
% 299.92/300.50 92637[7:SpR:497.0,82151.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),c_Set_Oinsert(v_x,w)))*.
% 299.92/300.50 93242[0:SpL:5878.1,284.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(w,c_Orderings_Obot__class_Obot(u))),hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1,v),x2)))* c_Fun_Oinj__on(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x1,v)* -> hBOOL(hAPP(hAPP(c_in(x1),c_Orderings_Obot__class_Obot(u)),x2)).
% 299.92/300.50 93297[4:SpR:497.0,85556.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),w),tc_bool)*.
% 299.92/300.50 93485[0:SpR:497.0,86147.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))),w))*.
% 299.92/300.50 93636[0:SpR:497.0,86148.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))),w,t_a)*.
% 299.92/300.50 93780[0:SpR:497.0,86342.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))))*.
% 299.92/300.50 19361[0:SSi:19314.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* c_lessequals(w,c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.92/300.50 21653[0:SpL:21267.0,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) -> c_Hoare__Mirabelle_Ohoare__valids(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x),tc_Com_Opname,v),w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x),tc_Com_Opname,v),w),u,t_a)*.
% 299.92/300.50 21322[0:SpR:21267.0,445.1] || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ofun__upd(u,v,w,x,y),hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v_x),tc_Com_Opname,z),v) equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Fun_Ofun__upd(u,v,w,x,y),hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v_x),tc_Com_Opname,z)),hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v_x))**.
% 299.92/300.50 22281[0:SpL:21893.0,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) -> c_Hoare__Mirabelle_Ohoare__valids(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname,v),w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname,v),w),u,t_a)*.
% 299.92/300.50 21948[0:SpR:21893.0,445.1] || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v_x),c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname,z),v) equal(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v_x),c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname,z)),hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v_x))**.
% 299.92/300.50 24484[0:SSi:24482.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool))* c_lessequals(y,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y)))* c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),x,tc_fun(w,tc_bool))*.
% 299.92/300.50 25376[0:SpR:512.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),z,x1),hAPP(c_Set_Oinsert(x2,z),x3)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),x2)),x1),hAPP(c_Set_Oimage(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),z,x1),x3)))*.
% 299.92/300.50 25375[0:SpR:512.0,99.1] || c_Fun_Oinj__on(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),z,x1),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),x2))),x2)**.
% 299.92/300.50 25374[0:SpR:512.0,438.1] || c_Fun_Oinj__on(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x,w),z,x1),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(y,x,v),x2))),x2)**.
% 299.92/300.50 27642[0:SpR:131.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Set_Ovimage(c_Fun_Ocomp(x,y,z,x1,x2),x2,x1),w,u,x3) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Ovimage(c_Fun_Ocomp(x,y,z,x1,x2),x2,x1),u,x3),hAPP(c_Set_Ovimage(y,x2,z),hAPP(c_Set_Ovimage(x,z,x1),v))),v)**.
% 299.92/300.50 27641[0:SpR:158.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ocomp(x,y,z,x1,x2),x2,x1),w,u,x3) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oimage(c_Fun_Ocomp(x,y,z,x1,x2),x2,x1),u,x3),hAPP(c_Set_Oimage(x,z,x1),hAPP(c_Set_Oimage(y,x2,z),v))),v)**.
% 299.92/300.50 27590[0:SpR:523.1,373.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),x),y),w,v,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),x),y),v,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(x,v_x)),hAPP(y,v_x))),v_x)**.
% 299.92/300.50 27589[0:SpR:460.1,373.2] || class_Lattices_Olattice(t_b) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v,u,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),v_x)**.
% 299.92/300.50 27557[0:SpR:131.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),z)) c_Fun_Oinj__on(c_Set_Ovimage(x1,x2,w),z,u,x3) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,c_Set_Ovimage(x1,x2,w),u,x3),hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,x1,w,x,x2),x2,x),y)),hAPP(c_Set_Ovimage(v,w,x),y))**.
% 299.92/300.50 27556[0:SpR:158.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) c_Fun_Oinj__on(c_Set_Oimage(x1,x,x2),z,u,x3) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,c_Set_Oimage(x1,x,x2),u,x3),hAPP(c_Set_Oimage(c_Fun_Ocomp(x1,v,x,x2,w),w,x2),y)),hAPP(c_Set_Oimage(v,w,x),y))**.
% 299.92/300.50 27525[0:SpR:373.2,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),x1)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(w,x,u,y),x1,z,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x2),v),hAPP(x,v))**.
% 299.92/300.50 27795[0:SpR:131.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Set_Ovimage(c_Fun_Ocomp(x,y,z,x1,x2),x2,x1),w,u,x3) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Ovimage(c_Fun_Ocomp(x,y,z,x1,x2),x2,x1),u,x3),hAPP(c_Set_Ovimage(y,x2,z),hAPP(c_Set_Ovimage(x,z,x1),v))),v)**.
% 299.92/300.50 27794[0:SpR:158.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ocomp(x,y,z,x1,x2),x2,x1),w,u,x3) -> equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oimage(c_Fun_Ocomp(x,y,z,x1,x2),x2,x1),u,x3),hAPP(c_Set_Oimage(x,z,x1),hAPP(c_Set_Oimage(y,x2,z),v))),v)**.
% 299.92/300.50 27743[0:SpR:523.1,71.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),x),y),w,v,z) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),x),y),v,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(x,v_x)),hAPP(y,v_x))),v_x)**.
% 299.92/300.50 27742[0:SpR:460.1,71.2] || class_Lattices_Olattice(t_b) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v,u,w) -> equal(hAPP(c_Fun_Othe__inv__into(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),v_x)**.
% 299.92/300.50 27710[0:SpR:373.2,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),x1)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(w,x,u,y),x1,z,x2) -> equal(hAPP(c_Fun_Othe__inv__into(x1,c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x2),v),hAPP(x,v))**.
% 299.92/300.50 27709[0:SpR:131.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),z)) c_Fun_Oinj__on(c_Set_Ovimage(x1,x2,w),z,u,x3) -> equal(hAPP(c_Fun_Othe__inv__into(z,c_Set_Ovimage(x1,x2,w),u,x3),hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,x1,w,x,x2),x2,x),y)),hAPP(c_Set_Ovimage(v,w,x),y))**.
% 299.92/300.50 27708[0:SpR:158.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) c_Fun_Oinj__on(c_Set_Oimage(x1,x,x2),z,u,x3) -> equal(hAPP(c_Fun_Othe__inv__into(z,c_Set_Oimage(x1,x,x2),u,x3),hAPP(c_Set_Oimage(c_Fun_Ocomp(x1,v,x,x2,w),w,x2),y)),hAPP(c_Set_Oimage(v,w,x),y))**.
% 299.92/300.50 27677[0:SpR:71.2,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),x1)) c_Fun_Oinj__on(c_Fun_Othe__inv__into(w,x,u,y),x1,z,x2) -> equal(hAPP(c_Fun_Othe__inv__into(x1,c_Fun_Othe__inv__into(w,x,u,y),z,x2),v),hAPP(x,v))**.
% 299.92/300.50 27676[0:SpR:71.2,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),x1)) c_Fun_Oinj__on(c_Fun_Othe__inv__into(w,x,u,y),x1,z,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Fun_Othe__inv__into(w,x,u,y),z,x2),v),hAPP(x,v))**.
% 299.92/300.50 27924[0:Res:468.0,263.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),y)),hAPP(c_Set_Oimage(z,v,w),hAPP(c_Set_Oinsert(x,v),y))) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oinsert(x,v),y),u,z,v,w)),y))* equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oinsert(x,v),y),u,z,v,w),x).
% 299.92/300.50 28194[0:SpR:465.1,317.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1,x2),hAPP(c_Set_Oinsert(w,x1),x3)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,u,z),w),x2),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1,x2),x3)))*.
% 299.92/300.50 28193[0:SpR:465.1,99.1] || c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> hBOOL(hAPP(hAPP(c_in(x),v),x2)) equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),z,x1),hAPP(c_Set_Oimage(u,x,y),x2)),x2)**.
% 299.92/300.50 28192[0:SpR:465.1,438.1] || c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> hBOOL(hAPP(hAPP(c_in(x),v),x2)) equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),z,x1),hAPP(c_Set_Oimage(u,x,y),x2)),x2)**.
% 299.92/300.50 28553[0:SpR:131.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Fun_Ofun__upd(z,x1,x2,x3,x4),x4,x5,x3),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x4,x5,x3),x1,hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x2)),x3,x5))*.
% 299.92/300.50 28552[0:SpR:158.0,118.0] || -> equal(c_Fun_Ocomp(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_Fun_Ofun__upd(z,x1,x2,x3,x4),x4,x5,x3),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x4,x5,x3),x1,hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x2)),x3,x5))*.
% 299.92/300.50 28501[0:SpR:523.1,118.0] class_Lattices_Olattice(u) || -> equal(c_Fun_Ocomp(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),c_Fun_Ofun__upd(x,y,v_x,z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x,x1,x2,z),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x)),z,x2))*.
% 299.92/300.50 28500[0:SpR:460.1,118.0] || class_Lattices_Olattice(t_b) -> equal(c_Fun_Ocomp(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Fun_Ofun__upd(u,v,v_x,w,x),x,y,w),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,x,y,w),v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),w,y))*.
% 299.92/300.50 29302[0:Rew:537.1,29102.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))**.
% 299.92/300.50 29303[0:Rew:537.1,29101.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_Com_Opname,x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))**.
% 299.92/300.50 29799[0:Rew:534.1,29626.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))**.
% 299.92/300.50 29800[0:Rew:534.1,29625.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)),tc_Com_Opname,x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))**.
% 299.92/300.50 32975[0:SpR:542.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,z),y)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,z),y))**.
% 299.92/300.50 32969[0:SpR:536.1,475.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x)),x1),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,x1),y)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,x1),y))**.
% 299.92/300.50 32968[0:SpR:535.1,475.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x)),x1),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,x1),y)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,x1),y))**.
% 299.92/300.50 32926[0:SpR:71.2,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),x1)) -> equal(hAPP(c_Set_Oinsert(v,x2),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(w,x,u,y),z,x2),x1)),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(w,x,u,y),z,x2),x1))**.
% 299.92/300.50 32925[0:SpR:373.2,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),x1)) -> equal(hAPP(c_Set_Oinsert(v,x2),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x2),x1)),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x2),x1))**.
% 299.92/300.50 32879[0:SpR:475.1,118.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Fun_Ocomp(c_Set_Oinsert(hAPP(x,v),y),c_Fun_Ofun__upd(z,x1,hAPP(c_Set_Oimage(x,u,y),w),x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(hAPP(x,v),y),z,x3,x4,x2),x1,hAPP(c_Set_Oimage(x,u,y),w),x2,x4))*.
% 299.92/300.50 33794[0:Res:248.4,430.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(tc_fun(u,tc_bool),tc_bool))* c_lessequals(c_Finite__Set_Olinorder__class_OMin(w,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,tc_bool),tc_bool))) c_lessequals(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))*.
% 299.92/300.50 33874[0:Res:247.4,430.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(tc_fun(u,tc_bool),tc_bool))* c_lessequals(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,tc_bool),tc_bool))) c_lessequals(c_Finite__Set_Olinorder__class_OMax(w,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))*.
% 299.92/300.50 34368[0:SpL:24914.0,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,w),hAPP(hAPP(c_in(u),v),v_x)),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,w),hAPP(hAPP(c_in(u),v),v_x)),u),v,u)*.
% 299.92/300.50 34367[0:SpL:24914.0,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,w),hAPP(hAPP(c_in(u),v),v_x)),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,w),hAPP(hAPP(c_in(u),v),v_x)),u),u)*.
% 299.92/300.50 35349[0:SpR:614.2,410.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u),y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),y,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,w,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),y,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 35330[0:SpR:188.1,410.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),y),c_Set_Ovimage(c_COMBK(v,u,z),z,u),x,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Ovimage(c_COMBK(v,u,z),z,u),x,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 37501[0:SpL:205.1,389.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x),y)* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v)* -> equal(x,hAPP(c_Set_Oimage(u,v,w),y))*.
% 299.92/300.50 38356[0:SSi:38279.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x)) c_Finite__Set_Ofinite(x,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y,x,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.92/300.50 38357[0:SSi:38275.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),w)) c_Finite__Set_Ofinite(w,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_Set_Oinsert(x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(x,u),y),w,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.92/300.50 38403[0:SpL:410.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(x,y)),hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x,x1,tc_fun(v,tc_bool)))) c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(y,x1),z),x,x1,tc_fun(v,tc_bool)),v,w)* -> equal(hAPP(x,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x,x1,tc_fun(v,tc_bool))).
% 299.92/300.50 38984[0:SpR:97.1,354.2] || c_Fun_Oinj__on(u,v,w,x) c_lessequals(hAPP(c_Set_Oimage(u,w,x),v),y,tc_fun(x,tc_bool)) c_Fun_Oinj__on(c_Fun_Othe__inv__into(v,u,w,x),y,x,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(y,c_Fun_Othe__inv__into(v,u,w,x),x,w),w,x),v),hAPP(c_Set_Oimage(u,w,x),v))**.
% 299.92/300.50 39398[0:Rew:533.0,39302.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x))),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v_x),x)))**.
% 299.92/300.50 39399[0:Rew:533.0,39241.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname))))*.
% 299.92/300.50 39400[0:Rew:533.0,39240.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname))))*.
% 299.92/300.50 39106[0:SpR:533.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_bool))* equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w))).
% 299.92/300.50 39786[0:SpR:24914.0,532.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)))**.
% 299.92/300.50 41378[0:SpL:338.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y))* hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x2,v),x))))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(x2,v),u,tc_fun(z,tc_bool))))*.
% 299.92/300.50 41328[0:SpL:339.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oinsert(z,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),x2),v))))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(c_Set_Oinsert(z,x1),x2)),u,tc_fun(x,tc_bool))))*.
% 299.92/300.50 41323[0:SpL:338.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y))* hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x2),x))))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x2),u,tc_fun(z,tc_bool))))*.
% 299.92/300.50 41302[0:SpL:465.1,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(z,x1,x2),v)))* -> hBOOL(hAPP(hAPP(c_in(x1),x3),v))* hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_Fun_Ofun__upd(z,x3,x4,x1,x2),x1,x2),u,tc_fun(x,tc_bool))))*.
% 299.92/300.50 41272[0:SpL:71.2,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),x1))* hBOOL(hAPP(hAPP(c_in(x2),x3),v))* -> hBOOL(hAPP(hAPP(c_in(x2),x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Fun_Othe__inv__into(w,x,u,y),z,tc_fun(x2,tc_bool))))*.
% 299.92/300.50 41271[0:SpL:373.2,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),x1))* hBOOL(hAPP(hAPP(c_in(x2),x3),v))* -> hBOOL(hAPP(hAPP(c_in(x2),x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Hilbert__Choice_Oinv__into(w,x,u,y),z,tc_fun(x2,tc_bool))))*.
% 299.92/300.50 41561[0:SpL:130.1,284.0] class_HOL_Ominus(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u)),y,v),z)))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,v)* -> hBOOL(hAPP(hAPP(c_in(y),v_x),z)).
% 299.92/300.50 41547[0:SpL:196.1,284.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),z,x),x1)))* c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x)* -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oimage(u,v,w),y)),x1)).
% 299.92/300.50 41738[0:SpL:24914.0,494.1] || hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),v_x),t_a)* c_Natural_Oevaln(y,w,x,z)* -> hBOOL(hAPP(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),tc_Com_Opname,x1),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),v_x)),v),z))*.
% 299.92/300.50 42267[0:SSi:42172.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(x,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),y))* -> hBOOL(hAPP(x,y)) hBOOL(hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),y)).
% 299.92/300.50 42268[0:SSi:42168.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(x,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))** -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))).
% 299.92/300.50 42470[0:SpL:9493.1,315.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,t_a),w,x),v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,t_a),w,x)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(v_x,t_a),w,x))** -> equal(hAPP(c_Set_Oimage(v,w,x),u),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,x),u)).
% 299.92/300.50 42468[0:SpL:8498.1,315.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(w,x),y,z),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(w,x),y,z)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,c_Set_Oinsert(w,x),y,z))** -> equal(hAPP(c_Set_Oimage(v,y,z),u),hAPP(c_Set_Oimage(c_Set_Oinsert(w,x),y,z),u)).
% 299.92/300.50 42429[0:SpL:9493.1,315.0] || equal(hAPP(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,t_a),v,w,x),v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,t_a),v,w,x)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v_x,t_a),v,w,x))** -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),w,x),u),hAPP(c_Set_Oimage(v,w,x),u)).
% 299.92/300.50 42427[0:SpL:8498.1,315.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v,w),x,y,z),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) equal(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v,w),x,y,z)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,c_Set_Oinsert(v,w),x,y,z))** -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(v,w),y,z),u),hAPP(c_Set_Oimage(x,y,z),u)).
% 299.92/300.50 43114[0:SpR:24914.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),tc_Com_Opname,x),u,tc_fun(v,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),tc_Com_Opname,x),u,tc_fun(v,tc_bool)))**.
% 299.92/300.50 43098[0:SpR:15172.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),y,z),x1,tc_fun(x2,tc_bool)),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),y,z),x1,tc_fun(x2,tc_bool)),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 43090[0:SpR:128.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(z,x1,w),v),tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Ovimage(z,x1,w),u,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Ovimage(z,x1,w),u,tc_fun(y,tc_bool)))**.
% 299.92/300.50 43049[0:SpR:337.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 43035[0:SpR:544.1,486.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(z,tc_bool)))**.
% 299.92/300.50 43034[0:SpR:543.1,486.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,tc_fun(z,tc_bool)))**.
% 299.92/300.50 43536[0:SpR:465.1,507.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(y,u,x),w)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x),u,x),x1)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x),u,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x1)))**.
% 299.92/300.50 43521[0:SpR:465.1,507.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x),u,x),x1)),hAPP(c_Set_Oimage(y,u,x),w)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x),u,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x1),w)))**.
% 299.92/300.50 43957[0:Res:424.2,231.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) c_lessequals(z,hAPP(c_Set_Oimage(w,x,u),y),tc_fun(u,tc_bool)) c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u) -> c_lessequals(hAPP(c_Set_Ovimage(w,x,u),hAPP(c_Set_Oinsert(v,u),z)),y,tc_fun(x,tc_bool))*.
% 299.92/300.50 43949[0:SpL:465.1,231.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) c_Fun_Oinj__on(c_Fun_Ofun__upd(v,z,x1,w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> hBOOL(hAPP(hAPP(c_in(w),z),y)) c_lessequals(hAPP(c_Set_Ovimage(c_Fun_Ofun__upd(v,z,x1,w,x),w,x),u),y,tc_fun(w,tc_bool))*.
% 299.92/300.50 44070[0:SpL:465.1,358.0] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),x1),tc_fun(w,tc_bool))* c_Fun_Oinj__on(c_Fun_Ofun__upd(u,y,z,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_in(v),y),x)) c_lessequals(x,x1,tc_fun(v,tc_bool)).
% 299.92/300.50 44055[0:SpL:465.1,358.0] || c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),z),hAPP(c_Set_Oimage(u,x,y),x1),tc_fun(y,tc_bool))* c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> hBOOL(hAPP(hAPP(c_in(x),v),x1)) c_lessequals(z,x1,tc_fun(x,tc_bool)).
% 299.92/300.50 44589[0:Rew:240.2,44587.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),v_x),c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),tc_Com_Opname,y),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,w,u)))**.
% 299.92/300.50 44590[0:Rew:240.2,44586.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),v_x),tc_Com_Opname,y),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,w,u)))**.
% 299.92/300.50 45099[0:SpR:161.0,326.2] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool)) c_lessequals(c_HOL_Ominus__class_Ominus(y,v,tc_fun(w,tc_bool)),z,tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),v,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z),tc_fun(w,tc_bool))*.
% 299.92/300.50 45098[0:SpR:162.0,326.2] || c_lessequals(hAPP(c_Set_Ovimage(u,v,w),x),y,tc_fun(v,tc_bool)) c_lessequals(hAPP(c_Set_Ovimage(u,v,w),z),x1,tc_fun(v,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x1),tc_fun(v,tc_bool))*.
% 299.92/300.50 45097[0:SpR:507.0,326.2] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Oimage(u,v,w),z),x1,tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),x1),tc_fun(w,tc_bool))*.
% 299.92/300.50 45038[0:SpR:486.1,326.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(x,hAPP(y,v),tc_fun(z,tc_bool))* c_lessequals(x1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))*.
% 299.92/300.50 45034[0:SpR:161.0,326.2] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)) c_lessequals(y,c_HOL_Ominus__class_Ominus(z,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),y),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),z),w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))*.
% 299.92/300.50 45033[0:SpR:162.0,326.2] || c_lessequals(u,hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool)) c_lessequals(z,hAPP(c_Set_Ovimage(v,w,x),x1),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),z),hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),x1)),tc_fun(w,tc_bool))*.
% 299.92/300.50 45032[0:SpR:507.0,326.2] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) c_lessequals(z,hAPP(c_Set_Oimage(v,w,x),x1),tc_fun(x,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),z),hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),x1)),tc_fun(x,tc_bool))*.
% 299.92/300.50 45313[0:SpL:161.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),z,tc_fun(w,tc_bool))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ominus__class_Ominus(x,z,tc_fun(w,tc_bool)),u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ominus__class_Ominus(y,z,tc_fun(w,tc_bool)),u,w)))*.
% 299.92/300.50 45312[0:SpL:162.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Ovimage(x,w,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Ovimage(x,w,y),z),u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Ovimage(x,w,y),x1),u,w)))*.
% 299.92/300.50 45311[0:SpL:507.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Oimage(x,y,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oimage(x,y,w),z),u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oimage(x,y,w),x1),u,w)))*.
% 299.92/300.50 45418[0:SpR:465.1,45357.1] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_x)) -> hBOOL(hAPP(hAPP(c_in(x),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),tc_Com_Opname)))* hBOOL(hAPP(c_Set_Oimage(u,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),tc_Com_Opname)))*.
% 299.92/300.50 45577[0:SpR:323.0,532.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,w,x,tc_fun(u,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),z),w,x,tc_fun(u,tc_bool))))**.
% 299.92/300.50 45571[0:SpR:323.0,533.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,x,tc_fun(u,tc_bool))),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),y),w,x,tc_fun(u,tc_bool))),z))**.
% 299.92/300.50 45553[0:SpR:323.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,y,tc_fun(z,tc_bool))),x1)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),x2),w),x,y,tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,x,y,tc_fun(z,tc_bool))),v,u),u)*.
% 299.92/300.50 45534[0:SpR:323.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),hAPP(c_Set_Ovimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,w,x,tc_fun(y,tc_bool))),u,x1),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),v),w,x,tc_fun(y,tc_bool)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))))))*.
% 299.92/300.50 45529[0:SpR:323.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,x,tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),y),w,x,tc_fun(u,tc_bool)),z,x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))))**.
% 299.92/300.50 45851[0:SpL:532.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),u,w)))* hBOOL(hAPP(hAPP(c_in(w),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y))))* -> hBOOL(hAPP(u,z))*.
% 299.92/300.50 45850[0:SpL:533.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,v)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,u,v)))* hBOOL(hAPP(hAPP(c_in(v),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))))* -> hBOOL(hAPP(u,z))*.
% 299.92/300.50 45933[0:SpL:465.1,45899.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),tc_Com_Opname)))* -> hBOOL(hAPP(hAPP(c_in(v),x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),tc_Com_Opname)))* hBOOL(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),v_x)).
% 299.92/300.50 46599[0:Rew:26153.0,46598.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(y,v,tc_fun(x,tc_bool)),u)),c_Set_Oinsert(z,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),hAPP(c_Set_Oinsert(z,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,y,v,tc_fun(x,tc_bool)))))**.
% 299.92/300.50 47362[0:SpL:339.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oinsert(x,w),y),u,w)),hAPP(c_Set_Oinsert(x,w),y)))*.
% 299.92/300.50 47588[0:SpL:338.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oinsert(x,w),z),u,w)),hAPP(c_Set_Oinsert(x,w),z)))*.
% 299.92/300.50 47931[0:SpL:339.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oinsert(y,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),v))))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(y,w),z),u,w)),hAPP(c_Set_Oinsert(y,w),z)))*.
% 299.92/300.50 48038[0:SpL:338.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oinsert(y,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),z))))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(y,w),z),u,w)),hAPP(c_Set_Oinsert(y,w),z)))*.
% 299.92/300.50 48439[0:SpL:9.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,x))),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,y,z,x1),x2,u),c_HOL_Ominus__class_Ominus(x3,hAPP(c_Set_Oinsert(x,x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))),tc_fun(x2,tc_bool)))))* c_Fun_Oinj__on(c_Fun_Ocomp(v,w,y,z,x1),hAPP(c_Set_Oinsert(x,x2),x3),x2,u) -> .
% 299.92/300.50 48430[0:SpL:1196.1,224.0] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),x),w,v) -> .
% 299.92/300.50 48420[0:SpL:1195.1,224.0] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),w),x),w,v) -> .
% 299.92/300.50 48377[0:SpL:87.1,224.0] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(w,u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(w,u),x),y),x,v) -> .
% 299.92/300.50 48376[0:SpL:88.1,224.0] class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),x,v),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(w,u)),hAPP(c_Set_Oinsert(w,x),y),x,v) -> .
% 299.92/300.50 48366[0:SpL:540.1,224.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y,v),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(w,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(c_Set_Oinsert(w,y),z),y,v) -> .
% 299.92/300.50 48365[0:SpL:539.1,224.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y,v),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(w,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(c_Set_Oinsert(w,y),z),y,v) -> .
% 299.92/300.50 48364[0:SpL:297.2,224.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) hBOOL(hAPP(hAPP(c_in(x),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,x),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(w,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Set_Oinsert(w,y),z),y,x) -> .
% 299.92/300.50 48361[0:SpL:2098.1,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,v),tc_Hoare__Mirabelle_Otriple(t_a)),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,v),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(v,x),y),x,u) -> c_Hoare__Mirabelle_Ohoare__valids(w,v,t_a).
% 299.92/300.50 48355[0:SpL:299.2,224.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,w,u) hBOOL(hAPP(hAPP(c_in(x),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,x),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(v,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Set_Oinsert(v,y),z),y,x) -> .
% 299.92/300.50 48474[0:Rew:9.0,48313.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,x))),hAPP(c_Set_Oimage(v,y,u),hAPP(c_Set_Oimage(w,z,y),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(x,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool))))))* c_Fun_Oinj__on(c_Fun_Ocomp(v,w,y,u,z),hAPP(c_Set_Oinsert(x,z),x1),z,u) -> .
% 299.92/300.50 48967[0:SpL:24914.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))* -> hBOOL(hAPP(x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x))))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.92/300.50 48938[0:SpL:104.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))))* -> hBOOL(hAPP(y,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),y,u)),c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool))))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,y,u)),x))*.
% 299.92/300.50 48932[0:SpL:600.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(y,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,y,u)),x)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),y,u)),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))))*.
% 299.92/300.50 49117[0:SpL:49017.1,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,v,tc_Com_Opname),tc_Com_Opname),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,v,tc_Com_Opname),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,w),x),w,u) -> hBOOL(hAPP(v,v_x)).
% 299.92/300.50 49172[0:SpL:24914.0,239.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) c_lessequals(x,y,tc_fun(w,tc_bool)) c_Fun_Oinj__on(v,x,w,u) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(x,v,w,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,z),hAPP(c_in(u),v_x)))),y))*.
% 299.92/300.50 49294[0:SpL:21893.0,488.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(v),v_x),c_in(v),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)),x))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,v)),y))*.
% 299.92/300.50 49293[0:SpL:21267.0,488.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(v),hAPP(c_in(v),v_x),tc_Com_Opname,w)))* hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)),x))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,v)),y))*.
% 299.92/300.50 49665[0:Rew:49662.2,49581.1] || c_Fun_Oinj__on(c_Set_Oimage(u,v,w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oimage(u,v,w),y,z),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),y),x))))* c_Fun_Oinj__on(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),y),x),y,z).
% 299.92/300.50 49666[0:Rew:49662.2,49582.1] || c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),y,z),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),y),x))))* c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),y),x),y,z).
% 299.92/300.50 49667[0:Rew:49662.2,49590.1] || c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),y,z),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),y),x))))* c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),y),x),y,z).
% 299.92/300.50 49673[0:Rew:49662.2,49485.1] || c_Fun_Oinj__on(c_Set_Oinsert(u,v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oinsert(u,v),z)),hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),z),x),w))))* c_Fun_Oinj__on(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),z),x),w),x,y).
% 299.92/300.50 49689[0:Rew:49662.2,49587.1] || c_Fun_Oinj__on(u,v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(u,v_x)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,y),hAPP(u,v_x)),w),v))))* c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,y),hAPP(u,v_x)),w),v),w,x).
% 299.92/300.50 49693[0:Rew:49662.2,49584.2] || equal(c_in(t_a),u) c_Fun_Oinj__on(hAPP(u,v_x),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(hAPP(u,v_x),w,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),w),v))))* c_Fun_Oinj__on(hAPP(u,v_x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),w),v),w,x).
% 299.92/300.50 49696[0:Rew:49662.2,49579.2] class_Lattices_Oboolean__algebra(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),w),v))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),w),v),w,x).
% 299.92/300.50 49697[0:Rew:49662.2,49589.2] class_Lattices_Oboolean__algebra(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),v))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),w),v),w,x).
% 299.92/300.50 49730[0:Rew:49662.2,49609.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),u,v,w) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,w),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v),u))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v),u),v,w).
% 299.92/300.50 49732[0:Rew:49662.2,49484.1] || c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),u,v,w) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),v,w),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs),v),u))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs),v),u),v,w).
% 299.92/300.50 49771[0:Rew:49662.2,49651.3,49662.2,49651.2] || c_Fun_Oinj__on(u,v,w,tc_Hoare__Mirabelle_Otriple(t_a)) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(x,w),v),w,tc_Hoare__Mirabelle_Otriple(t_a)) c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oimage(u,w,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(x,w),v)),y,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Set_Oimage(u,w,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(x,w),v)),y),hAPP(u,x),t_a)*.
% 299.92/300.50 50040[0:SpL:497.0,3698.2] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),c_Com_Ocom_OSKIP) -> .
% 299.92/300.50 50039[4:SpL:497.0,46565.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)))* -> .
% 299.92/300.50 50031[0:SpL:497.0,3493.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_in(tc_Com_Opname))** equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.92/300.50 49987[0:SpR:497.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))))*.
% 299.92/300.50 49964[0:SpR:497.0,3339.1] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)))* -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),x,y),u)**.
% 299.92/300.50 49963[0:SpR:497.0,3316.1] || equal(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)))* -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.92/300.50 49960[0:SpR:497.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),tc_Com_Opname,u),v_Procs)))*.
% 299.92/300.50 49949[0:SpR:497.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.92/300.50 49947[0:SpR:497.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_Com_Opname,w)),v_Procs))*.
% 299.92/300.50 49943[0:SpR:497.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.92/300.50 49941[0:SpR:497.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_Com_Opname,w)),v_Procs))*.
% 299.92/300.50 49940[0:SpR:497.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))))*.
% 299.92/300.50 49938[0:SpR:497.0,11030.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.92/300.50 49937[0:SpR:497.0,10090.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.92/300.50 49928[0:SpR:497.0,3284.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))))*.
% 299.92/300.50 49923[2:SpR:497.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool)).
% 299.92/300.50 49921[0:SpR:497.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool)).
% 299.92/300.50 49920[7:SpR:497.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool)).
% 299.92/300.50 49917[0:SpR:497.0,651.0] || -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.92/300.50 50076[0:Rew:497.0,50009.0] || -> equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_Com_Opname,u),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v_x))),v)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v_x),v)))**.
% 299.92/300.50 50077[0:Rew:497.0,50003.0] || -> equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_Com_Opname,v),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v_x)))),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v_x)))**.
% 299.92/300.50 50141[0:SpR:620.1,362.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oimage(w,x,tc_fun(u,tc_bool)),y))) -> equal(y,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,x,tc_fun(u,tc_bool))),tc_fun(u,tc_bool))*.
% 299.92/300.50 50174[0:Rew:620.1,50164.2] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(w,c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Fun_Ofun__upd(z,v,x1,u,tc_fun(x,tc_bool)),u,tc_fun(x,tc_bool))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,z,u,tc_fun(x,tc_bool))))**.
% 299.92/300.50 50481[0:SpR:66.0,223.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)))) -> equal(hAPP(c_Set_Oinsert(y,z),hAPP(c_Set_Oimage(x1,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool)))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x1,v,y,u,z),u,z),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))))**.
% 299.92/300.50 50854[0:SpL:622.0,3506.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_Com_Ocom_OSemi(w,x),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))))* -> .
% 299.92/300.50 50828[0:SpR:622.0,9566.0] || -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),hAPP(hAPP(c_Set_Oinsert(w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool))),v_x),tc_bool)*.
% 299.92/300.50 50806[0:SpR:622.0,32669.0] || -> hBOOL(hAPP(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,w),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))))))*.
% 299.92/300.50 50781[0:SpR:622.0,24020.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),v_x),v_x).
% 299.92/300.50 51104[0:SpL:3229.1,472.2] || equal(u,c_Hilbert__Choice_Oinv__into(v,w,x,y)) hBOOL(hAPP(hAPP(c_in(y),z),hAPP(c_Set_Oimage(w,x,y),v)))* hBOOL(hAPP(hAPP(c_in(y),v_x),hAPP(c_Set_Oimage(w,x,y),v)))* equal(hAPP(c_Hilbert__Choice_Oinv__into(v,w,x,y),z),hAPP(u,v_x))* -> equal(z,v_x).
% 299.92/300.50 51515[0:Res:376.0,195.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),x),tc_fun(w,tc_bool))* c_Fun_Oinj__on(y,hAPP(c_Set_Oinsert(v,w),x),w,z)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(y,w,z),x),hAPP(c_Set_Oimage(y,w,z),u),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,w,z),c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool))))**.
% 299.92/300.50 55996[0:SpL:497.0,55174.1] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)))* -> .
% 299.92/300.50 55914[0:SpL:497.0,55174.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),w)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool),hAPP(w,v_x))* -> .
% 299.92/300.50 58758[0:SpL:323.0,15629.0] || hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool))),z)))*.
% 299.92/300.50 59266[0:SpL:323.0,15857.0] || hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool))),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool))),x1)))*.
% 299.92/300.50 63794[0:MRR:63793.3,63779.3] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(hAPP(c_Set_Oimage(v,w,u),x),y)* c_Finite__Set_Ofinite(x,w) c_lessequals(hAPP(c_Set_Oimage(z,u,w),y),x,tc_fun(w,tc_bool))* c_Fun_Oinj__on(v,x,w,u) c_Fun_Oinj__on(z,y,u,w) -> equal(c_Finite__Set_Ocard(x,w),c_Finite__Set_Ocard(y,u)).
% 299.92/300.50 64619[0:SpL:26782.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,tc_fun(w,tc_bool)),x,u),y)))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,tc_fun(w,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u)* -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Obot__class_Obot(tc_bool)),y)).
% 299.92/300.50 74329[7:SpL:71835.1,472.2] || equal(c_Hilbert__Choice_Oinv__into(u,v,w,x),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(v,w,x),u)))* hBOOL(hAPP(hAPP(c_in(x),v_x),hAPP(c_Set_Oimage(v,w,x),u)))* equal(hAPP(c_Hilbert__Choice_Oinv__into(u,v,w,x),y),v_x) -> equal(y,v_x).
% 299.92/300.50 74531[7:Rew:71835.1,74221.2] || equal(c_Set_Oinsert(v_x,t_a),c_Hoare__Mirabelle_Otriple_Otriple(u)) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.50 76173[0:SpL:9915.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(v,w,x),y,z,x1,x2),x3,u),x4)))* c_Fun_Oinj__on(c_COMBS(c_Set_Ovimage(v,w,x),y,z,x1,x2),c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool)),x3,u)* -> hBOOL(hAPP(hAPP(c_in(x3),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),x4)).
% 299.92/300.50 76294[0:SpL:10469.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_Set_Oimage(v,w,x),y,z,x1,x2),x3,u),x4)))* c_Fun_Oinj__on(c_COMBS(c_Set_Oimage(v,w,x),y,z,x1,x2),c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool)),x3,u)* -> hBOOL(hAPP(hAPP(c_in(x3),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x4)).
% 299.92/300.50 76424[0:SpL:10470.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(v,w,x),y,z,x1,x2),x3,u),x4)))* c_Fun_Oinj__on(c_COMBS(c_Set_Ovimage(v,w,x),y,z,x1,x2),c_Orderings_Otop__class_Otop(tc_fun(x3,tc_bool)),x3,u)* -> hBOOL(hAPP(hAPP(c_in(x3),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),x4)).
% 299.92/300.50 77147[7:SpL:622.0,74788.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_x)** equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),w)* -> hBOOL(w)*.
% 299.92/300.50 80310[0:SpL:21268.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(w),hAPP(c_in(w),x),z,x1)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,u,w)),y))*.
% 299.92/300.50 80309[0:SpL:21268.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(w),hAPP(c_in(w),x),z,x1)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,u,w)),y))*.
% 299.92/300.50 80239[0:SpL:21268.0,516.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x))) -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),y,z)))*.
% 299.92/300.50 80172[0:SpL:21268.0,273.0] || equal(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w))* -> equal(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w),x,y))*.
% 299.92/300.50 80100[0:SpL:21268.0,485.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_in(w),hAPP(c_in(w),x),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x1)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x1,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)),z))*.
% 299.92/300.50 80099[0:SpL:21268.0,484.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_in(w),hAPP(c_in(w),x),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x1)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x1,u,w)),x1))*.
% 299.92/300.50 79969[0:SpR:131.0,21268.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x1)),z,x2)),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x1)))**.
% 299.92/300.50 79968[0:SpR:158.0,21268.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x1)),z,x2)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x1)))**.
% 299.92/300.50 79776[0:SpR:21268.0,131.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x1),z,x2))),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x1))**.
% 299.92/300.50 79774[0:SpR:21268.0,158.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x1),z,x2))),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x1))**.
% 299.92/300.50 81505[0:SpL:21894.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(w),x),c_in(w),z,x1)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,u,w)),y))*.
% 299.92/300.50 81504[0:SpL:21894.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(w),x),c_in(w),z,x1)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,u,w)),y))*.
% 299.92/300.50 81434[0:SpL:21894.0,516.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x))) -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y,z)))*.
% 299.92/300.50 81367[0:SpL:21894.0,273.0] || equal(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w))* -> equal(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w),c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),x,y))*.
% 299.92/300.50 81295[0:SpL:21894.0,485.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(w),x),c_in(w),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x1)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x1,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)),z))*.
% 299.92/300.50 81294[0:SpL:21894.0,484.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(w),x),c_in(w),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x1)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x1,u,w)),x1))*.
% 299.92/300.50 81163[0:SpR:131.0,21894.0] || -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x1)),c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x2)),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x1)))**.
% 299.92/300.50 81162[0:SpR:158.0,21894.0] || -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x1)),c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x2)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x1)))**.
% 299.92/300.50 80970[0:SpR:21894.0,131.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x1),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z,x2))),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x1))**.
% 299.92/300.50 80968[0:SpR:21894.0,158.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x1),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z,x2))),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x1))**.
% 299.92/300.50 83121[0:SpL:5924.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(v,w),x)),hAPP(c_Set_Oimage(c_COMBS(v,c_COMBK(x,y,z),x1,x2,x3),x4,u),x5)))* c_Fun_Oinj__on(c_COMBS(v,c_COMBK(x,y,z),x1,x2,x3),c_Orderings_Otop__class_Otop(tc_fun(x4,tc_bool)),x4,u)* -> hBOOL(hAPP(hAPP(c_in(x4),w),x5)).
% 299.92/300.50 83440[0:SpL:5961.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,x))),hAPP(c_Set_Oimage(c_COMBS(c_COMBK(v,y,z),w,x1,x2,x3),x4,u),x5)))* c_Fun_Oinj__on(c_COMBS(c_COMBK(v,y,z),w,x1,x2,x3),c_Orderings_Otop__class_Otop(tc_fun(x4,tc_bool)),x4,u)* -> hBOOL(hAPP(hAPP(c_in(x4),x),x5)).
% 299.92/300.50 84163[7:SpL:622.0,78767.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),tc_bool),v_x) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.92/300.50 84747[7:SpL:61.1,78178.0] || c_Finite__Set_Ofinite(u,v) c_Hoare__Mirabelle_Otriple__valid(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,v),u),v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),v_x),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),v_x,t_a).
% 299.92/300.50 85049[0:SpR:644.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oimage(c_COMBK(x,y,tc_Com_Opname),tc_Com_Opname,y),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oimage(c_COMBK(x,y,tc_Com_Opname),tc_Com_Opname,y),u,tc_fun(w,tc_bool)))**.
% 299.92/300.50 86595[0:Res:19823.1,199.0] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(y,u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool)),w,v,x))))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(y,u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool)),x1))*.
% 299.92/300.50 86708[4:SpL:622.0,86106.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),tc_bool),v_x) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.92/300.50 88615[7:SpL:622.0,88086.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_x)** hBOOL(c_HOL_Ominus__class_Ominus(w,hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),tc_bool))* -> .
% 299.92/300.50 89964[0:Rew:89962.0,47274.3] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* hBOOL(hAPP(hAPP(c_in(u),w),v)) -> c_lessequals(v,hAPP(c_Set_Oinsert(w,u),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),tc_fun(u,tc_bool))*.
% 299.92/300.50 91889[4:Rew:533.0,91839.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname))),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))).
% 299.92/300.50 93206[0:SpR:5878.1,486.1] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(u)),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,c_Orderings_Obot__class_Obot(u))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),y,z,x1,x2),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),y,z,x1,x2),v,tc_fun(x,tc_bool)))**.
% 299.92/300.50 93726[0:SpL:223.1,7462.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(x,hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),tc_fun(z,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,x1,u,z),u,z),w),z)* -> c_Finite__Set_Ofinite(x,z).
% 299.92/300.50 26022[0:Rew:339.0,25934.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),tc_Com_Opname,x))),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)))**.
% 299.92/300.50 26023[0:Rew:339.0,25933.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),tc_Com_Opname,x))),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)))**.
% 299.92/300.50 25899[0:SpR:339.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x,y),hAPP(c_Set_Oinsert(z,x),x1)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z)),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x,y),x1)))*.
% 299.92/300.50 26959[0:Res:424.2,202.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,u,u),hAPP(c_Set_Oinsert(v,u),x))))* c_lessequals(x,hAPP(c_Set_Oimage(w,u,u),hAPP(c_Set_Oinsert(v,u),x)),tc_fun(u,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(v,u),x),u) -> c_Fun_Oinj__on(w,hAPP(c_Set_Oinsert(v,u),x),u,u).
% 299.92/300.50 27645[0:SpR:317.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) c_Fun_Oinj__on(c_Set_Oinsert(hAPP(v,x1),x),z,u,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,c_Set_Oinsert(hAPP(v,x1),x),u,x2),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(x1,w),y))),hAPP(c_Set_Oimage(v,w,x),y))**.
% 299.92/300.50 27602[0:SpR:104.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))),w,u,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))),u,z),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(y,v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))),v)**.
% 299.92/300.50 27597[0:SpR:600.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),y,u,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),u,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),w)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)))**.
% 299.92/300.50 27595[0:SpR:614.2,373.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),z)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),z,x,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u))**.
% 299.92/300.50 27554[0:SpR:99.1,373.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),z)) c_Fun_Oinj__on(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,x1),y),hAPP(u,y))**.
% 299.92/300.50 27553[0:SpR:438.1,373.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),z)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,x1),y),hAPP(u,y))**.
% 299.92/300.50 27798[0:SpR:317.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) c_Fun_Oinj__on(c_Set_Oinsert(hAPP(v,x1),x),z,u,x2) -> equal(hAPP(c_Fun_Othe__inv__into(z,c_Set_Oinsert(hAPP(v,x1),x),u,x2),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(x1,w),y))),hAPP(c_Set_Oimage(v,w,x),y))**.
% 299.92/300.50 27755[0:SpR:104.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))),w,u,z) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))),u,z),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(y,v,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))),v)**.
% 299.92/300.50 27750[0:SpR:600.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),y,u,z) -> equal(hAPP(c_Fun_Othe__inv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),u,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),w)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)))**.
% 299.92/300.50 27748[0:SpR:614.2,71.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),z)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),z,x,x1) -> equal(hAPP(c_Fun_Othe__inv__into(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u))**.
% 299.92/300.50 27706[0:SpR:99.1,71.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),z)) c_Fun_Oinj__on(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x,x1) -> equal(hAPP(c_Fun_Othe__inv__into(z,c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,x1),y),hAPP(u,y))**.
% 299.92/300.50 27705[0:SpR:438.1,71.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),z)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x,x1) -> equal(hAPP(c_Fun_Othe__inv__into(z,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,x1),y),hAPP(u,y))**.
% 299.92/300.50 28513[0:SpR:104.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),c_Fun_Ofun__upd(w,x,y,z,x1),x1,x2,z),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w,x1,x2,z),x,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,y,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),z,x2))*.
% 299.92/300.50 28634[0:SpR:64.0,177.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))* equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),w),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))).
% 299.92/300.50 29055[0:SpR:537.1,317.0] class_Lattices_Olattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y),hAPP(c_Set_Oinsert(z,x),x1)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y),x1)))*.
% 299.92/300.50 29578[0:SpR:534.1,317.0] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y),hAPP(c_Set_Oinsert(z,x),x1)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y),x1)))*.
% 299.92/300.50 32336[0:SpL:393.1,477.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))) hBOOL(hAPP(hAPP(c_in(w),x),y))* -> equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z),c_Set_Oimage(c_COMBK(u,v,x1),x1,v),w),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))** hBOOL(hAPP(c_Set_Oimage(c_COMBK(u,v,x1),x1,v),x))*.
% 299.92/300.50 32409[0:Rew:104.0,32353.2] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(y,tc_bool))),v),tc_fun(y,tc_bool)),tc_fun(y,tc_bool)))* hBOOL(hAPP(hAPP(c_in(v),z),w))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,z,tc_fun(y,tc_bool)),tc_fun(y,tc_bool)))*.
% 299.92/300.50 32516[0:SpL:393.1,476.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))) hBOOL(hAPP(hAPP(c_in(w),x),y))* -> equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),y),c_Set_Oimage(c_COMBK(u,v,x1),x1,v),w),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))** hBOOL(hAPP(c_Set_Oimage(c_COMBK(u,v,x1),x1,v),x))*.
% 299.92/300.50 32587[0:Rew:104.0,32533.2] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(y,tc_bool))),v),tc_fun(y,tc_bool)),tc_fun(y,tc_bool)))* hBOOL(hAPP(hAPP(c_in(v),z),x))* -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,z,tc_fun(y,tc_bool)),tc_fun(y,tc_bool)))*.
% 299.92/300.50 32976[0:SpR:338.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x)),x1),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),u,x1),y)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),u,x1),y))**.
% 299.92/300.50 32922[0:SpR:97.1,475.1] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oimage(u,w,x),v)),z)) -> equal(hAPP(c_Set_Oinsert(v,x1),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,x1),z)),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,x1),z))**.
% 299.92/300.50 32921[0:SpR:99.1,475.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),z)) -> equal(hAPP(c_Set_Oinsert(y,x1),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,x1),z)),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,x1),z))**.
% 299.92/300.50 32920[0:SpR:438.1,475.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),z)) -> equal(hAPP(c_Set_Oinsert(y,x1),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,x1),z)),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,x1),z))**.
% 299.92/300.50 32908[0:SpR:393.1,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),x1),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(y,z,x),x,z),u,x1),w)),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(y,z,x),x,z),u,x1),w))**.
% 299.92/300.50 34534[0:Rew:537.1,34231.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))**.
% 299.92/300.50 34535[0:Rew:534.1,34230.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x))))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_x)))**.
% 299.92/300.50 34048[0:SpR:24914.0,177.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),hAPP(c_Set_Oinsert(v,u),v_x))))* equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),v_x),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),hAPP(c_Set_Oinsert(v,u),v_x)))*.
% 299.92/300.50 34600[0:SpR:55.1,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) -> hBOOL(hAPP(hAPP(c_in(x),z),w)) equal(hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(z,x),v),w,tc_fun(x,tc_bool)),x1),hAPP(c_Set_Oimage(c_Set_Oinsert(z,x),u,x1),y)),hAPP(c_Set_Oimage(c_Set_Oinsert(z,x),u,x1),y))**.
% 299.92/300.50 34579[0:SpR:55.1,246.2] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),w) -> hBOOL(hAPP(hAPP(c_in(w),x),v)) hBOOL(hAPP(hAPP(c_in(w),x),c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)))) equal(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,w),u),v,tc_fun(w,tc_bool)),w),c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),w)))**.
% 299.92/300.50 35352[0:SpR:542.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,tc_fun(z,tc_bool))))*.
% 299.92/300.50 35346[0:SpR:536.1,410.0] class_Lattices_Olattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 35345[0:SpR:535.1,410.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 35302[0:SpR:71.2,410.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(x,v),z),x1),c_Fun_Othe__inv__into(w,x,u,y),z,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Fun_Othe__inv__into(w,x,u,y),z,tc_fun(x2,tc_bool))))*.
% 299.92/300.50 35301[0:SpR:373.2,410.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(x,v),z),x1),c_Hilbert__Choice_Oinv__into(w,x,u,y),z,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Hilbert__Choice_Oinv__into(w,x,u,y),z,tc_fun(x2,tc_bool))))*.
% 299.92/300.50 36860[0:SpR:66.0,35.2] || c_lessequals(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w,tc_fun(v,tc_bool)) c_lessequals(w,c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(w,c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(u,v),y),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))**.
% 299.92/300.50 37313[0:SpL:338.0,274.0] || equal(hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(u,v),y)))* -> hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(v),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* equal(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)).
% 299.92/300.50 37307[0:SpL:317.0,274.0] || equal(hAPP(c_Set_Oinsert(hAPP(u,v),w),x),hAPP(c_Set_Oimage(u,y,w),hAPP(c_Set_Oinsert(v,y),z)))* -> hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v)),x))* hBOOL(hAPP(hAPP(c_in(w),hAPP(u,v)),hAPP(c_Set_Oimage(u,y,w),z)))* equal(x,hAPP(c_Set_Oimage(u,y,w),z)).
% 299.92/300.50 37696[0:Rew:9.0,37679.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Fun_Ocomp(c_Fun_Ocomp(x,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),v,y,w),c_Fun_Ofun__upd(u,z,x1,v,w),w,y,v),c_Fun_Ofun__upd(x,z,hAPP(x,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x1)),v,y))*.
% 299.92/300.50 38007[0:Res:83.0,441.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))**.
% 299.92/300.50 38492[0:Res:313.1,385.1] || c_lessequals(hAPP(c_Set_Oimage(u,v,v),w),w,tc_fun(v,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,v),w),v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(u,v,v),w),v,v) -> equal(hAPP(c_Set_Oimage(u,v,v),hAPP(c_Set_Oimage(u,v,v),w)),hAPP(c_Set_Oimage(u,v,v),w))**.
% 299.92/300.50 38487[0:Res:364.1,385.1] || c_lessequals(hAPP(c_Set_Oimage(u,v,v),hAPP(c_Set_Oinsert(w,v),x)),x,tc_fun(v,tc_bool))* c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(w,v),x),v) c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(w,v),x),v,v) -> equal(hAPP(c_Set_Oimage(u,v,v),hAPP(c_Set_Oinsert(w,v),x)),hAPP(c_Set_Oinsert(w,v),x)).
% 299.92/300.50 38650[0:SpL:24914.0,184.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),x))) c_Fun_Oinj__on(v,x,w,u) -> equal(hAPP(v,hAPP(c_Fun_Othe__inv__into(x,v,w,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x)))),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x)))**.
% 299.92/300.50 38976[0:SpR:354.2,205.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v,x,w,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),w,y),u),hAPP(c_Set_Oimage(x,w,y),u))**.
% 299.92/300.50 40925[0:Res:450.0,479.1] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(v),w,x,y))) -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(v)),x),w),t_a) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),w,x,y),z,u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),w,x,y)),z)))*.
% 299.92/300.50 41206[0:Res:450.0,478.1] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(v),w,x,y))) -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(v)),x),w),t_a) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),w,x,y),u,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),w,x,y))))*.
% 299.92/300.50 41318[0:SpL:537.1,275.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* hBOOL(hAPP(hAPP(c_in(y),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x2),w))))* -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x2)),v,tc_fun(y,tc_bool))))*.
% 299.92/300.50 41317[0:SpL:534.1,275.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x))* hBOOL(hAPP(hAPP(c_in(y),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x2),w))))* -> hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x2)),v,tc_fun(y,tc_bool))))*.
% 299.92/300.50 41316[0:SpL:536.1,275.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y))* hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x2),x))))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x2),v,tc_fun(z,tc_bool))))*.
% 299.92/300.50 41315[0:SpL:535.1,275.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y))* hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x2),x))))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x2),v,tc_fun(z,tc_bool))))*.
% 299.92/300.50 41554[0:SpL:131.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1)),hAPP(c_Set_Oimage(c_Set_Ovimage(w,z,x),x2,u),x3)))* c_Fun_Oinj__on(c_Set_Ovimage(w,z,x),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,u)* -> hBOOL(hAPP(hAPP(c_in(x2),hAPP(c_Set_Ovimage(v,x,y),x1)),x3)).
% 299.92/300.50 41552[0:SpL:158.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1)),hAPP(c_Set_Oimage(c_Set_Oimage(v,x,y),x2,u),x3)))* c_Fun_Oinj__on(c_Set_Oimage(v,x,y),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,u)* -> hBOOL(hAPP(hAPP(c_in(x2),hAPP(c_Set_Oimage(w,z,x),x1)),x3)).
% 299.92/300.50 41546[0:SpL:317.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(hAPP(v,w),x),hAPP(c_Set_Oimage(v,y,x),z))),hAPP(c_Set_Oimage(c_Set_Oimage(v,y,x),x1,u),x2)))* c_Fun_Oinj__on(c_Set_Oimage(v,y,x),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x1,u)* -> hBOOL(hAPP(hAPP(c_in(x1),hAPP(c_Set_Oinsert(w,y),z)),x2)).
% 299.92/300.50 41873[0:Rew:20446.2,41793.3] || c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) hBOOL(c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),x,y),v,u,w))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(v,z))*.
% 299.92/300.50 41874[0:Rew:20286.2,41792.3] || c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) hBOOL(c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),x,y),v,u,w))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(v,z))*.
% 299.92/300.50 42090[0:SpR:180.2,317.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y),hAPP(c_Set_Oinsert(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),z,v,u,u),x),x1)),hAPP(c_Set_Oinsert(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),z,hAPP(c_Set_Oinsert(w,u),v),u,u),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y),x1)))*.
% 299.92/300.50 43111[0:SpR:32668.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,x,tc_Com_Opname,y),hAPP(x,v_x)),tc_Com_Opname),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,x,tc_Com_Opname,y),hAPP(x,v_x)),tc_Com_Opname),u,tc_fun(w,tc_bool)))**.
% 299.92/300.50 43110[0:SpR:28910.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(x,y,z),x,tc_Com_Opname,x1),tc_Com_Opname),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(x,y,z),x,tc_Com_Opname,x1),tc_Com_Opname),u,tc_fun(w,tc_bool)))**.
% 299.92/300.50 43109[0:SpR:28926.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(w,tc_bool)))**.
% 299.92/300.50 43107[0:SpR:28755.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,x,c_COMBK(x,y,z),tc_Com_Opname,x1),tc_Com_Opname),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,x,c_COMBK(x,y,z),tc_Com_Opname,x1),tc_Com_Opname),u,tc_fun(w,tc_bool)))**.
% 299.92/300.50 43106[0:SpR:28771.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,x),tc_Com_Opname),u,tc_fun(w,tc_bool)))**.
% 299.92/300.50 43000[0:SpR:130.1,486.1] class_HOL_Ominus(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(y,v_x),hAPP(z,v_x),u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(y,z,tc_fun(t_a,u)),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_HOL_Ominus__class_Ominus(y,z,tc_fun(t_a,u)),v,tc_fun(x,tc_bool)))**.
% 299.92/300.50 42986[0:SpR:196.1,486.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w)* hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),z)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Ovimage(u,v,w),x,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Ovimage(u,v,w),x,tc_fun(x1,tc_bool)))**.
% 299.92/300.50 44138[0:SpR:465.1,232.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> hBOOL(hAPP(hAPP(c_in(x),v),z)) c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_HOL_Ouminus__class_Ouminus(z,tc_fun(x,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,x,y),z),tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.92/300.50 44312[0:Res:151.2,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(u),x),c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool))))* equal(hAPP(z,v),hAPP(z,x))* c_Fun_Oinj__on(z,c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool)),u,x1)* -> hBOOL(hAPP(hAPP(c_in(u),v),y))* equal(v,x).
% 299.92/300.50 44591[0:Rew:240.2,44585.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),tc_Com_Opname,y),hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),v_x)),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,v_x,w,u)))**.
% 299.92/300.50 44797[0:Res:31533.0,593.0] || c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x)))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))))),hAPP(v_Q,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x)))),t_a)*.
% 299.92/300.50 44796[0:Res:27443.0,593.0] || c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y))),t_a)*.
% 299.92/300.50 44795[0:Res:28312.0,593.0] || c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v))),t_a)*.
% 299.92/300.50 44793[0:Res:27383.0,593.0] || c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y))),t_a)*.
% 299.92/300.50 44792[0:Res:28009.0,593.0] || c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v))),t_a)*.
% 299.92/300.50 45591[0:SpR:323.0,584.0] || -> equal(hAPP(c_COMBS(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),y,z,x1,x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x3,w,x,tc_fun(u,tc_bool))),hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),x3),w,x,tc_fun(u,tc_bool)),hAPP(y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x3,w,x,tc_fun(u,tc_bool)))))*.
% 299.92/300.50 45590[0:SpR:323.0,584.0] || -> equal(hAPP(c_COMBS(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,y,tc_fun(v,tc_bool))),z,x1,x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x3,x,y,tc_fun(v,tc_bool))),hAPP(hAPP(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x3,x,y,tc_fun(v,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),w),x3),x,y,tc_fun(v,tc_bool))))*.
% 299.92/300.50 45539[0:SpR:323.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),z)) -> hBOOL(hAPP(hAPP(c_in(x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x2),v),w,x,tc_fun(y,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,w,x,tc_fun(y,tc_bool))),u,x1),z)))*.
% 299.92/300.50 45535[0:SpR:323.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),z)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),v),w,x,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(y,tc_bool))),u,tc_fun(x2,tc_bool)),tc_fun(x2,tc_bool))*.
% 299.92/300.50 45854[0:SpL:161.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),u,x)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ominus__class_Ominus(y,w,tc_fun(x,tc_bool)),u,x)))* hBOOL(hAPP(hAPP(c_in(x),z),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),y),w,tc_fun(x,tc_bool))))* -> hBOOL(hAPP(u,z))*.
% 299.92/300.50 45853[0:SpL:162.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Ovimage(v,w,x),y),u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Ovimage(v,w,x),z),u,w)))* hBOOL(hAPP(hAPP(c_in(w),x1),hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))))* -> hBOOL(hAPP(u,x1))*.
% 299.92/300.50 45852[0:SpL:507.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oimage(v,w,x),y),u,x)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oimage(v,w,x),z),u,x)))* hBOOL(hAPP(hAPP(c_in(x),x1),hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(u,x1))*.
% 299.92/300.50 46187[0:Res:687.1,481.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,hAPP(c_in(u),v),tc_Com_Opname)),y),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,v_Procs,hAPP(c_in(u),v),tc_Com_Opname)),y)))*.
% 299.92/300.50 46186[0:Res:686.1,481.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,hAPP(c_in(u),v),tc_Com_Opname)),y),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,x,hAPP(c_in(u),v),tc_Com_Opname)),y)))*.
% 299.92/300.50 46207[0:Rew:533.0,46136.2] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z)),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z))))*.
% 299.92/300.50 46505[0:Res:687.1,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,v_Procs,hAPP(c_in(u),v),tc_Com_Opname)),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,v_Procs,hAPP(c_in(u),v),tc_Com_Opname))))*.
% 299.92/300.50 46504[0:Res:686.1,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,y,hAPP(c_in(u),v),tc_Com_Opname)),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,y,hAPP(c_in(u),v),tc_Com_Opname))))*.
% 299.92/300.50 46454[0:Res:511.1,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),w)),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),w))))*.
% 299.92/300.50 46591[0:SpL:617.1,375.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oimage(w,x,tc_fun(u,tc_bool)),y)))* c_lessequals(hAPP(c_Set_Oinsert(z,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,x,tc_fun(u,tc_bool))),x1,tc_fun(u,tc_bool))* -> equal(y,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) c_lessequals(hAPP(c_Set_Oinsert(z,u),v),x1,tc_fun(u,tc_bool))*.
% 299.92/300.50 47371[0:SpL:410.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,y),z),x1,y,tc_fun(w,tc_bool))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x1,y,tc_fun(w,tc_bool)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(x1,x),u,w)),hAPP(x1,x)))*.
% 299.92/300.50 47940[0:SpL:410.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool)),u,y)))* hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x1,x),v),w,x,tc_fun(y,tc_bool))))* -> hBOOL(hAPP(u,z))* hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(w,x1),u,y)),hAPP(w,x1)))*.
% 299.92/300.50 48431[0:SpL:105.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(w,v,x),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(c_Set_Ovimage(w,v,x),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y),z),y,u) -> .
% 299.92/300.50 48423[0:SpL:38.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(w,v,x),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(c_Set_Ovimage(w,v,x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y),z),y,u) -> .
% 299.92/300.50 48422[0:SpL:321.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oimage(w,x,v),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oimage(w,x,v),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),y),z),y,u) -> .
% 299.92/300.50 48416[0:SpL:14216.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(x1,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(c_Set_Oinsert(x1,y),z),y,u) -> .
% 299.92/300.50 48414[0:SpL:584.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_COMBS(v,w,x,y,z),x1)),hAPP(c_Set_Oimage(hAPP(v,x1),x2,u),c_HOL_Ominus__class_Ominus(x3,hAPP(c_Set_Oinsert(hAPP(w,x1),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))),tc_fun(x2,tc_bool)))))* c_Fun_Oinj__on(hAPP(v,x1),hAPP(c_Set_Oinsert(hAPP(w,x1),x2),x3),x2,u) -> .
% 299.92/300.50 48342[0:SpL:25.1,224.0] class_HOL_Ouminus(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ouminus__class_Ouminus(hAPP(w,v_x),u)),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u)),x,v),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v_x,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(w,tc_fun(t_a,u)),hAPP(c_Set_Oinsert(v_x,x),y),x,v) -> .
% 299.92/300.50 48322[0:SpL:653.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,v),v,tc_Com_Opname),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,v),v,tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,w),x),w,u) -> .
% 299.92/300.50 48319[0:SpL:445.1,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(v,x,y,z,x1),x2,u),c_HOL_Ominus__class_Ominus(x3,hAPP(c_Set_Oinsert(w,x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))),tc_fun(x2,tc_bool)))))* c_Fun_Oinj__on(c_Fun_Ofun__upd(v,x,y,z,x1),hAPP(c_Set_Oinsert(w,x2),x3),x2,u) -> equal(w,x).
% 299.92/300.50 48839[0:Res:45357.1,619.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,u,tc_fun(x,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname)),c_Set_Oinsert(y,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,hAPP(c_in(u),v),tc_Com_Opname),w,u,tc_fun(x,tc_bool))))**.
% 299.92/300.50 48797[0:Res:153.1,619.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),x))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(y,z,tc_fun(x1,tc_bool)),hAPP(c_Set_Ovimage(v,z,u),x)),c_Set_Oinsert(x2,x1),tc_fun(x1,tc_bool),tc_fun(x1,tc_bool)),hAPP(c_Set_Oinsert(x2,x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Ovimage(v,z,u),x),y,z,tc_fun(x1,tc_bool))))**.
% 299.92/300.50 48983[0:Res:168.0,483.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w),t_a) hBOOL(hAPP(x,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v),w))))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,tc_Hoare__Mirabelle_Otriple(t_a))),v))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,tc_Hoare__Mirabelle_Otriple(t_a))),w))*.
% 299.92/300.50 49292[0:SpL:24914.0,488.1] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(v),tc_Com_Opname,w),hAPP(c_in(v),v_x))))* hBOOL(hAPP(hAPP(c_in(v),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)))* -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)),x))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,v)),y))*.
% 299.92/300.50 49263[0:SpL:104.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool)),u,w)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)),y))*.
% 299.92/300.50 49257[0:SpL:600.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)),y)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),u,w)),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool))))*.
% 299.92/300.50 49440[0:SpL:49342.1,224.0] || hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(v),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,w),x),w,v) -> .
% 299.92/300.50 49734[0:Rew:49662.2,49619.2] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w,x) -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(x),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),v))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,w),v),w,x).
% 299.92/300.50 49735[0:Rew:49662.2,49598.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),z,x1,x2) -> hBOOL(hAPP(hAPP(c_in(x2),hAPP(u,hAPP(v,x3))),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),x1,x2),hAPP(c_Set_Oinsert(x3,x1),z))))* c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),hAPP(c_Set_Oinsert(x3,x1),z),x1,x2).
% 299.92/300.50 49736[0:Rew:49662.2,49535.2] class_Lattices_Oboolean__algebra(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),x,y),hAPP(c_Set_Oinsert(v,x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ouminus__class_Ouminus(v,u)),hAPP(c_Set_Oinsert(v,x),w),x,y).
% 299.92/300.50 49737[0:Rew:49662.2,49520.2] || c_Fun_Oinj__on(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),w,x,y) -> c_Hoare__Mirabelle_Ohoare__valids(u,v,t_a) hBOOL(hAPP(hAPP(c_in(y),v),hAPP(c_Set_Oimage(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),x,y),hAPP(c_Set_Oinsert(v,x),w))))* c_Fun_Oinj__on(c_Set_Oinsert(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(u,v),tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(v,x),w),x,y).
% 299.92/300.50 49738[0:Rew:49662.2,49501.2] class_HOL_Ouminus(u) || c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),c_HOL_Ouminus__class_Ouminus(hAPP(v,v_x),u)),hAPP(c_Set_Oimage(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),x,y),hAPP(c_Set_Oinsert(v_x,x),w))))* c_Fun_Oinj__on(c_HOL_Ouminus__class_Ouminus(v,tc_fun(t_a,u)),hAPP(c_Set_Oinsert(v_x,x),w),x,y).
% 299.92/300.50 50044[0:SpL:497.0,3507.1] || equal(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)))* equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),x)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.92/300.50 50043[0:SpL:497.0,16327.1] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)))* equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_Procs) -> .
% 299.92/300.50 50042[7:SpL:497.0,31886.1] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)))* equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_x) -> .
% 299.92/300.50 50041[0:SpL:497.0,3499.1] || equal(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)))* hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.92/300.50 50038[0:SpL:497.0,24254.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.92/300.50 50033[0:SpL:497.0,13272.0] || equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.92/300.50 50032[0:SpL:497.0,3484.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Com_Ocom_OBODY)** equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(c_Com_Ocom_OBODY,w))* -> equal(v_x,w).
% 299.92/300.50 50006[0:SpR:8415.2,497.0] || equal(v_Procs,v_x) equal(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),c_Set_Oinsert(v_x,tc_Com_Opname)) -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v_x),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),v_x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v_x),u)))**.
% 299.92/300.50 49992[0:SpR:497.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),w,x),hAPP(c_Set_Oinsert(v_x,w),y)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))))*.
% 299.92/300.50 49977[0:SpR:497.0,9569.0] || -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v))),v_x),tc_bool)*.
% 299.92/300.50 49976[0:SpR:497.0,9568.0] || -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v))),x),v_x),tc_bool)*.
% 299.92/300.50 49972[0:SpR:497.0,3346.1] || equal(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),x))))*.
% 299.92/300.50 49971[0:SpR:497.0,28356.1] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),tc_Com_Opname,x)))*.
% 299.92/300.50 49970[0:SpR:497.0,28053.1] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),u,tc_Com_Opname,x)))*.
% 299.92/300.50 49969[0:SpR:497.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),tc_Com_Opname,x)))*.
% 299.92/300.50 49968[0:SpR:497.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),tc_Com_Opname,x)))*.
% 299.92/300.50 49967[0:SpR:497.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),tc_Com_Opname,x),u),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w))))*.
% 299.92/300.50 49966[0:SpR:497.0,3317.1] || equal(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)))* -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),hAPP(c_Set_Oinsert(v_x,u),x)))*.
% 299.92/300.50 49965[0:SpR:497.0,3305.1] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x),v_Procs),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w))))*.
% 299.92/300.50 49961[0:SpR:497.0,2771.1] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)))* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.92/300.50 49955[0:SpR:497.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_Com_Opname,w),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.92/300.50 49953[0:SpR:497.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_Com_Opname,w),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)))),v_Procs))*.
% 299.92/300.50 49946[0:SpR:497.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))))*.
% 299.92/300.50 49945[0:SpR:497.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))))*.
% 299.92/300.50 49939[0:SpR:497.0,15262.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))).
% 299.92/300.50 49936[0:SpR:497.0,8376.2] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_in(tc_Com_Opname))** equal(w,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),w))*.
% 299.92/300.50 49934[0:SpR:497.0,8415.2] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),v_x).
% 299.92/300.50 49933[4:SpR:497.0,39064.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))),y,t_a)*.
% 299.92/300.50 49932[4:SpR:497.0,39023.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))),y))*.
% 299.92/300.50 49931[0:SpR:497.0,3291.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))),v_Procs))*.
% 299.92/300.50 49930[0:SpR:497.0,3285.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.92/300.50 49926[0:SpR:497.0,3279.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),v_Procs),v_x)).
% 299.92/300.50 50444[0:SpR:223.1,20881.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Set_Oinsert(x,y),z,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x2,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),z),x3)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x2,v,x,u,y),u,y),w)))*.
% 299.92/300.50 50433[0:SpR:223.1,254.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(z,u,x),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))))* -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,x1,u,x),u,x),w)))*.
% 299.92/300.50 50409[0:SpR:223.1,9569.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),x2),c_Set_Oinsert(y,z)),hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),tc_bool)*.
% 299.92/300.50 50408[0:SpR:223.1,9568.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Set_Oinsert(y,z)),x2),hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),tc_bool)*.
% 299.92/300.50 50852[0:SpL:622.0,16217.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_Procs)** -> .
% 299.92/300.50 50851[7:SpL:622.0,31778.0] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),tc_bool),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_x)** -> .
% 299.92/300.50 50850[0:SpL:622.0,3929.0] || hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool)))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.92/300.50 50841[0:SpR:622.0,9567.0] || -> c_lessequals(hAPP(c_HOL_Ominus__class_Ominus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),w,tc_fun(x,tc_bool)),v_x),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),tc_bool)*.
% 299.92/300.50 50811[0:SpR:622.0,683.1] class_Complete__Lattice_Ocomplete__lattice(u) || -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,tc_fun(t_a,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,u),u)*.
% 299.92/300.50 50809[4:SpR:622.0,38236.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),tc_Com_Opname,tc_bool)).
% 299.92/300.50 50804[0:SpR:622.0,23902.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)),v_x).
% 299.92/300.50 54846[0:SpL:13749.2,224.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),y),x,v) -> .
% 299.92/300.50 55321[0:SpL:14043.2,224.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,v),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x),y),x,v) -> .
% 299.92/300.50 56360[0:SpL:30368.2,224.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oinsert(y,w),x),w,v) -> .
% 299.92/300.50 56802[0:SpL:30928.2,224.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oinsert(y,w),x),w,v) -> .
% 299.92/300.50 57943[0:SpL:497.0,55910.1] || equal(c_COMBK(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),y)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),x),y))) -> .
% 299.92/300.50 58100[0:SpL:497.0,55992.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool),w) -> .
% 299.92/300.50 58447[0:SpL:622.0,58248.0] || equal(c_COMBK(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),w,x),c_HOL_Ouminus__class_Ouminus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_fun(t_a,tc_bool)))* -> .
% 299.92/300.50 60212[0:SpL:497.0,58170.1] || equal(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),tc_bool),x,y),u)* -> .
% 299.92/300.50 60442[7:Res:58968.1,479.1] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(u),v),x),z,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(u),v),x)),z)))*.
% 299.92/300.50 60441[7:Res:58968.1,478.1] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y))))*.
% 299.92/300.50 60555[0:Res:58969.1,479.1] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(u),v),x),z,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(u),v),x)),z)))*.
% 299.92/300.50 60554[0:Res:58969.1,478.1] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y))))*.
% 299.92/300.50 60628[7:Res:59476.1,479.1] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),y),z,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),y)),z)))*.
% 299.92/300.50 60627[7:Res:59476.1,478.1] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z))))*.
% 299.92/300.50 60701[0:Res:59477.1,479.1] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),y),z,w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),y)),z)))*.
% 299.92/300.50 60700[0:Res:59477.1,478.1] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(w,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z))))*.
% 299.92/300.50 60886[0:Res:59017.1,479.1] || hBOOL(hAPP(u,v)) -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(x),v),t_a)* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(x),v),y),x1,u,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(x),v),y)),x1)))*.
% 299.92/300.50 60885[0:Res:59017.1,478.1] || hBOOL(hAPP(u,v)) -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(x),v),t_a)* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_in(x),v),z),u,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_in(x),v),z))))*.
% 299.92/300.50 60959[0:Res:59525.1,479.1] || hBOOL(hAPP(u,v)) -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(x),v),t_a)* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(x),v),z),x1,u,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(x),v),z)),x1)))*.
% 299.92/300.50 60958[0:Res:59525.1,478.1] || hBOOL(hAPP(u,v)) -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_in(x),v),t_a)* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_in(x),v),x1),u,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_in(x),v),x1))))*.
% 299.92/300.50 63792[0:SSi:63620.1,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || equal(v,w)* c_lessequals(x,w,tc_fun(u,tc_bool))* c_Fun_Oinj__on(y,w,u,z)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(y,u,z),v),hAPP(c_Set_Oimage(y,u,z),x),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool))))**.
% 299.92/300.50 64591[0:SpR:26782.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),x,tc_fun(y,tc_bool)),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),x,tc_fun(y,tc_bool)),u,tc_fun(w,tc_bool)))**.
% 299.92/300.50 76152[0:SpR:9915.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Set_Ovimage(y,z,v),x1,x2,x3,x4),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Set_Ovimage(y,z,v),x1,x2,x3,x4),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 76272[0:SpR:10469.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Set_Oimage(y,v,z),x1,x2,x3,x4),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Set_Oimage(y,v,z),x1,x2,x3,x4),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 76402[0:SpR:10470.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Set_Ovimage(y,z,v),x1,x2,x3,x4),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_Set_Ovimage(y,z,v),x1,x2,x3,x4),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 77381[0:Res:2399.2,471.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(y,v,u),x),tc_fun(u,tc_bool)) hBOOL(hAPP(hAPP(c_in(u),hAPP(y,w)),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(y,v,u),x),tc_fun(u,tc_bool))))*.
% 299.92/300.50 79039[0:Res:15630.1,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(x,y),z),x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),y)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(x,y),z),x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),y)))*.
% 299.92/300.50 79259[0:Res:15858.1,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(x,z),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),z)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(x,z),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),z)))*.
% 299.92/300.50 80194[0:SpL:21268.0,447.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w) c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),x),y,z),v,w)* -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),x),y,z),v).
% 299.92/300.50 79777[0:SpR:21268.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_COMBB(v,w,tc_fun(x,tc_bool),y),hAPP(c_COMBB(v,w,tc_fun(x,tc_bool),y),z),u,x1),y,w),x2),v,w,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,hAPP(c_COMBB(v,w,tc_fun(x,tc_bool),y),z),y,tc_fun(x,tc_bool)))**.
% 299.92/300.50 79546[0:SpR:21268.0,98.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(u,w,x),y),v,z),w,x)* -> equal(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(u,w,x),y),v,z),w),c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,w,x),y),x)).
% 299.92/300.50 81389[0:SpL:21894.0,447.0] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w) c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x),c_Set_Oimage(u,v,w),y,z),v,w)* -> c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x),c_Set_Oimage(u,v,w),y,z),v).
% 299.92/300.50 80971[0:SpR:21894.0,89.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_COMBB(v,w,tc_fun(x,tc_bool),y),z),c_COMBB(v,w,tc_fun(x,tc_bool),y),u,x1),y,w),x2),v,w,tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,hAPP(c_COMBB(v,w,tc_fun(x,tc_bool),y),z),y,tc_fun(x,tc_bool)))**.
% 299.92/300.50 80739[0:SpR:21894.0,98.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(u,w,x),y),c_Set_Oimage(u,w,x),v,z),w,x)* -> equal(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(u,w,x),y),c_Set_Oimage(u,w,x),v,z),w),c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,w,x),y),x)).
% 299.92/300.50 81760[0:MRR:51709.0,81757.2] || c_Finite__Set_Ofinite(u,v) c_lessequals(hAPP(c_Set_Oimage(w,v,x),u),hAPP(c_Set_Ovimage(y,x,v),u),tc_fun(x,tc_bool))* c_Fun_Oinj__on(y,hAPP(c_Set_Ovimage(y,x,v),u),x,v)* c_Fun_Oinj__on(w,u,v,x) -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Ovimage(y,x,v),u),x),c_Finite__Set_Ocard(u,v)).
% 299.92/300.50 83044[0:SpR:5924.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(y,v),z)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(y,c_COMBK(z,x1,x2),x3,x4,x5),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(y,c_COMBK(z,x1,x2),x3,x4,x5),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 83371[0:SpR:5961.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,hAPP(z,v))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_COMBK(y,x1,x2),z,x3,x4,x5),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_COMBS(c_COMBK(y,x1,x2),z,x3,x4,x5),u,tc_fun(x,tc_bool)))**.
% 299.92/300.50 85819[0:Res:9066.0,480.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),hAPP(c_Set_Oinsert(v,w),z))),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),hAPP(c_Set_Oinsert(v,w),z)))))*.
% 299.92/300.50 87284[7:SpR:622.0,71492.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))),w))*.
% 299.92/300.50 87432[7:SpR:622.0,71493.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_x)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))),w,t_a)*.
% 299.92/300.50 87562[7:SpR:622.0,71679.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))))*.
% 299.92/300.50 88303[0:Res:7227.0,481.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_COMBK(v,x,y),z,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))),x1),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_COMBK(v,x,y),z,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)))),x1)))*.
% 299.92/300.50 88302[0:Res:7227.0,480.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(c_COMBK(v,y,z),x1,w),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)))),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(c_COMBK(v,y,z),x1,w),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))))))*.
% 299.92/300.50 91831[4:SpL:465.1,78747.0] || equal(hAPP(c_Set_Oimage(u,v,w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),tc_Com_Opname)),v_x)** -> hBOOL(hAPP(hAPP(c_in(v),x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),tc_Com_Opname)))* hBOOL(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,x,y,v,w),v,w),v_x)).
% 299.92/300.50 92608[7:SpR:622.0,82151.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),c_Set_Oinsert(v_x,w)))*.
% 299.92/300.50 93268[4:SpR:622.0,85556.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_lessequals(v_x,hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),w),tc_bool)*.
% 299.92/300.50 93456[0:SpR:622.0,86147.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))),w))*.
% 299.92/300.50 93607[0:SpR:622.0,86148.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_Procs)** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))),w,t_a)*.
% 299.92/300.50 93751[0:SpR:622.0,86342.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))))*.
% 299.92/300.50 21664[0:SpL:21267.0,327.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)) -> c_lessequals(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),tc_Com_Opname,w),tc_fun(u,tc_bool))*.
% 299.92/300.50 21468[0:SpR:21267.0,329.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x),tc_Com_Opname,w),tc_fun(v,tc_bool))* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)).
% 299.92/300.50 22292[0:SpL:21893.0,327.0] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)) -> c_lessequals(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),tc_fun(u,tc_bool))*.
% 299.92/300.50 22094[0:SpR:21893.0,329.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),tc_fun(v,tc_bool))* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)).
% 299.92/300.50 26100[0:SpR:338.0,246.2] || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) -> hBOOL(hAPP(hAPP(c_in(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w))) equal(c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(x,u),w)),u),c_Suc(c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))**.
% 299.92/300.50 27200[0:Res:450.0,519.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w)),x),y),t_a) hBOOL(hAPP(w,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y,x,u))) hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y,x,u),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y,x,u)))*.
% 299.92/300.50 27372[0:SpL:21893.0,470.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,x,u),v_x),c_Set_Oimage(w,x,u),tc_Com_Opname,y),v,w,x,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,x,u),v_x),c_Set_Oimage(w,x,u),tc_Com_Opname,y)))*.
% 299.92/300.50 27371[0:SpL:21267.0,470.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),v_x),tc_Com_Opname,y),v,w,x,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),v_x),tc_Com_Opname,y)))*.
% 299.92/300.50 27432[0:SpL:21893.0,466.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,x,u),v_x),c_Set_Oimage(w,x,u),tc_Com_Opname,y),w,v,x,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,x,u),v_x),c_Set_Oimage(w,x,u),tc_Com_Opname,y)))*.
% 299.92/300.50 27431[0:SpL:21267.0,466.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),v_x),tc_Com_Opname,y),w,v,x,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),v_x),tc_Com_Opname,y)))*.
% 299.92/300.50 28200[0:SpR:465.1,687.1] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_x)) -> hBOOL(hAPP(hAPP(c_in(x),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),tc_Com_Opname)))* hBOOL(hAPP(c_Set_Oimage(u,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),tc_Com_Opname)))*.
% 299.92/300.50 28199[0:SpR:465.1,686.1] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_x)) -> hBOOL(hAPP(hAPP(c_in(x),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,z,c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),tc_Com_Opname)))* hBOOL(hAPP(c_Set_Oimage(u,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,z,c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),tc_Com_Opname)))*.
% 299.92/300.50 28184[0:SpR:465.1,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ofun__upd(x,y,z,x1,x2),x1,x2),w,u,x3) -> hBOOL(hAPP(hAPP(c_in(x1),y),v)) equal(hAPP(c_Fun_Othe__inv__into(w,c_Set_Oimage(c_Fun_Ofun__upd(x,y,z,x1,x2),x1,x2),u,x3),hAPP(c_Set_Oimage(x,x1,x2),v)),v)**.
% 299.92/300.50 28183[0:SpR:465.1,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ofun__upd(x,y,z,x1,x2),x1,x2),w,u,x3) -> hBOOL(hAPP(hAPP(c_in(x1),y),v)) equal(hAPP(c_Hilbert__Choice_Oinv__into(w,c_Set_Oimage(c_Fun_Ofun__upd(x,y,z,x1,x2),x1,x2),u,x3),hAPP(c_Set_Oimage(x,x1,x2),v)),v)**.
% 299.92/300.50 28495[0:SpR:465.1,118.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_Fun_Ocomp(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),c_Fun_Ofun__upd(x1,x2,w,x3,x4),x4,x5,x3),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1,x4,x5,x3),x2,hAPP(c_Set_Oimage(x,u,z),w),x3,x5))*.
% 299.92/300.50 32369[0:SpL:131.0,477.0] || hBOOL(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),x2),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z))))* hBOOL(hAPP(hAPP(c_in(z),x3),x1))* -> hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x3))*.
% 299.92/300.50 32368[0:SpL:158.0,477.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),x2),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z))))* hBOOL(hAPP(hAPP(c_in(z),x3),x1))* -> hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x3))*.
% 299.92/300.50 32549[0:SpL:131.0,476.0] || hBOOL(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),x2),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z))))* hBOOL(hAPP(hAPP(c_in(z),x3),x2))* -> hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x3))*.
% 299.92/300.50 32548[0:SpL:158.0,476.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),x2),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z))))* hBOOL(hAPP(hAPP(c_in(z),x3),x2))* -> hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x3))*.
% 299.92/300.50 33019[0:SpR:131.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(x,y,z),hAPP(c_Set_Ovimage(x1,z,x2),v)),x3),hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(x1,x,z,x2,y),y,x2),u,x3),w)),hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(x1,x,z,x2,y),y,x2),u,x3),w))**.
% 299.92/300.50 33018[0:SpR:158.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,y,z),hAPP(c_Set_Oimage(x1,x2,y),v)),x3),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(x,x1,y,z,x2),x2,z),u,x3),w)),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(x,x1,y,z,x2),x2,z),u,x3),w))**.
% 299.92/300.50 32961[0:SpR:523.1,475.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(x,v_x)),hAPP(y,v_x)),z),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),x),y),v,z),w)),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),x),y),v,z),w))**.
% 299.92/300.50 32960[0:SpR:460.1,475.1] || class_Lattices_Olattice(t_b) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x)),w),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,w),v)),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,w),v))**.
% 299.92/300.50 32858[0:SpR:475.1,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),w)),x1)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(y,u,z),w),x2),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(y,v),z),x,x2),x1)),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(y,v),z),x,x2),x1))**.
% 299.92/300.50 34378[0:SpL:24914.0,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname,v),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)),w,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname,v),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)),w),u,t_a)*.
% 299.92/300.50 34539[0:Rew:339.0,34236.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),tc_Com_Opname,x),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x))))),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)))**.
% 299.92/300.50 33954[0:SpR:24914.0,445.1] || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname,z),hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v_x)),v) equal(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ofun__upd(u,v,w,x,y),tc_Com_Opname,z),hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v_x))),hAPP(c_Fun_Ofun__upd(u,v,w,x,y),v_x))**.
% 299.92/300.50 35400[0:SpR:55.1,410.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),y),z),c_Set_Oinsert(v,u),y,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oinsert(v,u),y,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 35353[0:SpR:338.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(u,v),w),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),x,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),w))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),x,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 35298[0:SpR:97.1,410.0] || c_Fun_Oinj__on(u,v,w,x) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,w,x),v),y),z),c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 35297[0:SpR:99.1,410.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(u,x),y),z),c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),y,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),y,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 35296[0:SpR:438.1,410.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(u,x),y),z),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),y,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),y,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 35283[0:SpR:393.1,410.0] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,w),x),c_Set_Oimage(c_COMBK(y,z,v),v,z),w,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oimage(c_COMBK(y,z,v),v,z),w,tc_fun(x1,tc_bool))))*.
% 299.92/300.50 35221[0:SpR:410.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),x,y),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,v,x1,tc_fun(u,tc_bool)),x),x2)),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x1),z),v,x1,tc_fun(u,tc_bool)),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),x,y),x2)))*.
% 299.92/300.50 36852[0:SpR:66.0,55.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),c_HOL_Ominus__class_Ominus(x,y,tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(w,u),y),tc_fun(u,tc_bool))))**.
% 299.92/300.50 37323[0:SpL:21893.0,274.0] || equal(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(u,v),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(v),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,x)))* equal(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,x))*.
% 299.92/300.50 37322[0:SpL:21267.0,274.0] || equal(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(u,v),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(v),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,x)))* equal(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,x))*.
% 299.92/300.50 37306[0:SpL:55.1,274.0] || equal(hAPP(c_Set_Oinsert(u,v),w),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),x),y,tc_fun(v,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(v),u),y)) hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(v),u),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))))* equal(w,c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))).
% 299.92/300.50 38314[0:Res:201.3,251.1] class_Lattices_Oupper__semilattice(tc_fun(u,v)) class_HOL_Oord(v) || hBOOL(hAPP(hAPP(c_in(tc_fun(u,v)),w),x)) c_Finite__Set_Ofinite(x,tc_fun(u,v)) -> c_lessequals(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),w),y),z),hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,v)),y,x,tc_fun(u,v),tc_fun(u,v)),z),v)*.
% 299.92/300.50 38425[0:SSi:38391.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(c_Set_Oimage(u,v,w),z)) c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z)),v,w)* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y),z).
% 299.92/300.50 38426[0:SSi:38389.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z))) c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z)),v,w)* -> equal(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z)).
% 299.92/300.50 40894[0:Res:176.0,479.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Ovimage(x,w,y),hAPP(c_Set_Oinsert(hAPP(x,v),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),z,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(x,w,y),hAPP(c_Set_Oinsert(hAPP(x,v),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))),z)))*.
% 299.92/300.50 41175[0:Res:176.0,478.1] || hBOOL(hAPP(u,v)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Set_Ovimage(y,w,z),hAPP(c_Set_Oinsert(hAPP(y,v),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Ovimage(y,w,z),hAPP(c_Set_Oinsert(hAPP(y,v),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))))))*.
% 299.92/300.50 41376[0:SpL:475.1,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),w)),x1))* hBOOL(hAPP(hAPP(c_in(x2),x3),hAPP(c_Set_Oimage(y,u,z),w)))* -> hBOOL(hAPP(hAPP(c_in(x2),x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oinsert(hAPP(y,v),z),x,tc_fun(x2,tc_bool))))*.
% 299.92/300.50 41659[0:SpL:317.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(y,w),z))),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(v,y),x),x1,u),x2)))* c_Fun_Oinj__on(c_Set_Oinsert(hAPP(v,y),x),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x1,u)* -> hBOOL(hAPP(hAPP(c_in(x1),hAPP(c_Set_Oimage(v,w,x),z)),x2)).
% 299.92/300.50 41585[0:SpL:181.1,284.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(w,x,v),v,x),y,u),z)))* c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(w,x,v),v,x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,u)* -> hBOOL(hAPP(hAPP(c_in(x),w),x1))* hBOOL(hAPP(hAPP(c_in(y),x1),z))*.
% 299.92/300.50 41804[0:SpL:181.1,199.0] || hBOOL(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> hBOOL(hAPP(hAPP(c_in(y),z),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Ovimage(c_COMBK(z,y,u),u,y),v,w,x))))* hBOOL(hAPP(c_Set_Ovimage(c_COMBK(z,y,u),u,y),x1))*.
% 299.92/300.50 42269[0:SSi:42111.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(hAPP(c_in(v),w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(v),w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,hAPP(c_Set_Oinsert(y,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool))))*.
% 299.92/300.50 42503[0:SpL:586.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_COMBB(w,x,y,z),x1),x2,x3)),hAPP(w,hAPP(x1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_COMBB(w,x,y,z),x1),x2,x3))))* -> equal(hAPP(c_Set_Oimage(u,x2,x3),v),hAPP(c_Set_Oimage(hAPP(c_COMBB(w,x,y,z),x1),x2,x3),v)).
% 299.92/300.50 42502[0:SpL:585.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_COMBC(w,x,y,z),x1),x2,x3)),hAPP(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_COMBC(w,x,y,z),x1),x2,x3)),x1))* -> equal(hAPP(c_Set_Oimage(u,x2,x3),v),hAPP(c_Set_Oimage(hAPP(c_COMBC(w,x,y,z),x1),x2,x3),v)).
% 299.92/300.50 42495[0:SpL:11177.1,315.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,y),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,y)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,y))** -> equal(hAPP(c_Set_Oimage(v,x,y),u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w),x,y),u)).
% 299.92/300.50 42491[0:SpL:328.1,315.0] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y,z),x,tc_fun(w,tc_bool))* equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y,z)),x)** -> equal(hAPP(c_Set_Oimage(v,y,z),u),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y,z),u)).
% 299.92/300.50 42462[0:SpL:586.0,315.0] || equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,hAPP(c_COMBB(u,x,y,z),v),x1,x2,x3))),hAPP(x1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,hAPP(c_COMBB(u,x,y,z),v),x1,x2,x3)))* -> equal(hAPP(c_Set_Oimage(hAPP(c_COMBB(u,x,y,z),v),x2,x3),w),hAPP(c_Set_Oimage(x1,x2,x3),w)).
% 299.92/300.50 42461[0:SpL:585.0,315.0] || equal(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_COMBC(u,w,x,y),z),x1,x2,x3)),z),hAPP(x1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_COMBC(u,w,x,y),z),x1,x2,x3)))* -> equal(hAPP(c_Set_Oimage(hAPP(c_COMBC(u,w,x,y),z),x2,x3),v),hAPP(c_Set_Oimage(x1,x2,x3),v)).
% 299.92/300.50 42454[0:SpL:11177.1,315.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x,y),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x,y)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x,y))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),x,y),u),hAPP(c_Set_Oimage(w,x,y),u)).
% 299.92/300.50 42450[0:SpL:328.1,315.0] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y,z),w,tc_fun(v,tc_bool))* equal(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y,z)),w)** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y,z),u),hAPP(c_Set_Oimage(x,y,z),u)).
% 299.92/300.50 42720[0:SpR:35.2,161.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(v,x,tc_fun(w,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),c_HOL_Ominus__class_Ominus(y,c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)))*.
% 299.92/300.50 42776[0:Rew:538.0,42705.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(v,x,tc_fun(w,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),c_HOL_Ominus__class_Ominus(y,c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v),c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)))*.
% 299.92/300.50 42778[0:Rew:42777.1,42660.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),x,y),c_HOL_Ominus__class_Ominus(z,w,tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(z,w,tc_fun(u,tc_bool)))**.
% 299.92/300.50 42993[0:SpR:131.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),z)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,x2,w,x,x3),x3,x),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Ovimage(x2,x3,w),u,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Ovimage(x2,x3,w),u,tc_fun(x1,tc_bool)))**.
% 299.92/300.50 42991[0:SpR:158.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ocomp(x2,v,x,x3,w),w,x3),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(x2,x,x3),u,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(x2,x,x3),u,tc_fun(x1,tc_bool)))**.
% 299.92/300.50 42985[0:SpR:317.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(hAPP(x1,v),x2),hAPP(c_Set_Oimage(x1,w,x2),x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oimage(x1,w,x2),u,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oimage(x1,w,x2),u,tc_fun(z,tc_bool)))**.
% 299.92/300.50 43594[0:Rew:43593.1,43478.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,z) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),y,z),hAPP(c_Set_Oimage(v,w,u),x1)),hAPP(c_Set_Oimage(v,w,u),x1))**.
% 299.92/300.50 43822[0:Rew:43821.1,43700.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,z) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),y,z),hAPP(c_Set_Ovimage(v,u,w),x1)),hAPP(c_Set_Ovimage(v,u,w),x1))**.
% 299.92/300.50 43964[0:Res:340.2,231.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) c_lessequals(z,hAPP(c_Set_Oimage(v,w,x),y),tc_fun(x,tc_bool)) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> c_lessequals(hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),z)),y,tc_fun(w,tc_bool))*.
% 299.92/300.50 44280[0:SpL:21893.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v))* hBOOL(hAPP(hAPP(c_in(u),w),v))* equal(hAPP(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y)),hAPP(x,w))* c_Fun_Oinj__on(x,v,u,z)* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,y),w).
% 299.92/300.50 44279[0:SpL:21267.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v))* hBOOL(hAPP(hAPP(c_in(u),w),v))* equal(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y)),hAPP(x,w))* c_Fun_Oinj__on(x,v,u,z)* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,y),w).
% 299.92/300.50 45117[0:SpR:21893.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),tc_Com_Opname,x),y,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),tc_fun(w,tc_bool))*.
% 299.92/300.50 45116[0:SpR:21267.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v_x),tc_Com_Opname,x),y,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),tc_fun(w,tc_bool))*.
% 299.92/300.50 45052[0:SpR:21893.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),tc_Com_Opname,y),tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),tc_fun(w,tc_bool))*.
% 299.92/300.50 45051[0:SpR:21267.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),tc_Com_Opname,y),tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),tc_fun(w,tc_bool))*.
% 299.92/300.50 45331[0:SpL:21893.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_Com_Opname,y),u,w)))*.
% 299.92/300.50 45330[0:SpL:21267.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x),tc_Com_Opname,y),u,w)))*.
% 299.92/300.50 45513[0:Rew:9.0,45489.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))))))* c_Fun_Oinj__on(c_Fun_Ocomp(w,y,x,u,z),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,u)* -> equal(hAPP(w,hAPP(y,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v,c_Fun_Ocomp(w,y,x,u,z),u,z))),v)**.
% 299.92/300.50 47364[0:SpL:532.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)),y))*.
% 299.92/300.50 47594[0:SpL:533.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)),z))*.
% 299.92/300.50 47933[0:SpL:532.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,v)))* hBOOL(hAPP(hAPP(c_in(v),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),x))))* -> hBOOL(hAPP(u,y))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(z,u,v)),z))*.
% 299.92/300.50 48044[0:SpL:533.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,v)))* hBOOL(hAPP(hAPP(c_in(v),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z))))* -> hBOOL(hAPP(u,y))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(z,u,v)),z))*.
% 299.92/300.50 48462[0:SpL:24914.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(hAPP(c_in(u),v_x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),hAPP(c_Set_Oinsert(hAPP(c_in(u),v_x),w),x),w,u) -> .
% 299.92/300.50 48461[0:SpL:21893.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,v_x)),hAPP(c_Set_Oimage(v,w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,y),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(v,hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,y),w),x),w,u) -> .
% 299.92/300.50 48460[0:SpL:21267.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,v_x)),hAPP(c_Set_Oimage(v,w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,y),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(v,hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,y),w),x),w,u) -> .
% 299.92/300.50 48450[0:SpL:10063.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,t_a),v,u),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,t_a),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v),w),v,u) -> .
% 299.92/300.50 48442[0:SpL:584.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(v,w),hAPP(x,w))),hAPP(c_Set_Oimage(c_COMBS(v,x,y,z,x1),x2,u),c_HOL_Ominus__class_Ominus(x3,hAPP(c_Set_Oinsert(w,x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))),tc_fun(x2,tc_bool)))))* c_Fun_Oinj__on(c_COMBS(v,x,y,z,x1),hAPP(c_Set_Oinsert(w,x2),x3),x2,u) -> .
% 299.92/300.50 48441[0:SpL:586.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,x))),hAPP(c_Set_Oimage(hAPP(c_COMBB(v,y,z,x1),w),x2,u),c_HOL_Ominus__class_Ominus(x3,hAPP(c_Set_Oinsert(x,x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))),tc_fun(x2,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_COMBB(v,y,z,x1),w),hAPP(c_Set_Oinsert(x,x2),x3),x2,u) -> .
% 299.92/300.50 48440[0:SpL:585.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(v,w),x)),hAPP(c_Set_Oimage(hAPP(c_COMBC(v,y,z,x1),x),x2,u),c_HOL_Ominus__class_Ominus(x3,hAPP(c_Set_Oinsert(w,x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))),tc_fun(x2,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_COMBC(v,y,z,x1),x),hAPP(c_Set_Oinsert(w,x2),x3),x2,u) -> .
% 299.92/300.50 48425[0:SpL:3294.1,224.0] || equal(c_in(t_a),u) hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(hAPP(u,v_x),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(u,v_x),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),w),x),w,v) -> .
% 299.92/300.50 48421[0:SpL:330.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x),y),x,u) -> .
% 299.92/300.50 48359[0:SpL:331.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),hAPP(c_Set_Oinsert(v,x),y),x,u) -> .
% 299.92/300.50 48350[0:SpL:34428.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,v),hAPP(c_Set_Oinsert(v_x,w),x),w,u) -> .
% 299.92/300.50 48326[0:SpL:369.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Oimage(c_Set_Oinsert(v,w),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),x),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),x),y),z),y,u) -> .
% 299.92/300.50 48325[0:SpL:2089.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs)),hAPP(c_Set_Oimage(c_Set_Oinsert(v_x,tc_Com_Opname),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v_x,tc_Com_Opname),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,tc_Com_Opname),v_Procs),w),x),w,u) -> .
% 299.92/300.50 48324[0:SpL:34427.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,v),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,v),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w),x),w,u) -> .
% 299.92/300.50 48627[0:SpR:197.1,151.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oimage(u,v,w),y))) -> hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oimage(u,v,w),z))) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(y,z,tc_fun(v,tc_bool)))))*.
% 299.92/300.50 48939[0:SpL:339.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y))))* -> hBOOL(hAPP(z,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(w,u),x),z,u)),hAPP(c_Set_Oinsert(w,u),x)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,z,u)),y))*.
% 299.92/300.50 48934[0:SpL:338.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y))))* -> hBOOL(hAPP(z,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,z,u)),x))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oinsert(w,u),y),z,u)),hAPP(c_Set_Oinsert(w,u),y)))*.
% 299.92/300.50 49308[0:Res:168.0,488.1] || hBOOL(hAPP(u,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),x))))* -> c_Hoare__Mirabelle_Ohoare__valids(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),w),x),t_a) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,u,tc_Hoare__Mirabelle_Otriple(t_a))),w))* hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,tc_Hoare__Mirabelle_Otriple(t_a))),x))*.
% 299.92/300.50 49740[0:Rew:49662.2,49620.2] || hBOOL(hAPP(u,v_x)) c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),v))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,w),v),w,x).
% 299.92/300.50 49741[0:Rew:49662.2,49478.2] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),z,x1,x2) -> equal(x3,v) hBOOL(hAPP(hAPP(c_in(x2),hAPP(u,x3)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x1,x2),hAPP(c_Set_Oinsert(x3,x1),z))))* c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),hAPP(c_Set_Oinsert(x3,x1),z),x1,x2).
% 299.92/300.50 50037[0:SpL:497.0,3489.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_in(tc_Com_Opname))** hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)))) -> .
% 299.92/300.50 50036[0:SpL:497.0,3487.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> .
% 299.92/300.50 49951[0:SpR:497.0,3294.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_in(t_a))** -> equal(hAPP(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.92/300.50 50864[0:SpL:622.0,3698.2] || equal(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* equal(c_Com_Ocom_OBODY,u) equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool))),c_Com_Ocom_OSKIP) -> .
% 299.92/300.50 50863[4:SpL:622.0,46565.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))))* -> .
% 299.92/300.50 50855[0:SpL:622.0,3493.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_in(tc_Com_Opname))** equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))* -> .
% 299.92/300.50 50840[0:SpR:622.0,7253.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),w,x),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))))*.
% 299.92/300.50 50816[0:SpR:622.0,3339.1] || equal(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* -> equal(c_Fun_Ofun__upd(u,v_x,hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool))),x,y),u)**.
% 299.92/300.50 50815[0:SpR:622.0,3316.1] || equal(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))*.
% 299.92/300.50 50812[0:SpR:622.0,648.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,tc_fun(t_a,tc_bool)))),hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,u),v_Procs)))*.
% 299.92/300.50 50801[0:SpR:622.0,28031.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.92/300.50 50799[0:SpR:622.0,27381.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,w)),v_Procs))*.
% 299.92/300.50 50795[0:SpR:622.0,28334.0] || -> equal(hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),tc_Com_Opname,w),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.92/300.50 50793[0:SpR:622.0,27441.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),tc_Com_Opname,w)),v_Procs))*.
% 299.92/300.50 50792[0:SpR:622.0,21141.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),t_a,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))))*.
% 299.92/300.50 50790[0:SpR:622.0,11030.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))))*.
% 299.92/300.50 50789[0:SpR:622.0,10090.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> equal(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)),c_Orderings_Otop__class_Otop(tc_bool)).
% 299.92/300.50 50780[0:SpR:622.0,3284.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_in(w),v_Procs),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))))*.
% 299.92/300.50 50775[2:SpR:622.0,15483.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** -> c_Com_OWT(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),tc_bool)).
% 299.92/300.50 50773[0:SpR:622.0,15482.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_fun(t_a,tc_bool)),v_Procs)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),tc_bool)).
% 299.92/300.50 50772[7:SpR:622.0,27219.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_fun(t_a,tc_bool)),v_x)** -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),tc_bool)).
% 299.92/300.50 50769[0:SpR:622.0,651.0] || -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.92/300.50 51253[0:SpL:584.0,462.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(v),c_Option_Othe(tc_Com_Ocom),w,x,y),hAPP(c_Com_Obody,z)),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(c_Com_Obody,z)),hAPP(c_Com_Ocom_OBODY,z)),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.50 51526[0:Res:124.0,195.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,w,y),c_HOL_Ominus__class_Ominus(v,z,tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,w,y),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,z,tc_fun(w,tc_bool)),u,tc_fun(w,tc_bool))))**.
% 299.92/300.50 51523[0:Res:22741.1,195.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_in(t_a)) c_lessequals(v,c_Orderings_Obot__class_Obot(tc_bool),tc_fun(u,tc_bool)) c_Fun_Oinj__on(w,c_Orderings_Obot__class_Obot(tc_bool),u,x) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(w,u,x),v_x),hAPP(c_Set_Oimage(w,u,x),v),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(w,u,x),c_HOL_Ominus__class_Ominus(v_x,v,tc_fun(u,tc_bool))))**.
% 299.92/300.50 51522[0:Res:13018.1,195.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(v,c_Orderings_Otop__class_Otop(tc_bool),tc_fun(u,tc_bool)) c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_bool),u,x) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(w,u,x),v_x),hAPP(c_Set_Oimage(w,u,x),v),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(w,u,x),c_HOL_Ominus__class_Ominus(v_x,v,tc_fun(u,tc_bool))))**.
% 299.92/300.50 51520[0:Res:24939.1,195.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_lessequals(v,v_x,tc_fun(u,tc_bool)) c_Fun_Oinj__on(w,v_x,u,x) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(w,u,x),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(w,u,x),v),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(w,u,x),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_bool),v,tc_fun(u,tc_bool))))**.
% 299.92/300.50 51708[0:Res:13387.1,233.2] || equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** c_Finite__Set_Ofinite(x,v) c_Finite__Set_Ofinite(y,w) c_lessequals(hAPP(c_Set_Oimage(z,w,v),y),x,tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,x,v,w) c_Fun_Oinj__on(z,y,w,v) -> equal(c_Finite__Set_Ocard(x,v),c_Finite__Set_Ocard(y,w)).
% 299.92/300.50 51699[0:Res:420.0,233.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w) c_lessequals(hAPP(c_Set_Oimage(x,w,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(y,u,v,w)* c_Fun_Oinj__on(x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v) -> equal(c_Finite__Set_Ocard(u,v),c_Finite__Set_Ocard(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w)).
% 299.92/300.50 55969[0:SpL:622.0,55174.1] || equal(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool))))* -> .
% 299.92/300.50 55886[0:SpL:622.0,55174.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),w)* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),tc_bool),hAPP(w,v_x))* -> .
% 299.92/300.50 60399[7:SpR:533.0,58968.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x))))*.
% 299.92/300.50 60512[0:SpR:533.0,58969.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x))))*.
% 299.92/300.50 60585[7:SpR:533.0,59476.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),y))))*.
% 299.92/300.50 60658[0:SpR:533.0,59477.1] || equal(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_Procs) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),y))))*.
% 299.92/300.50 60843[0:SpR:533.0,59017.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),t_a)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y))))*.
% 299.92/300.50 60916[0:SpR:533.0,59525.1] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),t_a)* hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),z))))*.
% 299.92/300.50 61938[0:SpL:497.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.92/300.50 64532[0:SpL:497.0,24257.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.92/300.50 77382[0:Res:2399.2,375.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) c_lessequals(hAPP(y,w),c_HOL_Ouminus__class_Ouminus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.92/300.50 77747[0:SpL:323.0,5892.0] || hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x,u,tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))))* -> hBOOL(hAPP(c_COMBS(c_in(z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x,u,tc_fun(y,tc_bool))),x1,x2,x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))))*.
% 299.92/300.50 80266[0:SpL:21268.0,494.1] || hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),z),t_a)* c_Natural_Oevaln(y,w,x,x1)* -> hBOOL(hAPP(hAPP(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),z),x2,x3),v),x1))*.
% 299.92/300.50 80081[0:SpL:21268.0,239.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) c_lessequals(y,z,tc_fun(x,tc_bool)) c_Fun_Oinj__on(w,y,x,u) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Fun_Othe__inv__into(y,w,x,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_in(u),hAPP(c_in(u),v),x1,x2))),z))*.
% 299.92/300.50 80077[0:SpL:21268.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,y,u)),w))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,y,u)),x))*.
% 299.92/300.50 79915[0:SpR:532.0,21268.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)),w,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)))**.
% 299.92/300.50 79706[0:SpR:21268.0,532.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),x,z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)))**.
% 299.92/300.50 80455[0:Rew:533.0,79691.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),w,y)),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),z)))**.
% 299.92/300.50 80479[0:Rew:497.0,79560.0] || -> equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w),v,x))),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w)))**.
% 299.92/300.50 80480[0:Rew:497.0,79446.0] || -> equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v),u,w)),x)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),x)))**.
% 299.92/300.50 81461[0:SpL:21894.0,494.1] || hBOOL(hAPP(hAPP(u,v),w))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),z),t_a)* c_Natural_Oevaln(y,w,x,x1)* -> hBOOL(hAPP(hAPP(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),z),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),u),y),x2,x3),v),x1))*.
% 299.92/300.50 81276[0:SpL:21894.0,239.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) c_lessequals(y,z,tc_fun(x,tc_bool)) c_Fun_Oinj__on(w,y,x,u) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Fun_Othe__inv__into(y,w,x,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_in(u),v),c_in(u),x1,x2))),z))*.
% 299.92/300.50 81272[0:SpL:21894.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(y,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,y,u)),w))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,y,u)),x))*.
% 299.92/300.50 81109[0:SpR:532.0,21894.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)))**.
% 299.92/300.50 80900[0:SpR:21894.0,532.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)))**.
% 299.92/300.50 81650[0:Rew:533.0,80885.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,y)),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),z)))**.
% 299.92/300.50 81674[0:Rew:497.0,80753.0] || -> equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v,x))),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),w)))**.
% 299.92/300.50 81675[0:Rew:497.0,80639.0] || -> equal(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u,w)),x)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),x)))**.
% 299.92/300.50 83068[0:SpR:5924.0,450.0] || -> hBOOL(hAPP(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,x3,x4)),v),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_COMBS(u,c_COMBK(v,w,x),y,z,x1),x2,x3,x4)))* c_Hoare__Mirabelle_Otriple__valid(x4,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBS(u,c_COMBK(v,w,x),y,z,x1)),x3),x2),t_a).
% 299.92/300.50 83391[0:SpR:5961.0,450.0] || -> hBOOL(hAPP(hAPP(u,hAPP(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),x2,x3,x4))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_COMBS(c_COMBK(u,w,x),v,y,z,x1),x2,x3,x4)))* c_Hoare__Mirabelle_Otriple__valid(x4,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_COMBS(c_COMBK(u,w,x),v,y,z,x1)),x3),x2),t_a).
% 299.92/300.50 83894[0:SpL:5899.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_COMBS(w,x,y,z,x1),x2,x3)),hAPP(c_COMBS(w,x,x4,x5,x6),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_COMBS(w,x,y,z,x1),x2,x3)))* -> equal(hAPP(c_Set_Oimage(u,x2,x3),v),hAPP(c_Set_Oimage(c_COMBS(w,x,y,z,x1),x2,x3),v)).
% 299.92/300.50 83890[0:SpL:5899.0,315.0] || equal(hAPP(c_COMBS(u,v,w,x,y),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(z,c_COMBS(u,v,x1,x2,x3),x4,x5,x6)),hAPP(x4,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(z,c_COMBS(u,v,x1,x2,x3),x4,x5,x6)))* -> equal(hAPP(c_Set_Oimage(c_COMBS(u,v,x1,x2,x3),x5,x6),z),hAPP(c_Set_Oimage(x4,x5,x6),z)).
% 299.92/300.50 87208[0:Res:340.2,32820.0] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* c_lessequals(x,c_HOL_Ominus__class_Ominus(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))).
% 299.92/300.50 27137[0:SpR:445.1,450.0] || -> equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Fun_Ofun__upd(u,v,w,x,y),z,x1,x2),v) hBOOL(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Fun_Ofun__upd(u,v,w,x,y),z,x1,x2)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Fun_Ofun__upd(u,v,w,x,y),z,x1,x2)))* c_Hoare__Mirabelle_Otriple__valid(x2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Fun_Ofun__upd(u,v,w,x,y)),x1),z),t_a).
% 299.92/300.50 27649[0:SpR:338.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) c_Fun_Oinj__on(c_Set_Oinsert(z,v),y,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,c_Set_Oinsert(z,v),u,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(z,v),x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))**.
% 299.92/300.50 27603[0:SpR:339.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),z)),w,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),z)),u,x1),hAPP(c_Set_Oinsert(y,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),v))),v)**.
% 299.92/300.50 27599[0:SpR:338.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),y,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),u,x1),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x))),hAPP(c_Set_Oinsert(v,w),x))**.
% 299.92/300.50 27802[0:SpR:338.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) c_Fun_Oinj__on(c_Set_Oinsert(z,v),y,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(y,c_Set_Oinsert(z,v),u,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(z,v),x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))**.
% 299.92/300.50 27756[0:SpR:339.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),z)),w,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),z)),u,x1),hAPP(c_Set_Oinsert(y,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),v))),v)**.
% 299.92/300.50 27752[0:SpR:338.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),y,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),u,x1),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x))),hAPP(c_Set_Oinsert(v,w),x))**.
% 299.92/300.50 28514[0:SpR:339.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),c_Fun_Ofun__upd(x,y,z,x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x,x2,x3,x1),y,hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z)),x1,x3))*.
% 299.92/300.50 29057[0:SpR:537.1,118.0] class_Lattices_Olattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Fun_Ofun__upd(x,y,z,x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,x2,x3,x1),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)),x1,x3))*.
% 299.92/300.50 29037[0:SpR:537.1,71.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),x,v,x1) -> equal(hAPP(c_Fun_Othe__inv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w))),w)**.
% 299.92/300.50 29036[0:SpR:537.1,373.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),x,v,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w))),w)**.
% 299.92/300.50 29580[0:SpR:534.1,118.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),c_Fun_Ofun__upd(x,y,z,x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,x2,x3,x1),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),z)),x1,x3))*.
% 299.92/300.50 29559[0:SpR:534.1,71.2] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),x,v,x1) -> equal(hAPP(c_Fun_Othe__inv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w))),w)**.
% 299.92/300.50 29558[0:SpR:534.1,373.2] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),x,v,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w))),w)**.
% 299.92/300.50 30083[0:SpR:536.1,71.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),y,v,x1) -> equal(hAPP(c_Fun_Othe__inv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))**.
% 299.92/300.51 30082[0:SpR:536.1,373.2] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),y,v,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))**.
% 299.92/300.51 30639[0:SpR:535.1,71.2] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),y,v,x1) -> equal(hAPP(c_Fun_Othe__inv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))**.
% 299.92/300.51 30638[0:SpR:535.1,373.2] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),y,v,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x))**.
% 299.92/300.51 31524[0:SpL:21893.0,473.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,x,u),v_x),c_Set_Oimage(w,x,u),tc_Com_Opname,y),w,x,u),v)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,x,u),v_x),c_Set_Oimage(w,x,u),tc_Com_Opname,y)))*.
% 299.92/300.51 31523[0:SpL:21267.0,473.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),v_x),tc_Com_Opname,y),w,x,u),v)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),v_x),tc_Com_Opname,y)))*.
% 299.92/300.51 32344[0:SpL:297.2,477.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u)* hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)) hBOOL(hAPP(hAPP(c_in(w),z),x))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z))*.
% 299.92/300.51 32524[0:SpL:297.2,476.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w),u)* hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)) hBOOL(hAPP(hAPP(c_in(w),z),y))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z))*.
% 299.92/300.51 32979[0:SpR:104.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,v,tc_fun(y,tc_bool)),tc_fun(y,tc_bool)),z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(y,tc_bool))),u,z),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(y,tc_bool))),u,z),w))**.
% 299.92/300.51 33516[0:SpL:61.1,12979.0] || c_Finite__Set_Ofinite(u,v) c_Hoare__Mirabelle_Otriple__valid(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,v),u),v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),hAPP(c_in(tc_Com_Opname),v_x)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),v_Procs,t_a).
% 299.92/300.51 34607[0:SpR:55.1,244.2] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)))) equal(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),u),c_HOL_Ozero__class_Ozero(tc_nat)) equal(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),w,tc_fun(u,tc_bool)),u),c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(x,w,tc_fun(u,tc_bool)),u)))**.
% 299.92/300.51 35402[0:SpR:475.1,410.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,u,y),w),z),x1),c_Set_Oinsert(hAPP(x,v),y),z,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(x,u,y),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oinsert(hAPP(x,v),y),z,tc_fun(x2,tc_bool))))*.
% 299.92/300.51 35397[0:SpR:131.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Set_Ovimage(c_Fun_Ocomp(x,y,z,x1,x2),x2,x1),v,tc_fun(x3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x3,tc_bool)),hAPP(c_Set_Ovimage(y,x2,z),hAPP(c_Set_Ovimage(x,z,x1),u))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(c_Fun_Ocomp(x,y,z,x1,x2),x2,x1),v,tc_fun(x3,tc_bool))))*.
% 299.92/300.51 35396[0:SpR:158.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),c_Set_Oimage(c_Fun_Ocomp(x,y,z,x1,x2),x2,x1),v,tc_fun(x3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x3,tc_bool)),hAPP(c_Set_Oimage(x,z,x1),hAPP(c_Set_Oimage(y,x2,z),u))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_Fun_Ocomp(x,y,z,x1,x2),x2,x1),v,tc_fun(x3,tc_bool))))*.
% 299.92/300.51 35338[0:SpR:523.1,410.0] class_Lattices_Olattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,v),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),x),y),v,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(x,v_x)),hAPP(y,v_x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),x),y),v,tc_fun(z,tc_bool))))*.
% 299.92/300.51 35337[0:SpR:460.1,410.0] || class_Lattices_Olattice(t_b) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,tc_fun(w,tc_bool))))*.
% 299.92/300.51 37473[0:SpR:205.1,205.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),v,w),x),hAPP(c_Set_Oimage(u,v,w),x))**.
% 299.92/300.51 37683[0:SpR:198.1,198.1] || c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> equal(c_Fun_Ocomp(x,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),w,u),w,y,u),c_Fun_Ocomp(x,v,w,y,u))**.
% 299.92/300.51 38358[0:SSi:38282.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),hAPP(v,w)),x)) c_Finite__Set_Ofinite(x,tc_fun(u,tc_bool)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,y),z),v,y,tc_fun(u,tc_bool)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,v,y,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.92/300.51 38641[0:SpL:465.1,184.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) c_Fun_Oinj__on(c_Fun_Ofun__upd(w,z,x1,x,u),y,x,u) -> hBOOL(hAPP(hAPP(c_in(x),z),y)) equal(hAPP(c_Fun_Ofun__upd(w,z,x1,x,u),hAPP(c_Fun_Othe__inv__into(y,c_Fun_Ofun__upd(w,z,x1,x,u),x,u),v)),v)**.
% 299.92/300.51 39617[0:SpR:532.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),z),w),x1)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z)),x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x),x1)))*.
% 299.92/300.51 40187[0:SpR:21893.0,399.1] || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),tc_Com_Opname,v),w,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w),tc_fun(u,tc_bool)).
% 299.92/300.51 40186[0:SpR:21267.0,399.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),tc_Com_Opname,v),w,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w),tc_fun(u,tc_bool)).
% 299.92/300.51 40181[0:SpR:21893.0,399.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),v_x),c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),tc_Com_Opname,w),tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),u),hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),v_x),tc_fun(v,tc_bool)).
% 299.92/300.51 40180[0:SpR:21267.0,399.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),v_x),tc_Com_Opname,w),tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),u),hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),v_x),tc_fun(v,tc_bool)).
% 299.92/300.51 40282[0:SpL:21893.0,398.0] || c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),tc_fun(u,tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),tc_Com_Opname,w),v,tc_fun(u,tc_bool))*.
% 299.92/300.51 40281[0:SpL:21267.0,398.0] || c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),tc_fun(u,tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),tc_Com_Opname,w),v,tc_fun(u,tc_bool))*.
% 299.92/300.51 40276[0:SpL:21893.0,398.0] || c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),tc_fun(u,tc_bool)) -> c_lessequals(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),tc_Com_Opname,w),tc_fun(u,tc_bool))*.
% 299.92/300.51 40275[0:SpL:21267.0,398.0] || c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),tc_fun(u,tc_bool)) -> c_lessequals(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),tc_Com_Opname,w),tc_fun(u,tc_bool))*.
% 299.92/300.51 41374[0:SpL:55.1,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y))* hBOOL(hAPP(hAPP(c_in(z),x1),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x2,x),v),w,tc_fun(x,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(x),x2),w)) hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(x2,x),u,tc_fun(z,tc_bool))))*.
% 299.92/300.51 41333[0:SpL:410.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x3,x),v),w,x,tc_fun(y,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(w,x3)),u,tc_fun(x1,tc_bool))))*.
% 299.92/300.51 41603[0:SpL:614.2,284.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),z,x),x1)))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x)* -> hBOOL(hAPP(hAPP(c_in(z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),x1)).
% 299.92/300.51 41584[0:SpL:188.1,284.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,y),y,u),z,x),x1)))* c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v,u,y),y,u),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x)* -> hBOOL(hAPP(hAPP(c_in(z),w),x1))*.
% 299.92/300.51 41519[0:SpL:354.2,284.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(v,x,w,y),z)),u))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v,x,w,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,w)* -> hBOOL(hAPP(hAPP(c_in(y),z),hAPP(c_Set_Oimage(x,w,y),u)))*.
% 299.92/300.51 41803[0:SpL:188.1,199.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,y),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Ovimage(c_COMBK(v,u,z),z,u),x,w,y))))* hBOOL(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool))) c_Fun_Oinj__on(x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,y) -> hBOOL(hAPP(c_Set_Ovimage(c_COMBK(v,u,z),z,u),x1))*.
% 299.92/300.51 41788[0:SpL:8385.1,199.0] || equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oinsert(v_x,tc_Com_Opname),v,u,w)),v_Procs) hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oinsert(v_x,tc_Com_Opname),v,u,w)))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),x))*.
% 299.92/300.51 41973[0:SpR:354.2,82.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> c_lessequals(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,w,y),u),z,tc_fun(y,tc_bool))),tc_fun(w,tc_bool))*.
% 299.92/300.51 41958[0:SpR:354.2,82.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z),u,tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool))),tc_fun(w,tc_bool))*.
% 299.92/300.51 42092[0:SpR:180.2,118.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_Fun_Ofun__upd(x,y,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),z,v,u,u),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,x2,x3,x1),y,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),z,hAPP(c_Set_Oinsert(w,u),v),u,u),x1,x3))*.
% 299.92/300.51 42270[0:SSi:42112.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> equal(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)))**.
% 299.92/300.51 42719[0:SpR:113.0,161.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)))),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Ovimage(v,u,w),y),tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),z),hAPP(c_Set_Ovimage(v,u,w),y),tc_fun(u,tc_bool)))**.
% 299.92/300.51 42704[0:SpR:113.0,161.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Ovimage(w,u,x),y),tc_fun(u,tc_bool))),hAPP(c_Set_Ovimage(w,u,x),c_HOL_Ominus__class_Ominus(z,y,tc_fun(x,tc_bool)))),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Ovimage(w,u,x),z)),hAPP(c_Set_Ovimage(w,u,x),y),tc_fun(u,tc_bool)))**.
% 299.92/300.51 43103[0:SpR:338.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x1,v),x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(x1,v),u,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(x1,v),u,tc_fun(z,tc_bool)))**.
% 299.92/300.51 43100[0:SpR:317.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(x2,w),y))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oinsert(hAPP(v,x2),x),u,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oinsert(hAPP(v,x2),x),u,tc_fun(x1,tc_bool)))**.
% 299.92/300.51 43045[0:SpR:600.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),u,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),u,tc_fun(z,tc_bool)))**.
% 299.92/300.51 43024[0:SpR:181.1,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(x),y),v))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(c_COMBK(y,x,x1),x1,x),u,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(c_COMBK(y,x,x1),x1,x),u,tc_fun(z,tc_bool)))**.
% 299.92/300.51 45121[0:Res:326.2,402.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,y,tc_fun(w,tc_bool)) c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),tc_fun(w,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y)).
% 299.92/300.51 45111[0:SpR:24914.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v_x)),y,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),tc_fun(w,tc_bool))*.
% 299.92/300.51 45046[0:SpR:24914.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),tc_Com_Opname,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x)),tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),tc_fun(w,tc_bool))*.
% 299.92/300.51 45325[0:SpL:24914.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_Com_Opname,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)),u,w)))*.
% 299.92/300.51 45495[0:SpL:21893.0,237.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u) -> equal(hAPP(v,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,x),v,u,w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,x))**.
% 299.92/300.51 45494[0:SpL:21267.0,237.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u) -> equal(hAPP(v,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,x),v,u,w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,x))**.
% 299.92/300.51 45629[0:SpL:323.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),x1,x,tc_fun(w,tc_bool))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,x1,x,tc_fun(w,tc_bool)),u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x1,x,tc_fun(w,tc_bool)),u,w)))*.
% 299.92/300.51 45592[0:SpR:323.0,326.2] || c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool)),tc_fun(y,tc_bool)) c_lessequals(z,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(y,tc_bool)),tc_fun(y,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),x1),w,x,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.92/300.51 45585[0:SpR:323.0,326.2] || c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),y,tc_fun(x,tc_bool)) c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,v,w,tc_fun(x,tc_bool)),x1,tc_fun(x,tc_bool)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),z),v,w,tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),x1),tc_fun(x,tc_bool))*.
% 299.92/300.51 45873[0:SpL:21893.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),tc_Com_Opname,x),u,w)))* hBOOL(hAPP(hAPP(c_in(w),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x)))* -> hBOOL(hAPP(u,y))*.
% 299.92/300.51 45872[0:SpL:21267.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),tc_Com_Opname,x),u,w)))* hBOOL(hAPP(hAPP(c_in(w),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x)))* -> hBOOL(hAPP(u,y))*.
% 299.92/300.51 48445[0:SpL:12944.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)),z,u),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(x2,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)),hAPP(c_Set_Oinsert(x2,z),x1),z,u) -> .
% 299.92/300.51 48437[0:SpL:11499.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),x)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),y),z),y,u) -> .
% 299.92/300.51 48418[0:SpL:11695.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),x),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(v,w),c_Option_Othe(x)),hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),x),y),z),y,u) -> .
% 299.92/300.51 48417[0:SpL:11473.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(z,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Oinsert(z,x),y),x,u) -> .
% 299.92/300.51 48404[0:SpL:329.1,224.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) hBOOL(hAPP(hAPP(c_in(x),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y,x),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(v,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),hAPP(c_Set_Oinsert(v,y),z),y,x) -> .
% 299.92/300.51 48403[0:SpL:328.1,224.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) hBOOL(hAPP(hAPP(c_in(x),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y,x),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(u,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(c_Set_Oinsert(u,y),z),y,x) -> .
% 299.92/300.51 48394[0:SpL:538.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(w,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(w,y),z),y,u) -> .
% 299.92/300.51 48373[0:SpL:17045.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(x1,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(x1,y),z),y,u) -> .
% 299.92/300.51 48838[0:Res:687.1,619.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,u,tc_fun(x,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,v_Procs,hAPP(c_in(u),v),tc_Com_Opname)),c_Set_Oinsert(z,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(z,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,v_Procs,hAPP(c_in(u),v),tc_Com_Opname),w,u,tc_fun(x,tc_bool))))**.
% 299.92/300.51 48837[0:Res:686.1,619.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,u,tc_fun(x,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,y,hAPP(c_in(u),v),tc_Com_Opname)),c_Set_Oinsert(z,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(z,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(v_Procs,y,hAPP(c_in(u),v),tc_Com_Opname),w,u,tc_fun(x,tc_bool))))**.
% 299.92/300.51 48817[0:Res:450.0,619.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(v)),w),x),t_a) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(y,v,tc_fun(z,tc_bool)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),x,w,u)),c_Set_Oinsert(x1,z),tc_fun(z,tc_bool),tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(x1,z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),x,w,u),y,v,tc_fun(z,tc_bool))))**.
% 299.92/300.51 48788[0:Res:510.1,619.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z)),c_Set_Oinsert(x1,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(x1,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z),x,u,tc_fun(y,tc_bool))))**.
% 299.92/300.51 48787[0:Res:511.1,619.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),w)),c_Set_Oinsert(x1,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(x1,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),w),x,u,tc_fun(y,tc_bool))))**.
% 299.92/300.51 49264[0:SpL:339.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oinsert(x,w),y),u,w)),hAPP(c_Set_Oinsert(x,w),y)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)),z))*.
% 299.92/300.51 49259[0:SpL:338.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)),y))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oinsert(x,w),z),u,w)),hAPP(c_Set_Oinsert(x,w),z)))*.
% 299.92/300.51 49743[0:Rew:49662.2,49623.1] || c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),w,x,u) -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),x,u),hAPP(c_Set_Oinsert(hAPP(c_in(u),v_x),x),w))))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,v),hAPP(c_Set_Oinsert(hAPP(c_in(u),v_x),x),w),x,u).
% 299.92/300.51 49744[0:Rew:49662.2,49601.1] || c_Fun_Oinj__on(c_COMBS(u,v,w,x,y),z,x1,x2) -> hBOOL(hAPP(hAPP(c_in(x2),hAPP(hAPP(u,x3),hAPP(v,x3))),hAPP(c_Set_Oimage(c_COMBS(u,v,w,x,y),x1,x2),hAPP(c_Set_Oinsert(x3,x1),z))))* c_Fun_Oinj__on(c_COMBS(u,v,w,x,y),hAPP(c_Set_Oinsert(x3,x1),z),x1,x2).
% 299.92/300.51 49745[0:Rew:49662.2,49580.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,y),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),x),w),x,y).
% 299.92/300.51 49746[0:Rew:49662.2,49483.1] || c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),w,x),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w),v))))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,c_Lattices_Oupper__semilattice__class_Osup(tc_bool),tc_Com_Opname,u),hAPP(c_Set_Oinsert(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),w),v),w,x).
% 299.92/300.51 49747[0:Rew:49662.2,49481.1] || c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),v))))* c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v_x,tc_Com_Opname,u),u,tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,w),v),w,x).
% 299.92/300.51 50025[0:SpR:584.0,497.0] || -> equal(hAPP(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u,v,w),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)),v_x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),x),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x))))*.
% 299.92/300.51 49985[0:SpR:497.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.92/300.51 50506[0:SpL:223.1,62.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),w),tc_fun(x1,tc_bool)),x1)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oimage(y,u,x1),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),tc_fun(x1,tc_bool)),x1)*.
% 299.92/300.51 50484[0:SpR:158.0,223.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(x,y),hAPP(c_Set_Oimage(z,x1,y),hAPP(c_Set_Oimage(x2,u,x1),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(c_Fun_Ocomp(z,x2,x1,y,u),v,x,u,y),u,y),w))*.
% 299.92/300.51 50417[0:SpR:223.1,63.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),tc_fun(z,tc_bool)),z)* -> c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,x1,u,z),u,z),w),tc_fun(z,tc_bool)),z)*.
% 299.92/300.51 50416[0:SpR:223.1,446.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(x,hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),tc_fun(z,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(x1,z),x),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,x1,u,z),u,z),w),tc_fun(z,tc_bool))*.
% 299.92/300.51 50389[0:SpR:223.1,446.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),z,tc_fun(y,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,x1,u,y),u,y),w),hAPP(c_Set_Oinsert(x1,y),z),tc_fun(y,tc_bool))*.
% 299.92/300.51 50868[0:SpL:622.0,3507.1] || equal(c_Set_Oinsert(u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,x,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),w,x,tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))* -> .
% 299.92/300.51 50867[0:SpL:622.0,16327.1] || equal(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_Procs) -> .
% 299.92/300.51 50866[7:SpL:622.0,31886.1] || equal(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)) equal(u,v_x) -> .
% 299.92/300.51 50865[0:SpL:622.0,3499.1] || equal(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))* -> .
% 299.92/300.51 50862[0:SpL:622.0,24254.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),c_Com_Ocom_OBODY) equal(v_x,c_Com_Ocom_OSKIP) -> .
% 299.92/300.51 50857[0:SpL:622.0,13272.0] || equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),c_Orderings_Otop__class_Otop(tc_bool)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),w)* -> hBOOL(hAPP(w,v_x))*.
% 299.92/300.51 50856[0:SpL:622.0,3484.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),hAPP(c_Com_Ocom_OBODY,w))* -> equal(v_x,w).
% 299.92/300.51 50845[0:SpR:622.0,20881.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),w,x),hAPP(c_Set_Oinsert(v_x,w),y)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))))*.
% 299.92/300.51 50830[0:SpR:622.0,9569.0] || -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool))),v_x),tc_bool)*.
% 299.92/300.51 50829[0:SpR:622.0,9568.0] || -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool))),x),v_x),tc_bool)*.
% 299.92/300.51 50825[0:SpR:622.0,3346.1] || equal(c_Set_Oinsert(u,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,x,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),w,x,tc_fun(t_a,tc_bool)))))*.
% 299.92/300.51 50823[0:SpR:622.0,28356.1] || equal(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool))),tc_Com_Opname,x)))*.
% 299.92/300.51 50822[0:SpR:622.0,28053.1] || equal(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* -> hBOOL(hAPP(v_Procs,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool))),u,tc_Com_Opname,x)))*.
% 299.92/300.51 50821[0:SpR:622.0,28859.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool))),tc_Com_Opname,x)))*.
% 299.92/300.51 50820[0:SpR:622.0,28704.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,tc_Com_Opname),v_Procs),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,tc_fun(t_a,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,x)))*.
% 299.92/300.51 50819[0:SpR:622.0,21126.1] || equal(u,v_Procs) -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,x),u),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool)))))*.
% 299.92/300.51 50818[0:SpR:622.0,3317.1] || equal(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool))),hAPP(c_Set_Oinsert(v_x,u),x)))*.
% 299.92/300.51 50817[0:SpR:622.0,3305.1] || equal(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,tc_Com_Opname,x),v_Procs),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool)))))*.
% 299.92/300.51 50813[0:SpR:622.0,2771.1] || equal(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool))),tc_bool),c_HOL_Ouminus__class_Ouminus(hAPP(u,v_x),tc_bool))*.
% 299.92/300.51 50807[0:SpR:622.0,32668.0] || -> equal(hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,w),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))),tc_Com_Opname),v_Procs),v_Procs)**.
% 299.92/300.51 50805[0:SpR:622.0,31533.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,w),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))))),v_Procs))*.
% 299.92/300.51 50798[0:SpR:622.0,21131.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,w),hAPP(c_Set_Oinsert(x,tc_Com_Opname),v_Procs)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))))*.
% 299.92/300.51 50797[0:SpR:622.0,21143.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),t_a,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))))*.
% 299.92/300.51 50791[0:SpR:622.0,15262.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_in(t_a))** -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)))).
% 299.92/300.51 50788[0:SpR:622.0,8376.2] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_in(tc_Com_Opname))** equal(w,v_Procs) -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),w))*.
% 299.92/300.51 50786[0:SpR:622.0,8415.2] || equal(v_Procs,v_x) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** -> equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),v_x).
% 299.92/300.51 50785[4:SpR:622.0,39064.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> c_Hoare__Mirabelle_Ohoare__valids(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))),y,t_a)*.
% 299.92/300.51 50784[4:SpR:622.0,39023.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))),y))*.
% 299.92/300.51 50783[0:SpR:622.0,3291.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))),v_Procs))*.
% 299.92/300.51 50782[0:SpR:622.0,3285.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_in(tc_Com_Opname))** -> hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),hAPP(c_Set_Oinsert(w,tc_Com_Opname),v_Procs)))*.
% 299.92/300.51 50778[0:SpR:622.0,3279.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)))** -> hBOOL(hAPP(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),v_Procs),v_x)).
% 299.92/300.51 51256[0:SpL:3229.1,462.0] || equal(u,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))))* c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(u,v_x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),v_x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.51 51249[0:SpL:3229.1,462.0] || equal(u,c_Hoare__Mirabelle_Otriple_Otriple(v)) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(u,v_x),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),v_x),hAPP(c_Com_Ocom_OBODY,x)),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.51 51243[0:SpL:3229.1,462.0] || equal(u,c_Com_Obody) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),x),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(u,v_x))),y),tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),x),hAPP(c_Com_Ocom_OBODY,v_x)),y),tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w).
% 299.92/300.51 51323[0:SpR:622.0,51231.0] || -> equal(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),hAPP(hAPP(c_Set_Oinsert(w,t_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool))),v_x),tc_bool),c_Orderings_Obot__class_Obot(tc_bool))**.
% 299.92/300.51 51575[0:Res:448.1,195.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_lessequals(v,w,tc_fun(u,tc_bool))* c_Fun_Oinj__on(x,w,u,y)* -> c_lessequals(w,z,tc_fun(u,tc_bool))* equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,u,y),z),hAPP(c_Set_Oimage(x,u,y),v),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(z,v,tc_fun(u,tc_bool))))**.
% 299.92/300.51 52567[0:Rew:373.2,52557.3] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* c_Fun_Oinj__on(w,y,x,u) c_Fun_Oinj__on(z,hAPP(c_Set_Oimage(w,x,u),y),u,x1)* -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,c_Fun_Ocomp(z,w,u,x1,x),x,x1),hAPP(z,v)),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v))**.
% 299.92/300.51 52679[0:Rew:71.2,52669.3] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* c_Fun_Oinj__on(w,y,x,u) c_Fun_Oinj__on(z,hAPP(c_Set_Oimage(w,x,u),y),u,x1)* -> equal(hAPP(c_Fun_Othe__inv__into(y,c_Fun_Ocomp(z,w,u,x1,x),x,x1),hAPP(z,v)),hAPP(c_Fun_Othe__inv__into(y,w,x,u),v))**.
% 299.92/300.51 53428[0:SpR:33303.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,x),v_x),tc_Com_Opname),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,x),v_x),tc_Com_Opname),u,tc_fun(w,tc_bool)))**.
% 299.92/300.51 57913[0:SpL:622.0,55910.1] || equal(c_COMBK(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,y,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* equal(c_HOL_Ouminus__class_Ouminus(u,tc_bool),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),x,y,tc_fun(t_a,tc_bool)))) -> .
% 299.92/300.51 58070[0:SpL:622.0,55992.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_COMBK(w,x,y))* equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),tc_bool),w) -> .
% 299.92/300.51 59132[0:Rew:533.0,58753.1] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),y))))*.
% 299.92/300.51 59642[0:Rew:533.0,59261.1] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),z))))*.
% 299.92/300.51 60182[0:SpL:622.0,58170.1] || equal(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))* equal(c_COMBK(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool))),tc_bool),x,y),u)* -> .
% 299.92/300.51 60421[7:Res:58968.1,268.0] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(hAPP(c_in(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(u),v),x)))* equal(hAPP(z,v),hAPP(z,w))* c_Fun_Oinj__on(z,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(u),v),x),u,x1)* -> equal(v,w).
% 299.92/300.51 60534[0:Res:58969.1,268.0] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(hAPP(c_in(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(u),v),x)))* equal(hAPP(z,v),hAPP(z,w))* c_Fun_Oinj__on(z,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(u),v),x),u,x1)* -> equal(v,w).
% 299.92/300.51 60607[7:Res:59476.1,268.0] || equal(hAPP(c_in(u),v),v_x) hBOOL(hAPP(hAPP(c_in(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),y)))* equal(hAPP(z,v),hAPP(z,w))* c_Fun_Oinj__on(z,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),y),u,x1)* -> equal(v,w).
% 299.92/300.51 60680[0:Res:59477.1,268.0] || equal(hAPP(c_in(u),v),v_Procs) hBOOL(hAPP(hAPP(c_in(u),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),y)))* equal(hAPP(z,v),hAPP(z,w))* c_Fun_Oinj__on(z,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),y),u,x1)* -> equal(v,w).
% 299.92/300.51 60865[0:Res:59017.1,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),y),w)))* equal(hAPP(z,y),hAPP(z,v))* c_Fun_Oinj__on(z,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(c_in(u),y),w),u,x1)* -> c_Hoare__Mirabelle_Ohoare__valids(x2,hAPP(c_in(u),y),t_a)* equal(y,v).
% 299.92/300.51 60938[0:Res:59525.1,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),y),x)))* equal(hAPP(z,y),hAPP(z,v))* c_Fun_Oinj__on(z,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),y),x),u,x1)* -> c_Hoare__Mirabelle_Ohoare__valids(x2,hAPP(c_in(u),y),t_a)* equal(y,v).
% 299.92/300.51 61810[0:SpL:11167.1,224.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),v_Procs) hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,tc_Com_Opname)),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(v,w),c_Set_Oinsert(v_x,tc_Com_Opname)),hAPP(c_Set_Oinsert(v_Procs,x),y),x,u) -> .
% 299.92/300.51 62447[0:SSi:62231.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,y,tc_fun(w,tc_bool)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),tc_fun(w,tc_bool))*.
% 299.92/300.51 64818[0:SpR:28747.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),tc_Com_Opname,y),tc_Com_Opname),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),tc_Com_Opname,y),tc_Com_Opname),u,tc_fun(w,tc_bool)))**.
% 299.92/300.51 64938[0:SpR:28748.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),tc_Com_Opname,y),tc_Com_Opname),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),tc_Com_Opname,y),tc_Com_Opname),u,tc_fun(w,tc_bool)))**.
% 299.92/300.51 65058[0:SpR:28902.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,y),tc_Com_Opname),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,y),tc_Com_Opname),u,tc_fun(w,tc_bool)))**.
% 299.92/300.51 65178[0:SpR:28903.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v_Procs),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,y),tc_Com_Opname),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,y),tc_Com_Opname),u,tc_fun(w,tc_bool)))**.
% 299.92/300.51 66784[0:SpL:1188.2,224.0] class_OrderedGroup_Ogroup__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),hAPP(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(u),w),x),w,v) -> .
% 299.92/300.51 67540[0:SpL:1189.2,224.0] class_OrderedGroup_Oordered__ab__group__add(u) class_Lattices_Oboolean__algebra(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(u),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_HOL_Ozero__class_Ozero(u)),hAPP(c_Set_Oinsert(c_HOL_Ozero__class_Ozero(u),w),x),w,v) -> .
% 299.92/300.51 74339[7:SpL:71835.1,462.0] || equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),c_Set_Oinsert(v_x,t_a)) c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.51 74250[7:SpL:71835.1,462.0] || equal(c_Set_Oinsert(v_x,t_a),c_Com_Obody) c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),v_x)),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,v_x)),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.92/300.51 78619[0:Rew:584.0,78603.1,584.0,78603.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(v,v_x))) -> hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v_x),hAPP(v,v_x)),c_COMBS(c_in(u),v,w,x,y),tc_Com_Opname,z)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v_x),hAPP(v,v_x)),c_COMBS(c_in(u),v,w,x,y),tc_Com_Opname,z)))*.
% 299.92/300.51 78620[0:Rew:584.0,78602.1,584.0,78602.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(v,v_x))) -> hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(c_in(u),v,w,x,y),hAPP(hAPP(c_in(u),v_x),hAPP(v,v_x)),tc_Com_Opname,z)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBS(c_in(u),v,w,x,y),hAPP(hAPP(c_in(u),v_x),hAPP(v,v_x)),tc_Com_Opname,z)))*.
% 299.92/300.51 80257[0:SpL:21268.0,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(c_Set_Oinsert(u,v),w),x),y,z)))* equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(u,v),w),hAPP(hAPP(c_Set_Oinsert(u,v),w),x),y,z),u).
% 299.92/300.51 80098[0:SpL:21268.0,488.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_in(w),hAPP(c_in(w),x),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x1)))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)),z))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x1,u,w)),x1))*.
% 299.92/300.51 80457[0:Rew:537.1,79901.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),x,z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)))**.
% 299.92/300.51 80458[0:Rew:534.1,79900.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),x,z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)))**.
% 299.92/300.51 79547[0:SpR:21268.0,96.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(u,w,x),y),v,z),w,x) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(u,w,x),y),v,z),u,w,x),hAPP(c_Set_Oimage(u,w,x),y),x,w)*.
% 299.92/300.51 80472[0:Rew:240.2,79663.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),z),y,x1),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u)))**.
% 299.92/300.51 81452[0:SpL:21894.0,371.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),w),x)) -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Set_Oinsert(u,v),w),x),hAPP(c_Set_Oinsert(u,v),w),y,z)))* equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Set_Oinsert(u,v),w),x),hAPP(c_Set_Oinsert(u,v),w),y,z),u).
% 299.92/300.51 81293[0:SpL:21894.0,488.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_in(w),x),c_in(w),v,y)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),x1)))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)),z))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x1,u,w)),x1))*.
% 299.92/300.51 81652[0:Rew:537.1,81095.1] class_Lattices_Olattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)))**.
% 299.92/300.51 81653[0:Rew:534.1,81094.1] class_Lattices_Oupper__semilattice(u) || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y)))**.
% 299.92/300.51 80740[0:SpR:21894.0,96.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(u,w,x),y),c_Set_Oimage(u,w,x),v,z),w,x) -> c_Fun_Oinj__on(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(u,w,x),y),c_Set_Oimage(u,w,x),v,z),u,w,x),hAPP(c_Set_Oimage(u,w,x),y),x,w)*.
% 299.92/300.51 81667[0:Rew:240.2,80857.2] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),z),c_COMBB(c_Lattices_Oupper__semilattice__class_Osup(u),u,tc_fun(u,u),w),y,x1),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,z,w,u)))**.
% 299.92/300.51 81947[0:SpR:223.1,5879.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,w,z,v,x1),v,x1),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oinsert(z,x1),x2,x3,x4),hAPP(c_Set_Oimage(y,v,x1),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))),u)*.
% 299.92/300.51 82420[0:SpR:223.1,5880.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,w,z,v,x1),v,x1),x),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),c_Set_Oinsert(z,x1),x2,x3,x4),hAPP(c_Set_Oimage(y,v,x1),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))),u)*.
% 299.92/300.51 83123[0:SpL:5924.0,449.0] || hBOOL(hAPP(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,c_COMBS(u,c_COMBK(w,x,y),z,x1,x2),x3,x4)),w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,c_COMBS(u,c_COMBK(w,x,y),z,x1,x2),x3,x4)))* -> c_Hoare__Mirabelle_Otriple__valid(x4,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),x3),c_COMBS(u,c_COMBK(w,x,y),z,x1,x2)),t_a).
% 299.92/300.51 83442[0:SpL:5961.0,449.0] || hBOOL(hAPP(hAPP(u,hAPP(v,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(w,c_COMBS(c_COMBK(u,x,y),v,z,x1,x2),x3,x4))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(w,c_COMBS(c_COMBK(u,x,y),v,z,x1,x2),x3,x4)))* -> c_Hoare__Mirabelle_Otriple__valid(x4,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),w),x3),c_COMBS(c_COMBK(u,x,y),v,z,x1,x2)),t_a).
% 299.92/300.51 83883[0:SpL:5899.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_COMBS(v,w,x,y,z),x1)),hAPP(c_Set_Oimage(c_COMBS(v,w,x2,x3,x4),x5,u),c_HOL_Ominus__class_Ominus(x6,hAPP(c_Set_Oinsert(x1,x5),c_Orderings_Obot__class_Obot(tc_fun(x5,tc_bool))),tc_fun(x5,tc_bool)))))* c_Fun_Oinj__on(c_COMBS(v,w,x2,x3,x4),hAPP(c_Set_Oinsert(x1,x5),x6),x5,u) -> .
% 299.92/300.51 85142[0:MRR:85141.0,24395.1] || c_Finite__Set_Ofinite(u,v) c_lessequals(hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),u,tc_fun(v,tc_bool))* c_lessequals(hAPP(c_Set_Oimage(x,v,tc_Com_Opname),u),v_Procs,tc_fun(tc_Com_Opname,tc_bool))* c_Fun_Oinj__on(c_COMBK(w,v,tc_Com_Opname),v_Procs,tc_Com_Opname,v) c_Fun_Oinj__on(x,u,v,tc_Com_Opname) -> equal(c_Finite__Set_Ocard(u,v),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 299.92/300.51 85818[0:Res:9066.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(y,v),z))),c_Set_Oinsert(x1,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x1,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(y,v),z)),u,v,tc_fun(w,tc_bool))))**.
% 299.92/300.51 86475[0:SpL:86109.1,199.0] || equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oinsert(v_x,t_a),v,u,w)),v_Procs) hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oinsert(v_x,t_a),v,u,w)))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),x))*.
% 299.92/300.51 21651[0:SpL:21267.0,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x),tc_Com_Opname,w))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x),tc_Com_Opname,w)))* c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.92/300.51 22279[0:SpL:21893.0,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname,w))),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname,w)))* c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.92/300.51 26699[0:SpR:338.0,244.2] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x))) equal(c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),u),c_HOL_Ozero__class_Ozero(tc_nat)) equal(c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Set_Oinsert(v,u),x)),u),c_Suc(c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),u)))**.
% 299.92/300.51 27555[0:SpR:97.1,373.2] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oimage(u,w,x),v)),z)) c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),z,y,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,x1),v),hAPP(c_Set_Oimage(u,w,x),v))**.
% 299.92/300.51 27707[0:SpR:97.1,71.2] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oimage(u,w,x),v)),z)) c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),z,y,x1) -> equal(hAPP(c_Fun_Othe__inv__into(z,c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,x1),v),hAPP(c_Set_Oimage(u,w,x),v))**.
% 299.92/300.51 27939[0:Res:468.0,469.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(c_Set_Oimage(x1,v,w),hAPP(c_Set_Oimage(x,y,v),z))) equal(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(z,x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(x,y,v),z),u,x1,v,w),y,v)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(x,y,v),z),u,x1,v,w))**.
% 299.92/300.51 27938[0:Res:468.0,464.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(c_Set_Oimage(x1,v,w),hAPP(c_Set_Oimage(x,y,v),z))) equal(hAPP(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(z,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(x,y,v),z),u,x1,v,w),x,y,v)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(x,y,v),z),u,x1,v,w))**.
% 299.92/300.51 31374[0:SpL:445.1,449.0] || hBOOL(hAPP(hAPP(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,c_Fun_Ofun__upd(u,w,x,y,z),x1,x2)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,c_Fun_Ofun__upd(u,w,x,y,z),x1,x2)))* -> equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,c_Fun_Ofun__upd(u,w,x,y,z),x1,x2),w) c_Hoare__Mirabelle_Otriple__valid(x2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),x1),c_Fun_Ofun__upd(u,w,x,y,z)),t_a).
% 299.92/300.51 32955[0:SpR:465.1,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),y),v)) equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(z,x,x1),v),x2),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(z,y,x3,x,x1),x,x1),u,x2),w)),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(z,y,x3,x,x1),x,x1),u,x2),w))**.
% 299.92/300.51 33083[0:SpL:21893.0,94.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v,w) c_Fun_Oinj__on(y,hAPP(c_Set_Oimage(u,v,w),v_x),w,z) -> c_Fun_Oinj__on(c_Fun_Ocomp(y,u,w,z,v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v,z)*.
% 299.92/300.51 33082[0:SpL:21267.0,94.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v,w) c_Fun_Oinj__on(y,hAPP(c_Set_Oimage(u,v,w),v_x),w,z) -> c_Fun_Oinj__on(c_Fun_Ocomp(y,u,w,z,v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v,z)*.
% 299.92/300.51 34420[0:SpL:24914.0,470.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__XimageE__1__1(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,x,u),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,x,u),v_x)),v,w,x,u)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,x,u),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,x,u),v_x))))*.
% 299.92/300.51 34419[0:SpL:24914.0,466.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,x,u),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,x,u),v_x)),w,v,x,u)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,x,u),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,x,u),v_x))))*.
% 299.92/300.51 34389[0:SpL:24914.0,327.0] || equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)) -> c_lessequals(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),v_x)),tc_fun(u,tc_bool))*.
% 299.92/300.51 34138[0:SpR:24914.0,329.1] || c_lessequals(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)),tc_fun(v,tc_bool))* -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),tc_Com_Opname,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),v_x)).
% 299.92/300.51 34599[0:SpR:55.1,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) c_Fun_Oinj__on(c_Set_Oinsert(z,x),y,u,x1) -> hBOOL(hAPP(hAPP(c_in(x),z),w)) equal(hAPP(c_Fun_Othe__inv__into(y,c_Set_Oinsert(z,x),u,x1),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(z,x),v),w,tc_fun(x,tc_bool))),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)))**.
% 299.92/300.51 34598[0:SpR:55.1,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) c_Fun_Oinj__on(c_Set_Oinsert(z,x),y,u,x1) -> hBOOL(hAPP(hAPP(c_in(x),z),w)) equal(hAPP(c_Hilbert__Choice_Oinv__into(y,c_Set_Oinsert(z,x),u,x1),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(z,x),v),w,tc_fun(x,tc_bool))),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)))**.
% 299.92/300.51 35356[0:SpR:104.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))),v,tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(y,u,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool))),v,tc_fun(z,tc_bool))))*.
% 299.92/300.51 35223[0:SpR:410.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),c_Fun_Ofun__upd(x,y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,v,x1,tc_fun(u,tc_bool)),x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),x,x3,x4,x2),y,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x1),z),v,x1,tc_fun(u,tc_bool)),x2,x4))*.
% 299.92/300.51 37303[0:SpL:24914.0,274.0] || equal(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(u,v),v_x)) -> hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,x),hAPP(c_Set_Oinsert(u,v),v_x))))* equal(w,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,x),hAPP(c_Set_Oinsert(u,v),v_x)))*.
% 299.92/300.51 38972[0:SpR:354.2,317.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,w,y),u),z),x2)),hAPP(c_Set_Oinsert(u,x1),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x1),x2)))*.
% 299.92/300.51 38971[0:SpR:354.2,99.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x1),u),hAPP(c_Set_Oimage(x,w,y),u))**.
% 299.92/300.51 38970[0:SpR:354.2,438.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x1),u),hAPP(c_Set_Oimage(x,w,y),u))**.
% 299.92/300.51 40191[0:Res:399.1,402.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),u),tc_fun(w,tc_bool))* -> equal(hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),u),hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),v)).
% 299.92/300.51 40185[0:SpR:24914.0,399.1] || c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),tc_Com_Opname,v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x)),w,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w),tc_fun(u,tc_bool)).
% 299.92/300.51 40179[0:SpR:24914.0,399.1] || c_lessequals(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),tc_Com_Opname,w),hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),v_x)),tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),u),hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),v_x),tc_fun(v,tc_bool)).
% 299.92/300.51 40280[0:SpL:24914.0,398.0] || c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),tc_Com_Opname,w),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x)),v,tc_fun(u,tc_bool))*.
% 299.92/300.51 40274[0:SpL:24914.0,398.0] || c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x),tc_fun(u,tc_bool)) -> c_lessequals(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),tc_Com_Opname,w),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v_x)),tc_fun(u,tc_bool))*.
% 299.92/300.51 41269[0:SpL:205.1,275.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),y))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,tc_fun(x1,tc_bool))))*.
% 299.92/300.51 41556[0:SpL:71.2,284.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),v),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(w,x,u,y),x1,z),x2)))* c_Fun_Oinj__on(c_Fun_Othe__inv__into(w,x,u,y),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x1,z)* -> hBOOL(hAPP(hAPP(c_in(x1),hAPP(x,v)),x2)).
% 299.92/300.51 41555[0:SpL:373.2,284.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),v),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(w,x,u,y),x1,z),x2)))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(w,x,u,y),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x1,z)* -> hBOOL(hAPP(hAPP(c_in(x1),hAPP(x,v)),x2)).
% 299.92/300.51 41786[0:SpL:2097.1,199.0] || hBOOL(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oinsert(x,y),v,u,w)),x))* hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oinsert(x,y),v,u,w))) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(c_Set_Oinsert(x,y),z))*.
% 299.92/300.51 41953[0:SpR:465.1,82.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)))) c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),w),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),x),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(y,u,x1),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))),tc_fun(x1,tc_bool))*.
% 299.92/300.51 42274[0:SSi:42128.0,555.1,550.1] class_Lattices_Olattice(u) || c_Finite__Set_Ofinite(v,tc_fun(t_a,u)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),x,v,tc_fun(t_a,u),tc_fun(t_a,u)),v_x)),hAPP(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),x,hAPP(c_Set_Oinsert(w,tc_fun(t_a,u)),v),tc_fun(t_a,u),tc_fun(t_a,u)),v_x))**.
% 299.92/300.51 42279[0:SSi:42278.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> equal(hAPP(c_Set_Oinsert(w,v),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,hAPP(c_Set_Oinsert(y,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool))),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(w,v),y),tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)))**.
% 299.92/300.51 42476[0:SpL:331.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x,y)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x,y))** -> equal(hAPP(c_Set_Oimage(u,x,y),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x,y),v)).
% 299.92/300.51 42435[0:SpL:331.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),u,x,y)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),u,x,y))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),x,y),v),hAPP(c_Set_Oimage(u,x,y),v)).
% 299.92/300.51 43136[0:SpL:486.1,493.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* equal(hAPP(c_Set_Oimage(x,y,z),hAPP(x1,v)),hAPP(c_Set_Oimage(x,y,z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x1,u,tc_fun(y,tc_bool))))* c_Fun_Oinj__on(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x1,u,tc_fun(y,tc_bool)),y,z) -> equal(hAPP(x1,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x1,u,tc_fun(y,tc_bool))).
% 299.92/300.51 43043[0:SpR:614.2,486.1] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),z)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,tc_fun(x1,tc_bool)))**.
% 299.92/300.51 43023[0:SpR:188.1,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),w),y))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Ovimage(c_COMBK(v,u,x1),x1,u),x,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Ovimage(c_COMBK(v,u,x1),x1,u),x,tc_fun(z,tc_bool)))**.
% 299.92/300.51 42967[0:SpR:89.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(x1,v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_COMBB(x1,u,tc_fun(z,tc_bool),x),w),x,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_COMBB(x1,u,tc_fun(z,tc_bool),x),w),x,tc_fun(z,tc_bool)))**.
% 299.92/300.51 43530[0:SpR:354.2,507.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,w,y),u)),z)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z)))**.
% 299.92/300.51 43515[0:SpR:354.2,507.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Set_Oimage(x,w,y),u))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z)),u))**.
% 299.92/300.51 43943[0:SpL:354.2,231.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_lessequals(z,u,tc_fun(w,tc_bool)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v,x,w,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,w) -> c_lessequals(hAPP(c_Set_Ovimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z),hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool))*.
% 299.92/300.51 44064[0:SpL:354.2,358.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_lessequals(u,hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z),tc_fun(w,tc_bool))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v,x,w,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,w)* -> c_lessequals(hAPP(c_Set_Oimage(x,w,y),u),z,tc_fun(y,tc_bool)).
% 299.92/300.51 44049[0:SpL:354.2,358.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_lessequals(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z),u,tc_fun(w,tc_bool))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v,x,w,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,w)* -> c_lessequals(z,hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool)).
% 299.92/300.51 44306[0:Res:176.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),hAPP(c_Set_Oinsert(hAPP(w,y),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))* equal(hAPP(z,y),hAPP(z,v))* c_Fun_Oinj__on(z,hAPP(c_Set_Ovimage(w,u,x),hAPP(c_Set_Oinsert(hAPP(w,y),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),u,x1)* -> equal(y,v).
% 299.92/300.51 44278[0:SpL:24914.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),v))* hBOOL(hAPP(hAPP(c_in(u),w),v))* equal(hAPP(x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x))),hAPP(x,w))* c_Fun_Oinj__on(x,v,u,z)* -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,y),hAPP(c_in(u),v_x)),w).
% 299.92/300.51 45514[0:MRR:45507.3,17944.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u) -> equal(hAPP(v,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u),v,u,w)),c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u))**.
% 299.92/300.51 45515[0:MRR:45506.3,17944.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u) -> equal(hAPP(v,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u),v,u,w)),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),u))**.
% 299.92/300.51 45867[0:SpL:24914.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x)))* -> hBOOL(hAPP(u,y))*.
% 299.92/300.51 45855[0:SpL:323.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool)),u,y)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,w,x,tc_fun(y,tc_bool)),u,y)))* hBOOL(hAPP(hAPP(c_in(y),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),z),w,x,tc_fun(y,tc_bool))))* -> hBOOL(hAPP(u,x1))*.
% 299.92/300.51 46141[0:Res:151.2,481.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(u),v),x))* hBOOL(hAPP(y,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))),z),y,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))),z)))*.
% 299.92/300.51 46459[0:Res:151.2,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(u),v),x))* hBOOL(hAPP(y,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))),y,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)))))*.
% 299.92/300.51 46579[0:SpR:158.0,617.1] || -> equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(c_Fun_Ocomp(y,u,w,tc_fun(z,tc_bool),v),v,tc_fun(z,tc_bool)),x),c_Set_Oinsert(x1,z),tc_fun(z,tc_bool),tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(x1,z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,w),x),y,w,tc_fun(z,tc_bool))))*.
% 299.92/300.51 46601[0:Rew:26153.0,46600.2] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oimage(w,x,tc_fun(u,tc_bool)),y))) -> equal(y,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(z,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,x,tc_fun(u,tc_bool)))),hAPP(c_Set_Oinsert(z,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,x,tc_fun(u,tc_bool))))**.
% 299.92/300.51 46933[0:Res:241.2,402.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool)) c_lessequals(x,c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),x).
% 299.92/300.51 48456[0:SpL:28334.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w),tc_Com_Opname),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,x),y),x,u) -> .
% 299.92/300.51 48453[0:SpL:28031.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w),tc_Com_Opname),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,x),y),x,u) -> .
% 299.92/300.51 48428[0:SpL:24914.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,v_x)),hAPP(c_Set_Oimage(v,w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,y),hAPP(v,v_x)),w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(v,hAPP(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,y),hAPP(v,v_x)),w),x),w,u) -> .
% 299.92/300.51 48625[0:SpR:197.1,66.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),hAPP(c_Set_Oinsert(z,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oinsert(z,w),hAPP(c_Set_Oimage(u,v,w),y)),tc_fun(w,tc_bool)))*.
% 299.92/300.51 49154[0:SpL:393.1,239.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* c_lessequals(x,y,tc_fun(z,tc_bool)) c_Fun_Oinj__on(c_COMBK(w,u,z),x,z,u) -> equal(x,c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))) hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Fun_Othe__inv__into(x,c_COMBK(w,u,z),z,u),v)),y))*.
% 299.92/300.51 49639[0:Res:225.1,470.0] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,w),v),w,x) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),hAPP(u,y),u,w,x)),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))))*.
% 299.92/300.51 49638[0:Res:225.1,466.0] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,w),v),w,x) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),u,hAPP(u,y),w,x)),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))))*.
% 299.92/300.51 49634[0:Res:225.1,275.1] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(y),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(z,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))),x1))* -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(z,w),v),w,x)* hBOOL(hAPP(hAPP(c_in(x),hAPP(u,z)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oimage(u,w,x),y,tc_fun(x,tc_bool))))*.
% 299.92/300.51 49748[0:Rew:49662.2,49600.1] || c_Fun_Oinj__on(hAPP(c_COMBB(u,v,w,x),y),z,x1,x2) -> hBOOL(hAPP(hAPP(c_in(x2),hAPP(u,hAPP(y,x3))),hAPP(c_Set_Oimage(hAPP(c_COMBB(u,v,w,x),y),x1,x2),hAPP(c_Set_Oinsert(x3,x1),z))))* c_Fun_Oinj__on(hAPP(c_COMBB(u,v,w,x),y),hAPP(c_Set_Oinsert(x3,x1),z),x1,x2).
% 299.92/300.51 49749[0:Rew:49662.2,49599.1] || c_Fun_Oinj__on(hAPP(c_COMBC(u,v,w,x),y),z,x1,x2) -> hBOOL(hAPP(hAPP(c_in(x2),hAPP(hAPP(u,x3),y)),hAPP(c_Set_Oimage(hAPP(c_COMBC(u,v,w,x),y),x1,x2),hAPP(c_Set_Oinsert(x3,x1),z))))* c_Fun_Oinj__on(hAPP(c_COMBC(u,v,w,x),y),hAPP(c_Set_Oinsert(x3,x1),z),x1,x2).
% 299.92/300.51 49750[0:Rew:49662.2,49577.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),y,z),hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),w),y),x))))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_Option_Othe(w)),hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(c_Orderings_Otop__class_Otop(tc_bool),w),y),x),y,z).
% 299.92/300.51 49751[0:Rew:49662.2,49575.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),y,z),hAPP(c_Set_Oinsert(x1,y),x))))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),hAPP(c_Set_Oinsert(x1,y),x),y,z).
% 299.92/300.51 49752[0:Rew:49662.2,49563.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y,z),hAPP(c_Set_Oinsert(v,y),x))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),hAPP(c_Set_Oinsert(v,y),x),y,z).
% 299.92/300.51 49753[0:Rew:49662.2,49562.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y,z),hAPP(c_Set_Oinsert(u,y),x))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(c_Set_Oinsert(u,y),x),y,z).
% 299.92/300.51 49754[0:Rew:49662.2,49553.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),v)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,y),hAPP(c_Set_Oinsert(z,x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(z,x),w),x,y).
% 299.92/300.51 49756[0:Rew:49662.2,49487.1] || c_Fun_Oinj__on(c_Set_Oinsert(u,v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oinsert(z,v),hAPP(c_Set_Oinsert(u,v),x1))),hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(z,v),x1),x),w))))* c_Fun_Oinj__on(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(z,v),x1),x),w),x,y).
% 299.92/300.51 49774[0:Rew:6.0,49773.2] || c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)),x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(u,w)),hAPP(c_Set_Oimage(u,x,y),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(w,x),v),x,y).
% 299.92/300.51 49787[0:Rew:49662.2,49649.2] || c_Fun_Oinj__on(u,v,w,tc_Hoare__Mirabelle_Otriple(t_a)) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(x,w),v),w,tc_Hoare__Mirabelle_Otriple(t_a)) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(y,hAPP(c_Set_Oimage(u,w,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(x,w),v)))),hAPP(c_Set_Oimage(u,w,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oinsert(x,w),v))))* c_Hoare__Mirabelle_Otriple__valid(y,hAPP(u,x),t_a).
% 299.92/300.51 50510[0:SpL:223.1,263.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,x1,u,x),u,x),w)))* -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(z,u,x),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))))* equal(y,x1).
% 299.92/300.51 50482[0:SpR:393.1,223.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(c_COMBK(x,y,u),v,z,u,y),u,y),w),hAPP(c_Set_Oinsert(z,y),hAPP(c_Set_Oinsert(x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))))**.
% 299.92/300.51 50861[0:SpL:622.0,3489.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_in(tc_Com_Opname))** hBOOL(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),c_HOL_Ouminus__class_Ouminus(v_Procs,tc_fun(tc_Com_Opname,tc_bool)))) -> .
% 299.92/300.51 50860[0:SpL:622.0,3487.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname))** equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> .
% 299.92/300.51 50803[0:SpR:622.0,3294.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_in(t_a))** -> equal(hAPP(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),c_Orderings_Obot__class_Obot(tc_bool)).
% 299.92/300.51 51102[0:SpL:8415.2,472.2] || equal(v_Procs,v_x) equal(c_Hilbert__Choice_Oinv__into(u,v,w,x),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(v,w,x),u)))* hBOOL(hAPP(hAPP(c_in(x),v_x),hAPP(c_Set_Oimage(v,w,x),u)))* equal(hAPP(c_Hilbert__Choice_Oinv__into(u,v,w,x),y),v_x) -> equal(y,v_x).
% 299.92/300.51 51264[0:Rew:8415.2,51247.3] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(u)) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.51 52569[0:MRR:52568.2,96.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,x,u,y),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,u,y),w),c_Fun_Othe__inv__into(w,x,u,y),y,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(w,c_Fun_Ocomp(c_Fun_Othe__inv__into(w,x,u,y),x,y,u,u),u,u),v))*.
% 299.92/300.51 53355[0:Res:31543.0,593.0] || c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x)))),hAPP(v_Q,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x))),t_a)*.
% 299.92/300.51 53380[0:SpL:61.1,12982.0] || c_Finite__Set_Ofinite(u,v) c_Hoare__Mirabelle_Otriple__valid(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,v),u),v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool))),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),x,t_a)*.
% 299.92/300.51 60484[0:SpL:5882.1,224.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),c_Orderings_Otop__class_Otop(u)),hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1,v),c_HOL_Ominus__class_Ominus(x2,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),tc_fun(x1,tc_bool)))))* c_Fun_Oinj__on(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(u),x1),x2),x1,v) -> .
% 299.92/300.51 61908[0:SpL:622.0,15487.1] || equal(c_HOL_Ouminus__class_Ouminus(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_fun(t_a,tc_bool)),c_Com_Ocom_OBODY)** equal(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),tc_bool),c_Com_Ocom_OSKIP) -> .
% 299.92/300.51 62448[0:SSi:62230.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) equal(hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),u)) -> c_lessequals(hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),u),tc_fun(w,tc_bool))*.
% 299.92/300.51 62449[0:SSi:62210.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool)) equal(x,c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))) -> c_lessequals(x,c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.92/300.51 64256[0:SpL:646.1,224.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),x,w),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(hAPP(u,v_x),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Fun_Othe__inv__into(v_Procs,u,tc_Com_Opname,v),hAPP(c_Set_Oinsert(hAPP(u,v_x),x),y),x,w) -> .
% 299.92/300.51 64229[0:SpR:533.0,646.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),v_x)**.
% 299.92/300.51 64424[0:SpL:645.1,224.0] || c_Fun_Oinj__on(u,v_Procs,tc_Com_Opname,v) hBOOL(hAPP(hAPP(c_in(w),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),x,w),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(hAPP(u,v_x),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(c_Set_Oinsert(hAPP(u,v_x),x),y),x,w) -> .
% 299.92/300.51 64396[0:SpR:533.0,645.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))),v_x)**.
% 299.92/300.51 64502[0:SpL:622.0,24257.1] || equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Lattices_Oupper__semilattice__class_Osup(tc_bool))** equal(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),c_in(tc_Com_Opname)) -> hBOOL(hAPP(v_x,v_Procs)).
% 299.92/300.51 64691[0:Res:27986.0,593.0] || c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w))),t_a)*.
% 299.92/300.51 64711[0:Res:27987.0,593.0] || c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w))),t_a)*.
% 299.92/300.51 64731[0:Res:28288.0,593.0] || c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w))),t_a)*.
% 299.92/300.51 64751[0:Res:28289.0,593.0] || c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w))),t_a)*.
% 299.92/300.51 79036[0:Res:15630.1,479.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(x,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,y),z),x1,hAPP(c_in(u),v),y),x2,x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,y),z),x1,hAPP(c_in(u),v),y)),x2)))*.
% 299.92/300.51 79035[0:Res:15630.1,478.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(x,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,z),x1),x2,hAPP(c_in(u),v),z),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,z),x1),x2,hAPP(c_in(u),v),z))))*.
% 299.92/300.51 79060[0:Rew:533.0,78992.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(x,y),z),x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),y))))*.
% 299.92/300.51 79256[0:Res:15858.1,479.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(x,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(w,z),x1),hAPP(c_in(u),v),z),x2,x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(w,z),x1),hAPP(c_in(u),v),z)),x2)))*.
% 299.92/300.51 79255[0:Res:15858.1,478.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(x,v)) -> hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,hAPP(c_Set_Oinsert(w,x1),x2),hAPP(c_in(u),v),x1),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,hAPP(c_Set_Oinsert(w,x1),x2),hAPP(c_in(u),v),x1))))*.
% 299.92/300.51 79280[0:Rew:533.0,79212.0] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x))) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(x,z),x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),z))))*.
% 299.92/300.51 80207[0:SpL:21268.0,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),x,y),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),x,y),u),v,u)*.
% 299.92/300.51 80206[0:SpL:21268.0,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),x,y),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),x,y),u),u)*.
% 299.92/300.51 80464[0:Rew:339.0,79913.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)),x,z))),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)))**.
% 299.92/300.51 81402[0:SpL:21894.0,170.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),x,y),u) -> c_lessequals(c_Finite__Set_Olinorder__class_OMin(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),x,y),u),v,u)*.
% 299.92/300.51 81401[0:SpL:21894.0,169.1] class_Orderings_Olinorder(u) || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),x,y),u) -> c_lessequals(v,c_Finite__Set_Olinorder__class_OMax(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),x,y),u),u)*.
% 299.92/300.51 81659[0:Rew:339.0,81107.0] || -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),x,z))),hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y)))**.
% 299.92/300.51 89000[0:SpR:223.1,14196.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Set_Oinsert(x,y),z,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x2,v,x,u,y),u,y),w),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),hAPP(c_Set_Oimage(x2,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))))*.
% 299.92/300.51 88893[0:SpR:497.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_x))*.
% 299.92/300.51 92981[0:SpR:223.1,5876.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Set_Oinsert(y,z),x2,x3,x4),hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),tc_fun(x1,tc_bool))*.
% 299.92/300.51 27153[0:SpR:329.1,450.0] || c_lessequals(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w,x,y),tc_fun(v,tc_bool)) -> hBOOL(hAPP(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w,x,y),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u),w,x,y)))* c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),u)),x),w),t_a).
% 299.92/300.51 27136[0:SpR:393.1,450.0] || -> equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oimage(c_COMBK(u,v,w),w,v),x,y,z),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Set_Oimage(c_COMBK(u,v,w),w,v),x,y,z)))* c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Set_Oimage(c_COMBK(u,v,w),w,v)),y),x),t_a).
% 299.92/300.51 27598[0:SpR:542.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y,u,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))**.
% 299.92/300.51 27751[0:SpR:542.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y,u,z) -> equal(hAPP(c_Fun_Othe__inv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))**.
% 299.92/300.51 27937[0:Res:468.0,467.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(c_Set_Oimage(x1,v,w),hAPP(c_Set_Oimage(x,y,v),z))) equal(hAPP(x,hAPP(c_Hilbert__Choice_Oinv__into(z,x,y,v),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(x,y,v),z),u,x1,v,w))),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(x,y,v),z),u,x1,v,w))**.
% 299.92/300.51 32410[0:Rew:339.0,32354.2] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),x))))* hBOOL(hAPP(hAPP(c_in(x),x1),y))* -> hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x1)))*.
% 299.92/300.51 32411[0:Rew:537.1,32351.3] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x))))* hBOOL(hAPP(hAPP(c_in(x),x1),y))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1)))*.
% 299.92/300.51 32412[0:Rew:534.1,32350.3] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x))))* hBOOL(hAPP(hAPP(c_in(x),x1),y))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1)))*.
% 299.92/300.51 32588[0:Rew:339.0,32534.2] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),x))))* hBOOL(hAPP(hAPP(c_in(x),x1),z))* -> hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x1)))*.
% 299.92/300.51 32589[0:Rew:537.1,32531.3] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x))))* hBOOL(hAPP(hAPP(c_in(x),x1),z))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1)))*.
% 299.92/300.51 32590[0:Rew:534.1,32530.3] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x))))* hBOOL(hAPP(hAPP(c_in(x),x1),z))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1)))*.
% 299.92/300.51 32980[0:SpR:339.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),v)),x1),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(x,y),z)),u,x1),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(x,y),z)),u,x1),w))**.
% 299.92/300.51 32971[0:SpR:537.1,475.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w)),x1),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),v,x1),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),v,x1),x))**.
% 299.92/300.51 32970[0:SpR:534.1,475.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w)),x1),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),v,x1),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),v,x1),x))**.
% 299.92/300.51 32857[0:SpR:475.1,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),w)),x1)) c_Fun_Oinj__on(c_Set_Oinsert(hAPP(y,v),z),x1,x,x2) -> equal(hAPP(c_Fun_Othe__inv__into(x1,c_Set_Oinsert(hAPP(y,v),z),x,x2),hAPP(c_Set_Oimage(y,u,z),w)),hAPP(c_Set_Oimage(y,u,z),w))**.
% 299.92/300.51 32856[0:SpR:475.1,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),w)),x1)) c_Fun_Oinj__on(c_Set_Oinsert(hAPP(y,v),z),x1,x,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Set_Oinsert(hAPP(y,v),z),x,x2),hAPP(c_Set_Oimage(y,u,z),w)),hAPP(c_Set_Oimage(y,u,z),w))**.
% 299.92/300.51 33796[0:Res:248.4,402.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(tc_fun(u,tc_bool),tc_bool)) c_lessequals(c_Finite__Set_Olinorder__class_OMin(w,tc_fun(u,tc_bool)),c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,tc_bool),tc_bool))) equal(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),c_Finite__Set_Olinorder__class_OMin(w,tc_fun(u,tc_bool))).
% 299.92/300.51 33876[0:Res:247.4,402.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(tc_fun(u,tc_bool),tc_bool)) c_lessequals(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),c_Finite__Set_Olinorder__class_OMax(w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,tc_bool),tc_bool))) equal(c_Finite__Set_Olinorder__class_OMax(w,tc_fun(u,tc_bool)),c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool))).
% 299.92/300.51 34418[0:SpL:24914.0,473.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,x,u),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,x,u),v_x)),w,x,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,x,u),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,x,u),v_x))))*.
% 299.92/300.51 35332[0:SpR:465.1,410.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),y),c_Set_Oimage(c_Fun_Ofun__upd(z,v,x1,u,x2),u,x2),x,tc_fun(x3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x3,tc_bool)),hAPP(c_Set_Oimage(z,u,x2),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oimage(c_Fun_Ofun__upd(z,v,x1,u,x2),u,x2),x,tc_fun(x3,tc_bool))))*.
% 299.92/300.51 38669[0:Res:171.2,184.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) c_Fun_Oinj__on(v,x,w,u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(v,hAPP(c_Fun_Othe__inv__into(x,v,w,u),c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),x),u))),c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),x),u))**.
% 299.92/300.51 38668[0:Res:172.2,184.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) c_Fun_Oinj__on(v,x,w,u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(v,hAPP(c_Fun_Othe__inv__into(x,v,w,u),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),x),u))),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),x),u))**.
% 299.92/300.51 39619[0:SpR:532.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Fun_Ofun__upd(w,x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),z),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x2,x3,x1),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z)),x1,x3))*.
% 299.92/300.51 41267[0:SpL:354.2,275.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oimage(x,w,y),u)),x1))* hBOOL(hAPP(hAPP(c_in(x2),x3),u))* -> hBOOL(hAPP(hAPP(c_in(x2),x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,tc_fun(x2,tc_bool))))*.
% 299.92/300.51 41550[0:SpL:97.1,284.0] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(y),v),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),z,y),x1)))* c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,y)* -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oimage(u,w,x),v)),x1)).
% 299.92/300.51 41549[0:SpL:99.1,284.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x),x1)))* c_Fun_Oinj__on(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x)* -> hBOOL(hAPP(hAPP(c_in(z),hAPP(u,y)),x1)).
% 299.92/300.51 41548[0:SpL:438.1,284.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x),x1)))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x)* -> hBOOL(hAPP(hAPP(c_in(z),hAPP(u,y)),x1)).
% 299.92/300.51 41535[0:SpL:393.1,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(v,w,x),x,w),y,u),z)))* c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(v,w,x),x,w),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,u)* -> equal(x1,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* hBOOL(hAPP(hAPP(c_in(y),x1),z))*.
% 299.92/300.51 41521[0:SpL:205.1,284.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(v),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x)),y))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v)* -> hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oimage(u,v,w),y)))*.
% 299.92/300.51 41790[0:SpL:393.1,199.0] || hBOOL(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))) c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),w,x,y),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oimage(c_COMBK(u,v,z),z,v),w,x,y)),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))** hBOOL(hAPP(c_Set_Oimage(c_COMBK(u,v,z),z,v),x1))*.
% 299.92/300.51 41869[0:Rew:104.0,41811.2] || hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(y,tc_bool))),w,v,x)),tc_fun(y,tc_bool)),tc_fun(y,tc_bool)))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,z,tc_fun(y,tc_bool)),tc_fun(y,tc_bool)))*.
% 299.92/300.51 41975[0:SpR:205.1,82.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),y),tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool))),tc_fun(v,tc_bool))*.
% 299.92/300.51 41960[0:SpR:205.1,82.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x),y,tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))),tc_fun(v,tc_bool))*.
% 299.92/300.51 42071[0:SpR:180.2,475.1] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(hAPP(c_in(w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u)),y)) -> equal(hAPP(c_Set_Oinsert(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(z,u),v),u,u),x1),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w,x1),y)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w,x1),y))**.
% 299.92/300.51 42275[0:SSi:42176.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) c_lessequals(w,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,hAPP(c_Set_Oinsert(y,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(w,y,tc_fun(v,tc_bool)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)).
% 299.92/300.51 42276[0:SSi:42126.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) c_lessequals(c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)) -> c_lessequals(w,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,hAPP(c_Set_Oinsert(x,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.92/300.51 42281[0:Rew:42279.1,42277.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)))),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(x,v),w),tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)))**.
% 299.92/300.51 42479[0:SpL:297.2,315.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,z),u)* equal(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,z)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,z))** -> equal(hAPP(c_Set_Oimage(x,y,z),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,z),w)).
% 299.92/300.51 42438[0:SpL:297.2,315.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y,z),u)* equal(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y,z)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y,z))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,z),w),hAPP(c_Set_Oimage(x,y,z),w)).
% 299.92/300.51 43046[0:SpR:542.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,tc_fun(z,tc_bool)))**.
% 299.92/300.51 43039[0:SpR:536.1,486.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),v,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),v,tc_fun(z,tc_bool)))**.
% 299.92/300.51 43038[0:SpR:535.1,486.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),v,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),v,tc_fun(z,tc_bool)))**.
% 299.92/300.51 42995[0:SpR:71.2,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),x1)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Fun_Othe__inv__into(w,x,u,y),z,tc_fun(x2,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Fun_Othe__inv__into(w,x,u,y),z,tc_fun(x2,tc_bool)))**.
% 299.92/300.51 42994[0:SpR:373.2,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(x,v)),x1)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Hilbert__Choice_Oinv__into(w,x,u,y),z,tc_fun(x2,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Hilbert__Choice_Oinv__into(w,x,u,y),z,tc_fun(x2,tc_bool)))**.
% 299.92/300.51 42966[0:SpR:410.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),x)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(z,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(z,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,z,u,tc_fun(y,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(z,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,z,u,tc_fun(y,tc_bool))))**.
% 299.92/300.51 44176[0:SpR:465.1,232.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> hBOOL(hAPP(hAPP(c_in(x),v),c_HOL_Ouminus__class_Ouminus(z,tc_fun(x,tc_bool)))) c_lessequals(hAPP(c_Set_Oimage(u,x,y),c_HOL_Ouminus__class_Ouminus(z,tc_fun(x,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),z),tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.92/300.51 44132[0:SpR:354.2,232.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v,x,w,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,w) -> c_lessequals(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool))),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.92/300.51 44413[0:Rew:90.0,44399.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBB(c_Set_Oimage(u,v,w),tc_fun(v,tc_bool),tc_fun(w,tc_bool),y),v_x),c_COMBB(c_Set_Oimage(u,v,w),tc_fun(v,tc_bool),tc_fun(w,tc_bool),y),tc_Com_Opname,z),y,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v_x,y,tc_fun(v,tc_bool))))**.
% 299.92/300.51 44414[0:Rew:90.0,44398.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBB(c_Set_Oimage(u,v,w),tc_fun(v,tc_bool),tc_fun(w,tc_bool),y),hAPP(c_COMBB(c_Set_Oimage(u,v,w),tc_fun(v,tc_bool),tc_fun(w,tc_bool),y),v_x),tc_Com_Opname,z),y,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v_x,y,tc_fun(v,tc_bool))))**.
% 299.92/300.51 44467[0:Rew:30.0,44453.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBB(c_Set_Ovimage(u,v,w),tc_fun(w,tc_bool),tc_fun(v,tc_bool),y),v_x),c_COMBB(c_Set_Ovimage(u,v,w),tc_fun(w,tc_bool),tc_fun(v,tc_bool),y),tc_Com_Opname,z),y,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v_x,y,tc_fun(w,tc_bool))))**.
% 299.92/300.51 44468[0:Rew:30.0,44452.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBB(c_Set_Ovimage(u,v,w),tc_fun(w,tc_bool),tc_fun(v,tc_bool),y),hAPP(c_COMBB(c_Set_Ovimage(u,v,w),tc_fun(w,tc_bool),tc_fun(v,tc_bool),y),v_x),tc_Com_Opname,z),y,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v_x,y,tc_fun(w,tc_bool))))**.
% 299.92/300.51 44788[0:Res:468.0,593.0] || c_Hoare__Mirabelle_Otriple__valid(u,v_n(u),t_a)* -> equal(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),v_Procs),hAPP(c_Set_Oimage(x,tc_Com_Opname,w),v_Procs)) c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v_Procs,v,x,tc_Com_Opname,w))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v_Procs,v,x,tc_Com_Opname,w)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v_Procs,v,x,tc_Com_Opname,w))),t_a)*.
% 299.92/300.51 45493[0:SpL:24914.0,237.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,u) -> equal(hAPP(v,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,x),hAPP(c_in(u),v_x)),v,u,w)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,x),hAPP(c_in(u),v_x)))**.
% 299.92/300.51 47386[0:SpL:21893.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_Com_Opname,y),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)),x)).
% 299.92/300.51 47385[0:SpL:21267.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x),tc_Com_Opname,y),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)),x)).
% 299.92/300.51 47602[0:SpL:410.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,y),z),x1,y,tc_fun(w,tc_bool))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(x1,x),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x1,y,tc_fun(w,tc_bool)),u,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x1,y,tc_fun(w,tc_bool))))*.
% 299.92/300.51 47955[0:SpL:21893.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname,x),u,v)))* hBOOL(hAPP(hAPP(c_in(v),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)))* -> hBOOL(hAPP(u,y))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,u,v)),w)).
% 299.92/300.51 47954[0:SpL:21267.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x),tc_Com_Opname,x),u,v)))* hBOOL(hAPP(hAPP(c_in(v),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)))* -> hBOOL(hAPP(u,y))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,u,v)),w)).
% 299.92/300.51 48052[0:SpL:410.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(v,w),u,x)))* hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,z),x1),v,z,tc_fun(x,tc_bool))))* -> hBOOL(hAPP(u,y))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,v,z,tc_fun(x,tc_bool)),u,x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,v,z,tc_fun(x,tc_bool))))*.
% 299.92/300.51 48446[0:SpL:15172.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)),z,u),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(x2,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(x2,z),x1),z,u) -> .
% 299.92/300.51 48433[0:SpL:336.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x),y),x,u) -> .
% 299.92/300.51 48393[0:SpL:337.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),hAPP(c_Set_Oinsert(y,w),x),w,u) -> .
% 299.92/300.51 48371[0:SpL:14526.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Option_Othe(v),w,tc_fun(x,tc_bool)),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Option_Othe(v),w,tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),v),y),z),y,u) -> .
% 299.92/300.51 48635[0:SpR:197.1,13.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool)) c_lessequals(z,hAPP(c_Set_Oimage(u,v,w),x1),tc_fun(w,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,x1,tc_fun(v,tc_bool))),c_HOL_Ominus__class_Ominus(y,z,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.92/300.51 48634[0:SpR:197.1,13.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(x,hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Oimage(u,v,w),z),x1,tc_fun(w,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(x,x1,tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(y,z,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.92/300.51 49166[0:SpL:158.0,239.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1))))* c_lessequals(x1,x2,tc_fun(z,tc_bool)) c_Fun_Oinj__on(c_Fun_Ocomp(w,y,x,u,z),x1,z,u) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Fun_Othe__inv__into(x1,c_Fun_Ocomp(w,y,x,u,z),z,u),v)),x2))*.
% 299.92/300.51 49637[0:Res:225.1,473.0] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,w),v),w,x) hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Hilbert__Choice_Oinv__into(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),u,w,x),hAPP(u,y))),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))))*.
% 299.92/300.51 50167[0:SpR:158.0,620.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,x,tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(z,v,x),u)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),x1),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Fun_Ocomp(w,z,x,tc_fun(y,tc_bool),v),v,tc_fun(y,tc_bool))))*.
% 299.92/300.51 50448[0:SpR:223.1,317.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oimage(x,y,z),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x1,v,x2,u,y),u,y),w)),hAPP(c_Set_Oinsert(hAPP(x,x2),z),hAPP(c_Set_Oimage(x,y,z),hAPP(c_Set_Oimage(x1,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))))*.
% 299.92/300.51 50838[0:SpR:622.0,474.0] || -> hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,tc_fun(t_a,tc_bool)))),hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))*.
% 299.92/300.51 51759[0:MRR:51758.2,51758.6,20737.2,20734.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,v,w,y)* c_Finite__Set_Ofinite(z,w) c_lessequals(u,z,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Oimage(x1,w,y),z),hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool))* c_Fun_Oinj__on(x1,z,w,y) -> equal(c_Finite__Set_Ocard(u,w),c_Finite__Set_Ocard(z,w)).
% 299.92/300.51 70373[0:SpL:61.1,12983.0] || c_Finite__Set_Ofinite(u,v) c_Hoare__Mirabelle_Otriple__valid(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,v),u),v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),hAPP(c_Set_Oinsert(x,tc_Hoare__Mirabelle_Otriple(t_a)),y)),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),x,t_a).
% 299.92/300.51 72612[0:SpL:61.1,12988.1] || c_Finite__Set_Ofinite(u,v) hBOOL(hAPP(w,x))* c_Hoare__Mirabelle_Otriple__valid(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(y,v),u),v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(y,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),w),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(y,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),x,t_a)*.
% 299.92/300.51 78621[0:Rew:584.0,78600.1,584.0,78600.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(v,v_x))) -> hBOOL(hAPP(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(c_in(u),v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(c_in(u),v_x),hAPP(v,v_x)))),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBS(c_in(u),v,w,x,y),tc_Com_Opname,z),hAPP(hAPP(c_in(u),v_x),hAPP(v,v_x)))))*.
% 299.92/300.51 80276[0:SpL:21268.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),z,x1),u,w)))*.
% 299.92/300.51 80082[0:SpL:21268.0,184.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) c_Fun_Oinj__on(w,y,x,u) -> equal(hAPP(w,hAPP(c_Fun_Othe__inv__into(y,w,x,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1))**.
% 299.92/300.51 79785[0:SpR:21268.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),z),y,x1),tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),z),tc_fun(w,tc_bool))*.
% 299.92/300.51 79714[0:SpR:21268.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),x,z),x1,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x1),tc_fun(w,tc_bool))*.
% 299.92/300.51 81471[0:SpL:21894.0,487.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z,x1),u,w)))*.
% 299.92/300.51 81277[0:SpL:21894.0,184.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) c_Fun_Oinj__on(w,y,x,u) -> equal(hAPP(w,hAPP(c_Fun_Othe__inv__into(y,w,x,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1))),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1))**.
% 299.92/300.51 80979[0:SpR:21894.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y,x1),tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),z),tc_fun(w,tc_bool))*.
% 299.92/300.51 80908[0:SpR:21894.0,326.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,z),x1,tc_fun(w,tc_bool))* -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x1),tc_fun(w,tc_bool))*.
% 299.92/300.51 85090[0:SpL:644.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(v,w,tc_Com_Opname),tc_Com_Opname,w),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(v,w,tc_Com_Opname),tc_Com_Opname,w),hAPP(c_Set_Oinsert(v_Procs,x),y),x,u) -> .
% 299.92/300.51 87204[0:Res:241.2,32820.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),c_HOL_Ominus__class_Ominus(x,c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))),tc_fun(u,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))).
% 299.92/300.51 89564[7:SpL:78590.1,199.0] || equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oinsert(v_x,t_a),v,u,w)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oinsert(v_x,t_a),v,u,w)))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),x))*.
% 299.92/300.51 90355[4:SpL:78660.1,199.0] || equal(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oinsert(v_x,t_a),v,u,w)),v_x),v_x)** hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oinsert(v_x,t_a),v,u,w))) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),x))*.
% 299.92/300.51 27650[0:SpR:64.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool))),y))* c_Fun_Oinj__on(c_Set_Oinsert(w,x),y,u,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,c_Set_Oinsert(w,x),u,z),hAPP(c_Set_Oinsert(w,x),v)),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))*.
% 299.92/300.51 27803[0:SpR:64.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool))),y))* c_Fun_Oinj__on(c_Set_Oinsert(w,x),y,u,z) -> equal(hAPP(c_Fun_Othe__inv__into(y,c_Set_Oinsert(w,x),u,z),hAPP(c_Set_Oinsert(w,x),v)),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))*.
% 299.92/300.51 31373[0:SpL:393.1,449.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(w,c_Set_Oimage(c_COMBK(u,v,x),x,v),y,z)))* -> equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(w,c_Set_Oimage(c_COMBK(u,v,x),x,v),y,z),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),w),y),c_Set_Oimage(c_COMBK(u,v,x),x,v)),t_a).
% 299.92/300.51 32337[0:SpL:445.1,477.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),c_Fun_Ofun__upd(u,y,z,x1,x2),v)))* hBOOL(hAPP(hAPP(c_in(v),x3),w))* -> equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),c_Fun_Ofun__upd(u,y,z,x1,x2),v),y) hBOOL(hAPP(c_Fun_Ofun__upd(u,y,z,x1,x2),x3))*.
% 299.92/300.51 32517[0:SpL:445.1,476.0] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),c_Fun_Ofun__upd(u,y,z,x1,x2),v)))* hBOOL(hAPP(hAPP(c_in(v),x3),x))* -> equal(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),c_Fun_Ofun__upd(u,y,z,x1,x2),v),y) hBOOL(hAPP(c_Fun_Ofun__upd(u,y,z,x1,x2),x3))*.
% 299.92/300.51 34376[0:SpL:24914.0,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname,w),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x)))),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),tc_Com_Opname,w),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v_x))))* c_Hoare__Mirabelle_Otriple__valid(v,u,t_a).
% 299.92/300.51 34332[0:SpL:24914.0,94.1] || c_Fun_Oinj__on(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v,w) c_Fun_Oinj__on(y,hAPP(c_Set_Oimage(u,v,w),v_x),w,z) -> c_Fun_Oinj__on(c_Fun_Ocomp(y,u,w,z,v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v,z)*.
% 299.92/300.51 35357[0:SpR:339.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),z)),v,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(c_Set_Oinsert(y,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),u))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,x),z)),v,tc_fun(x1,tc_bool))))*.
% 299.92/300.51 35348[0:SpR:537.1,410.0] class_Lattices_Olattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),w,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),w,tc_fun(x1,tc_bool))))*.
% 299.92/300.51 35347[0:SpR:534.1,410.0] class_Lattices_Oupper__semilattice(u) || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),w,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),v))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z)),w,tc_fun(x1,tc_bool))))*.
% 299.92/300.51 35202[0:SpR:410.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),z)) -> equal(hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x1,x),v),w,x,tc_fun(y,tc_bool)),x2),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(w,x1)),u,x2),z)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(w,x1)),u,x2),z))**.
% 299.92/300.51 36733[0:SpR:67.0,35.2] || c_lessequals(u,c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* c_lessequals(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)),y,tc_fun(x,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,x),c_HOL_Ominus__class_Ominus(y,u,tc_fun(x,tc_bool))),tc_fun(x,tc_bool)),u)**.
% 299.92/300.51 37469[0:SpR:205.1,317.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),z),x),x1)),hAPP(c_Set_Oinsert(z,y),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,y),x1)))*.
% 299.92/300.51 37468[0:SpR:205.1,99.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,y),z),hAPP(c_Set_Oimage(u,v,w),z))**.
% 299.92/300.51 37467[0:SpR:205.1,438.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,y),z),hAPP(c_Set_Oimage(u,v,w),z))**.
% 299.92/300.51 38974[0:SpR:354.2,118.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(c_Fun_Ocomp(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),c_Fun_Ofun__upd(z,x1,hAPP(c_Set_Oimage(x,w,y),u),x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x3,x4,x2),x1,u,x2,x4))*.
% 299.92/300.51 41330[0:SpL:532.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y))* hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x2),x))))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x2),u,tc_fun(z,tc_bool))))*.
% 299.92/300.51 41329[0:SpL:533.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x2),v))))* -> hBOOL(hAPP(hAPP(c_in(x),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),x2)),u,tc_fun(x,tc_bool))))*.
% 299.92/300.51 41655[0:SpL:131.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),hAPP(c_Set_Ovimage(y,x,z),x1))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(y,v,x,z,w),w,z),x2,u),x3)))* c_Fun_Oinj__on(c_Set_Ovimage(c_Fun_Ocomp(y,v,x,z,w),w,z),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,u)* -> hBOOL(hAPP(hAPP(c_in(x2),x1),x3)).
% 299.92/300.51 41654[0:SpL:158.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,z,w),x1))),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(v,y,w,x,z),z,x),x2,u),x3)))* c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ocomp(v,y,w,x,z),z,x),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,u)* -> hBOOL(hAPP(hAPP(c_in(x2),x1),x3)).
% 299.92/300.51 41592[0:SpL:523.1,284.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x),y,v),z)))* c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,v)* -> hBOOL(hAPP(hAPP(c_in(y),v_x),z)).
% 299.92/300.51 41591[0:SpL:460.1,284.0] || class_Lattices_Olattice(t_b) hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v,u),w)))* c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,u)* -> hBOOL(hAPP(hAPP(c_in(v),v_x),w)).
% 299.92/300.51 41828[0:SpL:131.0,199.0] || hBOOL(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,z,x2),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x1,z,x2)))))* c_Fun_Oinj__on(x1,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x2) -> hBOOL(hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x3))*.
% 299.92/300.51 41827[0:SpL:158.0,199.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,z,x2),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x1,z,x2)))))* c_Fun_Oinj__on(x1,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x2) -> hBOOL(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x3))*.
% 299.92/300.51 41789[0:SpL:9493.1,199.0] || equal(hAPP(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oinsert(v_x,t_a),v,u,w)),v_x),c_Orderings_Otop__class_Otop(tc_bool))** hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oinsert(v_x,t_a),v,u,w))) c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(c_Set_Oinsert(v_x,t_a),x))*.
% 299.92/300.51 41787[0:SpL:8498.1,199.0] || equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oinsert(x,y),v,u,w)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))) hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,w),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oinsert(x,y),v,u,w)))* c_Fun_Oinj__on(v,c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),u,w) -> hBOOL(hAPP(c_Set_Oinsert(x,y),z))*.
% 299.92/300.51 42158[0:SpL:180.2,275.1] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(hAPP(c_in(w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u)),y))* hBOOL(hAPP(hAPP(c_in(z),x1),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(x2,u),v),u,u)))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x2),w,tc_fun(z,tc_bool))))*.
% 299.92/300.51 42049[0:SpR:180.2,410.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,v,u,u),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),w,hAPP(c_Set_Oinsert(z,u),v),u,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x,tc_fun(x1,tc_bool))))*.
% 299.92/300.51 42744[0:SpL:161.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(z,y,tc_fun(v,tc_bool)))) c_Fun_Oinj__on(u,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z),y,tc_fun(v,tc_bool)),v,w)* -> equal(c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(z,y,tc_fun(v,tc_bool))).
% 299.92/300.51 42722[0:SpR:66.0,161.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,u),x),tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,x,tc_fun(u,tc_bool))),y),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))**.
% 299.92/300.51 42707[0:SpR:66.0,161.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(w,u),y),tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_HOL_Ominus__class_Ominus(x,y,tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))**.
% 299.92/300.51 43099[0:SpR:55.1,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) -> hBOOL(hAPP(hAPP(c_in(x),z),w)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(z,x),v),w,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(z,x),u,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(z,x),u,tc_fun(x1,tc_bool)))**.
% 299.92/300.51 43047[0:SpR:338.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),u,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),u,tc_fun(z,tc_bool)))**.
% 299.92/300.51 42989[0:SpR:97.1,486.1] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oimage(u,w,x),v)),z)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,tc_fun(x1,tc_bool)))**.
% 299.92/300.51 42988[0:SpR:99.1,486.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),z)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,tc_fun(x1,tc_bool)))**.
% 299.92/300.51 42987[0:SpR:438.1,486.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(u,y)),z)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,tc_fun(x1,tc_bool)))**.
% 299.92/300.51 42974[0:SpR:393.1,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> equal(v,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(z,x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_COMBK(z,x1,x),x,x1),u,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_COMBK(z,x1,x),x,x1),u,tc_fun(y,tc_bool)))**.
% 299.92/300.51 42926[0:SpR:486.1,317.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),z,x1),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)),z),x2)),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)),x1),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),z,x1),x2)))*.
% 299.92/300.51 43563[0:SpL:507.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),x1))) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(x,y,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1)),v,w)* -> equal(hAPP(c_Set_Oimage(x,y,v),z),hAPP(c_Set_Oimage(x,y,v),x1)).
% 299.92/300.51 43532[0:SpR:205.1,507.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x)),y)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),y)))**.
% 299.92/300.51 43517[0:SpR:205.1,507.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(u,v,w),y))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x)),y))**.
% 299.92/300.51 43785[0:SpL:162.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(x,v,y),z)),hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(x,v,y),x1))) c_Fun_Oinj__on(u,hAPP(c_Set_Ovimage(x,v,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1)),v,w)* -> equal(hAPP(c_Set_Ovimage(x,v,y),z),hAPP(c_Set_Ovimage(x,v,y),x1)).
% 299.92/300.51 44066[0:SpL:205.1,358.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(x,hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),y),tc_fun(v,tc_bool))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v)* -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool)).
% 299.92/300.51 44051[0:SpL:205.1,358.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x),y,tc_fun(v,tc_bool))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v)* -> c_lessequals(x,hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)).
% 299.92/300.51 44181[0:Res:232.1,402.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))* -> equal(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool))),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool))).
% 299.92/300.51 44415[0:Rew:90.0,44397.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBB(c_Set_Oimage(u,v,w),tc_fun(v,tc_bool),tc_fun(w,tc_bool),y),tc_Com_Opname,z),hAPP(c_COMBB(c_Set_Oimage(u,v,w),tc_fun(v,tc_bool),tc_fun(w,tc_bool),y),v_x)),y,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v_x,y,tc_fun(v,tc_bool))))**.
% 299.92/300.51 44469[0:Rew:30.0,44451.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBB(c_Set_Ovimage(u,v,w),tc_fun(w,tc_bool),tc_fun(v,tc_bool),y),tc_Com_Opname,z),hAPP(c_COMBB(c_Set_Ovimage(u,v,w),tc_fun(w,tc_bool),tc_fun(v,tc_bool),y),v_x)),y,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,v_x,y,tc_fun(w,tc_bool))))**.
% 299.92/300.51 45353[0:Res:171.2,487.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)))*.
% 299.92/300.51 45352[0:Res:172.2,487.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)))*.
% 299.92/300.51 45505[0:Res:168.0,237.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,tc_Hoare__Mirabelle_Otriple(t_a)) -> c_Hoare__Mirabelle_Ohoare__valids(w,hAPP(c_Set_Oimage(u,v,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),t_a) equal(hAPP(u,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,hAPP(c_Set_Oimage(u,v,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))),u,tc_Hoare__Mirabelle_Otriple(t_a),v)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(w,hAPP(c_Set_Oimage(u,v,tc_Hoare__Mirabelle_Otriple(t_a)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))))**.
% 299.92/300.51 45653[0:Rew:45652.1,45557.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,z) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),y,z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(u,tc_bool)))**.
% 299.92/300.51 46166[0:Res:450.0,481.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(v)),w),x),t_a) hBOOL(hAPP(y,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(v),x,w,u))) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),x,w,u)),z),y,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),x,w,u)),z)))*.
% 299.92/300.51 46484[0:Res:450.0,480.0] || -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(v)),w),x),t_a) hBOOL(hAPP(y,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(v),x,w,u))) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),x,w,u)),y,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(v),x,w,u))))*.
% 299.92/300.51 47380[0:SpL:24914.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_Com_Opname,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)),x)).
% 299.92/300.51 47949[0:SpL:24914.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)),u,v)))* hBOOL(hAPP(hAPP(c_in(v),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_x)))* -> hBOOL(hAPP(u,y))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,u,v)),w)).
% 299.92/300.51 48459[0:SpL:32668.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x)),tc_Com_Opname),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x)),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,x),y),x,u) -> .
% 299.92/300.51 48458[0:SpL:28910.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y),tc_Com_Opname),z,u),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(v_Procs,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,z),x1),z,u) -> .
% 299.92/300.51 48457[0:SpL:28926.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v),tc_Com_Opname),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,w),x),w,u) -> .
% 299.92/300.51 48455[0:SpL:28755.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y),tc_Com_Opname),z,u),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(v_Procs,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,z),x1),z,u) -> .
% 299.92/300.51 48454[0:SpL:28771.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),tc_Com_Opname),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,w),x),w,u) -> .
% 299.92/300.51 48344[0:SpL:130.1,224.0] class_HOL_Ominus(u) || hBOOL(hAPP(hAPP(c_in(v),c_HOL_Ominus__class_Ominus(hAPP(w,v_x),hAPP(x,v_x),u)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u)),y,v),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(v_x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(w,x,tc_fun(t_a,u)),hAPP(c_Set_Oinsert(v_x,y),z),y,v) -> .
% 299.92/300.51 48328[0:SpL:353.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),y))),hAPP(c_Set_Oimage(c_Set_Oinsert(x,w),z,u),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),y),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(x,w),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),y),z),x1),z,u) -> .
% 299.92/300.51 48657[0:SpR:97.1,197.1] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(c_Fun_Othe__inv__into(v,u,w,x),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,w,x),v),y,tc_fun(x,tc_bool))),c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y),tc_fun(w,tc_bool)))**.
% 299.92/300.51 48642[0:SpR:97.1,197.1] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(c_Fun_Othe__inv__into(v,u,w,x),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,w) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oimage(u,w,x),v),tc_fun(x,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y),v,tc_fun(w,tc_bool)))**.
% 299.92/300.51 48631[0:SpR:197.1,82.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,w,y),hAPP(c_Set_Oimage(u,v,w),z)),hAPP(c_Set_Oimage(x,w,y),hAPP(c_Set_Oimage(u,v,w),x1)),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,w,y),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(z,x1,tc_fun(v,tc_bool)))),tc_fun(y,tc_bool))*.
% 299.92/300.51 48792[0:Res:151.2,619.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* -> hBOOL(hAPP(hAPP(c_in(u),v),x))* equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(y,u,tc_fun(z,tc_bool)),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))),c_Set_Oinsert(x1,z),tc_fun(z,tc_bool),tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(x1,z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool)),y,u,tc_fun(z,tc_bool))))**.
% 299.92/300.51 49198[0:MRR:49157.4,20734.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(w),z),u)) c_lessequals(hAPP(c_Set_Oimage(x,w,y),u),x1,tc_fun(y,tc_bool)) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,w,y),u),c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z)),x1))*.
% 299.92/300.51 49759[0:Rew:49662.2,49596.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),y,z),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),y),x))))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),w)),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),y),x),y,z).
% 299.92/300.51 49760[0:Rew:49662.2,49592.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,y),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),x),w),x,y).
% 299.92/300.51 49761[0:Rew:49662.2,49518.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),w,x),hAPP(c_Set_Oinsert(y,w),v))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(y,w),v),w,x).
% 299.92/300.51 49762[0:Rew:49662.2,49509.1] || c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),v_x),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),w,x),hAPP(c_Set_Oinsert(v_x,w),v))))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,u),hAPP(c_Set_Oinsert(v_x,w),v),w,x).
% 299.92/300.51 50178[0:Rew:542.0,50144.1,533.0,50144.1,532.0,50144.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(y,v,tc_fun(x,tc_bool)),u)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,y,v,tc_fun(x,tc_bool)))))**.
% 299.92/300.51 50507[0:SpL:223.1,208.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(x,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),w),tc_fun(x1,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(x1),z),x)) c_lessequals(x,hAPP(c_Set_Oimage(y,u,x1),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),tc_fun(x1,tc_bool))*.
% 299.92/300.51 50518[0:Rew:223.1,50483.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(u),x),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))* equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(c_Fun_Ofun__upd(y,x,z,u,x1),v,x2,u,x1),u,x1),w),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,x2,u,x1),u,x1),w))**.
% 299.92/300.51 51246[0:SpL:21893.0,462.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Obody,v_x),c_Com_Obody,tc_Com_Opname,y))),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.51 51245[0:SpL:21267.0,462.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Obody,hAPP(c_Com_Obody,v_x),tc_Com_Opname,y))),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.51 51528[0:Res:31315.0,195.0] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) c_Fun_Oinj__on(v,v_Procs,tc_Com_Opname,w) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(v,tc_Com_Opname,w),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool)))),hAPP(c_Set_Oimage(v,tc_Com_Opname,w),u),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(v,tc_Com_Opname,w),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_Orderings_Obot__class_Obot(tc_fun(tc_Com_Opname,tc_bool))),u,tc_fun(tc_Com_Opname,tc_bool))))**.
% 299.92/300.51 51514[0:Res:341.0,195.0] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool))* c_Fun_Oinj__on(y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v,z)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(y,v,z),x),hAPP(c_Set_Oimage(y,v,z),u),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,v,z),c_HOL_Ominus__class_Ominus(x,u,tc_fun(v,tc_bool))))**.
% 299.92/300.51 51513[0:Res:342.0,195.0] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),tc_fun(v,tc_bool))* c_Fun_Oinj__on(y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v,z)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(y,v,z),w),hAPP(c_Set_Oimage(y,v,z),u),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,v,z),c_HOL_Ominus__class_Ominus(w,u,tc_fun(v,tc_bool))))**.
% 299.92/300.51 51728[0:Res:448.1,233.2] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,w) c_Finite__Set_Ofinite(x,u) c_lessequals(hAPP(c_Set_Oimage(y,u,w),x),v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(z,v,w,u) c_Fun_Oinj__on(y,x,u,w) -> c_lessequals(x,hAPP(c_Set_Oimage(z,w,u),v),tc_fun(u,tc_bool))* equal(c_Finite__Set_Ocard(v,w),c_Finite__Set_Ocard(x,u)).
% 299.92/300.51 51691[0:SpL:3229.1,233.2] || equal(u,c_Set_Oimage(v,w,x))* c_Finite__Set_Ofinite(v_x,w) c_Finite__Set_Ofinite(y,x) c_lessequals(hAPP(u,v_x),y,tc_fun(x,tc_bool))* c_lessequals(hAPP(c_Set_Oimage(z,x,w),y),v_x,tc_fun(w,tc_bool))* c_Fun_Oinj__on(v,v_x,w,x)* c_Fun_Oinj__on(z,y,x,w) -> equal(c_Finite__Set_Ocard(v_x,w),c_Finite__Set_Ocard(y,x)).
% 299.92/300.51 51880[0:SpL:351.0,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_COMBK(v,w,x),y,z),hAPP(u,v)) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_COMBK(v,w,x),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),u)),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(u,x3),x4,z,x1))**.
% 299.92/300.51 53815[0:SpL:53771.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Option_Othe(w),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),v,c_Option_Othe(w),z,x1),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Option_Othe(w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),v,c_Option_Othe(w),z,x1),x),y),x,u) -> .
% 299.92/300.51 53846[0:SpL:53772.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Option_Othe(w),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Option_Othe(w),v,z,x1),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Option_Othe(w),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Option_Othe(w),v,z,x1),x),y),x,u) -> .
% 299.92/300.51 60420[7:Res:58968.1,481.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(u),v),x)),z),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(u),v),x)),z)))*.
% 299.92/300.51 60419[7:Res:58968.1,480.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y)),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y))))*.
% 299.92/300.51 60533[0:Res:58969.1,481.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(u),v),x)),z),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,hAPP(c_in(u),v),x)),z)))*.
% 299.92/300.51 60532[0:Res:58969.1,480.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y)),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y))))*.
% 299.92/300.51 60606[7:Res:59476.1,481.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),y)),z),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),y)),z)))*.
% 299.92/300.51 60605[7:Res:59476.1,480.0] || equal(hAPP(c_in(u),v),v_x) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z)),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z))))*.
% 299.92/300.51 60679[0:Res:59477.1,481.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),y)),z),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),y)),z)))*.
% 299.92/300.51 60678[0:Res:59477.1,480.0] || equal(hAPP(c_in(u),v),v_Procs) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z)),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z))))*.
% 299.92/300.51 60864[0:Res:59017.1,481.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a)* hBOOL(hAPP(x,w)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(v),w),y)),x1),x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(v),w),y)),x1)))*.
% 299.92/300.51 60863[0:Res:59017.1,480.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a)* hBOOL(hAPP(x,w)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_in(v),w),z)),x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_in(v),w),z))))*.
% 299.92/300.51 60937[0:Res:59525.1,481.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a)* hBOOL(hAPP(x,w)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(v),w),z)),x1),x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(v),w),z)),x1)))*.
% 299.92/300.51 60936[0:Res:59525.1,480.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a)* hBOOL(hAPP(x,w)) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_in(v),w),x1)),x,v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_in(v),w),x1))))*.
% 299.92/300.51 62450[0:SSi:62227.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool)))) -> c_lessequals(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool))),tc_fun(w,tc_bool))*.
% 299.92/300.51 73980[7:SpL:71835.1,233.2] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) c_Finite__Set_Ofinite(v_x,v) c_Finite__Set_Ofinite(x,w) c_lessequals(v_x,x,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Oimage(y,w,v),x),v_x,tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,v_x,v,w)* c_Fun_Oinj__on(y,x,w,v) -> equal(c_Finite__Set_Ocard(v_x,v),c_Finite__Set_Ocard(x,w)).
% 299.92/300.51 79013[0:Res:15630.1,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,y),z),x1,hAPP(c_in(u),v),y)))* equal(hAPP(x2,v),hAPP(x2,x))* c_Fun_Oinj__on(x2,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,y),z),x1,hAPP(c_in(u),v),y),u,x3)* -> equal(v,x).
% 299.92/300.51 79233[0:Res:15858.1,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(w,z),x1),hAPP(c_in(u),v),z)))* equal(hAPP(x2,v),hAPP(x2,x))* c_Fun_Oinj__on(x2,c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(w,z),x1),hAPP(c_in(u),v),z),u,x3)* -> equal(v,x).
% 299.92/300.51 80240[0:SpL:21268.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),x,z),u,w)))* hBOOL(hAPP(hAPP(c_in(w),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y)))* -> hBOOL(hAPP(u,x1))*.
% 299.92/300.51 80218[0:SpL:21268.0,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) -> c_Hoare__Mirabelle_Ohoare__valids(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),w,x),y,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),w,x),y),u,t_a)*.
% 299.92/300.51 80173[0:SpL:21268.0,398.0] || c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w),tc_fun(u,tc_bool)) -> c_lessequals(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w),x,y),tc_fun(u,tc_bool))*.
% 299.92/300.51 80138[0:SpL:21268.0,398.0] || c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w),tc_fun(u,tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),x,y),w,tc_fun(u,tc_bool))*.
% 299.92/300.51 79559[0:SpR:21268.0,399.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),x),v,y),tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),u),hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),x),tc_fun(w,tc_bool)).
% 299.92/300.51 79445[0:SpR:21268.0,399.1] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),w),u,x),y,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),w),hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),y),tc_fun(v,tc_bool)).
% 299.92/300.51 79437[0:SpR:21268.0,445.1] || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Fun_Ofun__upd(v,w,x,y,z),hAPP(c_Fun_Ofun__upd(v,w,x,y,z),x1),u,x2),w) equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Fun_Ofun__upd(v,w,x,y,z),hAPP(c_Fun_Ofun__upd(v,w,x,y,z),x1),u,x2)),hAPP(c_Fun_Ofun__upd(v,w,x,y,z),x1))**.
% 299.92/300.51 79351[1:SpR:21268.0,722.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_P,hAPP(v_P,v),u,w)),v_Procs)) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v)),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_P,hAPP(v_P,v),u,w))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_P,hAPP(v_P,v),u,w))),t_a)*.
% 299.92/300.51 79349[1:SpR:21268.0,722.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,v),u,w)),v_Procs)) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,v),u,w))),hAPP(c_Com_Ocom_OBODY,v)),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,v),u,w))),t_a)*.
% 299.92/300.51 79348[1:SpR:21268.0,722.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_Q,hAPP(v_Q,v),u,w)),v_Procs)) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_Q,hAPP(v_Q,v),u,w))),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v_Q,hAPP(v_Q,v),u,w))),hAPP(v_Q,v)),t_a)*.
% 299.92/300.51 81435[0:SpL:21894.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x,z),u,w)))* hBOOL(hAPP(hAPP(c_in(w),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y)))* -> hBOOL(hAPP(u,x1))*.
% 299.92/300.51 81413[0:SpL:21894.0,454.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) -> c_Hoare__Mirabelle_Ohoare__valids(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w,x),y,t_a) c_Hoare__Mirabelle_Otriple__valid(v_sko__Hoare__Mirabelle__Xhoare__valids__def__2(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),w,x),y),u,t_a)*.
% 299.92/300.51 81368[0:SpL:21894.0,398.0] || c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w),tc_fun(u,tc_bool)) -> c_lessequals(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w),c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),x,y),tc_fun(u,tc_bool))*.
% 299.92/300.51 81333[0:SpL:21894.0,398.0] || c_lessequals(hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),w),tc_fun(u,tc_bool)) -> c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),v),c_COMBC(c_in(u),u,tc_fun(u,tc_bool),tc_bool),x,y),w,tc_fun(u,tc_bool))*.
% 299.92/300.51 80752[0:SpR:21894.0,399.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),x),c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),v,y),tc_fun(w,tc_bool))* -> c_lessequals(hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),u),hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),x),tc_fun(w,tc_bool)).
% 299.92/300.51 80638[0:SpR:21894.0,399.1] || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),w),c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),u,x),y,tc_fun(v,tc_bool))* -> c_lessequals(hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),w),hAPP(c_COMBC(c_in(v),v,tc_fun(v,tc_bool),tc_bool),y),tc_fun(v,tc_bool)).
% 299.92/300.51 80630[0:SpR:21894.0,445.1] || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Fun_Ofun__upd(v,w,x,y,z),x1),c_Fun_Ofun__upd(v,w,x,y,z),u,x2),w) equal(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Fun_Ofun__upd(v,w,x,y,z),x1),c_Fun_Ofun__upd(v,w,x,y,z),u,x2)),hAPP(c_Fun_Ofun__upd(v,w,x,y,z),x1))**.
% 299.92/300.51 80544[1:SpR:21894.0,722.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(v_P,v),v_P,u,w)),v_Procs)) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v)),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(v_P,v),v_P,u,w))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(v_P,v),v_P,u,w))),t_a)*.
% 299.92/300.51 80542[1:SpR:21894.0,722.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Com_Ocom_OBODY,v),c_Com_Ocom_OBODY,u,w)),v_Procs)) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Com_Ocom_OBODY,v),c_Com_Ocom_OBODY,u,w))),hAPP(c_Com_Ocom_OBODY,v)),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Com_Ocom_OBODY,v),c_Com_Ocom_OBODY,u,w))),t_a)*.
% 299.92/300.51 80541[1:SpR:21894.0,722.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(v_Q,v),v_Q,u,w)),v_Procs)) -> c_Hoare__Mirabelle_Otriple__valid(v_na,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(v_Q,v),v_Q,u,w))),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(v_Q,v),v_Q,u,w))),hAPP(v_Q,v)),t_a)*.
% 299.92/300.51 83122[0:SpL:5924.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(v,w),x)),hAPP(c_Set_Oimage(c_COMBS(v,c_COMBK(x,y,z),x1,x2,x3),x4,u),c_HOL_Ominus__class_Ominus(x5,hAPP(c_Set_Oinsert(w,x4),c_Orderings_Obot__class_Obot(tc_fun(x4,tc_bool))),tc_fun(x4,tc_bool)))))* c_Fun_Oinj__on(c_COMBS(v,c_COMBK(x,y,z),x1,x2,x3),hAPP(c_Set_Oinsert(w,x4),x5),x4,u) -> .
% 299.92/300.51 83441[0:SpL:5961.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,hAPP(w,x))),hAPP(c_Set_Oimage(c_COMBS(c_COMBK(v,y,z),w,x1,x2,x3),x4,u),c_HOL_Ominus__class_Ominus(x5,hAPP(c_Set_Oinsert(x,x4),c_Orderings_Obot__class_Obot(tc_fun(x4,tc_bool))),tc_fun(x4,tc_bool)))))* c_Fun_Oinj__on(c_COMBS(c_COMBK(v,y,z),w,x1,x2,x3),hAPP(c_Set_Oinsert(x,x4),x5),x4,u) -> .
% 299.92/300.51 88729[0:SpL:61.1,12998.0] || c_Finite__Set_Ofinite(u,v) c_Hoare__Mirabelle_Otriple__valid(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,v),u),v),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),x),t_a)* -> c_Hoare__Mirabelle_Ohoare__valids(y,x,t_a) c_Hoare__Mirabelle_Otriple__valid(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)),v),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(y,x),t_a)*.
% 299.92/300.51 88862[0:SpR:622.0,14196.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),w,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))),v_x))*.
% 299.92/300.51 89904[0:SpR:223.1,26183.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(y,u,x),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x),u,x),w)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x),u,x),w))**.
% 299.92/300.51 93243[0:SpL:5878.1,224.0] class_Lattices_Obounded__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(w,c_Orderings_Obot__class_Obot(u))),hAPP(c_Set_Oimage(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),x1,v),c_HOL_Ominus__class_Ominus(x2,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),tc_fun(x1,tc_bool)))))* c_Fun_Oinj__on(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(u),w,x,y,z),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(u),x1),x2),x1,v) -> .
% 299.92/300.51 21297[0:SpR:21267.0,246.2] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),v) -> hBOOL(hAPP(hAPP(c_in(v),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w)))* equal(c_Suc(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),v_x),tc_Com_Opname,w),v)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(u,v),v_x),v)).
% 299.92/300.51 21923[0:SpR:21893.0,246.2] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),v) -> hBOOL(hAPP(hAPP(c_in(v),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w)))* equal(c_Suc(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(u,v),v_x),c_Set_Oinsert(u,v),tc_Com_Opname,w),v)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(u,v),v_x),v)).
% 299.92/300.51 27013[0:Res:171.2,175.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),u) -> equal(hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(v,c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),u)),x)**.
% 299.92/300.51 27012[0:Res:172.2,175.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),u) -> equal(hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(v,c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Ovimage(v,u,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),u)),x)**.
% 299.92/300.51 35186[0:SpR:410.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(v,x1)),y,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x1,w),u),v,w,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(v,x1)),y,tc_fun(x2,tc_bool))))*.
% 299.92/300.51 36730[0:SpR:67.0,61.1] || c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),w) -> equal(c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),tc_fun(w,tc_bool)),w)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(x,w),c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))),w))**.
% 299.92/300.51 37454[0:SpR:205.1,97.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Set_Oimage(u,v,w),x),w,v) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,v,w),x),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),v,w),x),hAPP(c_Set_Oimage(u,v,w),x))**.
% 299.92/300.51 38516[0:Rew:205.1,38476.4] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,v) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,v),w),v) c_lessequals(w,hAPP(c_Set_Oimage(u,v,v),w),tc_fun(v,tc_bool))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,v),hAPP(c_Set_Oimage(u,v,v),w),v,v)* -> equal(hAPP(c_Set_Oimage(u,v,v),w),w).
% 299.92/300.51 38646[0:SpL:21893.0,184.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) c_Fun_Oinj__on(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,x,u),v_x),c_Set_Oimage(w,x,u),tc_Com_Opname,y),x,u) -> equal(hAPP(w,hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,x,u),v_x),c_Set_Oimage(w,x,u),tc_Com_Opname,y),w,x,u),v)),v)**.
% 299.92/300.51 38645[0:SpL:21267.0,184.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) c_Fun_Oinj__on(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),v_x),tc_Com_Opname,y),x,u) -> equal(hAPP(w,hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),v_x),tc_Com_Opname,y),w,x,u),v)),v)**.
% 299.92/300.51 38995[0:SpR:21893.0,354.2] || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),y,tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,y,v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(y,u,v,w),w,v),hAPP(c_Set_Oimage(u,v,w),v_x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x))*.
% 299.92/300.51 38994[0:SpR:21267.0,354.2] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),y,tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,y,v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(y,u,v,w),w,v),hAPP(c_Set_Oimage(u,v,w),v_x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x))*.
% 299.92/300.51 38942[0:SpR:354.2,354.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_lessequals(hAPP(c_Set_Oimage(x,w,y),u),z,tc_fun(y,tc_bool)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v,x,w,y),z,y,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(z,c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),w,y),u),hAPP(c_Set_Oimage(x,w,y),u))**.
% 299.92/300.51 39598[0:SpR:532.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),x)),x1),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),u,x1),y)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),u,x1),y))**.
% 299.92/300.51 42282[0:SSi:42177.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,hAPP(c_Set_Oinsert(y,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),w,v)))* hBOOL(hAPP(hAPP(c_in(v),z),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool))))* -> hBOOL(hAPP(w,z))*.
% 299.92/300.51 42723[0:SpL:161.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y))* hBOOL(hAPP(hAPP(c_in(z),x1),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x2),v),w,tc_fun(x,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(z),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(x2,w,tc_fun(x,tc_bool))),u,tc_fun(z,tc_bool))))*.
% 299.92/300.51 42779[0:SSi:42667.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),x)) c_Finite__Set_Ofinite(x,tc_fun(u,tc_bool)) -> c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),w,tc_fun(u,tc_bool)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(y,w,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.92/300.51 43115[0:SpL:486.1,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool))),x1))* hBOOL(hAPP(hAPP(c_in(x2),x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(x2),x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x,tc_fun(x2,tc_bool))))*.
% 299.92/300.51 43101[0:SpR:475.1,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),w)),x1)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(y,u,z),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oinsert(hAPP(y,v),z),x,tc_fun(x2,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oinsert(hAPP(y,v),z),x,tc_fun(x2,tc_bool)))**.
% 299.92/300.51 43096[0:SpR:131.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Ovimage(y,z,x1),hAPP(c_Set_Ovimage(x2,x1,x3),v))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(c_Fun_Ocomp(x2,y,x1,x3,z),z,x3),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Ovimage(c_Fun_Ocomp(x2,y,x1,x3,z),z,x3),u,tc_fun(x,tc_bool)))**.
% 299.92/300.51 43095[0:SpR:158.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(y,z,x1),hAPP(c_Set_Oimage(x2,x3,z),v))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_Fun_Ocomp(y,x2,z,x1,x3),x3,x1),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_Fun_Ocomp(y,x2,z,x1,x3),x3,x1),u,tc_fun(x,tc_bool)))**.
% 299.92/300.51 43031[0:SpR:523.1,486.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(y,v_x)),hAPP(z,v_x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),y),z),v,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),y),z),v,tc_fun(x,tc_bool)))**.
% 299.92/300.51 43030[0:SpR:460.1,486.1] || class_Lattices_Olattice(t_b) hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,tc_fun(w,tc_bool)))**.
% 299.92/300.51 43542[0:SpL:507.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x3),y))))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),x3)),u,tc_fun(x1,tc_bool))))*.
% 299.92/300.51 43595[0:SSi:43485.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),y)) c_Finite__Set_Ofinite(y,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),z),y,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.92/300.51 43764[0:SpL:162.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x3),y))))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),x3)),u,tc_fun(x1,tc_bool))))*.
% 299.92/300.51 43823[0:SSi:43707.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),y)) c_Finite__Set_Ofinite(y,tc_fun(u,tc_bool)) -> c_lessequals(hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),z),y,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.92/300.51 44134[0:SpR:205.1,232.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v) -> c_lessequals(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.92/300.51 45603[0:SpR:89.0,323.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,x),y),z,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,hAPP(c_COMBB(z,x,tc_fun(u,tc_bool),w),v),w,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),x1),hAPP(c_COMBB(z,x,tc_fun(u,tc_bool),w),v),w,tc_fun(u,tc_bool)))**.
% 299.92/300.51 45596[0:SpR:89.0,323.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_COMBB(w,x,tc_fun(u,tc_bool),y),z),y,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(z,y,x),x1),w,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),v),x1),hAPP(c_COMBB(w,x,tc_fun(u,tc_bool),y),z),y,tc_fun(u,tc_bool)))**.
% 299.92/300.51 45895[0:Res:171.2,482.2] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))*.
% 299.92/300.51 45894[0:Res:172.2,482.2] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)))* hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))*.
% 299.92/300.51 46135[0:Res:176.0,481.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(x,w,y),hAPP(c_Set_Oinsert(hAPP(x,v),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))),z),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(x,w,y),hAPP(c_Set_Oinsert(hAPP(x,v),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))),z)))*.
% 299.92/300.51 46453[0:Res:176.0,480.0] || -> hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Ovimage(y,w,z),hAPP(c_Set_Oinsert(hAPP(y,v),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))))),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Ovimage(y,w,z),hAPP(c_Set_Oinsert(hAPP(y,v),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool)))))))*.
% 299.92/300.51 46935[0:Res:241.2,231.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oimage(x,y,u),z)),tc_fun(u,tc_bool)) c_Fun_Oinj__on(x,c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,u) -> c_lessequals(hAPP(c_Set_Ovimage(x,y,u),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),z,tc_fun(y,tc_bool))*.
% 299.92/300.51 48636[0:SpR:197.1,35.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool)) c_lessequals(y,hAPP(c_Set_Oimage(u,v,w),z),tc_fun(w,tc_bool)) -> equal(c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(z,x,tc_fun(v,tc_bool))),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x))**.
% 299.92/300.51 49191[0:Res:171.2,239.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) c_lessequals(x,y,tc_fun(w,tc_bool)) c_Fun_Oinj__on(v,x,w,u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(x,v,w,u),c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),x),u))),y))*.
% 299.92/300.51 49190[0:Res:172.2,239.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),x),u) c_lessequals(x,y,tc_fun(w,tc_bool)) c_Fun_Oinj__on(v,x,w,u) -> equal(hAPP(c_Set_Oimage(v,w,u),x),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(x,v,w,u),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),x),u))),y))*.
% 299.92/300.51 49163[0:SpL:465.1,239.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) c_lessequals(y,z,tc_fun(x,tc_bool)) c_Fun_Oinj__on(c_Fun_Ofun__upd(w,x1,x2,x,u),y,x,u) -> hBOOL(hAPP(hAPP(c_in(x),x1),y)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Fun_Othe__inv__into(y,c_Fun_Ofun__upd(w,x1,x2,x,u),x,u),v)),z))*.
% 299.92/300.51 49765[0:Rew:49662.2,49604.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),y,z,x1) -> hBOOL(hAPP(hAPP(c_in(x1),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),z,x1),hAPP(c_Set_Oinsert(x2,z),y))))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),w,x)),hAPP(c_Set_Oinsert(x2,z),y),z,x1).
% 299.92/300.51 49766[0:Rew:49662.2,49576.1] || c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),x,y),hAPP(c_Set_Oinsert(z,x),w))))* c_Fun_Oinj__on(hAPP(c_Set_Oinsert(u,v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),hAPP(c_Set_Oinsert(z,x),w),x,y).
% 299.92/300.51 49767[0:Rew:49662.2,49532.1] || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),y,z),hAPP(c_Set_Oinsert(x1,y),x))))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)),v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x1,y),x),y,z).
% 299.92/300.51 49768[0:Rew:49662.2,49530.1] || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),y,z),hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),u),y),x))))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_Option_Othe(u),v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(c_Option_Ooption_OSome(c_Orderings_Obot__class_Obot(tc_bool),u),y),x),y,z).
% 299.92/300.51 49769[0:Rew:49662.2,49503.2] class_HOL_Ominus(u) || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),hAPP(w,v_x),u)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),y,z),hAPP(c_Set_Oinsert(v_x,y),x))))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(v,w,tc_fun(t_a,u)),hAPP(c_Set_Oinsert(v_x,y),x),y,z).
% 299.92/300.51 49986[0:SpR:497.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),x),y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),y)),v,u),u)*.
% 299.92/300.51 49978[0:SpR:497.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),u,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w)),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.92/300.51 50171[0:SpL:620.1,375.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oimage(w,x,tc_fun(u,tc_bool)),y)))* c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,x,tc_fun(u,tc_bool))),x1,tc_fun(u,tc_bool))* -> equal(y,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),v),x1,tc_fun(u,tc_bool))*.
% 299.92/300.51 50170[0:SpL:620.1,372.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oimage(w,x,tc_fun(u,tc_bool)),y)))* equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,x,tc_fun(u,tc_bool))),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))** -> equal(y,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),v),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))**.
% 299.92/300.51 50461[0:SpR:223.1,338.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Set_Oimage(x1,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x1,v,x,u,y),u,y),w)))**.
% 299.92/300.51 50452[0:SpR:223.1,424.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),y),z)) c_lessequals(hAPP(c_Set_Oimage(x1,u,x),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),z,tc_fun(x,tc_bool))* -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x1,v,y,u,x),u,x),w),z,tc_fun(x,tc_bool))*.
% 299.92/300.51 50451[0:SpR:223.1,56.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),y),z)) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x1,v,y,u,x),u,x),w),z,tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x1,u,x),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),z,tc_fun(x,tc_bool)))*.
% 299.92/300.51 50435[0:SpR:223.1,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oimage(z,v,x1),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))),x2))* -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,w,x3,v,x1),v,x1),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,c_Set_Oinsert(x3,x1),y,u),u)*.
% 299.92/300.51 50430[0:SpR:223.1,339.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(x,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(z,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,x,u,y),u,y),w)),x1))**.
% 299.92/300.51 50410[0:SpR:223.1,176.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),hAPP(c_Set_Ovimage(c_Set_Oinsert(x1,z),x,x2),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,x1,u,z),u,z),w),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))))))*.
% 299.92/300.51 50849[0:SpR:158.0,622.0] || -> equal(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),hAPP(c_Set_Oimage(w,x,v),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_x),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Fun_Ocomp(u,w,v,tc_fun(t_a,tc_bool),x),x,tc_fun(t_a,tc_bool))))*.
% 299.92/300.51 51254[0:SpL:8415.2,462.0] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.51 51244[0:SpL:24914.0,462.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Obody,tc_Com_Opname,y),hAPP(c_Com_Obody,v_x)))),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.51 51241[0:SpL:8415.2,462.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Com_Obody) c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),v_x)),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,v_x)),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.92/300.51 51517[0:Res:364.1,195.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,hAPP(c_Set_Oinsert(y,w),v),tc_fun(w,tc_bool))* c_Fun_Oinj__on(z,hAPP(c_Set_Oinsert(y,w),v),w,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,w,x1),u),hAPP(c_Set_Oimage(z,w,x1),x),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,w,x1),c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool))))**.
% 299.92/300.51 51875[0:SpL:10463.0,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,x),hAPP(u,c_Orderings_Obot__class_Obot(tc_bool))) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),u)),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(u,x1),x2,x,y))**.
% 299.92/300.51 51874[0:SpL:9911.0,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,x),hAPP(u,c_Orderings_Otop__class_Otop(tc_bool))) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),u)),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(u,x1),x2,x,y))**.
% 299.92/300.51 54310[0:Rew:50512.0,54219.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))) -> equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))))**.
% 299.92/300.51 60391[7:SpR:465.1,58968.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_x) -> hBOOL(hAPP(hAPP(c_in(x),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),z)))* hBOOL(hAPP(c_Set_Oimage(u,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),z)))*.
% 299.92/300.51 60504[0:SpR:465.1,58969.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_Procs) -> hBOOL(hAPP(hAPP(c_in(x),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),z)))* hBOOL(hAPP(c_Set_Oimage(u,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),z)))*.
% 299.92/300.51 60577[7:SpR:465.1,59476.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_x) -> hBOOL(hAPP(hAPP(c_in(x),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),x1)))* hBOOL(hAPP(c_Set_Oimage(u,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),x1)))*.
% 299.92/300.51 60650[0:SpR:465.1,59477.1] || equal(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),v_Procs) -> hBOOL(hAPP(hAPP(c_in(x),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),x1)))* hBOOL(hAPP(c_Set_Oimage(u,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),x1)))*.
% 299.92/300.51 60835[0:SpR:465.1,59017.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),w)))* c_Hoare__Mirabelle_Ohoare__valids(x2,c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),t_a)* hBOOL(hAPP(c_Set_Oimage(y,u,x1),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),w)))*.
% 299.92/300.51 60908[0:SpR:465.1,59525.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),x)))* c_Hoare__Mirabelle_Ohoare__valids(x2,c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),t_a)* hBOOL(hAPP(c_Set_Oimage(y,u,x1),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),x)))*.
% 299.92/300.51 64103[0:Res:679.1,195.0] || c_lessequals(u,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) c_lessequals(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)) c_Fun_Oinj__on(w,v_Procs,tc_Com_Opname,x) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(w,tc_Com_Opname,x),hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u)),hAPP(c_Set_Oimage(w,tc_Com_Opname,x),v),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(w,tc_Com_Opname,x),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),u),v,tc_fun(tc_Com_Opname,tc_bool))))**.
% 299.92/300.51 64620[0:SpL:26782.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,tc_fun(w,tc_bool)),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),x),y),x,u) -> .
% 299.92/300.51 27166[0:SpR:131.0,450.0] || -> hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z,x1,x2))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z,x1,x2)))* c_Hoare__Mirabelle_Otriple__valid(x2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y)),x1),z),t_a).
% 299.92/300.51 27165[0:SpR:158.0,450.0] || -> hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z,x1,x2))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z,x1,x2)))* c_Hoare__Mirabelle_Otriple__valid(x2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w)),x1),z),t_a).
% 299.92/300.51 32356[0:SpL:329.1,477.0] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),v),tc_fun(y,tc_bool))* hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),v)) hBOOL(hAPP(hAPP(c_in(v),z),w))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),z))*.
% 299.92/300.51 32536[0:SpL:329.1,476.0] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),v),tc_fun(y,tc_bool))* hBOOL(c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),v)) hBOOL(hAPP(hAPP(c_in(v),z),x))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),z))*.
% 299.92/300.51 37471[0:SpR:205.1,118.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Fun_Ocomp(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),c_Fun_Ofun__upd(x,y,hAPP(c_Set_Oimage(u,v,w),z),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,x2,x3,x1),y,z,x1,x3))*.
% 299.92/300.51 38962[0:SpR:354.2,475.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oimage(x,w,y),u)),x1)) -> equal(hAPP(c_Set_Oinsert(u,x2),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x2),x1)),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x2),x1))**.
% 299.92/300.51 39576[0:SpR:532.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),x,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),w))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),x,tc_fun(x1,tc_bool))))*.
% 299.92/300.51 40880[0:SpL:21893.0,479.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(w),v),v_x),hAPP(c_in(w),v),tc_Com_Opname,x),y,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(w),v),v_x),hAPP(c_in(w),v),tc_Com_Opname,x)),y)))*.
% 299.92/300.51 40879[0:SpL:21267.0,479.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(w),v),hAPP(hAPP(c_in(w),v),v_x),tc_Com_Opname,x),y,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(w),v),hAPP(hAPP(c_in(w),v),v_x),tc_Com_Opname,x)),y)))*.
% 299.92/300.51 41161[0:SpL:21893.0,478.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(w),v),v_x),hAPP(c_in(w),v),tc_Com_Opname,y),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(w),v),v_x),hAPP(c_in(w),v),tc_Com_Opname,y))))*.
% 299.92/300.51 41160[0:SpL:21267.0,478.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(w),v),hAPP(hAPP(c_in(w),v),v_x),tc_Com_Opname,y),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(w),v),hAPP(hAPP(c_in(w),v),v_x),tc_Com_Opname,y))))*.
% 299.92/300.51 41586[0:SpL:465.1,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(v,z,x1,w,x),w,x),x2,u),x3)))* c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ofun__upd(v,z,x1,w,x),w,x),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,u)* -> hBOOL(hAPP(hAPP(c_in(w),z),y)) hBOOL(hAPP(hAPP(c_in(x2),y),x3)).
% 299.92/300.51 42481[0:SpL:181.1,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Set_Ovimage(c_COMBK(w,x,y),y,x),z,x1)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(x),w),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Set_Ovimage(c_COMBK(w,x,y),y,x),z,x1)))* equal(hAPP(c_Set_Oimage(u,z,x1),v),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(w,x,y),y,x),z,x1),v)).
% 299.92/300.51 42440[0:SpL:181.1,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,c_Set_Ovimage(c_COMBK(w,x,y),y,x),u,z,x1)),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))** -> hBOOL(hAPP(hAPP(c_in(x),w),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,c_Set_Ovimage(c_COMBK(w,x,y),y,x),u,z,x1)))* equal(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(w,x,y),y,x),z,x1),v),hAPP(c_Set_Oimage(u,z,x1),v)).
% 299.92/300.51 43051[0:SpR:104.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(y,v,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_HOL_Ouminus__class_Ouminus(y,tc_fun(z,tc_bool))),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_HOL_Ouminus__class_Ouminus(y,tc_fun(z,tc_bool))),u,tc_fun(x,tc_bool)))**.
% 299.92/300.51 42928[0:SpR:486.1,118.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),c_Fun_Ofun__upd(z,x1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)),x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),z,x3,x4,x2),x1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)),x2,x4))*.
% 299.92/300.51 44337[0:Res:450.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(u),w,x,y)))* equal(hAPP(z,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(u),w,x,y)),hAPP(z,v))* c_Fun_Oinj__on(z,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_in(u),w,x,y),u,x1)* -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_in(u)),x),w),t_a)* equal(v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_in(u),w,x,y),v).
% 299.92/300.51 46577[0:SpR:97.1,617.1] || c_Fun_Oinj__on(u,v,tc_fun(w,tc_bool),x) -> equal(hAPP(c_Set_Oimage(u,tc_fun(w,tc_bool),x),v),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) equal(hAPP(c_Set_Oinsert(y,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,tc_fun(w,tc_bool),x),v),c_Fun_Othe__inv__into(v,u,tc_fun(w,tc_bool),x),x,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oinsert(y,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)))**.
% 299.92/300.51 46602[0:Rew:410.0,46569.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_fun(w,tc_bool),tc_bool)),hAPP(c_Set_Oimage(x,v,tc_fun(w,tc_bool)),u)),y),c_Set_Oinsert(z,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,x,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),y),c_Set_Oinsert(z,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)))**.
% 299.92/300.51 47367[0:SpL:161.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),z,tc_fun(w,tc_bool))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ominus__class_Ominus(y,z,tc_fun(w,tc_bool)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ominus__class_Ominus(x,z,tc_fun(w,tc_bool)),u,w)),c_HOL_Ominus__class_Ominus(x,z,tc_fun(w,tc_bool))))*.
% 299.92/300.51 47366[0:SpL:162.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Ovimage(x,w,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Ovimage(x,w,y),x1),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Ovimage(x,w,y),z),u,w)),hAPP(c_Set_Ovimage(x,w,y),z)))*.
% 299.92/300.51 47365[0:SpL:507.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Oimage(x,y,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oimage(x,y,w),x1),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oimage(x,y,w),z),u,w)),hAPP(c_Set_Oimage(x,y,w),z)))*.
% 299.92/300.51 47598[0:SpL:161.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),z,tc_fun(w,tc_bool))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ominus__class_Ominus(x,z,tc_fun(w,tc_bool)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ominus__class_Ominus(y,z,tc_fun(w,tc_bool)),u,w)),c_HOL_Ominus__class_Ominus(y,z,tc_fun(w,tc_bool))))*.
% 299.92/300.51 47597[0:SpL:162.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Ovimage(x,w,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Ovimage(x,w,y),z),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Ovimage(x,w,y),x1),u,w)),hAPP(c_Set_Ovimage(x,w,y),x1)))*.
% 299.92/300.51 47596[0:SpL:507.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Oimage(x,y,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oimage(x,y,w),z),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oimage(x,y,w),x1),u,w)),hAPP(c_Set_Oimage(x,y,w),x1)))*.
% 299.92/300.51 47936[0:SpL:161.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),u,x)))* hBOOL(hAPP(hAPP(c_in(x),y),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),v),w,tc_fun(x,tc_bool))))* -> hBOOL(hAPP(u,y))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ominus__class_Ominus(z,w,tc_fun(x,tc_bool)),u,x)),c_HOL_Ominus__class_Ominus(z,w,tc_fun(x,tc_bool))))*.
% 299.92/300.51 47935[0:SpL:162.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Ovimage(v,w,x),y),u,w)))* hBOOL(hAPP(hAPP(c_in(w),z),hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),y))))* -> hBOOL(hAPP(u,z))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Ovimage(v,w,x),x1),u,w)),hAPP(c_Set_Ovimage(v,w,x),x1)))*.
% 299.92/300.51 47934[0:SpL:507.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oimage(v,w,x),y),u,x)))* hBOOL(hAPP(hAPP(c_in(x),z),hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),y))))* -> hBOOL(hAPP(u,z))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oimage(v,w,x),x1),u,x)),hAPP(c_Set_Oimage(v,w,x),x1)))*.
% 299.92/300.51 48048[0:SpL:161.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),u,x)))* hBOOL(hAPP(hAPP(c_in(x),y),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),z),w,tc_fun(x,tc_bool))))* -> hBOOL(hAPP(u,y))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ominus__class_Ominus(z,w,tc_fun(x,tc_bool)),u,x)),c_HOL_Ominus__class_Ominus(z,w,tc_fun(x,tc_bool))))*.
% 299.92/300.51 48047[0:SpL:162.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Ovimage(v,w,x),y),u,w)))* hBOOL(hAPP(hAPP(c_in(w),z),hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),x1))))* -> hBOOL(hAPP(u,z))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Ovimage(v,w,x),x1),u,w)),hAPP(c_Set_Ovimage(v,w,x),x1)))*.
% 299.92/300.51 48046[0:SpL:507.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oimage(v,w,x),y),u,x)))* hBOOL(hAPP(hAPP(c_in(x),z),hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),x1))))* -> hBOOL(hAPP(u,z))* hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oimage(v,w,x),x1),u,x)),hAPP(c_Set_Oimage(v,w,x),x1)))*.
% 299.92/300.51 48368[0:SpL:181.1,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(w,x,v),v,x),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(x1,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(w,x,v),v,x),hAPP(c_Set_Oinsert(x1,y),z),y,u) -> hBOOL(hAPP(hAPP(c_in(x),w),x1)).
% 299.92/300.51 48667[0:SpR:158.0,197.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,x) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),z)),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),x1),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_HOL_Ominus__class_Ominus(z,x1,tc_fun(y,tc_bool))))**.
% 299.92/300.51 48652[0:SpR:158.0,197.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,x) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x1)),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_HOL_Ominus__class_Ominus(z,x1,tc_fun(y,tc_bool))))**.
% 299.92/300.51 48628[0:SpR:197.1,55.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> hBOOL(hAPP(hAPP(c_in(w),x),hAPP(c_Set_Oimage(u,v,w),y))) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oimage(u,v,w),z)),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(z,y,tc_fun(v,tc_bool)))))**.
% 299.92/300.51 49155[0:SpL:317.0,239.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(hAPP(w,x),u),hAPP(c_Set_Oimage(w,y,u),z))))* c_lessequals(hAPP(c_Set_Oinsert(x,y),z),x1,tc_fun(y,tc_bool)) c_Fun_Oinj__on(w,hAPP(c_Set_Oinsert(x,y),z),y,u) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oinsert(x,y),z),w,y,u),v)),x1))*.
% 299.92/300.51 49772[0:Rew:49662.2,49597.1] || c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(u,v,w),x1),tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),y,z),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(x1,tc_fun(w,tc_bool)),y),x))))* c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(x1,tc_fun(w,tc_bool)),y),x),y,z).
% 299.92/300.51 49983[0:SpR:497.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),x),y))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),y)),u,w),v)))*.
% 299.92/300.51 49979[0:SpR:497.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),x)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.92/300.51 50422[0:SpR:223.1,545.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),x1))* -> hBOOL(hAPP(hAPP(c_in(x2),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,x3,u,z),u,z),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(x3,z),x,x2),x1)))*.
% 299.92/300.51 50418[0:SpR:223.1,362.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),x1))* -> c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,x2,u,z),u,z),w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oinsert(x2,z),x,tc_fun(x3,tc_bool)),tc_fun(x3,tc_bool))*.
% 299.92/300.51 51530[0:Res:7542.0,195.0] || c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oinsert(v,w),tc_Com_Opname,tc_fun(w,tc_bool)),w,y)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,w,y),v_x),hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,w,y),c_HOL_Ominus__class_Ominus(v_x,u,tc_fun(w,tc_bool))))**.
% 299.92/300.51 51529[0:Res:651.0,195.0] || c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,v,tc_Com_Opname,tc_fun(w,tc_bool)),w,y) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,w,y),hAPP(v,v_x)),hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,w,y),c_HOL_Ominus__class_Ominus(hAPP(v,v_x),u,tc_fun(w,tc_bool))))**.
% 299.92/300.51 51516[0:Res:7539.0,195.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),y)),tc_fun(w,tc_bool))* c_Fun_Oinj__on(z,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),y)),w,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,w,x1),y),hAPP(c_Set_Oimage(z,w,x1),u),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,w,x1),c_HOL_Ominus__class_Ominus(y,u,tc_fun(w,tc_bool))))**.
% 299.92/300.51 53099[0:SpL:23955.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,u),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,x),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,x),v),w),v,u) -> .
% 299.92/300.51 53231[0:SpL:23958.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v,u),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,x),v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,x),v),w),v,u) -> .
% 299.92/300.51 53486[0:SpL:33303.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x),tc_Com_Opname),w,u),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(v_Procs,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,w),x),w,u) -> .
% 299.92/300.51 60418[7:Res:58968.1,619.0] || equal(hAPP(c_in(u),v),v_x) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,u,tc_fun(x,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y)),c_Set_Oinsert(x1,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(x1,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y),w,u,tc_fun(x,tc_bool))))**.
% 299.92/300.51 60531[0:Res:58969.1,619.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,u,tc_fun(x,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y)),c_Set_Oinsert(x1,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(x1,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,hAPP(c_in(u),v),y),w,u,tc_fun(x,tc_bool))))**.
% 299.92/300.51 60604[7:Res:59476.1,619.0] || equal(hAPP(c_in(u),v),v_x) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,u,tc_fun(x,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z)),c_Set_Oinsert(x1,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(x1,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z),w,u,tc_fun(x,tc_bool))))**.
% 299.92/300.51 60677[0:Res:59477.1,619.0] || equal(hAPP(c_in(u),v),v_Procs) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,u,tc_fun(x,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z)),c_Set_Oinsert(x1,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(x1,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),z),w,u,tc_fun(x,tc_bool))))**.
% 299.92/300.51 60862[0:Res:59017.1,619.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a)* equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,v,tc_fun(y,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_in(v),w),z)),c_Set_Oinsert(x2,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(x2,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),x1,hAPP(c_in(v),w),z),x,v,tc_fun(y,tc_bool))))**.
% 299.92/300.51 60935[0:Res:59525.1,619.0] || -> c_Hoare__Mirabelle_Ohoare__valids(u,hAPP(c_in(v),w),t_a)* equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,v,tc_fun(y,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_in(v),w),x1)),c_Set_Oinsert(x2,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(x2,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_in(v),w),x1),x,v,tc_fun(y,tc_bool))))**.
% 299.92/300.51 64874[0:SpL:28747.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w),tc_Com_Opname),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,x),y),x,u) -> .
% 299.92/300.51 64994[0:SpL:28748.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w),tc_Com_Opname),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,x),y),x,u) -> .
% 299.92/300.51 65114[0:SpL:28902.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w),tc_Com_Opname),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,x),y),x,u) -> .
% 299.92/300.51 65234[0:SpL:28903.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w),tc_Com_Opname),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v_Procs,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,x),y),x,u) -> .
% 299.92/300.51 74533[7:Rew:71835.1,74272.2] || equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),c_Set_Oinsert(v_x,t_a)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),v_x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.51 80294[0:SpL:21268.0,470.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),y),z,x1),v,w,x,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),y),z,x1)))*.
% 299.92/300.51 80293[0:SpL:21268.0,466.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),y),z,x1),w,v,x,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),y),z,x1)))*.
% 299.92/300.51 80275[0:SpL:21268.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),z,x1),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)),x)).
% 299.92/300.51 80241[0:SpL:21268.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),v,z),u,w)))* hBOOL(hAPP(hAPP(c_in(w),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(u,x1))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)),x)).
% 299.92/300.51 80231[0:SpL:21268.0,327.0] || equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)) -> c_lessequals(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),u,y),tc_fun(v,tc_bool))*.
% 299.92/300.51 80183[0:SpL:21268.0,274.0] || equal(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(u,v),x))* -> hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(v),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),x),y,z)))* equal(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(u,v),x),y,z))*.
% 299.92/300.51 80166[0:SpL:21268.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(v,x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),v,hAPP(v,w),z,x1),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(v,hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),v,hAPP(v,w),z,x1),x),y),x,u) -> .
% 299.92/300.51 80065[0:SpL:21268.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(u),x),w))* equal(hAPP(y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1)),hAPP(y,x))* c_Fun_Oinj__on(y,w,u,x2)* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_in(u),hAPP(c_in(u),v),z,x1),x).
% 299.92/300.51 79918[0:SpR:161.0,21268.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),w,tc_fun(u,tc_bool)),x,z)),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),w,tc_fun(u,tc_bool)))**.
% 299.92/300.51 79917[0:SpR:162.0,21268.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)),y,x1)),hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)))**.
% 299.92/300.51 79916[0:SpR:507.0,21268.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)),y,x1)),hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)))**.
% 299.92/300.51 79716[0:SpR:21268.0,329.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v,y),tc_fun(w,tc_bool))* -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),v,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x)).
% 299.92/300.51 80476[0:Rew:30.0,79779.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_COMBB(c_Set_Ovimage(u,v,w),tc_fun(w,tc_bool),tc_fun(v,tc_bool),z),hAPP(c_COMBB(c_Set_Ovimage(u,v,w),tc_fun(w,tc_bool),tc_fun(v,tc_bool),z),x1),y,x2),z,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,x1,z,tc_fun(w,tc_bool))))**.
% 299.92/300.51 80477[0:Rew:90.0,79778.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_COMBB(c_Set_Oimage(u,v,w),tc_fun(v,tc_bool),tc_fun(w,tc_bool),z),hAPP(c_COMBB(c_Set_Oimage(u,v,w),tc_fun(v,tc_bool),tc_fun(w,tc_bool),z),x1),y,x2),z,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,x1,z,tc_fun(v,tc_bool))))**.
% 299.92/300.51 81489[0:SpL:21894.0,470.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(w,x,u),y),c_Set_Oimage(w,x,u),z,x1),v,w,x,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(w,x,u),y),c_Set_Oimage(w,x,u),z,x1)))*.
% 299.92/300.51 81488[0:SpL:21894.0,466.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(w,x,u),y),c_Set_Oimage(w,x,u),z,x1),w,v,x,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(w,x,u),y),c_Set_Oimage(w,x,u),z,x1)))*.
% 299.92/300.51 81470[0:SpL:21894.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z,x1),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)),x)).
% 299.92/300.51 81436[0:SpL:21894.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v,z),u,w)))* hBOOL(hAPP(hAPP(c_in(w),x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(u,x1))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)),x)).
% 299.92/300.51 81426[0:SpL:21894.0,327.0] || equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)) -> c_lessequals(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,y),tc_fun(v,tc_bool))*.
% 299.92/300.51 81378[0:SpL:21894.0,274.0] || equal(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Set_Oinsert(u,v),x))* -> hBOOL(hAPP(hAPP(c_in(v),u),w))* hBOOL(hAPP(hAPP(c_in(v),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(u,v),x),c_Set_Oinsert(u,v),y,z)))* equal(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(u,v),x),c_Set_Oinsert(u,v),y,z))*.
% 299.92/300.51 81361[0:SpL:21894.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(v,w)),hAPP(c_Set_Oimage(v,x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(v,w),v,z,x1),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(v,hAPP(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(v,w),v,z,x1),x),y),x,u) -> .
% 299.92/300.51 81260[0:SpL:21894.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* hBOOL(hAPP(hAPP(c_in(u),x),w))* equal(hAPP(y,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1)),hAPP(y,x))* c_Fun_Oinj__on(y,w,u,x2)* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),c_in(u),z,x1),x).
% 299.92/300.51 81112[0:SpR:161.0,21894.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),w,tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),x,z)),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),w,tc_fun(u,tc_bool)))**.
% 299.92/300.51 81111[0:SpR:162.0,21894.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),y,x1)),hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)))**.
% 299.92/300.51 81110[0:SpR:507.0,21894.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),y,x1)),hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)))**.
% 299.92/300.51 80910[0:SpR:21894.0,329.1] || c_lessequals(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v,y),tc_fun(w,tc_bool))* -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x)).
% 299.92/300.51 81671[0:Rew:30.0,80973.0] || -> equal(hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_COMBB(c_Set_Ovimage(u,v,w),tc_fun(w,tc_bool),tc_fun(v,tc_bool),z),x1),c_COMBB(c_Set_Ovimage(u,v,w),tc_fun(w,tc_bool),tc_fun(v,tc_bool),z),y,x2),z,tc_fun(w,tc_bool))),hAPP(c_Set_Ovimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,x1,z,tc_fun(w,tc_bool))))**.
% 299.92/300.51 81672[0:Rew:90.0,80972.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_COMBB(c_Set_Oimage(u,v,w),tc_fun(v,tc_bool),tc_fun(w,tc_bool),z),x1),c_COMBB(c_Set_Oimage(u,v,w),tc_fun(v,tc_bool),tc_fun(w,tc_bool),z),y,x2),z,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,x1,z,tc_fun(v,tc_bool))))**.
% 299.92/300.51 83133[0:SpL:5924.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_COMBS(w,c_COMBK(x,y,z),x1,x2,x3),x4,x5)),hAPP(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_COMBS(w,c_COMBK(x,y,z),x1,x2,x3),x4,x5)),x))* -> equal(hAPP(c_Set_Oimage(u,x4,x5),v),hAPP(c_Set_Oimage(c_COMBS(w,c_COMBK(x,y,z),x1,x2,x3),x4,x5),v)).
% 299.92/300.51 83129[0:SpL:5924.0,315.0] || equal(hAPP(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,c_COMBS(u,c_COMBK(w,x,y),z,x1,x2),x3,x4,x5)),w),hAPP(x3,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,c_COMBS(u,c_COMBK(w,x,y),z,x1,x2),x3,x4,x5)))* -> equal(hAPP(c_Set_Oimage(c_COMBS(u,c_COMBK(w,x,y),z,x1,x2),x4,x5),v),hAPP(c_Set_Oimage(x3,x4,x5),v)).
% 299.92/300.51 83450[0:SpL:5961.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_COMBS(c_COMBK(w,x,y),z,x1,x2,x3),x4,x5)),hAPP(w,hAPP(z,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_COMBS(c_COMBK(w,x,y),z,x1,x2,x3),x4,x5))))* -> equal(hAPP(c_Set_Oimage(u,x4,x5),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBK(w,x,y),z,x1,x2,x3),x4,x5),v)).
% 299.92/300.51 83448[0:SpL:5961.0,315.0] || equal(hAPP(u,hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,c_COMBS(c_COMBK(u,x,y),v,z,x1,x2),x3,x4,x5))),hAPP(x3,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,c_COMBS(c_COMBK(u,x,y),v,z,x1,x2),x3,x4,x5)))* -> equal(hAPP(c_Set_Oimage(c_COMBS(c_COMBK(u,x,y),v,z,x1,x2),x4,x5),w),hAPP(c_Set_Oimage(x3,x4,x5),w)).
% 299.92/300.51 89930[0:SpL:26183.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),x),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),x),y),z),y,u) -> .
% 299.92/300.51 26702[0:SpR:21893.0,244.2] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,u),v_x),c_Set_Oinsert(v,u),tc_Com_Opname,w)))* equal(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,u),v_x),c_Set_Oinsert(v,u),tc_Com_Opname,w),u),c_HOL_Ozero__class_Ozero(tc_nat)) equal(c_Suc(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(v,u),v_x),c_Set_Oinsert(v,u),tc_Com_Opname,w),u)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(v,u),v_x),u)).
% 299.92/300.51 26701[0:SpR:21267.0,244.2] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v,u),v_x),tc_Com_Opname,w)))* equal(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v,u),v_x),tc_Com_Opname,w),u),c_HOL_Ozero__class_Ozero(tc_nat)) equal(c_Suc(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v,u),v_x),tc_Com_Opname,w),u)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(v,u),v_x),u)).
% 299.92/300.51 31406[0:SpL:131.0,449.0] || hBOOL(hAPP(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(z,c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x1,x2))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(z,c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x1,x2)))* -> c_Hoare__Mirabelle_Otriple__valid(x2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),z),x1),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y)),t_a).
% 299.92/300.51 31405[0:SpL:158.0,449.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(z,c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x1,x2))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(z,c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x1,x2)))* -> c_Hoare__Mirabelle_Otriple__valid(x2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),z),x1),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w)),t_a).
% 299.92/300.51 38010[0:Res:340.2,441.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))* c_lessequals(x,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))*.
% 299.92/300.51 38643[0:SpL:24914.0,184.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) c_Fun_Oinj__on(w,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,x,u),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,x,u),v_x)),x,u) -> equal(hAPP(w,hAPP(c_Fun_Othe__inv__into(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,x,u),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,x,u),v_x)),w,x,u),v)),v)**.
% 299.92/300.51 38992[0:SpR:24914.0,354.2] || c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),y,tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,y,v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(y,u,v,w),w,v),hAPP(c_Set_Oimage(u,v,w),v_x)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)))*.
% 299.92/300.51 38986[0:SpR:205.1,354.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),y,w,v) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(y,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),v,w),x),hAPP(c_Set_Oimage(u,v,w),x))**.
% 299.92/300.51 38945[0:SpR:354.2,410.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,w,y),u),z),x1),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,tc_fun(x2,tc_bool))))*.
% 299.92/300.51 40457[0:SpL:21893.0,529.0] || c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),v) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),tc_Com_Opname,y)),v)*.
% 299.92/300.51 40456[0:SpL:21267.0,529.0] || c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),v) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),tc_Com_Opname,y)),v)*.
% 299.92/300.51 40706[0:SpR:21893.0,530.1] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),tc_Com_Opname,y)),v)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),v).
% 299.92/300.51 40705[0:SpR:21267.0,530.1] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),tc_Com_Opname,y)),v)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),v).
% 299.92/300.51 41870[0:Rew:339.0,41812.2] || hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,x,z),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),y,x,z)))))* c_Fun_Oinj__on(y,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,z) -> hBOOL(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x1)))*.
% 299.92/300.51 41871[0:Rew:537.1,41809.3] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,x,z),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y,x,z)))))* c_Fun_Oinj__on(y,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,z) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1)))*.
% 299.92/300.51 41872[0:Rew:534.1,41808.3] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,x,z),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y,x,z)))))* c_Fun_Oinj__on(y,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,z) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1)))*.
% 299.92/300.51 42070[0:SpR:180.2,71.2] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(hAPP(c_in(w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),y,w,x1) -> equal(hAPP(c_Fun_Othe__inv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w,x1),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(z,u),v),u,u)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u))**.
% 299.92/300.51 42069[0:SpR:180.2,373.2] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(hAPP(c_in(w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),y,w,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),w,x1),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(z,u),v),u,u)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u))**.
% 299.92/300.51 42283[0:SSi:42173.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(hAPP(c_in(v),w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,hAPP(c_Set_Oinsert(y,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(v),w),y)) hBOOL(hAPP(hAPP(c_in(v),w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)))).
% 299.92/300.51 42480[0:SpL:188.1,315.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,x,c_Set_Ovimage(c_COMBK(v,u,y),y,u),z,x1)))* equal(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,x,c_Set_Ovimage(c_COMBK(v,u,y),y,u),z,x1)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)))** -> equal(hAPP(c_Set_Oimage(x,z,x1),w),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,y),y,u),z,x1),w)).
% 299.92/300.51 42439[0:SpL:188.1,315.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z,x1)))* equal(hAPP(y,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z,x1)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))** -> equal(hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,x),x,u),z,x1),w),hAPP(c_Set_Oimage(y,z,x1),w)).
% 299.92/300.51 42661[0:SpR:161.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),x,y),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(z,w,tc_fun(u,tc_bool)),x),x1)),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z),w,tc_fun(u,tc_bool)),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),x,y),x1)))*.
% 299.92/300.51 43025[0:SpR:465.1,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),y),v)) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(x1,x,x2),v)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_Fun_Ofun__upd(x1,y,x3,x,x2),x,x2),u,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(c_Fun_Ofun__upd(x1,y,x3,x,x2),x,x2),u,tc_fun(z,tc_bool)))**.
% 299.92/300.51 43479[0:SpR:507.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),y,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(v,w,u),x1),y),x2)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x1)),z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),y,z),x2)))*.
% 299.92/300.51 43701[0:SpR:162.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),y,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(v,u,w),x1),y),x2)),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x1)),z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),y,z),x2)))*.
% 299.92/300.51 45354[0:Res:468.0,487.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,z,v,x1)))* -> equal(hAPP(c_Set_Oimage(y,v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Oimage(z,v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,u,v)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)))*.
% 299.92/300.51 46966[0:Rew:223.1,46940.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v,u,u),u,u),w),tc_fun(u,tc_bool))* c_Finite__Set_Ofinite(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),u) -> c_Fun_Oinj__on(x,c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),u,u)*.
% 299.92/300.51 47408[0:Res:171.2,485.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)),v))*.
% 299.92/300.51 47407[0:Res:172.2,485.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)),v))*.
% 299.92/300.51 47363[0:SpL:533.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))*.
% 299.92/300.51 47639[0:Res:171.2,484.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)),w))*.
% 299.92/300.51 47638[0:Res:172.2,484.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)),w))*.
% 299.92/300.51 47595[0:SpL:532.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)))*.
% 299.92/300.51 47977[0:Res:171.2,490.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)),v))*.
% 299.92/300.51 47976[0:Res:172.2,490.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)),v))*.
% 299.92/300.51 47932[0:SpL:533.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),v))))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)))*.
% 299.92/300.51 48089[0:Res:171.2,489.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.92/300.51 48088[0:Res:172.2,489.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) hBOOL(hAPP(x,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.92/300.51 48045[0:SpL:532.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),z))))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)))*.
% 299.92/300.51 48438[0:SpL:128.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Ovimage(v,w,x),y),tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(v,w,x),z,u),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(c_Set_Ovimage(v,w,x),hAPP(c_Set_Oinsert(c_HOL_Ouminus__class_Ouminus(y,tc_fun(x,tc_bool)),z),x1),z,u) -> .
% 299.92/300.51 48367[0:SpL:188.1,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,y),y,u),z,x),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(w,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v,u,y),y,u),hAPP(c_Set_Oinsert(w,z),x1),z,x) -> .
% 299.92/300.51 48786[0:Res:176.0,619.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(x,v,y),hAPP(c_Set_Oinsert(hAPP(x,z),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))),c_Set_Oinsert(x1,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x1,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Ovimage(x,v,y),hAPP(c_Set_Oinsert(hAPP(x,z),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),u,v,tc_fun(w,tc_bool))))**.
% 299.92/300.51 48948[0:SpL:410.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x),y),z,x,tc_fun(u,tc_bool))))* -> hBOOL(hAPP(x1,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(z,w),x1,u)),hAPP(z,w)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,z,x,tc_fun(u,tc_bool)),x1,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,z,x,tc_fun(u,tc_bool))))*.
% 299.92/300.51 49758[0:Rew:9.0,49472.1] || c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),z,y,x) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(u,hAPP(v,x1))),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(x1,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool))))))* c_Fun_Oinj__on(c_Fun_Ocomp(u,v,w,x,y),hAPP(c_Set_Oinsert(x1,y),z),y,x).
% 299.92/300.51 49775[0:Rew:49662.2,49615.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),x,y),hAPP(c_Set_Oinsert(v_Procs,x),w))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,u,hAPP(u,v_x),tc_Com_Opname,v),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,x),w),x,y).
% 299.92/300.51 49776[0:Rew:49662.2,49612.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),x,y),hAPP(c_Set_Oinsert(v_Procs,x),w))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(u,v_x),u,tc_Com_Opname,v),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,x),w),x,y).
% 299.92/300.51 49777[0:Rew:49662.2,49552.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),w,x),hAPP(c_Set_Oinsert(y,w),v))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(y,w),v),w,x).
% 299.92/300.51 49778[0:Rew:49662.2,49538.2] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z),x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z),x),w),x,y).
% 299.92/300.51 49779[0:Rew:49662.2,49537.2] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z),x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z),x),w),x,y).
% 299.92/300.51 49812[0:Rew:49662.2,49653.3] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(y,hAPP(u,z))) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(z,w),v),w,x) hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(z,w),v)),x1,y,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(z,w),v))),x1)))*.
% 299.92/300.51 49813[0:Rew:49662.2,49652.3] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(y,hAPP(u,z))) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(z,w),v),w,x) hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(z,w),v)),y,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(z,w),v)))))*.
% 299.92/300.51 50839[0:SpR:622.0,361.2] class_Complete__Lattice_Ocomplete__lattice(u) || hBOOL(hAPP(hAPP(c_in(v),v_x),w)) -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,x,tc_fun(t_a,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(y,x,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v,u),u)*.
% 299.92/300.51 50831[0:SpR:622.0,176.0] || -> hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Ovimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),u,x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),v,w,tc_fun(t_a,tc_bool))),x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))*.
% 299.92/300.51 51257[0:SpL:584.0,462.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(c_COMBS(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x,y,z,x1),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x2))),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x2)),hAPP(x,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x2)))),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.51 51751[0:MRR:51750.0,24395.1] || c_Finite__Set_Ofinite(u,v) c_lessequals(hAPP(c_Set_Oinsert(w,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),u,tc_fun(v,tc_bool))* c_lessequals(hAPP(c_Set_Oimage(x,v,y),u),z,tc_fun(y,tc_bool))* c_Fun_Oinj__on(c_COMBK(w,v,y),z,y,v)* c_Fun_Oinj__on(x,u,v,y) -> equal(z,c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))) equal(c_Finite__Set_Ocard(u,v),c_Suc(c_HOL_Ozero__class_Ozero(tc_nat))).
% 299.92/300.51 51890[0:SpL:9924.0,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),v,w),hAPP(u,c_Orderings_Otop__class_Otop(tc_bool))) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool)),w,v,x),tc_fun(x,w),tc_fun(x,v),v),hAPP(c_COMBB(y,w,tc_fun(x,w),v),u)),z,x1,v,x)),c_List_Ofoldl(y,hAPP(u,z),x1,w,x))**.
% 299.92/300.51 76174[0:SpL:9915.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(v,w,x),y,z,x1,x2),x3,u),c_HOL_Ominus__class_Ominus(x4,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x3),c_Orderings_Obot__class_Obot(tc_fun(x3,tc_bool))),tc_fun(x3,tc_bool)))))* c_Fun_Oinj__on(c_COMBS(c_Set_Ovimage(v,w,x),y,z,x1,x2),hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x3),x4),x3,u) -> .
% 299.92/300.51 76295[0:SpL:10469.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_Set_Oimage(v,w,x),y,z,x1,x2),x3,u),c_HOL_Ominus__class_Ominus(x4,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x3),c_Orderings_Obot__class_Obot(tc_fun(x3,tc_bool))),tc_fun(x3,tc_bool)))))* c_Fun_Oinj__on(c_COMBS(c_Set_Oimage(v,w,x),y,z,x1,x2),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)),x3),x4),x3,u) -> .
% 299.92/300.51 76425[0:SpL:10470.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_Set_Ovimage(v,w,x),y,z,x1,x2),x3,u),c_HOL_Ominus__class_Ominus(x4,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),x3),c_Orderings_Obot__class_Obot(tc_fun(x3,tc_bool))),tc_fun(x3,tc_bool)))))* c_Fun_Oinj__on(c_COMBS(c_Set_Ovimage(v,w,x),y,z,x1,x2),hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)),x3),x4),x3,u) -> .
% 299.92/300.51 79012[0:Res:15630.1,481.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(x,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,y),z),x1,hAPP(c_in(u),v),y)),x2),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,y),z),x1,hAPP(c_in(u),v),y)),x2)))*.
% 299.92/300.51 79011[0:Res:15630.1,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(x,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,z),x1),x2,hAPP(c_in(u),v),z)),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,z),x1),x2,hAPP(c_in(u),v),z))))*.
% 299.92/300.51 79232[0:Res:15858.1,481.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(x,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(w,z),x1),hAPP(c_in(u),v),z)),x2),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,hAPP(c_Set_Oinsert(w,z),x1),hAPP(c_in(u),v),z)),x2)))*.
% 299.92/300.51 79231[0:Res:15858.1,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(x,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,hAPP(c_Set_Oinsert(w,x1),x2),hAPP(c_in(u),v),x1)),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,hAPP(c_Set_Oinsert(w,x1),x2),hAPP(c_in(u),v),x1))))*.
% 299.92/300.51 80292[0:SpL:21268.0,473.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),y),z,x1),w,x,u),v)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),y),z,x1)))*.
% 299.92/300.51 80198[0:SpL:21268.0,462.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Com_Obody,hAPP(c_Com_Obody,x),z,x1))),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.51 80091[0:SpL:21268.0,237.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u) -> equal(hAPP(w,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_in(u),hAPP(c_in(u),v),y,z),w,u,x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_in(u),hAPP(c_in(u),v),y,z))**.
% 299.92/300.51 81487[0:SpL:21894.0,473.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(w,x,u),y),c_Set_Oimage(w,x,u),z,x1),w,x,u),v)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(w,x,u),y),c_Set_Oimage(w,x,u),z,x1)))*.
% 299.92/300.51 81393[0:SpL:21894.0,462.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Com_Obody,x),c_Com_Obody,z,x1))),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.51 81286[0:SpL:21894.0,237.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u) -> equal(hAPP(w,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),c_in(u),y,z),w,u,x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),c_in(u),y,z))**.
% 299.92/300.51 88421[0:Res:8176.1,195.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(y,v,w,z)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(y,w,z),c_HOL_Ominus__class_Ominus(u,x1,tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(y,w,z),x),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,w,z),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,x1,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))))**.
% 299.92/300.51 27150[0:SpR:104.0,450.0] || -> hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),w,x,y),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool))),w,x,y)))* c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(v,tc_bool)))),x),w),t_a).
% 299.92/300.51 27940[0:Res:468.0,175.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Ovimage(x,v,y),hAPP(c_Set_Oinsert(z,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))))),hAPP(c_Set_Oimage(x1,v,w),hAPP(c_Set_Ovimage(x,v,y),hAPP(c_Set_Oinsert(z,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))))) equal(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Ovimage(x,v,y),hAPP(c_Set_Oinsert(z,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool)))),u,x1,v,w)),z)**.
% 299.92/300.51 33918[0:SpR:24914.0,246.2] || c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),v) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x))))* equal(c_Suc(c_Finite__Set_Ocard(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(u,v),tc_Com_Opname,w),hAPP(c_Set_Oinsert(u,v),v_x)),v)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(u,v),v_x),v)).
% 299.92/300.51 35201[0:SpR:410.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),z)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(w,x1)),z,u,x2) -> equal(hAPP(c_Fun_Othe__inv__into(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(w,x1)),u,x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x1,x),v),w,x,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool)))**.
% 299.92/300.51 35200[0:SpR:410.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),z)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(w,x1)),z,u,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(w,x1)),u,x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x1,x),v),w,x,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool)))**.
% 299.92/300.51 36194[0:Res:171.2,516.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)),w))*.
% 299.92/300.51 36193[0:Res:172.2,516.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)),w))*.
% 299.92/300.51 37459[0:SpR:205.1,475.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),z)) -> equal(hAPP(c_Set_Oinsert(y,x1),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,x1),z)),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,x1),z))**.
% 299.92/300.51 39191[0:SpR:533.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,y),hAPP(c_Set_Oinsert(z,x),x1)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z)),y),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,y),x1)))*.
% 299.92/300.51 40455[0:SpL:24914.0,529.0] || c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),v) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),tc_Com_Opname,y),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x))),v)*.
% 299.92/300.51 40704[0:SpR:24914.0,530.1] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),tc_Com_Opname,y),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x))),v)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),v).
% 299.92/300.51 40877[0:SpL:24914.0,479.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(w),v),tc_Com_Opname,x),hAPP(hAPP(c_in(w),v),v_x)),y,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(w),v),tc_Com_Opname,x),hAPP(hAPP(c_in(w),v),v_x))),y)))*.
% 299.92/300.51 41158[0:SpL:24914.0,478.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),v_x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(w),v),tc_Com_Opname,y),hAPP(hAPP(c_in(w),v),v_x)),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(w),v),tc_Com_Opname,y),hAPP(hAPP(c_in(w),v),v_x)))))*.
% 299.92/300.51 41802[0:SpL:297.2,199.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,y),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,w,y)),u)* hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,y),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,w,y))) c_Fun_Oinj__on(x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,y) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),z))*.
% 299.92/300.51 42472[0:SpL:445.1,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Fun_Ofun__upd(w,x,y,z,x1),x2,x3)),hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Fun_Ofun__upd(w,x,y,z,x1),x2,x3)))* -> equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Fun_Ofun__upd(w,x,y,z,x1),x2,x3),x) equal(hAPP(c_Set_Oimage(u,x2,x3),v),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,x,y,z,x1),x2,x3),v)).
% 299.92/300.51 42431[0:SpL:445.1,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,c_Fun_Ofun__upd(u,w,x,y,z),x1,x2,x3)),hAPP(x1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,c_Fun_Ofun__upd(u,w,x,y,z),x1,x2,x3)))* -> equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,c_Fun_Ofun__upd(u,w,x,y,z),x1,x2,x3),w) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,w,x,y,z),x2,x3),v),hAPP(c_Set_Oimage(x1,x2,x3),v)).
% 299.92/300.51 43052[0:SpR:339.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(y,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),v))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(y,z),x1)),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(y,z),x1)),u,tc_fun(x,tc_bool)))**.
% 299.92/300.51 43042[0:SpR:537.1,486.1] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),w))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1)),v,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1)),v,tc_fun(y,tc_bool)))**.
% 299.92/300.51 43041[0:SpR:534.1,486.1] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),w),x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),w))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1)),v,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1)),v,tc_fun(y,tc_bool)))**.
% 299.92/300.51 43040[0:SpR:180.2,486.1] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(hAPP(c_in(w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u)),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(x1,u),v),u,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),w,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x1),w,tc_fun(z,tc_bool)))**.
% 299.92/300.51 42906[0:SpR:486.1,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool))),x1)) -> equal(hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)),x2),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x,x2),x1)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x,x2),x1))**.
% 299.92/300.51 44292[0:SpL:21893.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(u),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,x)))* equal(hAPP(y,v),hAPP(y,w))* c_Fun_Oinj__on(y,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,x),u,z)* -> equal(v,w).
% 299.92/300.51 44291[0:SpL:21267.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(u),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,x)))* equal(hAPP(y,v),hAPP(y,w))* c_Fun_Oinj__on(y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,x),u,z)* -> equal(v,w).
% 299.92/300.51 45607[0:SpL:323.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),z))* hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x3),v),w,x,tc_fun(y,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(x1),x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x3,w,x,tc_fun(y,tc_bool))),u,tc_fun(x1,tc_bool))))*.
% 299.92/300.51 45654[0:SSi:45564.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),y)) c_Finite__Set_Ofinite(y,tc_fun(u,tc_bool)) -> c_lessequals(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),z),w,x,tc_fun(u,tc_bool)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,w,x,tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))*.
% 299.92/300.51 45896[0:Res:468.0,482.2] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,u,w)))* -> equal(hAPP(c_Set_Oimage(y,w,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x)),hAPP(c_Set_Oimage(x1,w,z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),y,x1,w,z)))*.
% 299.92/300.51 48379[0:SpL:544.1,224.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,v),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),y),z),y,v) -> .
% 299.92/300.51 48378[0:SpL:543.1,224.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,v),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x),y),z),y,v) -> .
% 299.92/300.51 48664[0:SpR:465.1,197.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> hBOOL(hAPP(hAPP(c_in(x),v),z)) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,x,y),z),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),x1),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_HOL_Ominus__class_Ominus(z,x1,tc_fun(x,tc_bool))))**.
% 299.92/300.51 48649[0:SpR:465.1,197.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,y) -> hBOOL(hAPP(hAPP(c_in(x),v),z)) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),x1),hAPP(c_Set_Oimage(u,x,y),z),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),c_HOL_Ominus__class_Ominus(x1,z,tc_fun(x,tc_bool))))**.
% 299.92/300.51 49192[0:Res:468.0,239.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,u,w,y) -> equal(hAPP(c_Set_Oimage(z,y,x1),hAPP(c_Set_Oimage(x,w,y),u)),hAPP(c_Set_Oimage(x2,y,x1),hAPP(c_Set_Oimage(x,w,y),u))) hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(u,x,w,y),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(x,w,y),u),z,x2,y,x1))),v))*.
% 299.92/300.51 49158[0:SpL:158.0,239.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Fun_Ocomp(w,x,y,u,z),z,u),x1)))* c_lessequals(hAPP(c_Set_Oimage(x,z,y),x1),x2,tc_fun(y,tc_bool)) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(x,z,y),x1),y,u) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,z,y),x1),w,y,u),v)),x2))*.
% 299.92/300.51 49273[0:SpL:410.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x,y),z),x1,y,tc_fun(w,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(x1,x),u,w)),hAPP(x1,x)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x1,y,tc_fun(w,tc_bool)),u,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x1,y,tc_fun(w,tc_bool))))*.
% 299.92/300.51 49780[0:Rew:49662.2,49605.1] || c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),y,z,x1) -> hBOOL(hAPP(hAPP(c_in(x1),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),z,x1),hAPP(c_Set_Oinsert(x2,z),y))))* c_Fun_Oinj__on(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),u,v),w,tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(x2,z),y),z,x1).
% 299.92/300.51 49781[0:Rew:49662.2,49527.2] || c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(u,v,w),w,v),x,y,z) -> hBOOL(hAPP(hAPP(c_in(v),u),x1)) hBOOL(hAPP(hAPP(c_in(z),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(u,v,w),w,v),y,z),hAPP(c_Set_Oinsert(x1,y),x))))* c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(u,v,w),w,v),hAPP(c_Set_Oinsert(x1,y),x),y,z).
% 299.92/300.51 49782[0:Rew:49662.2,49489.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),y,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),x1),y),x))))* c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),x1),y),x),y,z).
% 299.92/300.51 49783[0:Rew:49662.2,49488.1] || c_Fun_Oinj__on(c_Set_Oimage(u,v,w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oinsert(hAPP(u,x1),w),hAPP(c_Set_Oimage(u,v,w),x2))),hAPP(c_Set_Oimage(c_Set_Oimage(u,v,w),y,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(x1,v),x2),y),x))))* c_Fun_Oinj__on(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(x1,v),x2),y),x),y,z).
% 299.92/300.51 50159[0:SpR:158.0,620.1] || -> equal(hAPP(c_Set_Oimage(u,v,w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(c_Fun_Ocomp(y,u,w,tc_fun(z,tc_bool),v),v,tc_fun(z,tc_bool)),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),tc_fun(z,tc_bool),tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,w),x),y,w,tc_fun(z,tc_bool))))*.
% 299.92/300.51 50179[0:Rew:542.0,50146.2,533.0,50146.2,532.0,50146.2] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oimage(w,x,tc_fun(u,tc_bool)),y))) -> equal(y,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,x,tc_fun(u,tc_bool)))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,w,x,tc_fun(u,tc_bool))))**.
% 299.92/300.51 50427[0:SpR:223.1,410.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),x1,z,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),hAPP(x1,y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),x1,z,tc_fun(x2,tc_bool))))*.
% 299.92/300.51 50395[0:SpR:223.1,8385.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(x,u,tc_Com_Opname),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),v_Procs)** -> equal(hAPP(c_Set_Oimage(x,u,tc_Com_Opname),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,tc_Com_Opname),u,tc_Com_Opname),w)).
% 299.92/300.51 50836[0:SpR:622.0,545.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,x,tc_fun(t_a,tc_bool)))),hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(y,x,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),u,w),v)))*.
% 299.92/300.51 50832[0:SpR:622.0,362.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> c_lessequals(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,tc_fun(t_a,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),u,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))*.
% 299.92/300.51 51542[0:Res:20152.0,195.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,w,y),c_HOL_Ominus__class_Ominus(z,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,w,y),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(z,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),u,tc_fun(w,tc_bool))))**.
% 299.92/300.51 51535[0:Res:20186.0,195.0] || c_lessequals(u,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),w,y) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,w,y),c_HOL_Ominus__class_Ominus(z,v,tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,w,y),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(z,v,tc_fun(w,tc_bool)),u,tc_fun(w,tc_bool))))**.
% 299.92/300.51 51534[0:Res:19747.0,195.0] || c_lessequals(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),tc_fun(x,tc_bool))* c_Fun_Oinj__on(y,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool)),x,z)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(y,x,z),w),hAPP(c_Set_Oimage(y,x,z),u),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,x,z),c_HOL_Ominus__class_Ominus(w,u,tc_fun(x,tc_bool))))**.
% 299.92/300.51 51524[0:Res:23936.0,195.0] || c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)) c_Fun_Oinj__on(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,tc_fun(v,tc_bool)),v,x) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(w,v,x),v_x),hAPP(c_Set_Oimage(w,v,x),u),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(w,v,x),c_HOL_Ominus__class_Ominus(v_x,u,tc_fun(v,tc_bool))))**.
% 299.92/300.51 51518[0:Res:1145.0,195.0] || c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v,w,x),tc_Com_Opname,tc_fun(y,tc_bool)),tc_fun(y,tc_bool))* c_Fun_Oinj__on(z,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(v,w,x),tc_Com_Opname,tc_fun(y,tc_bool)),y,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,y,x1),v),hAPP(c_Set_Oimage(z,y,x1),u),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,y,x1),c_HOL_Ominus__class_Ominus(v,u,tc_fun(y,tc_bool))))**.
% 299.92/300.51 51689[0:SpL:8415.2,233.2] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Finite__Set_Ofinite(v_x,v) c_Finite__Set_Ofinite(x,w) c_lessequals(v_x,x,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Oimage(y,w,v),x),v_x,tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,v_x,v,w)* c_Fun_Oinj__on(y,x,w,v) -> equal(c_Finite__Set_Ocard(v_x,v),c_Finite__Set_Ocard(x,w)).
% 299.92/300.51 64057[0:Res:63953.0,195.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),tc_fun(tc_Com_Opname,tc_bool)) c_Fun_Oinj__on(w,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),v),tc_Com_Opname,x) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(w,tc_Com_Opname,x),c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool))),hAPP(c_Set_Oimage(w,tc_Com_Opname,x),u),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(w,tc_Com_Opname,x),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(v,v_Procs,tc_fun(tc_Com_Opname,tc_bool)),u,tc_fun(tc_Com_Opname,tc_bool))))**.
% 299.92/300.51 71716[7:SpR:71455.1,223.1] || equal(hAPP(c_Set_Oimage(u,v,t_a),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),v_x)** hBOOL(hAPP(hAPP(c_in(v),x),w)) -> equal(hAPP(c_Set_Oimage(u,v,t_a),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,x,v_x,v,t_a),v,t_a),w)).
% 299.92/300.51 78984[0:SpR:465.1,15630.1] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),z)) -> hBOOL(hAPP(hAPP(c_in(x),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(z,x1),x2),x3,c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),x1)))* hBOOL(hAPP(c_Set_Oimage(u,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(z,x1),x2),x3,c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),x1)))*.
% 299.92/300.51 79204[0:SpR:465.1,15858.1] || hBOOL(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),z)) -> hBOOL(hAPP(hAPP(c_in(x),v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,hAPP(c_Set_Oinsert(z,x2),x3),c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),x2)))* hBOOL(hAPP(c_Set_Oimage(u,x,y),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(x1,hAPP(c_Set_Oinsert(z,x2),x3),c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),x2)))*.
% 299.92/300.51 80216[0:SpL:21268.0,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),x,y))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),x,y)))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a).
% 299.92/300.51 80133[0:SpL:21268.0,94.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(u,w,x),y),v,z),w,x) c_Fun_Oinj__on(x1,hAPP(c_Set_Oimage(u,w,x),y),x,x2) -> c_Fun_Oinj__on(c_Fun_Ocomp(x1,u,x,x2,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(u,w,x),y),v,z),w,x2)*.
% 299.92/300.51 81411[0:SpL:21894.0,496.0] || hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xtriples__valid__Suc__1(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x,y))),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),v),hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),u),x,y)))* c_Hoare__Mirabelle_Otriple__valid(w,u,t_a).
% 299.92/300.51 81328[0:SpL:21894.0,94.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(u,w,x),y),c_Set_Oimage(u,w,x),v,z),w,x) c_Fun_Oinj__on(x1,hAPP(c_Set_Oimage(u,w,x),y),x,x2) -> c_Fun_Oinj__on(c_Fun_Ocomp(x1,u,x,x2,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(u,w,x),y),c_Set_Oimage(u,w,x),v,z),w,x2)*.
% 299.92/300.51 84978[0:SpR:223.1,84957.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),u,z),u,z),w)))*.
% 299.92/300.51 86388[0:SpR:86109.1,223.1] || equal(hAPP(c_Set_Oimage(u,v,t_a),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),v_Procs)** hBOOL(hAPP(hAPP(c_in(v),x),w)) -> equal(hAPP(c_Set_Oimage(u,v,t_a),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,x,v_x,v,t_a),v,t_a),w)).
% 299.92/300.51 94272[0:Res:14491.3,385.1] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Set_Oimage(w,u,u),c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)))))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_Finite__Set_Ofinite(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),u) c_Fun_Oinj__on(w,c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),u,u) -> equal(hAPP(c_Set_Oimage(w,u,u),c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool))),c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool))).
% 299.92/300.51 21572[0:SpL:21267.0,202.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,v),hAPP(c_Set_Oimage(u,v,v),v_x),tc_Com_Opname,w),v) c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,v),hAPP(c_Set_Oimage(u,v,v),v_x),tc_Com_Opname,w),hAPP(c_Set_Oimage(u,v,v),v_x),tc_fun(v,tc_bool))* -> c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,v),hAPP(c_Set_Oimage(u,v,v),v_x),tc_Com_Opname,w),v,v).
% 299.92/300.51 22199[0:SpL:21893.0,202.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,v),v_x),c_Set_Oimage(u,v,v),tc_Com_Opname,w),v) c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,v),v_x),c_Set_Oimage(u,v,v),tc_Com_Opname,w),hAPP(c_Set_Oimage(u,v,v),v_x),tc_fun(v,tc_bool))* -> c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,v),v_x),c_Set_Oimage(u,v,v),tc_Com_Opname,w),v,v).
% 299.92/300.51 29094[0:SpR:537.1,450.0] class_Lattices_Olattice(u) || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y,z))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y,z)))* c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))),y),x),t_a).
% 299.92/300.51 29618[0:SpR:534.1,450.0] class_Lattices_Oupper__semilattice(u) || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y,z))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y,z)))* c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))),y),x),t_a).
% 299.92/300.51 31390[0:SpL:104.0,449.0] || hBOOL(hAPP(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),x,y),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),x,y)))* -> c_Hoare__Mirabelle_Otriple__valid(y,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),v),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)))),t_a).
% 299.92/300.51 37443[0:SpR:205.1,410.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),x),y),z),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),y,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),y,tc_fun(x1,tc_bool))))*.
% 299.92/300.51 38025[0:Res:47.2,441.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))* -> equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))).
% 299.92/300.51 38670[0:Res:468.0,184.0] || c_Fun_Oinj__on(u,v,w,x) -> equal(hAPP(c_Set_Oimage(y,x,z),hAPP(c_Set_Oimage(u,w,x),v)),hAPP(c_Set_Oimage(x1,x,z),hAPP(c_Set_Oimage(u,w,x),v))) equal(hAPP(u,hAPP(c_Fun_Othe__inv__into(v,u,w,x),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(u,w,x),v),y,x1,x,z))),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(u,w,x),v),y,x1,x,z))**.
% 299.92/300.51 38961[0:SpR:354.2,71.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oimage(x,w,y),u)),x1)) c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),x1,z,x2) -> equal(hAPP(c_Fun_Othe__inv__into(x1,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x2),u),hAPP(c_Set_Oimage(x,w,y),u))**.
% 299.92/300.51 38960[0:SpR:354.2,373.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oimage(x,w,y),u)),x1)) c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),x1,z,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x2),u),hAPP(c_Set_Oimage(x,w,y),u))**.
% 299.92/300.51 41992[0:Res:82.0,402.0] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)))).
% 299.92/300.51 42471[0:SpL:393.1,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Set_Oimage(c_COMBK(w,x,y),y,x),z,x1)),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))** -> equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Set_Oimage(c_COMBK(w,x,y),y,x),z,x1),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))) equal(hAPP(c_Set_Oimage(u,z,x1),v),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(w,x,y),y,x),z,x1),v)).
% 299.92/300.51 42430[0:SpL:393.1,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,c_Set_Oimage(c_COMBK(w,x,y),y,x),u,z,x1)),hAPP(c_Set_Oinsert(w,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))** -> equal(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,c_Set_Oimage(c_COMBK(w,x,y),y,x),u,z,x1),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))) equal(hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(w,x,y),y,x),z,x1),v),hAPP(c_Set_Oimage(u,z,x1),v)).
% 299.92/300.51 42663[0:SpR:161.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),c_Fun_Ofun__upd(x,y,c_HOL_Ominus__class_Ominus(z,w,tc_fun(u,tc_bool)),x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),x,x2,x3,x1),y,c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z),w,tc_fun(u,tc_bool)),x1,x3))*.
% 299.92/300.51 43058[0:SpR:410.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),z)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(x2,x),v),w,x,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(w,x2)),u,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(w,x2)),u,tc_fun(x1,tc_bool)))**.
% 299.92/300.51 42890[0:SpR:486.1,410.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool)),z),x1),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,v)),z,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,x,u,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(x,v)),z,tc_fun(x2,tc_bool))))*.
% 299.92/300.51 43481[0:SpR:507.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),c_Fun_Ofun__upd(y,z,hAPP(c_Set_Oimage(v,w,u),x1),x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),y,x3,x4,x2),z,hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x1)),x2,x4))*.
% 299.92/300.51 43703[0:SpR:162.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),c_Fun_Ofun__upd(y,z,hAPP(c_Set_Ovimage(v,u,w),x1),x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),y,x3,x4,x2),z,hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x1)),x2,x4))*.
% 299.92/300.51 45628[0:SpL:323.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,z,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(u,v,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,y,z,tc_fun(v,tc_bool)))) c_Fun_Oinj__on(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),x),x1),y,z,tc_fun(v,tc_bool)),v,w)* -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,z,tc_fun(v,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,y,z,tc_fun(v,tc_bool))).
% 299.92/300.51 46942[0:Res:241.2,208.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(x,u),y)),tc_fun(u,tc_bool))* -> hBOOL(hAPP(hAPP(c_in(u),x),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))* c_lessequals(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool))*.
% 299.92/300.51 46925[0:SpR:56.1,241.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* hBOOL(hAPP(hAPP(c_in(u),w),hAPP(c_Set_Oinsert(v,u),x))) c_lessequals(hAPP(c_Set_Oinsert(v,u),x),hAPP(c_Set_Oinsert(w,u),y),tc_fun(u,tc_bool))* -> c_lessequals(c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool))*.
% 299.92/300.51 47182[0:SpL:56.1,242.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* hBOOL(hAPP(hAPP(c_in(u),w),hAPP(c_Set_Oinsert(v,u),x))) c_lessequals(c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),y,tc_fun(u,tc_bool))* -> c_lessequals(hAPP(c_Set_Oinsert(v,u),x),hAPP(c_Set_Oinsert(w,u),y),tc_fun(u,tc_bool))*.
% 299.92/300.51 48330[0:SpL:196.1,224.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),z,x),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),y),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),y),z),x1),z,x) -> .
% 299.92/300.51 48329[0:SpL:317.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(hAPP(v,w),x),hAPP(c_Set_Oimage(v,y,x),z))),hAPP(c_Set_Oimage(c_Set_Oimage(v,y,x),x1,u),c_HOL_Ominus__class_Ominus(x2,hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(w,y),z),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),tc_fun(x1,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oimage(v,y,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(w,y),z),x1),x2),x1,u) -> .
% 299.92/300.51 48318[0:SpL:393.1,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(v,w,x),x,w),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(x1,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(v,w,x),x,w),hAPP(c_Set_Oinsert(x1,y),z),y,u) -> equal(x1,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))).
% 299.92/300.51 48985[0:Res:171.2,483.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.92/300.51 48984[0:Res:172.2,483.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,x,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w))*.
% 299.92/300.51 48941[0:SpL:532.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y))))* -> hBOOL(hAPP(z,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,z,u)),x))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y),z,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)))*.
% 299.92/300.51 48940[0:SpL:533.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),y))))* -> hBOOL(hAPP(z,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),z,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,z,u)),y))*.
% 299.92/300.51 49770[0:Rew:26884.1,49467.3] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))))* c_Fun_Oinj__on(x,hAPP(c_Set_Oinsert(v,u),y),u,z)* -> hBOOL(hAPP(hAPP(c_in(z),hAPP(x,w)),hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))))* c_Fun_Oinj__on(x,hAPP(c_Set_Oinsert(w,u),y),u,z).
% 299.92/300.51 49784[0:Rew:49662.2,49526.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z,x1) -> hBOOL(hAPP(hAPP(c_in(x1),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_COMBK(v,u,x),x,u),z,x1),hAPP(c_Set_Oinsert(w,z),y))))* c_Fun_Oinj__on(c_Set_Ovimage(c_COMBK(v,u,x),x,u),hAPP(c_Set_Oinsert(w,z),y),z,x1).
% 299.92/300.51 49785[0:Rew:49662.2,49496.1] || c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Ovimage(c_Fun_Ocomp(x1,u,w,x2,v),v,x2),x3)),hAPP(c_Set_Oimage(c_Set_Ovimage(u,v,w),y,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(x1,w,x2),x3),y),x))))* c_Fun_Oinj__on(c_Set_Ovimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(x1,w,x2),x3),y),x),y,z).
% 299.92/300.51 49786[0:Rew:49662.2,49494.1] || c_Fun_Oinj__on(c_Set_Oimage(u,v,w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x1,v,w,x2),x2,w),x3)),hAPP(c_Set_Oimage(c_Set_Oimage(u,v,w),y,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x1,x2,v),x3),y),x))))* c_Fun_Oinj__on(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x1,x2,v),x3),y),x),y,z).
% 299.92/300.51 50455[0:SpR:223.1,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),x),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))* -> equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,hAPP(y,x),u,z),u,z),w),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))*.
% 299.92/300.51 50443[0:SpR:223.1,317.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oimage(c_Set_Oinsert(x,y),z,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x2,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),z),x3)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x2,v,x,u,y),u,y),w),x1),hAPP(c_Set_Oimage(c_Set_Oinsert(x,y),z,x1),x3)))*.
% 299.92/300.51 50442[0:SpR:223.1,99.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Set_Oinsert(x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oinsert(x,y),z,x1),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x2,v,x,u,y),u,y),w)),hAPP(c_Set_Oimage(x2,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))*.
% 299.92/300.51 50441[0:SpR:223.1,438.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Set_Oinsert(x,y),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oinsert(x,y),z,x1),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x2,v,x,u,y),u,y),w)),hAPP(c_Set_Oimage(x2,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))*.
% 299.92/300.51 50385[0:SpR:223.1,2097.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),z))* -> equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,z,u,y),u,y),w),hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))*.
% 299.92/300.51 51895[0:SpL:11176.1,459.0] || equal(c_Orderings_Otop__class_Otop(tc_bool),u) equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,x),hAPP(v,u)) -> equal(hAPP(v,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),v)),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(v,x1),x2,x,y))**.
% 299.92/300.51 51990[0:Obv:51915.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Ovimage(u,v,w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oimage(u,v,w),x,y,z),tc_fun(z,x),tc_fun(z,y),y),hAPP(c_COMBB(x1,x,tc_fun(z,x),y),c_Set_Ovimage(u,v,w))),x2,x3,y,z)),c_List_Ofoldl(x1,hAPP(c_Set_Ovimage(u,v,w),x2),x3,x,z))**.
% 299.92/300.51 52573[0:MRR:52572.3,20734.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(w),z),u)) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(u,x,w,y),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,w,y),u),c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z)),hAPP(c_Hilbert__Choice_Oinv__into(u,c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(v,x,w,y),x,y,w,w),w,w),z))*.
% 299.92/300.51 52686[0:MRR:52685.3,20734.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(w),z),u)) -> equal(hAPP(c_Fun_Othe__inv__into(u,x,w,y),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,w,y),u),c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z)),hAPP(c_Fun_Othe__inv__into(u,c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(v,x,w,y),x,y,w,w),w,w),z))*.
% 299.92/300.51 62451[0:SSi:62232.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)))) -> c_lessequals(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))*.
% 299.92/300.51 74532[7:Rew:71835.1,74181.2] || equal(c_Set_Oinsert(v_x,t_a),c_Hoare__Mirabelle_Otriple_Otriple(u)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,hAPP(c_Com_Ocom_OBODY,v)),w),tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v))),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,hAPP(c_Com_Ocom_OBODY,v)),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.51 74536[7:Rew:71835.1,74379.4,71835.1,74379.3] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(z,w,x),v_x))) c_Fun_Oinj__on(u,v_x,v,w) c_Fun_Oinj__on(z,v_x,w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_x,u,v,w),hAPP(c_Hilbert__Choice_Oinv__into(v_x,z,w,x),y)),hAPP(c_Hilbert__Choice_Oinv__into(v_x,c_Fun_Ocomp(z,u,w,x,v),v,x),y))*.
% 299.92/300.51 74537[7:Rew:71835.1,74378.4,71835.1,74378.3] || equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(z,w,x),v_x))) c_Fun_Oinj__on(u,v_x,v,w) c_Fun_Oinj__on(z,v_x,w,x) -> equal(hAPP(c_Fun_Othe__inv__into(v_x,u,v,w),hAPP(c_Fun_Othe__inv__into(v_x,z,w,x),y)),hAPP(c_Fun_Othe__inv__into(v_x,c_Fun_Ocomp(z,u,w,x,v),v,x),y))*.
% 299.92/300.51 79010[0:Res:15630.1,619.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,u,tc_fun(y,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,z),x1),x2,hAPP(c_in(u),v),z)),c_Set_Oinsert(x3,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(x3,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(hAPP(c_Set_Oinsert(w,z),x1),x2,hAPP(c_in(u),v),z),x,u,tc_fun(y,tc_bool))))**.
% 299.92/300.51 79230[0:Res:15858.1,619.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,u,tc_fun(y,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,hAPP(c_Set_Oinsert(w,x1),x2),hAPP(c_in(u),v),x1)),c_Set_Oinsert(x3,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(x3,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(z,hAPP(c_Set_Oinsert(w,x1),x2),hAPP(c_in(u),v),x1),x,u,tc_fun(y,tc_bool))))**.
% 299.92/300.51 19362[0:SSi:19315.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x)),tc_fun(w,tc_bool))* c_lessequals(x,hAPP(c_Set_Oimage(v,w,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x)),tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),w) -> c_Fun_Oinj__on(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),w,w).
% 299.92/300.51 21571[0:SpL:21267.0,193.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v) equal(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v),c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),v_x),w)) -> c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v,w)*.
% 299.92/300.51 22198[0:SpL:21893.0,193.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v) equal(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v),c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),v_x),w)) -> c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v,w)*.
% 299.92/300.51 26700[0:SpR:64.0,244.2] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))* equal(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),u),c_HOL_Ozero__class_Ozero(tc_nat)) equal(c_Suc(c_Finite__Set_Ocard(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),u)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(v,u),w),u)).
% 299.92/300.51 27151[0:SpR:339.0,450.0] || -> hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),x,y,z))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),x,y,z)))* c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w))),y),x),t_a).
% 299.92/300.51 31388[0:SpL:537.1,449.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y,z))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y,z)))* -> c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))),t_a).
% 299.92/300.51 31387[0:SpL:534.1,449.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y,z))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y,z)))* -> c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w))),t_a).
% 299.92/300.51 34047[0:SpR:24914.0,244.2] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),hAPP(c_Set_Oinsert(v,u),v_x))))* equal(c_Finite__Set_Ocard(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),hAPP(c_Set_Oinsert(v,u),v_x)),u),c_HOL_Ozero__class_Ozero(tc_nat)) equal(c_Suc(c_Finite__Set_Ocard(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(v,u),tc_Com_Opname,w),hAPP(c_Set_Oinsert(v,u),v_x)),u)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(v,u),v_x),u)).
% 299.92/300.51 39193[0:SpR:533.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),c_Fun_Ofun__upd(x,y,z,x1,x2),x2,x3,x1),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,x2,x3,x1),y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z)),x1,x3))*.
% 299.92/300.51 39171[0:SpR:533.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),w,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),u,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),v))),v)**.
% 299.92/300.51 39170[0:SpR:533.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),w,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),u,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),v))),v)**.
% 299.92/300.51 39597[0:SpR:532.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),y,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),u,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))**.
% 299.92/300.51 39596[0:SpR:532.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),y,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),u,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))**.
% 299.92/300.51 41551[0:SpL:354.2,284.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(z),u),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),x1,z),x2)))* c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),x1,z)* -> hBOOL(hAPP(hAPP(c_in(x1),hAPP(c_Set_Oimage(x,w,y),u)),x2)).
% 299.92/300.51 42492[0:SpL:329.1,315.0] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),y,z),tc_fun(x,tc_bool))* equal(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),y,z)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),y,z))** -> equal(hAPP(c_Set_Oimage(w,y,z),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),u),y,z),v)).
% 299.92/300.51 42451[0:SpL:329.1,315.0] || c_lessequals(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y,z),tc_fun(w,tc_bool))* equal(hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y,z)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y,z))** -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y,z),v),hAPP(c_Set_Oimage(x,y,z),v)).
% 299.92/300.51 43054[0:SpR:532.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),u,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),u,tc_fun(z,tc_bool)))**.
% 299.92/300.51 44289[0:SpL:24914.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) hBOOL(hAPP(hAPP(c_in(u),w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,x),hAPP(hAPP(c_in(u),v),v_x))))* equal(hAPP(y,v),hAPP(y,w))* c_Fun_Oinj__on(y,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,x),hAPP(hAPP(c_in(u),v),v_x)),u,z)* -> equal(v,w).
% 299.92/300.51 47409[0:Res:468.0,485.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,z,v,x1)))* -> equal(hAPP(c_Set_Oimage(y,v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Oimage(z,v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,u,v)),w))*.
% 299.92/300.51 47368[0:SpL:323.0,485.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),x1,x,tc_fun(w,tc_bool))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x1,x,tc_fun(w,tc_bool)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,x1,x,tc_fun(w,tc_bool)),u,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,x1,x,tc_fun(w,tc_bool))))*.
% 299.92/300.51 47640[0:Res:468.0,484.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,z,v,x1)))* -> equal(hAPP(c_Set_Oimage(y,v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Oimage(z,v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,u,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)),x))*.
% 299.92/300.51 47599[0:SpL:323.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),x1,x,tc_fun(w,tc_bool))))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,x1,x,tc_fun(w,tc_bool)),u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x1,x,tc_fun(w,tc_bool)),u,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x1,x,tc_fun(w,tc_bool))))*.
% 299.92/300.51 47978[0:Res:468.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* -> equal(hAPP(c_Set_Oimage(x,w,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),v)),hAPP(c_Set_Oimage(x1,w,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),v))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),v),x,x1,w,y)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(z,u,w)),z))*.
% 299.92/300.51 47937[0:SpL:323.0,490.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool)),u,y)))* hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),v),w,x,tc_fun(y,tc_bool))))* -> hBOOL(hAPP(u,z))* hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(y,tc_bool)),u,y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(y,tc_bool))))*.
% 299.92/300.51 48090[0:Res:468.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* -> equal(hAPP(c_Set_Oimage(x,w,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),z)),hAPP(c_Set_Oimage(x1,w,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),z))) hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),z),x,x1,w,y)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(z,u,w)),z))*.
% 299.92/300.51 48049[0:SpL:323.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool)),u,y)))* hBOOL(hAPP(hAPP(c_in(y),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),x1),w,x,tc_fun(y,tc_bool))))* -> hBOOL(hAPP(u,z))* hBOOL(hAPP(hAPP(c_in(y),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(y,tc_bool)),u,y)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(y,tc_bool))))*.
% 299.92/300.51 48444[0:SpL:131.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),hAPP(c_Set_Ovimage(y,x,z),x1))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(y,v,x,z,w),w,z),x2,u),c_HOL_Ominus__class_Ominus(x3,hAPP(c_Set_Oinsert(x1,x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))),tc_fun(x2,tc_bool)))))* c_Fun_Oinj__on(c_Set_Ovimage(c_Fun_Ocomp(y,v,x,z,w),w,z),hAPP(c_Set_Oinsert(x1,x2),x3),x2,u) -> .
% 299.92/300.51 48443[0:SpL:158.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,z,w),x1))),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(v,y,w,x,z),z,x),x2,u),c_HOL_Ominus__class_Ominus(x3,hAPP(c_Set_Oinsert(x1,x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))),tc_fun(x2,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ocomp(v,y,w,x,z),z,x),hAPP(c_Set_Oinsert(x1,x2),x3),x2,u) -> .
% 299.92/300.51 48375[0:SpL:523.1,224.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(w,v_x)),hAPP(x,v_x))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x),y,v),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(v_x,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),w),x),hAPP(c_Set_Oinsert(v_x,y),z),y,v) -> .
% 299.92/300.51 48374[0:SpL:460.1,224.0] || class_Lattices_Olattice(t_b) hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v,u),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v_x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool)))))* c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),hAPP(c_Set_Oinsert(v_x,v),w),v,u) -> .
% 299.92/300.51 48339[0:SpL:71.2,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),v),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(w,x,u,y),x1,z),c_HOL_Ominus__class_Ominus(x2,hAPP(c_Set_Oinsert(hAPP(x,v),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),tc_fun(x1,tc_bool)))))* c_Fun_Oinj__on(c_Fun_Othe__inv__into(w,x,u,y),hAPP(c_Set_Oinsert(hAPP(x,v),x1),x2),x1,z) -> .
% 299.92/300.51 48338[0:SpL:373.2,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) hBOOL(hAPP(hAPP(c_in(z),v),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(w,x,u,y),x1,z),c_HOL_Ominus__class_Ominus(x2,hAPP(c_Set_Oinsert(hAPP(x,v),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),tc_fun(x1,tc_bool)))))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(w,x,u,y),hAPP(c_Set_Oinsert(hAPP(x,v),x1),x2),x1,z) -> .
% 299.92/300.51 48337[0:SpL:131.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1)),hAPP(c_Set_Oimage(c_Set_Ovimage(w,z,x),x2,u),c_HOL_Ominus__class_Ominus(x3,hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(v,x,y),x1),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))),tc_fun(x2,tc_bool)))))* c_Fun_Oinj__on(c_Set_Ovimage(w,z,x),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(v,x,y),x1),x2),x3),x2,u) -> .
% 299.92/300.51 48335[0:SpL:158.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(c_Fun_Ocomp(v,w,x,y,z),z,y),x1)),hAPP(c_Set_Oimage(c_Set_Oimage(v,x,y),x2,u),c_HOL_Ominus__class_Ominus(x3,hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(w,z,x),x1),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))),tc_fun(x2,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oimage(v,x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(w,z,x),x1),x2),x3),x2,u) -> .
% 299.92/300.51 48630[0:SpR:197.1,161.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)))),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x)),z),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)))**.
% 299.92/300.51 48629[0:SpR:197.1,161.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ominus__class_Ominus(z,y,tc_fun(v,tc_bool)))),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(u,v,w),z)),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)))**.
% 299.92/300.51 49310[0:Res:171.2,488.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMin(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)),w))*.
% 299.92/300.51 49309[0:Res:172.2,488.1] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u) hBOOL(hAPP(x,c_Finite__Set_Olinorder__class_OMax(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),u)))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v,x,u)),v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,x,u)),w))*.
% 299.92/300.51 49266[0:SpL:532.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(y,u,w)),y))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z)))*.
% 299.92/300.51 49265[0:SpL:533.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,u,w)),z))*.
% 299.92/300.51 49788[0:Rew:49662.2,49618.1] || c_Fun_Oinj__on(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),x,y),hAPP(c_Set_Oinsert(v_Procs,x),w))))* c_Fun_Oinj__on(c_Set_Oinsert(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,u,tc_Com_Opname,v),hAPP(u,v_x)),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,x),w),x,y).
% 299.92/300.51 49789[0:Rew:49662.2,49617.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),y,z,x1) -> hBOOL(hAPP(hAPP(c_in(x1),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),z,x1),hAPP(c_Set_Oinsert(v_Procs,z),y))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(u,v,w),u,tc_Com_Opname,x),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,z),y),z,x1).
% 299.92/300.51 49790[0:Rew:49662.2,49616.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),v))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,u),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,w),v),w,x).
% 299.92/300.51 49791[0:Rew:49662.2,49614.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),y,z,x1) -> hBOOL(hAPP(hAPP(c_in(x1),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),z,x1),hAPP(c_Set_Oinsert(v_Procs,z),y))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,u,c_COMBK(u,v,w),tc_Com_Opname,x),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,z),y),z,x1).
% 299.92/300.51 49792[0:Rew:49662.2,49613.1] || c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),v,w,x) -> hBOOL(hAPP(hAPP(c_in(x),v_Procs),hAPP(c_Set_Oimage(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),w,x),hAPP(c_Set_Oinsert(v_Procs,w),v))))* c_Fun_Oinj__on(c_Set_Oinsert(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,u),tc_Com_Opname),hAPP(c_Set_Oinsert(v_Procs,w),v),w,x).
% 299.92/300.51 49793[0:Rew:49662.2,49498.3] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) c_Fun_Oinj__on(c_Fun_Othe__inv__into(w,x,u,y),z,x1,x2) -> hBOOL(hAPP(hAPP(c_in(x2),v),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(w,x,u,y),x1,x2),hAPP(c_Set_Oinsert(hAPP(x,v),x1),z))))* c_Fun_Oinj__on(c_Fun_Othe__inv__into(w,x,u,y),hAPP(c_Set_Oinsert(hAPP(x,v),x1),z),x1,x2).
% 299.92/300.51 49794[0:Rew:49662.2,49497.3] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(x,w,u,y) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(w,x,u,y),z,x1,x2) -> hBOOL(hAPP(hAPP(c_in(x2),v),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(w,x,u,y),x1,x2),hAPP(c_Set_Oinsert(hAPP(x,v),x1),z))))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(w,x,u,y),hAPP(c_Set_Oinsert(hAPP(x,v),x1),z),x1,x2).
% 299.92/300.51 49824[0:MRR:49635.2,114.1] || c_Fun_Oinj__on(u,v,w,x) c_lessequals(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),z,tc_fun(w,tc_bool)) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,w),v),w,x) hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(c_HOL_Ominus__class_Ominus(v,hAPP(c_Set_Oinsert(y,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))),tc_fun(w,tc_bool)),u,w,x),hAPP(u,y))),z))*.
% 299.92/300.51 51532[0:Res:83.0,195.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,w,y),hAPP(c_Set_Oimage(z,x1,w),hAPP(c_Set_Ovimage(z,x1,w),v))),hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,w,y),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,x1,w),hAPP(c_Set_Ovimage(z,x1,w),v)),u,tc_fun(w,tc_bool))))**.
% 299.92/300.51 51636[0:SSi:51619.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),tc_fun(v,tc_bool)) c_Fun_Oinj__on(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),tc_Com_Opname,tc_fun(v,tc_bool)),v,x) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(w,v,x),v_x),hAPP(c_Set_Oimage(w,v,x),u),tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(w,v,x),c_HOL_Ominus__class_Ominus(v_x,u,tc_fun(v,tc_bool))))**.
% 299.92/300.51 51637[0:SSi:51590.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,tc_fun(w,tc_bool)),w,y)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,w,y),c_Orderings_Obot__class_Obot(tc_bool)),hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,w,y),c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_bool),u,tc_fun(w,tc_bool))))**.
% 299.92/300.51 51638[0:SSi:51589.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,tc_fun(w,tc_bool)),w,y)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,w,y),c_Orderings_Otop__class_Otop(tc_bool)),hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,w,y),c_HOL_Ominus__class_Ominus(c_Orderings_Otop__class_Otop(tc_bool),u,tc_fun(w,tc_bool))))**.
% 299.92/300.51 51639[0:SSi:51583.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),x1),tc_fun(v,tc_bool))* c_Fun_Oinj__on(x2,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),x1),v,x3)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x2,v,x3),x1),hAPP(c_Set_Oimage(x2,v,x3),u),tc_fun(x3,tc_bool)),hAPP(c_Set_Oimage(x2,v,x3),c_HOL_Ominus__class_Ominus(x1,u,tc_fun(v,tc_bool))))**.
% 299.92/300.51 51695[0:SpL:158.0,233.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(w,x) c_lessequals(hAPP(c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(x1,v,z),u)),w,tc_fun(x,tc_bool))* c_lessequals(hAPP(c_Set_Oimage(x2,x,v),w),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(c_Fun_Ocomp(y,x1,z,x,v),u,v,x)* c_Fun_Oinj__on(x2,w,x,v) -> equal(c_Finite__Set_Ocard(u,v),c_Finite__Set_Ocard(w,x)).
% 299.92/300.51 51872[0:SpL:302.1,459.0] class_Lattices_Obounded__lattice(u) || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,x),hAPP(v,c_Orderings_Otop__class_Otop(u))) -> equal(hAPP(v,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),v)),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(v,x1),x2,x,y))**.
% 299.92/300.51 51981[0:Rew:23682.0,51959.1,23682.0,51959.1] || equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v,w)),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),u,v,w))** -> equal(c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(u,w,v,x),tc_fun(x,w),tc_fun(x,v),v),hAPP(c_COMBB(y,w,tc_fun(x,w),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)))),z,x1,v,x),c_List_Ofoldl(y,z,x1,w,x))**.
% 299.92/300.51 52226[0:Rew:8415.2,52197.3] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),v_x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.51 80279[0:SpL:21268.0,529.0] || c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),v) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),z,x1)),v)*.
% 299.92/300.51 80267[0:SpL:21268.0,5986.0] || hBOOL(hAPP(c_COMBS(c_in(u),v,w,x,y),z)) -> hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_COMBS(c_in(u),v,w,x,y),hAPP(c_COMBS(c_in(u),v,w,x,y),z),x1,x2)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_COMBS(c_in(u),v,w,x,y),hAPP(c_COMBS(c_in(u),v,w,x,y),z),x1,x2)))*.
% 299.92/300.51 79919[0:SpR:323.0,21268.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),z),w,x,tc_fun(u,tc_bool)),y,x1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),z),w,x,tc_fun(u,tc_bool)))**.
% 299.92/300.51 79784[0:SpR:21268.0,530.1] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),z),y,x1)),v)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),z),v).
% 299.92/300.51 81474[0:SpL:21894.0,529.0] || c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),v) -> c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),z,x1)),v)*.
% 299.92/300.51 81462[0:SpL:21894.0,5986.0] || hBOOL(hAPP(c_COMBS(c_in(u),v,w,x,y),z)) -> hBOOL(hAPP(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_COMBS(c_in(u),v,w,x,y),z),c_COMBS(c_in(u),v,w,x,y),x1,x2)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_COMBS(c_in(u),v,w,x,y),z),c_COMBS(c_in(u),v,w,x,y),x1,x2)))*.
% 299.92/300.51 81113[0:SpR:323.0,21894.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),z),w,x,tc_fun(u,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),y,x1)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),z),w,x,tc_fun(u,tc_bool)))**.
% 299.92/300.51 80978[0:SpR:21894.0,530.1] || c_Hoare__Mirabelle_Otriple__valid(c_Suc(u),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),z),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y,x1)),v)* -> c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),z),v).
% 299.92/300.51 89475[7:SpR:78590.1,223.1] || equal(hAPP(c_Set_Oimage(u,v,t_a),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),c_Set_Oinsert(v_x,t_a))** hBOOL(hAPP(hAPP(c_in(v),x),w)) -> equal(hAPP(c_Set_Oimage(u,v,t_a),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,x,v_x,v,t_a),v,t_a),w)).
% 299.92/300.51 90266[4:SpR:78660.1,223.1] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),v_x),v_x)** hBOOL(hAPP(hAPP(c_in(v),x),w)) -> equal(hAPP(c_Set_Oimage(u,v,t_a),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(x,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,x,v_x,v,t_a),v,t_a),w)).
% 299.92/300.51 21661[0:SpL:21267.0,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x),tc_Com_Opname,x)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x),tc_Com_Opname,x)))*.
% 299.92/300.51 22289[0:SpL:21893.0,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_Com_Opname,x)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_Com_Opname,x)))*.
% 299.92/300.51 22427[0:SpR:21893.0,97.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v,w) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),u,v,w),w,v),hAPP(c_Set_Oimage(u,v,w),v_x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x))**.
% 299.92/300.51 22426[0:SpR:21267.0,97.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v,w) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),u,v,w),w,v),hAPP(c_Set_Oimage(u,v,w),v_x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x))**.
% 299.92/300.51 31391[0:SpL:339.0,449.0] || hBOOL(hAPP(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),y,z))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),y,z)))* -> c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w))),t_a).
% 299.92/300.51 37458[0:SpR:205.1,71.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),z)) c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),z,x,x1) -> equal(hAPP(c_Fun_Othe__inv__into(z,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,x1),y),hAPP(c_Set_Oimage(u,v,w),y))**.
% 299.92/300.51 37457[0:SpR:205.1,373.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),z)) c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),z,x,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,x1),y),hAPP(c_Set_Oimage(u,v,w),y))**.
% 299.92/300.51 39422[0:Rew:533.0,39251.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname,x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))**.
% 299.92/300.51 39423[0:Rew:533.0,39250.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),tc_Com_Opname,x))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))**.
% 299.92/300.51 41791[0:SpL:445.1,199.0] || hBOOL(hAPP(u,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Fun_Ofun__upd(u,y,z,x1,x2),w,v,x))))* c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Fun_Ofun__upd(u,y,z,x1,x2),w,v,x)),y) hBOOL(hAPP(c_Fun_Ofun__upd(u,y,z,x1,x2),x3))*.
% 299.92/300.51 42642[0:SpR:161.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) -> equal(hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),v),w,tc_fun(x,tc_bool)),x1),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(z,w,tc_fun(x,tc_bool))),u,x1),y)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(z,w,tc_fun(x,tc_bool))),u,x1),y))**.
% 299.92/300.51 42990[0:SpR:354.2,486.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oimage(x,w,y),u)),x1)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,tc_fun(x2,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,tc_fun(x2,tc_bool)))**.
% 299.92/300.51 43459[0:SpR:507.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),y)),x2),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),x1)),u,x2),z)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),x1)),u,x2),z))**.
% 299.92/300.51 43681[0:SpR:162.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),z)) -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),y)),x2),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),x1)),u,x2),z)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),x1)),u,x2),z))**.
% 299.92/300.51 45558[0:SpR:323.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),y,z),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(u,tc_bool)),y),x2)),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),x1),w,x,tc_fun(u,tc_bool)),z),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),y,z),x2)))*.
% 299.92/300.51 46121[0:SpL:21893.0,481.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,x)),y),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,x)),y)))*.
% 299.92/300.51 46120[0:SpL:21267.0,481.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,x)),y),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,x)),y)))*.
% 299.92/300.51 46439[0:SpL:21893.0,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,y)),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,y))))*.
% 299.92/300.51 46438[0:SpL:21267.0,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,y)),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,y))))*.
% 299.92/300.51 46603[0:Rew:338.0,46568.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,c_Set_Oinsert(w,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,z,v,tc_fun(x,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_fun(x,tc_bool),tc_bool)),y),hAPP(c_Set_Oimage(z,v,tc_fun(x,tc_bool)),u)),c_Set_Oinsert(w,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)))**.
% 299.92/300.51 48448[0:SpL:317.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oinsert(y,w),z))),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(v,y),x),x1,u),c_HOL_Ominus__class_Ominus(x2,hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(v,w,x),z),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),tc_fun(x1,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(hAPP(v,y),x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(v,w,x),z),x1),x2),x1,u) -> .
% 299.92/300.51 48395[0:SpL:104.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)),tc_fun(x,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(x,tc_bool))),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(w,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(x,tc_bool))),hAPP(c_Set_Oinsert(w,y),z),y,u) -> .
% 299.92/300.51 48389[0:SpL:600.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(w,x,tc_fun(v,tc_bool)),y),z),y,u) -> .
% 299.92/300.51 48387[0:SpL:614.2,224.0] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),z,x),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,y,w,u),z),x1),z,x) -> .
% 299.92/300.51 48332[0:SpL:99.1,224.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(hAPP(u,y),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Set_Oinsert(hAPP(u,y),z),x1),z,x) -> .
% 299.92/300.51 48331[0:SpL:438.1,224.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),z,x),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(hAPP(u,y),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Set_Oinsert(hAPP(u,y),z),x1),z,x) -> .
% 299.92/300.51 48658[0:SpR:354.2,197.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v,x,w,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,w,y),u),z,tc_fun(y,tc_bool))),c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z),tc_fun(w,tc_bool)))**.
% 299.92/300.51 48643[0:SpR:354.2,197.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(v,x,w,y),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),y,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oimage(x,w,y),u),tc_fun(y,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z),u,tc_fun(w,tc_bool)))**.
% 299.92/300.51 49795[0:Rew:49662.2,49610.1] || c_Fun_Oinj__on(c_Set_Oinsert(u,v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),hAPP(c_Set_Oinsert(u,v),x1))),hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),x,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),x1),x),w))))* c_Fun_Oinj__on(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z),x1),x),w),x,y).
% 299.92/300.51 49796[0:Rew:49662.2,49607.1] || c_Fun_Oinj__on(c_Set_Oinsert(hAPP(u,v),w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oimage(u,x1,w),hAPP(c_Set_Oinsert(v,x1),x2))),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(u,v),w),y,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,x1,w),x2),y),x))))* c_Fun_Oinj__on(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,x1,w),x2),y),x),y,z).
% 299.92/300.51 49797[0:Rew:49662.2,49546.3] class_Complete__Lattice_Ocomplete__lattice(u) || c_Finite__Set_Ofinite(v,w) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x1,w,u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),y,z),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x1,w,u),y),x))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,x1,w,u),y),x),y,z).
% 299.92/300.51 49798[0:Rew:49662.2,49477.2] || c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(u,v,w),w,v),x,y,z) -> equal(x1,c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))),hAPP(c_Set_Oimage(c_Set_Oimage(c_COMBK(u,v,w),w,v),y,z),hAPP(c_Set_Oinsert(x1,y),x))))* c_Fun_Oinj__on(c_Set_Oimage(c_COMBK(u,v,w),w,v),hAPP(c_Set_Oinsert(x1,y),x),y,z).
% 299.92/300.51 49823[0:Rew:49662.2,49627.3,49662.2,49627.1] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(z,w),v))))* equal(hAPP(x1,hAPP(u,z)),hAPP(x1,y))* c_Fun_Oinj__on(x1,hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(z,w),v)),x,x2)* -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(z,w),v),w,x) equal(hAPP(u,z),y).
% 299.92/300.51 50445[0:SpR:223.1,118.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Fun_Ocomp(c_Set_Oinsert(x,y),c_Fun_Ofun__upd(z,x1,hAPP(c_Set_Oimage(x2,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),x3,x4),x4,x5,x3),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Set_Oinsert(x,y),z,x4,x5,x3),x1,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x2,v,x,u,y),u,y),w),x3,x5))*.
% 299.92/300.51 50399[0:SpR:223.1,9493.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(hAPP(c_Set_Oimage(x,u,t_a),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),v_x),c_Orderings_Otop__class_Otop(tc_bool))** -> equal(hAPP(c_Set_Oimage(x,u,t_a),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,v_x,u,t_a),u,t_a),w)).
% 299.92/300.51 50391[0:SpR:223.1,8498.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))) -> equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,z,u,y),u,y),w),hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))*.
% 299.92/300.51 51644[0:SSi:51581.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),tc_fun(w,tc_bool))* c_Fun_Oinj__on(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),w,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,w,x1),u),hAPP(c_Set_Oimage(z,w,x1),x),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,w,x1),c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool))))**.
% 299.92/300.51 51645[0:SSi:51578.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v),tc_fun(w,tc_bool))* c_Fun_Oinj__on(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),v),w,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,w,x1),u),hAPP(c_Set_Oimage(z,w,x1),x),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,w,x1),c_HOL_Ominus__class_Ominus(u,x,tc_fun(w,tc_bool))))**.
% 299.92/300.51 51894[0:SpL:9936.1,459.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),u,tc_bool) equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),w,x),hAPP(v,c_Orderings_Otop__class_Otop(tc_bool))) -> equal(hAPP(v,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),u),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),v)),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(v,x1),x2,x,y))**.
% 299.92/300.51 52554[0:Res:8366.1,624.0] || equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),hAPP(c_Set_Oimage(w,x,v),y)),v_Procs) c_Fun_Oinj__on(w,y,x,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(w,x,v),y),v,tc_Com_Opname) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,v),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(w,x,v),y),u,v,tc_Com_Opname),v_x)),hAPP(c_Hilbert__Choice_Oinv__into(y,c_Fun_Ocomp(u,w,v,tc_Com_Opname,x),x,tc_Com_Opname),v_x))**.
% 299.92/300.51 52666[0:Res:8366.1,623.0] || equal(hAPP(c_Set_Oimage(u,v,tc_Com_Opname),hAPP(c_Set_Oimage(w,x,v),y)),v_Procs) c_Fun_Oinj__on(w,y,x,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(w,x,v),y),v,tc_Com_Opname) -> equal(hAPP(c_Fun_Othe__inv__into(y,w,x,v),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(w,x,v),y),u,v,tc_Com_Opname),v_x)),hAPP(c_Fun_Othe__inv__into(y,c_Fun_Ocomp(u,w,v,tc_Com_Opname,x),x,tc_Com_Opname),v_x))**.
% 299.92/300.51 73081[7:Res:71608.1,624.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),hAPP(c_Set_Oimage(w,x,v),y)),v_x) c_Fun_Oinj__on(w,y,x,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(w,x,v),y),v,t_a) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,v),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(w,x,v),y),u,v,t_a),v_x)),hAPP(c_Hilbert__Choice_Oinv__into(y,c_Fun_Ocomp(u,w,v,t_a,x),x,t_a),v_x))**.
% 299.92/300.51 73080[7:Res:71608.1,623.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),hAPP(c_Set_Oimage(w,x,v),y)),v_x) c_Fun_Oinj__on(w,y,x,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(w,x,v),y),v,t_a) -> equal(hAPP(c_Fun_Othe__inv__into(y,w,x,v),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(w,x,v),y),u,v,t_a),v_x)),hAPP(c_Fun_Othe__inv__into(y,c_Fun_Ocomp(u,w,v,t_a,x),x,t_a),v_x))**.
% 299.92/300.51 80291[0:SpL:21268.0,184.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) c_Fun_Oinj__on(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),y),z,x1),x,u) -> equal(hAPP(w,hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),y),z,x1),w,x,u),v)),v)**.
% 299.92/300.51 79390[0:SpR:21268.0,354.2] || c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),u,z),x1,tc_fun(w,tc_bool))* c_Fun_Oinj__on(v,x1,w,x) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(x1,v,w,x),x,w),hAPP(c_Set_Oimage(v,w,x),y)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),u,z))*.
% 299.92/300.51 81486[0:SpL:21894.0,184.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) c_Fun_Oinj__on(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(w,x,u),y),c_Set_Oimage(w,x,u),z,x1),x,u) -> equal(hAPP(w,hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(w,x,u),y),c_Set_Oimage(w,x,u),z,x1),w,x,u),v)),v)**.
% 299.92/300.51 80583[0:SpR:21894.0,354.2] || c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),u,z),x1,tc_fun(w,tc_bool))* c_Fun_Oinj__on(v,x1,w,x) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(x1,v,w,x),x,w),hAPP(c_Set_Oimage(v,w,x),y)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),u,z))*.
% 299.92/300.51 86675[0:Res:86261.1,624.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),hAPP(c_Set_Oimage(w,x,v),y)),v_Procs) c_Fun_Oinj__on(w,y,x,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(w,x,v),y),v,t_a) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,v),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(w,x,v),y),u,v,t_a),v_x)),hAPP(c_Hilbert__Choice_Oinv__into(y,c_Fun_Ocomp(u,w,v,t_a,x),x,t_a),v_x))**.
% 299.92/300.51 86674[0:Res:86261.1,623.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),hAPP(c_Set_Oimage(w,x,v),y)),v_Procs) c_Fun_Oinj__on(w,y,x,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(w,x,v),y),v,t_a) -> equal(hAPP(c_Fun_Othe__inv__into(y,w,x,v),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(w,x,v),y),u,v,t_a),v_x)),hAPP(c_Fun_Othe__inv__into(y,c_Fun_Ocomp(u,w,v,t_a,x),x,t_a),v_x))**.
% 299.92/300.51 34276[0:SpL:24914.0,202.1] || c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,v),tc_Com_Opname,w),hAPP(c_Set_Oimage(u,v,v),v_x)),v) c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,v),tc_Com_Opname,w),hAPP(c_Set_Oimage(u,v,v),v_x)),hAPP(c_Set_Oimage(u,v,v),v_x),tc_fun(v,tc_bool))* -> c_Fun_Oinj__on(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,v),tc_Com_Opname,w),hAPP(c_Set_Oimage(u,v,v),v_x)),v,v).
% 299.92/300.51 39426[0:Rew:533.0,39352.2] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x))))* hBOOL(hAPP(hAPP(c_in(x),x1),y))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x1)))*.
% 299.92/300.51 39427[0:Rew:533.0,39351.2] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x))))* hBOOL(hAPP(hAPP(c_in(x),x1),z))* -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x1)))*.
% 299.92/300.51 39428[0:Rew:533.0,39243.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),tc_Com_Opname,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))**.
% 299.92/300.51 39172[0:SpR:533.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),v)),x1),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),u,x1),w)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),u,x1),w))**.
% 299.92/300.51 41553[0:SpL:205.1,284.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),z,x),x1)))* c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),z,x)* -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oimage(u,v,w),y)),x1)).
% 299.92/300.51 42505[0:SpL:131.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Set_Ovimage(c_Fun_Ocomp(w,x,y,z,x1),x1,z),x2,x3)),hAPP(c_Set_Ovimage(x,x1,y),hAPP(c_Set_Ovimage(w,y,z),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Set_Ovimage(c_Fun_Ocomp(w,x,y,z,x1),x1,z),x2,x3))))* -> equal(hAPP(c_Set_Oimage(u,x2,x3),v),hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(w,x,y,z,x1),x1,z),x2,x3),v)).
% 299.92/300.51 42504[0:SpL:158.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Set_Oimage(c_Fun_Ocomp(w,x,y,z,x1),x1,z),x2,x3)),hAPP(c_Set_Oimage(w,y,z),hAPP(c_Set_Oimage(x,x1,y),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Set_Oimage(c_Fun_Ocomp(w,x,y,z,x1),x1,z),x2,x3))))* -> equal(hAPP(c_Set_Oimage(u,x2,x3),v),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(w,x,y,z,x1),x1,z),x2,x3),v)).
% 299.92/300.51 42464[0:SpL:131.0,315.0] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(z,c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x1,x2,x3))),hAPP(x1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(z,c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x1,x2,x3)))* -> equal(hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x2,x3),z),hAPP(c_Set_Oimage(x1,x2,x3),z)).
% 299.92/300.51 42463[0:SpL:158.0,315.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(z,c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x1,x2,x3))),hAPP(x1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(z,c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x1,x2,x3)))* -> equal(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x2,x3),z),hAPP(c_Set_Oimage(x1,x2,x3),z)).
% 299.92/300.51 42624[0:SpR:161.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(z,v,tc_fun(w,tc_bool))),x,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),u),v,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ominus__class_Ominus(z,v,tc_fun(w,tc_bool))),x,tc_fun(x1,tc_bool))))*.
% 299.92/300.51 42905[0:SpR:486.1,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool))),x1)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x1,x,x2) -> equal(hAPP(c_Fun_Othe__inv__into(x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x,x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)))**.
% 299.92/300.51 42904[0:SpR:486.1,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool))),x1)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x1,x,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x,x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)))**.
% 299.92/300.51 43441[0:SpR:507.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),x),y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x1)),y,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x1),x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x1)),y,tc_fun(x2,tc_bool))))*.
% 299.92/300.51 43663[0:SpR:162.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(u,v,w),x),y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x1)),y,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x1)),y,tc_fun(x2,tc_bool))))*.
% 299.92/300.51 45142[0:SSi:45082.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) c_lessequals(w,x,tc_fun(v,tc_bool)) c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),z,tc_fun(v,tc_bool)) -> c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,hAPP(c_Set_Oinsert(w,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z),tc_fun(v,tc_bool))*.
% 299.92/300.51 45143[0:SSi:45017.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) c_lessequals(w,x,tc_fun(v,tc_bool)) c_lessequals(y,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),tc_fun(v,tc_bool)) -> c_lessequals(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z,hAPP(c_Set_Oinsert(x,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),tc_fun(v,tc_bool))*.
% 299.92/300.51 45375[0:SSi:45296.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(w,x))* hBOOL(hAPP(hAPP(c_in(v),x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,hAPP(c_Set_Oinsert(z,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool))))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,w,v)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),w,v)))*.
% 299.92/300.51 48369[0:SpL:465.1,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(v,z,x1,w,x),w,x),x2,u),c_HOL_Ominus__class_Ominus(x3,hAPP(c_Set_Oinsert(y,x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))),tc_fun(x2,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ofun__upd(v,z,x1,w,x),w,x),hAPP(c_Set_Oinsert(y,x2),x3),x2,u) -> hBOOL(hAPP(hAPP(c_in(w),z),y)).
% 299.92/300.51 48986[0:Res:468.0,483.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(c_Set_Oimage(z,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))) hBOOL(hAPP(x1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y),u,z,v,w)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,x1,v)),x))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,x1,v)),y))*.
% 299.92/300.51 49799[0:Rew:49662.2,49606.2] || c_Fun_Oinj__on(c_Set_Oinsert(u,v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(v),u),z)) hBOOL(hAPP(hAPP(c_in(y),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(u,v),x1),z,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(u,v),x,y),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(x1,z,tc_fun(v,tc_bool)),x),w))))* c_Fun_Oinj__on(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(x1,z,tc_fun(v,tc_bool)),x),w),x,y).
% 299.92/300.51 49800[0:Rew:49662.2,49548.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),v)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,y),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(z,v,tc_fun(u,tc_bool)),x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(z,v,tc_fun(u,tc_bool)),x),w),x,y).
% 299.92/300.51 49801[0:Rew:49662.2,49542.2] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x1))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1),x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1),x),w),x,y).
% 299.92/300.51 49802[0:Rew:49662.2,49541.2] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x1))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1),x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),z),x1),x),w),x,y).
% 299.92/300.51 49825[0:Rew:49662.2,49626.3] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,w),v),w,x) hBOOL(hAPP(z,hAPP(u,y))) hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(y,w),v))),x1),z,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(y,w),v))),x1)))*.
% 299.92/300.51 49826[0:Rew:49662.2,49625.3] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,w),v),w,x) hBOOL(hAPP(z,hAPP(u,y))) hBOOL(hAPP(hAPP(c_in(x),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(y,w),v))),z,x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(y,w),v)))))*.
% 299.92/300.51 49827[0:Rew:49662.2,49624.2] || c_Fun_Oinj__on(u,v,w,x) -> c_Fun_Oinj__on(u,hAPP(c_Set_Oinsert(y,w),v),w,x) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(z,x,tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(y,w),v))),c_Set_Oinsert(x2,x1),tc_fun(x1,tc_bool),tc_fun(x1,tc_bool)),hAPP(c_Set_Oinsert(x2,x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oinsert(y,w),v)),z,x,tc_fun(x1,tc_bool))))**.
% 299.92/300.51 50157[0:SpR:97.1,620.1] || c_Fun_Oinj__on(u,v,tc_fun(w,tc_bool),x) -> equal(hAPP(c_Set_Oimage(u,tc_fun(w,tc_bool),x),v),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,tc_fun(w,tc_bool),x),v),c_Fun_Othe__inv__into(v,u,tc_fun(w,tc_bool),x),x,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),tc_fun(w,tc_bool),tc_fun(w,tc_bool)))**.
% 299.92/300.51 50180[0:Rew:410.0,50143.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_fun(w,tc_bool),tc_bool)),hAPP(c_Set_Oimage(x,v,tc_fun(w,tc_bool)),u)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),tc_fun(w,tc_bool),tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,x,v,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),tc_fun(w,tc_bool),tc_fun(w,tc_bool)))**.
% 299.92/300.51 51692[0:SpL:465.1,233.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(w,x) c_lessequals(hAPP(c_Set_Oimage(y,v,x),u),w,tc_fun(x,tc_bool))* c_lessequals(hAPP(c_Set_Oimage(z,x,v),w),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(c_Fun_Ofun__upd(y,x1,x2,v,x),u,v,x)* c_Fun_Oinj__on(z,w,x,v) -> hBOOL(hAPP(hAPP(c_in(v),x1),u)) equal(c_Finite__Set_Ocard(u,v),c_Finite__Set_Ocard(w,x)).
% 299.92/300.51 52196[0:SpL:584.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Com_Ocom_OBODY,v,w,x),y),z),tc_Hoare__Mirabelle_Otriple(u)),x1),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,y))),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),y),hAPP(c_Com_Ocom_OBODY,y)),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.51 52556[0:Res:526.1,624.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),x1)) c_Fun_Oinj__on(x,z,y,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(x,y,v),z),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,x,y,v),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,y,v),z),u,v,w),x1)),hAPP(c_Hilbert__Choice_Oinv__into(z,c_Fun_Ocomp(u,x,v,w,y),y,w),x1))*.
% 299.92/300.51 52668[0:Res:526.1,623.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),x1)) c_Fun_Oinj__on(x,z,y,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(x,y,v),z),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(z,x,y,v),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,y,v),z),u,v,w),x1)),hAPP(c_Fun_Othe__inv__into(z,c_Fun_Ocomp(u,x,v,w,y),y,w),x1))*.
% 299.92/300.51 71092[0:Res:7568.0,195.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),tc_fun(w,tc_bool))* c_Fun_Oinj__on(z,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),w,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,w,x1),x),hAPP(c_Set_Oimage(z,w,x1),u),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,w,x1),c_HOL_Ominus__class_Ominus(x,u,tc_fun(w,tc_bool))))**.
% 299.92/300.51 71302[0:Res:7538.0,195.0] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),y)),tc_fun(v,tc_bool))* c_Fun_Oinj__on(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),y)),v,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,v,x1),y),hAPP(c_Set_Oimage(z,v,x1),u),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,v,x1),c_HOL_Ominus__class_Ominus(y,u,tc_fun(v,tc_bool))))**.
% 299.92/300.51 72117[0:Res:7830.0,195.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),tc_fun(w,tc_bool))* c_Fun_Oinj__on(z,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),w,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,w,x1),y),hAPP(c_Set_Oimage(z,w,x1),u),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,w,x1),c_HOL_Ominus__class_Ominus(y,u,tc_fun(w,tc_bool))))**.
% 299.92/300.51 78213[7:Rew:78159.0,46589.1] || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x),c_Set_Oimage(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(c_Set_Oinsert(y,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x),c_Set_Oimage(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x),u,v,tc_fun(w,tc_bool))),hAPP(c_Set_Oinsert(y,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,u,v,tc_fun(w,tc_bool))))**.
% 299.92/300.51 78214[7:Rew:78159.0,46588.1] || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x),tc_Com_Opname,x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(c_Set_Oinsert(y,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x),tc_Com_Opname,x),u,v,tc_fun(w,tc_bool))),hAPP(c_Set_Oinsert(y,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,u,v,tc_fun(w,tc_bool))))**.
% 299.92/300.51 80211[0:SpL:21268.0,479.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(w),v),hAPP(hAPP(c_in(w),v),x),y,z),x1,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(w),v),hAPP(hAPP(c_in(w),v),x),y,z)),x1)))*.
% 299.92/300.51 80210[0:SpL:21268.0,478.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(w),v),hAPP(hAPP(c_in(w),v),x),z,x1),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(w),v),hAPP(hAPP(c_in(w),v),x),z,x1))))*.
% 299.92/300.51 81406[0:SpL:21894.0,479.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_in(w),v),x),hAPP(c_in(w),v),y,z),x1,u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_in(w),v),x),hAPP(c_in(w),v),y,z)),x1)))*.
% 299.92/300.51 81405[0:SpL:21894.0,478.1] || hBOOL(hAPP(u,v)) hBOOL(hAPP(hAPP(c_in(w),v),x)) -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(y,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_in(w),v),x),hAPP(c_in(w),v),z,x1),u,w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_in(w),v),x),hAPP(c_in(w),v),z,x1))))*.
% 299.92/300.51 34386[0:SpL:24914.0,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x)) -> hBOOL(hAPP(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_Com_Opname,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x))))* hBOOL(hAPP(w,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),tc_Com_Opname,x),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),v_x))))*.
% 299.92/300.51 34275[0:SpL:24914.0,193.1] || c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v) equal(c_Finite__Set_Ocard(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v),c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),v_x),w)) -> c_Fun_Oinj__on(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v,w)*.
% 299.92/300.51 38359[0:SSi:38309.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),w)) c_Finite__Set_Ofinite(w,tc_fun(u,tc_bool)) c_lessequals(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x,w,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),tc_fun(u,tc_bool))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x,w,tc_fun(u,tc_bool),tc_fun(u,tc_bool))).
% 299.92/300.51 38417[0:SpL:21893.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),tc_Com_Opname,y)),hAPP(c_Set_Oimage(u,v,w),x))** c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x),v,w) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),tc_Com_Opname,y),x).
% 299.92/300.51 38416[0:SpL:21267.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x),tc_Com_Opname,y)),hAPP(c_Set_Oimage(u,v,w),x))** c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x),v,w) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x),tc_Com_Opname,y),x).
% 299.92/300.51 39094[0:SpR:533.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(u,v),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),v,tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),u))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z)),v,tc_fun(x1,tc_bool))))*.
% 299.92/300.51 41815[0:SpL:329.1,199.0] || c_lessequals(u,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),w,v,x)),tc_fun(y,tc_bool))* hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,x),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),w,v,x))) c_Fun_Oinj__on(w,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,x) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),u),z))*.
% 299.92/300.51 42992[0:SpR:205.1,486.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(u,v,w),y)),z)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,tc_fun(x1,tc_bool)))**.
% 299.92/300.51 42908[0:SpR:486.1,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool))),x1)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x,tc_fun(x2,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x,tc_fun(x2,tc_bool)))**.
% 299.92/300.51 45560[0:SpR:323.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),c_Fun_Ofun__upd(y,z,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(u,tc_bool)),x2,x3),x3,x4,x2),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),y,x3,x4,x2),z,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),x1),w,x,tc_fun(u,tc_bool)),x2,x4))*.
% 299.92/300.51 45917[0:SSi:45837.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,w,v)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),w,v)))* hBOOL(hAPP(hAPP(c_in(v),z),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,hAPP(c_Set_Oinsert(x,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool))))* -> hBOOL(hAPP(w,z))*.
% 299.92/300.51 46118[0:SpL:24914.0,481.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,x),hAPP(hAPP(c_in(u),v),v_x))),y),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,x),hAPP(hAPP(c_in(u),v),v_x))),y)))*.
% 299.92/300.51 46436[0:SpL:24914.0,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> hBOOL(hAPP(w,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,y),hAPP(hAPP(c_in(u),v),v_x))),w,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,y),hAPP(hAPP(c_in(u),v),v_x)))))*.
% 299.92/300.51 48451[0:SpL:338.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(x,v),y))),hAPP(c_Set_Oimage(c_Set_Oinsert(x,v),z,u),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(x,v),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y),z),x1),z,u) -> .
% 299.92/300.51 48396[0:SpL:339.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),x)),z,u),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),x)),hAPP(c_Set_Oinsert(y,z),x1),z,u) -> .
% 299.92/300.51 48391[0:SpL:338.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z,u),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),y),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(v,w),y),z),x1),z,u) -> .
% 299.92/300.51 48386[0:SpL:537.1,224.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),z,v),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_Set_Oinsert(y,z),x1),z,v) -> .
% 299.92/300.51 48385[0:SpL:534.1,224.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),z,v),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),hAPP(c_Set_Oinsert(y,z),x1),z,v) -> .
% 299.92/300.51 48383[0:SpL:536.1,224.0] class_Lattices_Olattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z,v),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y),z),x1),z,v) -> .
% 299.92/300.51 48382[0:SpL:535.1,224.0] class_Lattices_Oupper__semilattice(u) || hBOOL(hAPP(hAPP(c_in(v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),z,v),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y),z),x1),z,v) -> .
% 299.92/300.51 48772[0:SpL:21893.0,619.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,u,tc_fun(x,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,y)),c_Set_Oinsert(z,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(z,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(u),v),v_x),hAPP(c_in(u),v),tc_Com_Opname,y),w,u,tc_fun(x,tc_bool))))**.
% 299.92/300.51 48771[0:SpL:21267.0,619.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,u,tc_fun(x,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,y)),c_Set_Oinsert(z,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(z,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),v_x),tc_Com_Opname,y),w,u,tc_fun(x,tc_bool))))**.
% 299.92/300.51 48944[0:SpL:161.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),y,tc_fun(u,tc_bool))))* -> hBOOL(hAPP(z,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool)),z,u)),c_HOL_Ominus__class_Ominus(w,y,tc_fun(u,tc_bool))))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_HOL_Ominus__class_Ominus(x,y,tc_fun(u,tc_bool)),z,u)),c_HOL_Ominus__class_Ominus(x,y,tc_fun(u,tc_bool))))*.
% 299.92/300.51 48943[0:SpL:162.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Ovimage(w,u,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))))* -> hBOOL(hAPP(x1,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Ovimage(w,u,x),y),x1,u)),hAPP(c_Set_Ovimage(w,u,x),y)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Ovimage(w,u,x),z),x1,u)),hAPP(c_Set_Ovimage(w,u,x),z)))*.
% 299.92/300.51 48942[0:SpL:507.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))))* -> hBOOL(hAPP(x1,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oimage(w,x,u),y),x1,u)),hAPP(c_Set_Oimage(w,x,u),y)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Set_Oimage(w,x,u),z),x1,u)),hAPP(c_Set_Oimage(w,x,u),z)))*.
% 299.92/300.51 49311[0:Res:468.0,488.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,z,v,x1)))* -> equal(hAPP(c_Set_Oimage(y,v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Oimage(z,v,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x))) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(w,u,v)),w))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,v)),x))*.
% 299.92/300.51 49805[0:Rew:49662.2,49534.2] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(v,v_x)),hAPP(w,v_x))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),y,z),hAPP(c_Set_Oinsert(v_x,y),x))))* c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,u)),v),w),hAPP(c_Set_Oinsert(v_x,y),x),y,z).
% 299.92/300.51 49806[0:Rew:49662.2,49533.2] || class_Lattices_Olattice(t_b) c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),u,v,w) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(t_b),hAPP(v_f,v_x)),hAPP(v_g,v_x))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),v,w),hAPP(c_Set_Oinsert(v_x,v),u))))* c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,t_b)),v_f),v_g),hAPP(c_Set_Oinsert(v_x,v),u),v,w).
% 299.92/300.51 50421[0:SpR:223.1,475.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),x1))* -> equal(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,x2,u,z),u,z),w),x3),hAPP(c_Set_Oimage(c_Set_Oinsert(x2,z),x,x3),x1)),hAPP(c_Set_Oimage(c_Set_Oinsert(x2,z),x,x3),x1))**.
% 299.92/300.51 51586[0:Res:49.2,195.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(v,c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) c_lessequals(w,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) c_Fun_Oinj__on(x,c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),u,y) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,u,y),v),hAPP(c_Set_Oimage(x,u,y),w),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))))**.
% 299.92/300.51 51562[0:Res:47.2,195.0] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(u,tc_bool)) c_Fun_Oinj__on(x,v,u,y) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(x,u,y),w),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool))))**.
% 299.92/300.51 51537[0:Res:446.1,195.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,hAPP(c_Set_Oinsert(y,w),v),tc_fun(w,tc_bool))* c_Fun_Oinj__on(z,hAPP(c_Set_Oinsert(y,w),v),w,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,w,x1),hAPP(c_Set_Oinsert(y,w),u)),hAPP(c_Set_Oimage(z,w,x1),x),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,w,x1),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(y,w),u),x,tc_fun(w,tc_bool))))**.
% 299.92/300.51 51533[0:Res:108.1,195.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* c_Fun_Oinj__on(y,c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool)),w,z)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(y,w,z),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(y,w,z),x),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,w,z),c_HOL_Ominus__class_Ominus(c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))))**.
% 299.92/300.51 51525[0:Res:424.2,195.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(x,w,tc_fun(u,tc_bool))* c_lessequals(y,w,tc_fun(u,tc_bool))* c_Fun_Oinj__on(z,w,u,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,u,x1),hAPP(c_Set_Oinsert(v,u),x)),hAPP(c_Set_Oimage(z,u,x1),y),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,u,x1),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,u),x),y,tc_fun(u,tc_bool))))**.
% 299.92/300.51 51896[0:SpL:14216.0,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),y,z),hAPP(u,c_Orderings_Otop__class_Otop(tc_bool))) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Set_Oinsert(v,w),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),u)),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(u,x3),x4,z,x1))**.
% 299.92/300.51 51983[0:Rew:300.1,51924.2,300.1,51924.2] class_Lattices_Obounded__lattice(u) || equal(hAPP(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w,x)),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),v,w,x))** -> equal(c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(v,x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)))),x1,x2,w,y),c_List_Ofoldl(z,x1,x2,x,y))**.
% 299.92/300.51 52224[0:Rew:8415.2,52190.3] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(u)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,hAPP(c_Com_Ocom_OBODY,v)),w),tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v))),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,hAPP(c_Com_Ocom_OBODY,v)),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.51 52560[0:Res:9258.0,624.0] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(y,hAPP(c_Set_Oimage(u,w,x),v),x,t_a) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(y,x,t_a),hAPP(c_Set_Oimage(u,w,x),v)),v_x),tc_bool)) equal(hAPP(c_Hilbert__Choice_Oinv__into(v,u,w,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,w,x),v),y,x,t_a),v_x)),hAPP(c_Hilbert__Choice_Oinv__into(v,c_Fun_Ocomp(y,u,x,t_a,w),w,t_a),v_x))**.
% 299.92/300.51 52570[0:Rew:8415.2,52531.5,8415.2,52531.4] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(z,w,x),v_x))) c_Fun_Oinj__on(u,v_x,v,w) c_Fun_Oinj__on(z,v_x,w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_x,u,v,w),hAPP(c_Hilbert__Choice_Oinv__into(v_x,z,w,x),y)),hAPP(c_Hilbert__Choice_Oinv__into(v_x,c_Fun_Ocomp(z,u,w,x,v),v,x),y))*.
% 299.92/300.51 52672[0:Res:9258.0,623.0] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(y,hAPP(c_Set_Oimage(u,w,x),v),x,t_a) -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_Set_Oimage(y,x,t_a),hAPP(c_Set_Oimage(u,w,x),v)),v_x),tc_bool)) equal(hAPP(c_Fun_Othe__inv__into(v,u,w,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,w,x),v),y,x,t_a),v_x)),hAPP(c_Fun_Othe__inv__into(v,c_Fun_Ocomp(y,u,x,t_a,w),w,t_a),v_x))**.
% 299.92/300.51 52683[0:Rew:8415.2,52643.5,8415.2,52643.4] || equal(v_Procs,v_x) equal(c_Set_Oimage(u,v,w),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(z,w,x),v_x))) c_Fun_Oinj__on(u,v_x,v,w) c_Fun_Oinj__on(z,v_x,w,x) -> equal(hAPP(c_Fun_Othe__inv__into(v_x,u,v,w),hAPP(c_Fun_Othe__inv__into(v_x,z,w,x),y)),hAPP(c_Fun_Othe__inv__into(v_x,c_Fun_Ocomp(z,u,w,x,v),v,x),y))*.
% 299.92/300.51 56405[0:SpL:30368.2,459.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Olattice(u) || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,x),hAPP(v,c_Orderings_Otop__class_Otop(u))) -> equal(hAPP(v,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),v)),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(v,x1),x2,x,y))**.
% 299.92/300.51 56847[0:SpL:30928.2,459.0] class_Lattices_Oboolean__algebra(u) class_Lattices_Oupper__semilattice(u) || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),w,x),hAPP(v,c_Orderings_Otop__class_Otop(u))) -> equal(hAPP(v,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Otop__class_Otop(u)),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),v)),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(v,x1),x2,x,y))**.
% 299.92/300.51 74534[7:Rew:71835.1,74193.2] || equal(c_Set_Oinsert(v_x,t_a),c_Com_Ocom_OBODY) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),v_x),w),tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),v_x),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.51 89731[7:Res:89344.1,624.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),hAPP(c_Set_Oimage(w,x,v),y)),c_Set_Oinsert(v_x,t_a)) c_Fun_Oinj__on(w,y,x,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(w,x,v),y),v,t_a) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,v),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(w,x,v),y),u,v,t_a),v_x)),hAPP(c_Hilbert__Choice_Oinv__into(y,c_Fun_Ocomp(u,w,v,t_a,x),x,t_a),v_x))**.
% 299.92/300.51 89730[7:Res:89344.1,623.0] || equal(hAPP(c_Set_Oimage(u,v,t_a),hAPP(c_Set_Oimage(w,x,v),y)),c_Set_Oinsert(v_x,t_a)) c_Fun_Oinj__on(w,y,x,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(w,x,v),y),v,t_a) -> equal(hAPP(c_Fun_Othe__inv__into(y,w,x,v),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(w,x,v),y),u,v,t_a),v_x)),hAPP(c_Fun_Othe__inv__into(y,c_Fun_Ocomp(u,w,v,t_a,x),x,t_a),v_x))**.
% 299.92/300.51 90875[4:Res:90134.1,624.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),hAPP(c_Set_Oimage(w,x,v),y)),v_x),v_x) c_Fun_Oinj__on(w,y,x,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(w,x,v),y),v,t_a) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,v),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(w,x,v),y),u,v,t_a),v_x)),hAPP(c_Hilbert__Choice_Oinv__into(y,c_Fun_Ocomp(u,w,v,t_a,x),x,t_a),v_x))**.
% 299.92/300.51 90874[4:Res:90134.1,623.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),hAPP(c_Set_Oimage(w,x,v),y)),v_x),v_x) c_Fun_Oinj__on(w,y,x,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(w,x,v),y),v,t_a) -> equal(hAPP(c_Fun_Othe__inv__into(y,w,x,v),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(w,x,v),y),u,v,t_a),v_x)),hAPP(c_Fun_Othe__inv__into(y,c_Fun_Ocomp(u,w,v,t_a,x),x,t_a),v_x))**.
% 299.92/300.51 721[0:MRR:719.0,589.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v_na)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))*.
% 299.92/300.51 34031[0:SpR:24914.0,97.1] || c_Fun_Oinj__on(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v,w) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),u,v,w),w,v),hAPP(c_Set_Oimage(u,v,w),v_x)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)))**.
% 299.92/300.51 36195[0:Res:468.0,516.0] || -> equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),hAPP(c_Set_Oimage(z,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))) hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y),u,z,v,w)),x))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y),u,z,v,w)),y))*.
% 299.92/300.51 38513[0:SSi:38502.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oimage(u,v,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),w,tc_fun(v,tc_bool))* c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v) c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v,v) -> equal(hAPP(c_Set_Oimage(u,v,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)).
% 299.92/300.51 38514[0:SSi:38501.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oimage(u,v,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),x,tc_fun(v,tc_bool))* c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v) c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v,v) -> equal(hAPP(c_Set_Oimage(u,v,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)).
% 299.92/300.51 38637[0:SpL:205.1,184.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(v),x),y)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Set_Oimage(u,v,w),y),w,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,v,w),y),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x)),x)**.
% 299.92/300.51 42488[0:SpL:104.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),y,z)),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),y,z),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)))* -> equal(hAPP(c_Set_Oimage(u,y,z),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(x,tc_fun(w,tc_bool))),y,z),v)).
% 299.92/300.51 42447[0:SpL:104.0,315.0] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),x,y,z),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),hAPP(x,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),x,y,z)))* -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),y,z),v),hAPP(c_Set_Oimage(x,y,z),v)).
% 299.92/300.51 42641[0:SpR:161.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(z,w,tc_fun(x,tc_bool))),y,u,x1) -> equal(hAPP(c_Fun_Othe__inv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(z,w,tc_fun(x,tc_bool))),u,x1),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),v),w,tc_fun(x,tc_bool))),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)))**.
% 299.92/300.51 42640[0:SpR:161.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(z,w,tc_fun(x,tc_bool))),y,u,x1) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(z,w,tc_fun(x,tc_bool))),u,x1),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),z),v),w,tc_fun(x,tc_bool))),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool)))**.
% 299.92/300.51 43458[0:SpR:507.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),x1)),z,u,x2) -> equal(hAPP(c_Fun_Othe__inv__into(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),x1)),u,x2),hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),y))),hAPP(c_Set_Oimage(v,w,x),y))**.
% 299.92/300.51 43457[0:SpR:507.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),x1)),z,u,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),x1)),u,x2),hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),y))),hAPP(c_Set_Oimage(v,w,x),y))**.
% 299.92/300.51 43680[0:SpR:162.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),z)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),x1)),z,u,x2) -> equal(hAPP(c_Fun_Othe__inv__into(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),x1)),u,x2),hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),y))),hAPP(c_Set_Ovimage(v,w,x),y))**.
% 299.92/300.51 43679[0:SpR:162.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),z)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),x1)),z,u,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),x1)),u,x2),hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),y))),hAPP(c_Set_Ovimage(v,w,x),y))**.
% 299.92/300.51 48447[0:SpL:55.1,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,w),x),y,tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(c_Set_Oinsert(v,w),z,u),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(x,y,tc_fun(w,tc_bool)),z),x1),z,u) -> hBOOL(hAPP(hAPP(c_in(w),v),y)).
% 299.92/300.51 48333[0:SpL:97.1,224.0] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(y),v),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),z,y),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,w,x),v),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,w,x),v),z),x1),z,y) -> .
% 299.92/300.51 49269[0:SpL:161.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),z,tc_fun(w,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ominus__class_Ominus(x,z,tc_fun(w,tc_bool)),u,w)),c_HOL_Ominus__class_Ominus(x,z,tc_fun(w,tc_bool))))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_HOL_Ominus__class_Ominus(y,z,tc_fun(w,tc_bool)),u,w)),c_HOL_Ominus__class_Ominus(y,z,tc_fun(w,tc_bool))))*.
% 299.92/300.51 49268[0:SpL:162.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Ovimage(x,w,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1))))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Ovimage(x,w,y),z),u,w)),hAPP(c_Set_Ovimage(x,w,y),z)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Ovimage(x,w,y),x1),u,w)),hAPP(c_Set_Ovimage(x,w,y),x1)))*.
% 299.92/300.51 49267[0:SpL:507.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(c_Set_Oimage(x,y,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1))))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oimage(x,y,w),z),u,w)),hAPP(c_Set_Oimage(x,y,w),z)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Set_Oimage(x,y,w),x1),u,w)),hAPP(c_Set_Oimage(x,y,w),x1)))*.
% 299.92/300.51 49807[0:Rew:49662.2,49603.1] || c_Fun_Oinj__on(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1,x2) -> hBOOL(hAPP(hAPP(c_in(x2),hAPP(c_Set_Ovimage(v,y,w),hAPP(c_Set_Ovimage(u,w,x),x3))),hAPP(c_Set_Oimage(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),x1,x2),hAPP(c_Set_Oinsert(x3,x1),z))))* c_Fun_Oinj__on(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Oinsert(x3,x1),z),x1,x2).
% 299.92/300.51 49808[0:Rew:49662.2,49602.1] || c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),z,x1,x2) -> hBOOL(hAPP(hAPP(c_in(x2),hAPP(c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(v,y,w),x3))),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),x1,x2),hAPP(c_Set_Oinsert(x3,x1),z))))* c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),hAPP(c_Set_Oinsert(x3,x1),z),x1,x2).
% 299.92/300.51 49809[0:Rew:49662.2,49550.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Set_Oinsert(z,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x1))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(z,u),x1),x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(hAPP(c_Set_Oinsert(z,u),x1),x),w),x,y).
% 299.92/300.51 49810[0:Rew:49662.2,49491.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),y,z),hAPP(c_Set_Oinsert(hAPP(u,x1),y),x))))* c_Fun_Oinj__on(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Set_Oinsert(hAPP(u,x1),y),x),y,z).
% 299.92/300.51 49811[0:Rew:49662.2,49490.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),y,z),hAPP(c_Set_Oinsert(hAPP(u,x1),y),x))))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Set_Oinsert(hAPP(u,x1),y),x),y,z).
% 299.92/300.51 50479[0:SpR:56.1,223.1] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))) hBOOL(hAPP(hAPP(c_in(u),w),hAPP(c_Set_Oinsert(v,u),x))) -> equal(hAPP(c_Set_Oinsert(y,z),hAPP(c_Set_Oimage(x1,u,z),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x1,w,y,u,z),u,z),hAPP(c_Set_Oinsert(v,u),x)))*.
% 299.92/300.51 50404[0:SpR:223.1,410.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),z),x1),c_Set_Oinsert(x2,y),z,tc_fun(x3,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x3,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,x2,u,y),u,y),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oinsert(x2,y),z,tc_fun(x3,tc_bool))))*.
% 299.92/300.51 51545[0:Res:362.1,195.0] || hBOOL(hAPP(hAPP(c_in(u),v),w))* c_lessequals(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)),tc_fun(z,tc_bool))* c_Fun_Oinj__on(x1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)),z,x2)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x1,z,x2),hAPP(y,v)),hAPP(c_Set_Oimage(x1,z,x2),x),tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(x1,z,x2),c_HOL_Ominus__class_Ominus(hAPP(y,v),x,tc_fun(z,tc_bool))))**.
% 299.92/300.51 51893[0:SpL:23682.0,459.0] || equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,w)),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),v,w)) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Obot__class_Obot(tc_bool)),w,v,x),tc_fun(x,w),tc_fun(x,v),v),hAPP(c_COMBB(y,w,tc_fun(x,w),v),u)),z,x1,v,x)),c_List_Ofoldl(y,hAPP(u,z),x1,w,x))**.
% 299.92/300.51 52192[0:SpL:3229.1,461.0] || equal(u,c_Hoare__Mirabelle_Otriple_Otriple(v)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(u,v_x),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(v)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(u,v_x),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),v_x),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.92/300.51 52454[0:SpL:24020.1,228.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v_x),x),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Com_Ocom_OSemi(v_x,x)),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.51 52443[0:SpL:24020.1,228.0] || equal(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(v_x,w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v_x),c_Com_Ocom_OSemi(v_x,x)),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.51 52559[0:Res:13238.1,624.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),hAPP(c_Set_Oimage(w,x,v),y)),v_x),c_Orderings_Otop__class_Otop(tc_bool)) c_Fun_Oinj__on(w,y,x,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(w,x,v),y),v,t_a) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,v),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(w,x,v),y),u,v,t_a),v_x)),hAPP(c_Hilbert__Choice_Oinv__into(y,c_Fun_Ocomp(u,w,v,t_a,x),x,t_a),v_x))**.
% 299.92/300.51 52558[0:Res:8375.1,624.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) c_Fun_Oinj__on(x,z,y,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(x,y,v),z),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,x,y,v),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,y,v),z),u,v,w),x1)),hAPP(c_Hilbert__Choice_Oinv__into(z,c_Fun_Ocomp(u,x,v,w,y),y,w),x1))*.
% 299.92/300.51 52555[0:Res:652.1,624.0] || c_lessequals(v_Procs,hAPP(c_Set_Oimage(u,v,tc_Com_Opname),hAPP(c_Set_Oimage(w,x,v),y)),tc_fun(tc_Com_Opname,tc_bool)) c_Fun_Oinj__on(w,y,x,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(w,x,v),y),v,tc_Com_Opname) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,v),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(w,x,v),y),u,v,tc_Com_Opname),v_x)),hAPP(c_Hilbert__Choice_Oinv__into(y,c_Fun_Ocomp(u,w,v,tc_Com_Opname,x),x,tc_Com_Opname),v_x))**.
% 299.92/300.51 52671[0:Res:13238.1,623.0] || equal(hAPP(hAPP(c_Set_Oimage(u,v,t_a),hAPP(c_Set_Oimage(w,x,v),y)),v_x),c_Orderings_Otop__class_Otop(tc_bool)) c_Fun_Oinj__on(w,y,x,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(w,x,v),y),v,t_a) -> equal(hAPP(c_Fun_Othe__inv__into(y,w,x,v),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(w,x,v),y),u,v,t_a),v_x)),hAPP(c_Fun_Othe__inv__into(y,c_Fun_Ocomp(u,w,v,t_a,x),x,t_a),v_x))**.
% 299.92/300.51 52670[0:Res:8375.1,623.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),z)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) c_Fun_Oinj__on(x,z,y,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(x,y,v),z),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(z,x,y,v),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,y,v),z),u,v,w),x1)),hAPP(c_Fun_Othe__inv__into(z,c_Fun_Ocomp(u,x,v,w,y),y,w),x1))*.
% 299.92/300.51 52667[0:Res:652.1,623.0] || c_lessequals(v_Procs,hAPP(c_Set_Oimage(u,v,tc_Com_Opname),hAPP(c_Set_Oimage(w,x,v),y)),tc_fun(tc_Com_Opname,tc_bool)) c_Fun_Oinj__on(w,y,x,v) c_Fun_Oinj__on(u,hAPP(c_Set_Oimage(w,x,v),y),v,tc_Com_Opname) -> equal(hAPP(c_Fun_Othe__inv__into(y,w,x,v),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(w,x,v),y),u,v,tc_Com_Opname),v_x)),hAPP(c_Fun_Othe__inv__into(y,c_Fun_Ocomp(u,w,v,tc_Com_Opname,x),x,tc_Com_Opname),v_x))**.
% 299.92/300.51 74535[7:Rew:71835.1,74222.3] || equal(c_Set_Oinsert(v_x,t_a),c_Hoare__Mirabelle_Otriple_Otriple(u)) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,w),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),x),y),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,c_Com_Ocom_OSemi(w,y)),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.51 78215[7:Rew:78159.0,46586.1] || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(c_Set_Oinsert(y,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x)),u,v,tc_fun(w,tc_bool))),hAPP(c_Set_Oinsert(y,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_x,u,v,tc_fun(w,tc_bool))))**.
% 299.92/300.51 80203[0:SpL:21268.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),y,z)))* equal(hAPP(x1,v),hAPP(x1,x))* c_Fun_Oinj__on(x1,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),y,z),u,x2)* -> equal(v,x).
% 299.92/300.51 80475[0:Rew:533.0,79914.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)),x,z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)))**.
% 299.92/300.51 79367[0:SpR:21268.0,246.2] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),w) -> hBOOL(hAPP(hAPP(c_in(w),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y)))* equal(c_Suc(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(v,w),x),u,y),w)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(v,w),x),w)).
% 299.92/300.51 81398[0:SpL:21894.0,268.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(u),x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),y,z)))* equal(hAPP(x1,v),hAPP(x1,x))* c_Fun_Oinj__on(x1,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),y,z),u,x2)* -> equal(v,x).
% 299.92/300.51 81670[0:Rew:533.0,81108.0] || -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,z))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),y)))**.
% 299.92/300.51 80560[0:SpR:21894.0,246.2] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),w) -> hBOOL(hAPP(hAPP(c_in(w),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y)))* equal(c_Suc(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,w),x),c_Set_Oinsert(v,w),u,y),w)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(v,w),x),w)).
% 299.92/300.51 82090[0:SSi:81957.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),x1),tc_fun(v,tc_bool))* c_Fun_Oinj__on(x2,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w,x,y,z),x1),v,x3)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x2,v,x3),hAPP(w,x1)),hAPP(c_Set_Oimage(x2,v,x3),u),tc_fun(x3,tc_bool)),hAPP(c_Set_Oimage(x2,v,x3),c_HOL_Ominus__class_Ominus(hAPP(w,x1),u,tc_fun(v,tc_bool))))**.
% 299.92/300.51 94060[0:Res:10791.0,195.0] || c_lessequals(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),y)),tc_fun(w,tc_bool))* c_Fun_Oinj__on(z,hAPP(c_Set_Oinsert(v,w),hAPP(c_Set_Oinsert(x,w),y)),w,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,w,x1),hAPP(c_Set_Oinsert(v,w),y)),hAPP(c_Set_Oimage(z,w,x1),u),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,w,x1),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(v,w),y),u,tc_fun(w,tc_bool))))**.
% 299.92/300.51 94143[0:Res:14364.3,195.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(x,w,tc_fun(u,tc_bool))* c_Fun_Oinj__on(y,w,u,z)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(y,u,z),c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(y,u,z),x),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))))**.
% 299.92/300.51 94248[0:Res:14491.3,195.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,w))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* c_Fun_Oinj__on(y,c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),u,z)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(y,u,z),w),hAPP(c_Set_Oimage(y,u,z),x),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,x,tc_fun(u,tc_bool))))**.
% 299.92/300.51 38411[0:SpL:24914.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),tc_Com_Opname,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x))),hAPP(c_Set_Oimage(u,v,w),x))** c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),tc_Com_Opname,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),v_x)),x).
% 299.92/300.51 42486[0:SpL:537.1,315.0] class_Lattices_Olattice(u) || equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),z,x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),z,x1))))* -> equal(hAPP(c_Set_Oimage(v,z,x1),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),z,x1),w)).
% 299.92/300.51 42485[0:SpL:534.1,315.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),z,x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(w,v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),z,x1))))* -> equal(hAPP(c_Set_Oimage(v,z,x1),w),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),y)),z,x1),w)).
% 299.92/300.51 42445[0:SpL:537.1,315.0] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y,z,x1))),hAPP(y,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y,z,x1)))* -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),z,x1),x),hAPP(c_Set_Oimage(y,z,x1),x)).
% 299.92/300.51 42444[0:SpL:534.1,315.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y,z,x1))),hAPP(y,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y,z,x1)))* -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),z,x1),x),hAPP(c_Set_Oimage(y,z,x1),x)).
% 299.92/300.51 45538[0:SpR:323.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),z)) -> equal(hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),v),w,x,tc_fun(y,tc_bool)),x2),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(y,tc_bool))),u,x2),z)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(y,tc_bool))),u,x2),z))**.
% 299.92/300.51 46578[0:SpR:354.2,617.1] || c_lessequals(u,v,tc_fun(tc_fun(w,tc_bool),tc_bool)) c_Fun_Oinj__on(x,v,tc_fun(w,tc_bool),y) -> equal(hAPP(c_Set_Oimage(x,tc_fun(w,tc_bool),y),u),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))) equal(hAPP(c_Set_Oinsert(z,w),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,tc_fun(w,tc_bool),y),u),c_Hilbert__Choice_Oinv__into(v,x,tc_fun(w,tc_bool),y),y,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,c_Set_Oinsert(z,w),tc_fun(w,tc_bool),tc_fun(w,tc_bool)))**.
% 299.92/300.51 46943[0:Res:241.2,441.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(x,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))),tc_fun(u,tc_bool))* -> equal(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(x,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool)))).
% 299.92/300.51 47419[0:SSi:47350.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(w,x))* hBOOL(hAPP(hAPP(c_in(v),x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,hAPP(c_Set_Oinsert(z,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool))))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),w,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,w,v)),z))*.
% 299.92/300.51 47988[0:SSi:47919.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),w,v)))* hBOOL(hAPP(hAPP(c_in(v),y),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,hAPP(c_Set_Oinsert(z,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool))))* -> hBOOL(hAPP(w,y))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(z,w,v)),z))*.
% 299.92/300.51 48449[0:SpL:475.1,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(y,v),z),x1,x),c_HOL_Ominus__class_Ominus(x2,hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(y,u,z),w),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),tc_fun(x1,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(hAPP(y,v),z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(y,u,z),w),x1),x2),x1,x) -> .
% 299.92/300.51 48390[0:SpL:542.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y,u),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y),z),y,u) -> .
% 299.92/300.51 48312[0:SpL:465.1,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Fun_Ofun__upd(v,w,x,y,u),z)),hAPP(c_Set_Oimage(v,y,u),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(z,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))))* c_Fun_Oinj__on(c_Fun_Ofun__upd(v,w,x,y,u),hAPP(c_Set_Oinsert(z,y),x1),y,u) -> hBOOL(hAPP(hAPP(c_in(y),w),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(z,y),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))),tc_fun(y,tc_bool)))).
% 299.92/300.51 48769[0:SpL:24914.0,619.0] || hBOOL(hAPP(hAPP(c_in(u),v),v_x)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,u,tc_fun(x,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,y),hAPP(hAPP(c_in(u),v),v_x))),c_Set_Oinsert(z,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)),hAPP(c_Set_Oinsert(z,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_in(u),v),tc_Com_Opname,y),hAPP(hAPP(c_in(u),v),v_x)),w,u,tc_fun(x,tc_bool))))**.
% 299.92/300.51 49814[0:Rew:49662.2,49608.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(c_Set_Oinsert(hAPP(x,v),y),z,x1,x2) -> hBOOL(hAPP(hAPP(c_in(x2),hAPP(c_Set_Oimage(x,u,y),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(hAPP(x,v),y),x1,x2),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,u,y),w),x1),z))))* c_Fun_Oinj__on(c_Set_Oinsert(hAPP(x,v),y),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,u,y),w),x1),z),x1,x2).
% 299.92/300.51 50045[0:SpL:497.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),y),z)))) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),y)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),z)),u,tc_fun(w,tc_bool))))*.
% 299.92/300.51 50492[0:SpL:223.1,275.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),x1))* hBOOL(hAPP(hAPP(c_in(x2),x3),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,x4,u,z),u,z),w)))* -> hBOOL(hAPP(hAPP(c_in(x2),x3),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oinsert(x4,z),x,tc_fun(x2,tc_bool))))*.
% 299.92/300.51 50480[0:SpR:117.0,223.1] || hBOOL(hAPP(hAPP(c_in(u),v),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))) -> equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(y,z),hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))))**.
% 299.92/300.51 50463[0:SpR:223.1,10931.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(x,hAPP(c_Set_Oimage(y,u,tc_Hoare__Mirabelle_Otriple(t_a)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),t_a) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,tc_Hoare__Mirabelle_Otriple(t_a)),u,tc_Hoare__Mirabelle_Otriple(t_a)),w),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,hAPP(c_Set_Oimage(y,u,tc_Hoare__Mirabelle_Otriple(t_a)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))))*.
% 299.92/300.51 51714[0:Res:313.1,233.2] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Finite__Set_Ofinite(u,w) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x,w,y),v),y) c_lessequals(hAPP(c_Set_Oimage(z,y,w),hAPP(c_Set_Oimage(x,w,y),v)),u,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,u,w,y) c_Fun_Oinj__on(z,hAPP(c_Set_Oimage(x,w,y),v),y,w) -> equal(c_Finite__Set_Ocard(u,w),c_Finite__Set_Ocard(hAPP(c_Set_Oimage(x,w,y),v),y)).
% 299.92/300.51 51903[0:SpL:12944.0,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)),z,x1),hAPP(u,c_Orderings_Otop__class_Otop(tc_bool))) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Set_Oinsert(v,w),c_COMBK(c_Orderings_Otop__class_Otop(tc_bool),x,y)),x1,z,x2),tc_fun(x2,x1),tc_fun(x2,z),z),hAPP(c_COMBB(x3,x1,tc_fun(x2,x1),z),u)),x4,x5,z,x2)),c_List_Ofoldl(x3,hAPP(u,x4),x5,x1,x2))**.
% 299.92/300.51 51897[0:SpL:11473.0,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),x,y),hAPP(u,c_Orderings_Otop__class_Otop(tc_bool))) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Set_Oinsert(v,w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),c_Orderings_Otop__class_Otop(tc_bool))),y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),u)),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(u,x2),x3,y,z))**.
% 299.92/300.51 51881[0:SpL:17045.0,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)),y,z),hAPP(u,c_Orderings_Obot__class_Obot(tc_bool))) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_HOL_Ominus__class_Ominus(c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),w,tc_fun(x,tc_bool)),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),u)),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(u,x3),x4,z,x1))**.
% 299.92/300.51 52211[0:SpL:3229.1,461.0] || equal(u,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),y),tc_Hoare__Mirabelle_Otriple(v))) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(u,v_x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(v_x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.92/300.51 52199[0:SpL:3229.1,461.0] || equal(u,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x))) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(u,v_x),tc_Hoare__Mirabelle_Otriple(v)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),v_x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.92/300.51 52186[0:SpL:3229.1,461.0] || equal(u,c_Com_Ocom_OBODY) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(u,v_x)),x),tc_Hoare__Mirabelle_Otriple(v)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,v_x)),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.92/300.51 52177[0:SpL:3229.1,461.0] || equal(u,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x)))) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),v_x),tc_Hoare__Mirabelle_Otriple(v)),y),hAPP(c_Set_Oinsert(hAPP(u,v_x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),v_x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.92/300.51 52164[0:SpL:3229.1,461.0] || equal(u,c_Com_Obody) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,v_x)),x),tc_Hoare__Mirabelle_Otriple(v)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(u,v_x))),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,v_x)),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.92/300.51 52456[0:SpL:23902.1,228.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Orderings_Obot__class_Obot(tc_bool)),x),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Com_Ocom_OSemi(v_x,x)),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.51 52445[0:SpL:23902.1,228.0] || equal(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(v_x,w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v_x),c_Com_Ocom_OSemi(c_Orderings_Obot__class_Obot(tc_bool),x)),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.51 52543[0:SpL:158.0,624.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Fun_Ocomp(w,x,y,u,z),z,u),x1)))* c_Fun_Oinj__on(x,x1,z,y) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(x,z,y),x1),y,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x1,x,z,y),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,z,y),x1),w,y,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Fun_Ocomp(w,x,y,u,z),z,u),v))*.
% 299.92/300.51 52655[0:SpL:158.0,623.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(c_Fun_Ocomp(w,x,y,u,z),z,u),x1)))* c_Fun_Oinj__on(x,x1,z,y) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(x,z,y),x1),y,u) -> equal(hAPP(c_Fun_Othe__inv__into(x1,x,z,y),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,z,y),x1),w,y,u),v)),hAPP(c_Fun_Othe__inv__into(x1,c_Fun_Ocomp(w,x,y,u,z),z,u),v))*.
% 299.92/300.51 74279[7:SpL:71835.1,461.0] || equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),c_Set_Oinsert(v_x,t_a)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.51 74227[7:SpL:71835.1,461.0] || equal(c_Set_Oinsert(v_x,t_a),c_Com_Obody) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,v_x)),w),tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),v_x)),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,v_x)),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.51 41875[0:Rew:533.0,41813.2] || hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,x,z),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),y,x,z)))))* c_Fun_Oinj__on(y,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,z) -> hBOOL(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x1)))*.
% 299.92/300.51 42489[0:SpL:339.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),y)),z,x1)),hAPP(c_Set_Oinsert(x,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),y)),z,x1))))* -> equal(hAPP(c_Set_Oimage(u,z,x1),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(x,w),y)),z,x1),v)).
% 299.92/300.51 42448[0:SpL:339.0,315.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),y,z,x1))),hAPP(y,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),y,z,x1)))* -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),z,x1),x),hAPP(c_Set_Oimage(y,z,x1),x)).
% 299.92/300.51 43055[0:SpR:161.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(v,w,tc_fun(x,tc_bool))),y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),v),w,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(x1,w,tc_fun(x,tc_bool))),u,tc_fun(z,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_HOL_Ominus__class_Ominus(x1,w,tc_fun(x,tc_bool))),u,tc_fun(z,tc_bool)))**.
% 299.92/300.51 43461[0:SpR:507.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),y)),z)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x2),y))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),x2)),u,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),x2)),u,tc_fun(x1,tc_bool)))**.
% 299.92/300.51 43683[0:SpR:162.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),y)),z)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x2),y))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),x2)),u,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),x2)),u,tc_fun(x1,tc_bool)))**.
% 299.92/300.51 45520[0:SpR:323.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,v,w,tc_fun(x,tc_bool)),y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,v,w,tc_fun(x,tc_bool))),y,tc_fun(x2,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x1),u),v,w,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,v,w,tc_fun(x,tc_bool))),y,tc_fun(x2,tc_bool))))*.
% 299.92/300.51 46580[0:SpR:205.1,617.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(tc_fun(v,tc_bool),tc_bool)),tc_fun(v,tc_bool),w) -> equal(hAPP(c_Set_Oimage(u,tc_fun(v,tc_bool),w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(hAPP(c_Set_Oinsert(y,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,tc_fun(v,tc_bool),w),x),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(tc_fun(v,tc_bool),tc_bool)),u,tc_fun(v,tc_bool),w),w,tc_fun(v,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,c_Set_Oinsert(y,v),tc_fun(v,tc_bool),tc_fun(v,tc_bool)))**.
% 299.92/300.51 48660[0:SpR:205.1,197.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool))),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),y),tc_fun(v,tc_bool)))**.
% 299.92/300.51 48645[0:SpR:205.1,197.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,v) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),c_HOL_Ominus__class_Ominus(x,hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x),y,tc_fun(v,tc_bool)))**.
% 299.92/300.51 49815[0:Rew:49662.2,49554.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,z,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),x,y),hAPP(c_Set_Oinsert(z,x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(z,x),w),x,y).
% 299.92/300.51 49816[0:Rew:49662.2,49549.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z),x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),z),x),w),x,y).
% 299.92/300.51 49817[0:Rew:49662.2,49528.2] || c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),z,x1,x2) -> hBOOL(hAPP(hAPP(c_in(x),v),x3)) hBOOL(hAPP(hAPP(c_in(x2),hAPP(c_Set_Oimage(u,x,y),x3)),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),x1,x2),hAPP(c_Set_Oinsert(x3,x1),z))))* c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Ofun__upd(u,v,w,x,y),x,y),hAPP(c_Set_Oinsert(x3,x1),z),x1,x2).
% 299.92/300.51 51538[0:Res:84.1,195.0] || c_lessequals(c_HOL_Ominus__class_Ominus(u,v,tc_fun(w,tc_bool)),x,tc_fun(w,tc_bool))* c_lessequals(y,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),tc_fun(w,tc_bool))* c_Fun_Oinj__on(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),x),w,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,w,x1),u),hAPP(c_Set_Oimage(z,w,x1),y),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,w,x1),c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool))))**.
% 299.92/300.51 51704[0:Res:364.1,233.2] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(x,v) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(z,w),y),w) c_lessequals(hAPP(c_Set_Oimage(x1,w,v),hAPP(c_Set_Oinsert(z,w),y)),x,tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,x,v,w) c_Fun_Oinj__on(x1,hAPP(c_Set_Oinsert(z,w),y),w,v) -> equal(c_Finite__Set_Ocard(x,v),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(z,w),y),w)).
% 299.92/300.51 52174[0:SpL:584.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),hAPP(c_Com_Obody,v)),hAPP(c_Com_Ocom_OBODY,v)),w),tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Option_Othe(tc_Com_Ocom),y,z,x1),hAPP(c_Com_Obody,v)),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),hAPP(c_Com_Obody,v)),hAPP(c_Com_Ocom_OBODY,v)),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52458[0:SpL:10090.1,228.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(c_Orderings_Otop__class_Otop(tc_bool),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Orderings_Otop__class_Otop(tc_bool)),x),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Com_Ocom_OSemi(v_x,x)),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 52447[0:SpL:10090.1,228.0] || equal(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Lattices_Oupper__semilattice__class_Osup(tc_bool)) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(c_Orderings_Otop__class_Otop(tc_bool),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v_x),c_Com_Ocom_OSemi(c_Orderings_Otop__class_Otop(tc_bool),x)),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 78727[4:Res:78665.1,624.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1))),v_x)** c_Fun_Oinj__on(y,x1,z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x1,y,z,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Fun_Ocomp(w,y,x,u,z),z,u),v))*.
% 299.92/300.52 78726[4:Res:78665.1,623.0] || equal(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1))),v_x)** c_Fun_Oinj__on(y,x1,z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> equal(hAPP(c_Fun_Othe__inv__into(x1,y,z,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,u),v)),hAPP(c_Fun_Othe__inv__into(x1,c_Fun_Ocomp(w,y,x,u,z),z,u),v))*.
% 299.92/300.52 79572[0:SpR:21268.0,244.2] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v,u),x),w,y)))* equal(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v,u),x),w,y),u),c_HOL_Ozero__class_Ozero(tc_nat)) equal(c_Suc(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oinsert(v,u),hAPP(c_Set_Oinsert(v,u),x),w,y),u)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(v,u),x),u)).
% 299.92/300.52 80765[0:SpR:21894.0,244.2] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,u),x),c_Set_Oinsert(v,u),w,y)))* equal(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,u),x),c_Set_Oinsert(v,u),w,y),u),c_HOL_Ozero__class_Ozero(tc_nat)) equal(c_Suc(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,u),x),c_Set_Oinsert(v,u),w,y),u)),c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(v,u),x),u)).
% 299.92/300.52 43053[0:SpR:533.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),x1),v))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1)),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),z),x1)),u,tc_fun(x,tc_bool)))**.
% 299.92/300.52 49818[0:Rew:49662.2,49545.2] class_Lattices_Olattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y,z),hAPP(c_Set_Oinsert(x1,y),x))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),hAPP(c_Set_Oinsert(x1,y),x),y,z).
% 299.92/300.52 49819[0:Rew:49662.2,49544.2] class_Lattices_Oupper__semilattice(u) || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x1))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),y,z),hAPP(c_Set_Oinsert(x1,y),x))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),hAPP(c_Set_Oinsert(x1,y),x),y,z).
% 299.92/300.52 49820[0:Rew:49662.2,49492.2] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),y,z,x1) -> hBOOL(hAPP(hAPP(c_in(x1),v),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),z,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,w,x),v),z),y))))* c_Fun_Oinj__on(c_Set_Oimage(c_Fun_Othe__inv__into(v,u,w,x),x,w),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,w,x),v),z),y),z,x1).
% 299.92/300.52 50501[0:SpL:223.1,284.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(z,x1),x2,x),x3)))* c_Fun_Oinj__on(c_Set_Oinsert(z,x1),c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),x2,x)* -> hBOOL(hAPP(hAPP(c_in(x2),hAPP(c_Set_Oimage(y,u,x1),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),x3))*.
% 299.92/300.52 50447[0:SpR:223.1,584.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_COMBS(c_Set_Oinsert(x,y),z,x1,x2,x3),hAPP(c_Set_Oimage(x4,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x4,v,x,u,y),u,y),w),hAPP(z,hAPP(c_Set_Oimage(x4,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))))*.
% 299.92/300.52 50446[0:SpR:223.1,584.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(hAPP(c_COMBS(x,c_Set_Oinsert(y,z),x1,x2,x3),hAPP(c_Set_Oimage(x4,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),hAPP(hAPP(x,hAPP(c_Set_Oimage(x4,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x4,v,y,u,z),u,z),w)))*.
% 299.92/300.52 50869[0:SpL:622.0,275.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),z,y,tc_fun(t_a,tc_bool))))) -> hBOOL(hAPP(hAPP(c_in(w),x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(z,y,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),u,tc_fun(w,tc_bool))))*.
% 299.92/300.52 51547[0:Res:129.1,195.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,hAPP(c_Set_Ovimage(y,z,w),v),tc_fun(z,tc_bool))* c_Fun_Oinj__on(x1,hAPP(c_Set_Ovimage(y,z,w),v),z,x2)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x1,z,x2),hAPP(c_Set_Ovimage(y,z,w),u)),hAPP(c_Set_Oimage(x1,z,x2),x),tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(x1,z,x2),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Ovimage(y,z,w),u),x,tc_fun(z,tc_bool))))**.
% 299.92/300.52 51546[0:Res:313.1,195.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,hAPP(c_Set_Oimage(y,w,z),v),tc_fun(z,tc_bool))* c_Fun_Oinj__on(x1,hAPP(c_Set_Oimage(y,w,z),v),z,x2)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x1,z,x2),hAPP(c_Set_Oimage(y,w,z),u)),hAPP(c_Set_Oimage(x1,z,x2),x),tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(x1,z,x2),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(y,w,z),u),x,tc_fun(z,tc_bool))))**.
% 299.92/300.52 51757[0:MRR:51756.1,20737.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Finite__Set_Ofinite(x,v) c_lessequals(y,x,tc_fun(v,tc_bool)) c_lessequals(hAPP(c_Set_Oimage(z,v,w),x),hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Set_Oimage(u,v,w),y),w,v)* c_Fun_Oinj__on(z,x,v,w) -> equal(c_Finite__Set_Ocard(y,v),c_Finite__Set_Ocard(x,v)).
% 299.92/300.52 51904[0:SpL:15172.0,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)),z,x1),hAPP(u,c_Orderings_Obot__class_Obot(tc_bool))) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_HOL_Ominus__class_Ominus(c_COMBK(c_Orderings_Obot__class_Obot(tc_bool),v,w),x,tc_fun(y,tc_bool)),x1,z,x2),tc_fun(x2,x1),tc_fun(x2,z),z),hAPP(c_COMBB(x3,x1,tc_fun(x2,x1),z),u)),x4,x5,z,x2)),c_List_Ofoldl(x3,hAPP(u,x4),x5,x1,x2))**.
% 299.92/300.52 51884[0:SpL:337.0,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),w,x),hAPP(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),u)),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(u,x1),x2,x,y))**.
% 299.92/300.52 51870[0:SpL:300.1,459.0] class_Lattices_Obounded__lattice(u) || equal(hAPP(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,x)),c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),w,x)) -> equal(hAPP(v,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),c_Orderings_Obot__class_Obot(u)),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),v)),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(v,x1),x2,x,y))**.
% 299.92/300.52 52227[0:Rew:8415.2,52184.3] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Com_Ocom_OBODY) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),v_x),w),tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),v_x),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52452[0:SpL:3229.1,228.0] || equal(u,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x))* c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(u,v_x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),v_x),z),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSemi(x,z)),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 52441[0:SpL:3229.1,228.0] || equal(u,hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w))* c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(u,v_x),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),y),z),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSemi(v_x,z)),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 52435[0:SpL:3229.1,228.0] || equal(u,c_Hoare__Mirabelle_Otriple_Otriple(v)) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(u,v_x),x),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),y),z),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),v_x),c_Com_Ocom_OSemi(x,z)),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 52566[0:Res:8376.2,624.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),v_Procs) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,x,y,w),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),v_x)),hAPP(c_Hilbert__Choice_Oinv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),v_x))*.
% 299.92/300.52 52678[0:Res:8376.2,623.0] || equal(c_in(tc_Com_Opname),c_in(u)) equal(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),v_Procs) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Fun_Othe__inv__into(z,x,y,w),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),v_x)),hAPP(c_Fun_Othe__inv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),v_x))*.
% 299.92/300.52 74336[7:SpL:71835.1,228.0] || equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),c_Set_Oinsert(v_x,t_a)) c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v_x),y),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Com_Ocom_OSemi(w,y)),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 74316[7:SpL:71835.1,228.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Set_Oinsert(v_x,t_a)) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(v_x,x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),x),y),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Com_Ocom_OSemi(v_x,y)),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 77346[0:Res:2399.2,195.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(v,c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) c_Fun_Oinj__on(x,c_HOL_Ouminus__class_Ouminus(w,tc_fun(u,tc_bool)),u,y) -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),w,tc_fun(u,tc_bool)) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x,u,y),w),hAPP(c_Set_Oimage(x,u,y),v),tc_fun(y,tc_bool)),hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,v,tc_fun(u,tc_bool))))**.
% 299.92/300.52 80228[0:SpL:21268.0,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),y,z)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),y,z)))*.
% 299.92/300.52 80202[0:SpL:21268.0,481.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(x,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),y,z)),x1),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),y,z)),x1)))*.
% 299.92/300.52 80201[0:SpL:21268.0,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(x,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),z,x1)),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),z,x1))))*.
% 299.92/300.52 81423[0:SpL:21894.0,519.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x)) -> hBOOL(hAPP(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),y,z)))* hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w),y,z)))*.
% 299.92/300.52 81397[0:SpL:21894.0,481.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(x,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),y,z)),x1),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(y,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),y,z)),x1)))*.
% 299.92/300.52 81396[0:SpL:21894.0,480.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(x,v)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),z,x1)),x,u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),z,x1))))*.
% 299.92/300.52 85144[0:MRR:85143.2,49657.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oinsert(y,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))* c_Fun_Oinj__on(c_COMBK(y,x,tc_Com_Opname),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBK(y,x,tc_Com_Opname),tc_Com_Opname,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oinsert(y,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),w,x,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Fun_Ocomp(w,c_COMBK(y,x,tc_Com_Opname),x,u,tc_Com_Opname),tc_Com_Opname,u),v))*.
% 299.92/300.52 85146[0:MRR:85145.2,49657.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oinsert(y,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))* c_Fun_Oinj__on(c_COMBK(y,x,tc_Com_Opname),v_Procs,tc_Com_Opname,x) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_COMBK(y,x,tc_Com_Opname),tc_Com_Opname,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oinsert(y,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),w,x,u),v)),hAPP(c_Fun_Othe__inv__into(v_Procs,c_Fun_Ocomp(w,c_COMBK(y,x,tc_Com_Opname),x,u,tc_Com_Opname),tc_Com_Opname,u),v))*.
% 299.92/300.52 48945[0:SpL:323.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),z,w,tc_fun(u,tc_bool))))* -> hBOOL(hAPP(x1,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,z,w,tc_fun(u,tc_bool)),x1,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,z,w,tc_fun(u,tc_bool))))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,z,w,tc_fun(u,tc_bool)),x1,u)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,z,w,tc_fun(u,tc_bool))))*.
% 299.92/300.52 49821[0:Rew:49662.2,49555.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(c_Set_Oinsert(v,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x1))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),y,z),hAPP(c_Set_Oinsert(x1,y),x))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oinsert(v,u),w)),hAPP(c_Set_Oinsert(x1,y),x),y,z).
% 299.92/300.52 49822[0:Rew:49662.2,49543.3] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x1,hAPP(c_Set_Oinsert(w,u),v),u,u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,z),hAPP(c_Set_Oinsert(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x1,v,u,u),y),x))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Set_Oinsert(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x1,v,u,u),y),x),y,z).
% 299.92/300.52 50423[0:SpR:223.1,486.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),x1))* -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,x3,u,z),u,z),w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oinsert(x3,z),x,tc_fun(x2,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,c_Set_Oinsert(x3,z),x,tc_fun(x2,tc_bool)))**.
% 299.92/300.52 51543[0:Res:340.2,195.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,v,tc_fun(w,tc_bool))* c_lessequals(y,v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(z,v,w,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,w,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x)),hAPP(c_Set_Oimage(z,w,x1),y),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,w,x1),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),y,tc_fun(w,tc_bool))))**.
% 299.92/300.52 51891[0:SpL:9935.1,459.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),tc_bool) equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),hAPP(u,c_Orderings_Otop__class_Otop(tc_bool))) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),u)),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(u,x1),x2,x,y))**.
% 299.92/300.52 51866[0:SpL:8385.1,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,tc_Com_Opname),v,w),v_Procs) equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,tc_Com_Opname),v,w)),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,tc_Com_Opname),v,w)) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oinsert(v_x,tc_Com_Opname),w,v,x),tc_fun(x,w),tc_fun(x,v),v),hAPP(c_COMBB(y,w,tc_fun(x,w),v),u)),z,x1,v,x)),c_List_Ofoldl(y,hAPP(u,z),x1,w,x))**.
% 299.92/300.52 51996[0:Obv:51917.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(u,x,y,z),tc_fun(z,x),tc_fun(z,y),y),hAPP(c_COMBB(x1,x,tc_fun(z,x),y),c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w))),x2,x3,y,z)),c_List_Ofoldl(x1,hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x2),x3,x,z))**.
% 299.92/300.52 51997[0:Obv:51916.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(u,x,y,z),tc_fun(z,x),tc_fun(z,y),y),hAPP(c_COMBB(x1,x,tc_fun(z,x),y),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w))),x2,x3,y,z)),c_List_Ofoldl(x1,hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),x2),x3,x,z))**.
% 299.92/300.52 52234[0:Rew:21893.0,52189.1] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,v_x)),w),tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Ocom_OBODY,v_x),c_Com_Ocom_OBODY,tc_Com_Opname,y)))),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,v_x)),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52235[0:Rew:21267.0,52188.1] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,v_x)),w),tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,v_x),tc_Com_Opname,y)))),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,v_x)),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52455[0:SpL:3294.1,228.0] || equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_in(t_a)) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(c_Orderings_Obot__class_Obot(tc_bool),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool))),x),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Com_Ocom_OSemi(v_x,x)),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 52453[0:SpL:584.0,228.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(c_COMBS(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x,y,z,x1),x2),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(x,x2)),x3),x4),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSemi(x2,x3)),x4),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 52444[0:SpL:3294.1,228.0] || equal(c_Hoare__Mirabelle_Otriple_Otriple(u),c_in(t_a)) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(c_Orderings_Obot__class_Obot(tc_bool),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),x),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v_x),c_Com_Ocom_OSemi(c_Orderings_Obot__class_Obot(tc_fun(t_a,tc_bool)),x)),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 52442[0:SpL:584.0,228.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(c_COMBS(c_Hoare__Mirabelle_Otriple_Otriple(v),w,x,y,z),x1),x2),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),x2),x3),x4),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),x1),c_Com_Ocom_OSemi(hAPP(w,x1),x3)),x4),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 52465[0:Rew:8415.2,52433.4] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Hoare__Mirabelle_Otriple_Otriple(u)) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,w),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),x),y),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(v_x,c_Com_Ocom_OSemi(w,y)),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 52579[0:MRR:52578.2,96.1] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(y),z),hAPP(c_Set_Oimage(x1,w,y),v))) c_Fun_Oinj__on(x1,v,w,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,w,x),v),c_Fun_Othe__inv__into(v,u,w,x),x,w),hAPP(c_Hilbert__Choice_Oinv__into(v,x1,w,y),z)),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,w,x),v),c_Fun_Ocomp(x1,c_Fun_Othe__inv__into(v,u,w,x),w,y,x),x,y),z))*.
% 299.92/300.52 52692[0:MRR:52691.2,96.1] || c_Fun_Oinj__on(u,v,w,x) hBOOL(hAPP(hAPP(c_in(y),z),hAPP(c_Set_Oimage(x1,w,y),v))) c_Fun_Oinj__on(x1,v,w,y) -> equal(hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,w,x),v),c_Fun_Othe__inv__into(v,u,w,x),x,w),hAPP(c_Fun_Othe__inv__into(v,x1,w,y),z)),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,w,x),v),c_Fun_Ocomp(x1,c_Fun_Othe__inv__into(v,u,w,x),w,y,x),x,y),z))*.
% 299.92/300.52 71823[7:SpL:71455.1,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,t_a),v,w),v_x) equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,t_a),v,w)),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,t_a),v,w)) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oinsert(v_x,t_a),w,v,x),tc_fun(x,w),tc_fun(x,v),v),hAPP(c_COMBB(y,w,tc_fun(x,w),v),u)),z,x1,v,x)),c_List_Ofoldl(y,hAPP(u,z),x1,w,x))**.
% 299.92/300.52 75624[0:SSi:75463.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),tc_fun(v,tc_bool))* c_Fun_Oinj__on(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),v,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,v,x1),y),hAPP(c_Set_Oimage(z,v,x1),u),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,v,x1),c_HOL_Ominus__class_Ominus(y,u,tc_fun(v,tc_bool))))**.
% 299.92/300.52 76092[0:SSi:75917.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),tc_fun(v,tc_bool))* c_Fun_Oinj__on(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y)),v,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,v,x1),x),hAPP(c_Set_Oimage(z,v,x1),u),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,v,x1),c_HOL_Ominus__class_Ominus(x,u,tc_fun(v,tc_bool))))**.
% 299.92/300.52 77823[0:SpL:223.1,5892.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))))* -> hBOOL(hAPP(c_COMBS(c_in(x1),c_Set_Oinsert(y,z),x2,x3,x4),hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))))*.
% 299.92/300.52 80032[0:SpL:21268.0,202.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,w),hAPP(c_Set_Oimage(v,w,w),x),u,y),w) c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,w),hAPP(c_Set_Oimage(v,w,w),x),u,y),hAPP(c_Set_Oimage(v,w,w),x),tc_fun(w,tc_bool))* -> c_Fun_Oinj__on(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,w),hAPP(c_Set_Oimage(v,w,w),x),u,y),w,w).
% 299.92/300.52 81227[0:SpL:21894.0,202.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,w),x),c_Set_Oimage(v,w,w),u,y),w) c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,w),x),c_Set_Oimage(v,w,w),u,y),hAPP(c_Set_Oimage(v,w,w),x),tc_fun(w,tc_bool))* -> c_Fun_Oinj__on(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,w),x),c_Set_Oimage(v,w,w),u,y),w,w).
% 299.92/300.52 86511[0:SpL:86109.1,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,t_a),v,w),v_Procs) equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,t_a),v,w)),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,t_a),v,w)) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oinsert(v_x,t_a),w,v,x),tc_fun(x,w),tc_fun(x,v),v),hAPP(c_COMBB(y,w,tc_fun(x,w),v),u)),z,x1,v,x)),c_List_Ofoldl(y,hAPP(u,z),x1,w,x))**.
% 299.92/300.52 38490[0:Res:84.1,385.1] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),w,tc_fun(v,tc_bool)),x,tc_fun(v,tc_bool))* c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v) c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),v,v) -> equal(hAPP(c_Set_Oimage(u,v,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)).
% 299.92/300.52 45537[0:SpR:323.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),z)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(y,tc_bool))),z,u,x2) -> equal(hAPP(c_Fun_Othe__inv__into(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(y,tc_bool))),u,x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),v),w,x,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool)))**.
% 299.92/300.52 45536[0:SpR:323.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),z)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(y,tc_bool))),z,u,x2) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x1,w,x,tc_fun(y,tc_bool))),u,x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),v),w,x,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool)))**.
% 299.92/300.52 48384[0:SpL:180.2,224.0] class_Lattices_Oupper__semilattice(u) || c_Finite__Set_Ofinite(v,u) hBOOL(hAPP(hAPP(c_in(w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,hAPP(c_Set_Oinsert(y,u),v),u,u)),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),z,w),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),y),hAPP(c_Set_Oinsert(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(u),x,v,u,u),z),x1),z,w) -> .
% 299.92/300.52 49270[0:SpL:323.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),x1,x,tc_fun(w,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,x1,x,tc_fun(w,tc_bool)),u,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,x1,x,tc_fun(w,tc_bool))))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x1,x,tc_fun(w,tc_bool)),u,w)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,x1,x,tc_fun(w,tc_bool))))*.
% 299.92/300.52 49973[0:SpR:497.0,415.0] || -> equal(c_Fun_Ofun__upd(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_x,hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)))**.
% 299.92/300.52 51871[0:SpL:299.2,459.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y),w,u)* equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x,y),hAPP(v,w)) -> equal(hAPP(v,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),v)),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(v,x2),x3,y,z))**.
% 299.92/300.52 51864[0:SpL:2097.1,459.0] || hBOOL(hAPP(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v,w),x,y),v))* equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v,w),x,y)),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v,w),x,y)) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oinsert(v,w),y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),u)),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(u,x2),x3,y,z))**.
% 299.92/300.52 52175[0:SpL:8415.2,461.0] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52162[0:SpL:8415.2,461.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_Com_Obody) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,v_x)),w),tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),v_x)),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,v_x)),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52236[0:Rew:24914.0,52187.1] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,v_x)),w),tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Ocom_OBODY,tc_Com_Opname,y),hAPP(c_Com_Ocom_OBODY,v_x))))),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,v_x)),w),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52549[0:SpL:3229.1,624.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(w,x,v),hAPP(c_Set_Oimage(y,z,x),x1))))* c_Fun_Oinj__on(y,x1,z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x1,y,z,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,v),v_x)),hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Fun_Ocomp(w,y,x,v,z),z,v),v_x))*.
% 299.92/300.52 52533[0:SpL:3229.1,624.0] || equal(u,c_Set_Oimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(y),z),hAPP(c_Set_Oimage(x1,x,y),hAPP(u,v_x))))* c_Fun_Oinj__on(v,v_x,w,x) c_Fun_Oinj__on(x1,hAPP(c_Set_Oimage(v,w,x),v_x),x,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_x,v,w,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(v,w,x),v_x),x1,x,y),z)),hAPP(c_Hilbert__Choice_Oinv__into(v_x,c_Fun_Ocomp(x1,v,x,y,w),w,y),z))*.
% 299.92/300.52 52661[0:SpL:3229.1,623.0] || equal(u,c_in(v)) hBOOL(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(w,x,v),hAPP(c_Set_Oimage(y,z,x),x1))))* c_Fun_Oinj__on(y,x1,z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,v) -> equal(hAPP(c_Fun_Othe__inv__into(x1,y,z,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,v),v_x)),hAPP(c_Fun_Othe__inv__into(x1,c_Fun_Ocomp(w,y,x,v,z),z,v),v_x))*.
% 299.92/300.52 52645[0:SpL:3229.1,623.0] || equal(u,c_Set_Oimage(v,w,x))* hBOOL(hAPP(hAPP(c_in(y),z),hAPP(c_Set_Oimage(x1,x,y),hAPP(u,v_x))))* c_Fun_Oinj__on(v,v_x,w,x) c_Fun_Oinj__on(x1,hAPP(c_Set_Oimage(v,w,x),v_x),x,y) -> equal(hAPP(c_Fun_Othe__inv__into(v_x,v,w,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(v,w,x),v_x),x1,x,y),z)),hAPP(c_Fun_Othe__inv__into(v_x,c_Fun_Ocomp(x1,v,x,y,w),w,y),z))*.
% 299.92/300.52 74146[7:SpL:71835.1,624.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)))) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,x,y,w),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),v_x)),hAPP(c_Hilbert__Choice_Oinv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),v_x))*.
% 299.92/300.52 74145[7:SpL:71835.1,623.0] || equal(c_Set_Oinsert(v_x,t_a),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)))) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Fun_Othe__inv__into(z,x,y,w),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),v_x)),hAPP(c_Fun_Othe__inv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),v_x))*.
% 299.92/300.52 80272[0:SpL:21268.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z),x,x1)),hAPP(c_Set_Oimage(u,v,w),y))** c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z),v,w) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z),x,x1),y).
% 299.92/300.52 80200[0:SpL:21268.0,619.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,u,tc_fun(y,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),z,x1)),c_Set_Oinsert(x2,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(x2,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_in(u),v),hAPP(hAPP(c_in(u),v),w),z,x1),x,u,tc_fun(y,tc_bool))))**.
% 299.92/300.52 80031[0:SpL:21268.0,193.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),u,z),w) equal(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),u,z),w),c_Finite__Set_Ocard(hAPP(c_Set_Oimage(v,w,x),y),x)) -> c_Fun_Oinj__on(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),u,z),w,x)*.
% 299.92/300.52 80006[0:SpL:21268.0,593.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs)) c_Hoare__Mirabelle_Otriple__valid(v,v_n(v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(tc_Com_Opname),hAPP(c_in(tc_Com_Opname),u),w,x))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(tc_Com_Opname),hAPP(c_in(tc_Com_Opname),u),w,x)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(tc_Com_Opname),hAPP(c_in(tc_Com_Opname),u),w,x))),t_a)*.
% 299.92/300.52 81467[0:SpL:21894.0,493.1] || equal(hAPP(c_Set_Oimage(u,v,w),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x,x1)),hAPP(c_Set_Oimage(u,v,w),y))** c_Fun_Oinj__on(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z),v,w) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),z),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),x,x1),y).
% 299.92/300.52 81395[0:SpL:21894.0,619.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,u,tc_fun(y,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),z,x1)),c_Set_Oinsert(x2,y),tc_fun(y,tc_bool),tc_fun(y,tc_bool)),hAPP(c_Set_Oinsert(x2,y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_in(u),v),w),hAPP(c_in(u),v),z,x1),x,u,tc_fun(y,tc_bool))))**.
% 299.92/300.52 81226[0:SpL:21894.0,193.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),u,z),w) equal(c_Finite__Set_Ocard(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),u,z),w),c_Finite__Set_Ocard(hAPP(c_Set_Oimage(v,w,x),y),x)) -> c_Fun_Oinj__on(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),u,z),w,x)*.
% 299.92/300.52 81201[0:SpL:21894.0,593.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs)) c_Hoare__Mirabelle_Otriple__valid(v,v_n(v),t_a)* -> c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(tc_Com_Opname),u),c_in(tc_Com_Opname),w,x))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(tc_Com_Opname),u),c_in(tc_Com_Opname),w,x)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(tc_Com_Opname),u),c_in(tc_Com_Opname),w,x))),t_a)*.
% 299.92/300.52 28211[0:SpR:465.1,21893.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),v_x),c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),tc_Com_Opname,z)))* equal(hAPP(c_Set_Oimage(w,u,y),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),v_x),c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),tc_Com_Opname,z)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),v_x))**.
% 299.92/300.52 28210[0:SpR:465.1,21267.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),v_x),tc_Com_Opname,z)))* equal(hAPP(c_Set_Oimage(w,u,y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),v_x),tc_Com_Opname,z)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),v_x))**.
% 299.92/300.52 28201[0:SpR:465.1,450.0] || -> hBOOL(hAPP(hAPP(c_in(u),v),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),z,x1,x2))) hBOOL(hAPP(hAPP(c_Set_Oimage(w,u,y),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),z,x1,x2)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),z,x1,x2)))* c_Hoare__Mirabelle_Otriple__valid(x2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y)),x1),z),t_a).
% 299.92/300.52 32347[0:SpL:465.1,477.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),c_Set_Oimage(c_Fun_Ofun__upd(u,x1,x2,v,w),v,w),x)))* hBOOL(hAPP(hAPP(c_in(x),x3),y))* -> hBOOL(hAPP(hAPP(c_in(v),x1),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),c_Set_Oimage(c_Fun_Ofun__upd(u,x1,x2,v,w),v,w),x)))* hBOOL(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,x1,x2,v,w),v,w),x3))*.
% 299.92/300.52 32527[0:SpL:465.1,476.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),c_Set_Oimage(c_Fun_Ofun__upd(u,x1,x2,v,w),v,w),x)))* hBOOL(hAPP(hAPP(c_in(x),x3),z))* -> hBOOL(hAPP(hAPP(c_in(v),x1),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z),c_Set_Oimage(c_Fun_Ofun__upd(u,x1,x2,v,w),v,w),x)))* hBOOL(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,x1,x2,v,w),v,w),x3))*.
% 299.92/300.52 38491[0:Res:362.1,385.1] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oimage(w,x,x),u,tc_fun(x,tc_bool))),v))* c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oimage(w,x,x),u,tc_fun(x,tc_bool)),x) c_Fun_Oinj__on(w,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oimage(w,x,x),u,tc_fun(x,tc_bool)),x,x) -> equal(hAPP(c_Set_Oimage(w,x,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oimage(w,x,x),u,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Set_Oimage(w,x,x),u,tc_fun(x,tc_bool)))**.
% 299.92/300.52 42290[0:SSi:42184.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) equal(hAPP(c_Set_Oimage(w,v,x),y),hAPP(c_Set_Oimage(w,v,x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)))) c_Fun_Oinj__on(w,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z,hAPP(c_Set_Oinsert(y,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool)),v,x)* -> equal(y,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool))).
% 299.92/300.52 45540[0:SpR:323.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(y,tc_bool))),z)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x1,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x2),v),w,x,tc_fun(y,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,w,x,tc_fun(y,tc_bool))),u,tc_fun(x1,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(z,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,w,x,tc_fun(y,tc_bool))),u,tc_fun(x1,tc_bool)))**.
% 299.92/300.52 47617[0:SpL:21893.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_Com_Opname,y),u,w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_Com_Opname,y)))*.
% 299.92/300.52 47616[0:SpL:21267.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x),tc_Com_Opname,y),u,w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x),tc_Com_Opname,y)))*.
% 299.92/300.52 48067[0:SpL:21893.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x)))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),tc_Com_Opname,y),u,w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),tc_Com_Opname,y)))*.
% 299.92/300.52 48066[0:SpL:21267.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x)))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),tc_Com_Opname,y),u,w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x),tc_Com_Opname,y)))*.
% 299.92/300.52 48405[0:SpL:410.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v,w),x),y,w,tc_fun(z,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x1,u),c_HOL_Ominus__class_Ominus(x2,hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,w,tc_fun(z,tc_bool)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),tc_fun(x1,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,w,tc_fun(z,tc_bool)),x1),x2),x1,u) -> .
% 299.92/300.52 50181[0:Rew:532.0,50142.1] || -> equal(u,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(y,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_fun(w,tc_bool),tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,z,v,tc_fun(w,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_fun(w,tc_bool),tc_bool)),y),hAPP(c_Set_Oimage(z,v,tc_fun(w,tc_bool)),u)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_fun(w,tc_bool),tc_fun(w,tc_bool)))**.
% 299.92/300.52 51911[0:SpL:369.0,459.0] || equal(hAPP(c_Set_Oinsert(u,v),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(u,v),c_Set_Oinsert(u,v),w,x)),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(u,v),c_Set_Oinsert(u,v),w,x)) -> equal(hAPP(c_Set_Oinsert(u,v),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oinsert(u,v),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),c_Set_Oinsert(u,v))),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(c_Set_Oinsert(u,v),x1),x2,x,y))**.
% 299.92/300.52 79548[0:SpR:21268.0,97.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(u,w,x),y),v,z),w,x) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(u,w,x),y),v,z),u,w,x),x,w),hAPP(c_Set_Oimage(u,w,x),y)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oimage(u,w,x),hAPP(c_Set_Oimage(u,w,x),y),v,z))**.
% 299.92/300.52 80741[0:SpR:21894.0,97.1] || c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(u,w,x),y),c_Set_Oimage(u,w,x),v,z),w,x) -> equal(hAPP(c_Set_Oimage(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(u,w,x),y),c_Set_Oimage(u,w,x),v,z),u,w,x),x,w),hAPP(c_Set_Oimage(u,w,x),y)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(u,w,x),y),c_Set_Oimage(u,w,x),v,z))**.
% 299.92/300.52 89603[7:SpL:78590.1,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,t_a),v,w),c_Set_Oinsert(v_x,t_a)) equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,t_a),v,w)),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,t_a),v,w)) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oinsert(v_x,t_a),w,v,x),tc_fun(x,w),tc_fun(x,v),v),hAPP(c_COMBB(y,w,tc_fun(x,w),v),u)),z,x1,v,x)),c_List_Ofoldl(y,hAPP(u,z),x1,w,x))**.
% 299.92/300.52 90394[4:SpL:78660.1,459.0] || equal(hAPP(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,t_a),v,w),v_x),v_x) equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,t_a),v,w)),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,t_a),v,w)) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oinsert(v_x,t_a),w,v,x),tc_fun(x,w),tc_fun(x,v),v),hAPP(c_COMBB(y,w,tc_fun(x,w),v),u)),z,x1,v,x)),c_List_Ofoldl(y,hAPP(u,z),x1,w,x))**.
% 299.92/300.52 31384[0:SpL:465.1,449.0] || hBOOL(hAPP(hAPP(c_Set_Oimage(u,v,w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(x,c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),x1,x2)),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(x,c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),x1,x2)))* -> hBOOL(hAPP(hAPP(c_in(v),y),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(x,c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),x1,x2))) c_Hoare__Mirabelle_Otriple__valid(x2,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),x),x1),c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w)),t_a).
% 299.92/300.52 48334[0:SpL:354.2,224.0] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(z),u),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),x1,z),c_HOL_Ominus__class_Ominus(x2,hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,w,y),u),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),tc_fun(x1,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,w,y),u),x1),x2),x1,z) -> .
% 299.92/300.52 49159[0:SpL:205.1,239.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(v),x),y)) c_lessequals(hAPP(c_Set_Oimage(u,v,w),y),z,tc_fun(w,tc_bool)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Set_Oimage(u,v,w),y),w,v) -> hBOOL(hAPP(hAPP(c_in(w),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,v,w),y),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x)),z))*.
% 299.92/300.52 50158[0:SpR:354.2,620.1] || c_lessequals(u,v,tc_fun(tc_fun(w,tc_bool),tc_bool)) c_Fun_Oinj__on(x,v,tc_fun(w,tc_bool),y) -> equal(hAPP(c_Set_Oimage(x,tc_fun(w,tc_bool),y),u),c_Orderings_Obot__class_Obot(tc_fun(y,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,tc_fun(w,tc_bool),y),u),c_Hilbert__Choice_Oinv__into(v,x,tc_fun(w,tc_bool),y),y,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),tc_fun(w,tc_bool),tc_fun(w,tc_bool)))**.
% 299.92/300.52 50826[0:SpR:622.0,415.0] || -> equal(c_Fun_Ofun__upd(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_x,hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),w,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))**.
% 299.92/300.52 51898[0:SpL:9.0,459.0] || equal(hAPP(u,hAPP(v,hAPP(w,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Fun_Ocomp(v,w,x,y,z),x1,x2)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Fun_Ocomp(v,w,x,y,z),x1,x2))** -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Fun_Ocomp(v,w,x,y,z),x2,x1,x3),tc_fun(x3,x2),tc_fun(x3,x1),x1),hAPP(c_COMBB(x4,x2,tc_fun(x3,x2),x1),u)),x5,x6,x1,x3)),c_List_Ofoldl(x4,hAPP(u,x5),x6,x2,x3))**.
% 299.92/300.52 51867[0:SpL:9493.1,459.0] || equal(hAPP(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,t_a),v,w),v_x),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,t_a),v,w)),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v_x,t_a),v,w)) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oinsert(v_x,t_a),w,v,x),tc_fun(x,w),tc_fun(x,v),v),hAPP(c_COMBB(y,w,tc_fun(x,w),v),u)),z,x1,v,x)),c_List_Ofoldl(y,hAPP(u,z),x1,w,x))**.
% 299.92/300.52 51865[0:SpL:8498.1,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v,w),x,y),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v,w),x,y)),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oinsert(v,w),x,y)) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oinsert(v,w),y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),u)),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(u,x2),x3,y,z))**.
% 299.92/300.52 52208[0:SpL:353.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(v)),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),y),tc_Hoare__Mirabelle_Otriple(v)),z)),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(v)),z),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.92/300.52 52450[0:SpL:8415.2,228.0] || equal(v_Procs,v_x) equal(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(v_x,tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v_x),y),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Com_Ocom_OSemi(w,y)),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 52439[0:SpL:8415.2,228.0] || equal(v_Procs,v_x) equal(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(v_x,x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),x),y),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),c_Com_Ocom_OSemi(v_x,y)),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 80487[0:Rew:21268.0,80141.1] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Com_Ocom_OBODY,hAPP(c_Com_Ocom_OBODY,w),z,x1)))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 81682[0:Rew:21894.0,81336.1] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Com_Ocom_OBODY,w),c_Com_Ocom_OBODY,z,x1)))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 92431[0:Rew:223.1,92380.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),tc_fun(z,tc_bool))* -> equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w),hAPP(c_Set_Oimage(x,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))).
% 299.92/300.52 34080[0:SpR:24914.0,465.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),tc_Com_Opname,z),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),v_x))))* equal(hAPP(c_Set_Oimage(w,u,y),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),tc_Com_Opname,z),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),v_x))),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(w,v,x,u,y),u,y),v_x))**.
% 299.92/300.52 39242[0:SpR:533.0,450.0] || -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,y,z))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__2(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,y,z)))* c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w))),y),x),t_a).
% 299.92/300.52 45508[0:Res:468.0,237.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(x,w,y),hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)))),hAPP(c_Set_Oimage(z,w,y),hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))))) equal(hAPP(u,c_ATP__Linkup_Osko__Fun__Xrange__ex1__eq__1__1(c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),x,z,w,y),u,w,v)),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(u,v,w),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),x,z,w,y))**.
% 299.92/300.52 47611[0:SpL:24914.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_Com_Opname,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)),u,w)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_Com_Opname,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x))))*.
% 299.92/300.52 48061[0:SpL:24914.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x)))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),tc_Com_Opname,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x)),u,w)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),tc_Com_Opname,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),v_x))))*.
% 299.92/300.52 48398[0:SpL:532.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),z,u),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y),z),x1),z,u) -> .
% 299.92/300.52 48397[0:SpL:533.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),y))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),z,u),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(y,z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),hAPP(c_Set_Oinsert(y,z),x1),z,u) -> .
% 299.92/300.52 48963[0:SpL:21893.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),tc_Com_Opname,y),x,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),tc_Com_Opname,y)))*.
% 299.92/300.52 48962[0:SpL:21267.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x),tc_Com_Opname,y),x,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x),tc_Com_Opname,y)))*.
% 299.92/300.52 49922[0:SpR:497.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v))),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)))**.
% 299.92/300.52 50160[0:SpR:205.1,620.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(tc_fun(v,tc_bool),tc_bool)),tc_fun(v,tc_bool),w) -> equal(hAPP(c_Set_Oimage(u,tc_fun(v,tc_bool),w),x),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,tc_fun(v,tc_bool),w),x),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(tc_fun(v,tc_bool),tc_bool)),u,tc_fun(v,tc_bool),w),w,tc_fun(v,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y),tc_fun(v,tc_bool),tc_fun(v,tc_bool)))**.
% 299.92/300.52 51684[0:SpL:317.0,233.2] || c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(u,v),w),v) c_Finite__Set_Ofinite(x,y) c_lessequals(hAPP(c_Set_Oinsert(hAPP(z,u),y),hAPP(c_Set_Oimage(z,v,y),w)),x,tc_fun(y,tc_bool))* c_lessequals(hAPP(c_Set_Oimage(x1,y,v),x),hAPP(c_Set_Oinsert(u,v),w),tc_fun(v,tc_bool))* c_Fun_Oinj__on(z,hAPP(c_Set_Oinsert(u,v),w),v,y)* c_Fun_Oinj__on(x1,x,y,v) -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(u,v),w),v),c_Finite__Set_Ocard(x,y)).
% 299.92/300.52 51993[0:Rew:331.0,51927.1,331.0,51927.1] || equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),u,w,x)),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),u,w,x))** -> equal(c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(u,x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))))),x1,x2,w,y),c_List_Ofoldl(z,x1,x2,x,y))**.
% 299.92/300.52 51994[0:Obv:51923.2] || hBOOL(hAPP(hAPP(c_in(u),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Fun_Othe__inv__into(v,w,u,x),w,y,z)),v)) c_Fun_Oinj__on(w,v,u,x) -> equal(hAPP(c_Fun_Othe__inv__into(v,w,u,x),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(w,z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),c_Fun_Othe__inv__into(v,w,u,x))),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(c_Fun_Othe__inv__into(v,w,u,x),x3),x4,z,x1))**.
% 299.92/300.52 51995[0:Obv:51922.2] || hBOOL(hAPP(hAPP(c_in(u),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Hilbert__Choice_Oinv__into(v,w,u,x),w,y,z)),v)) c_Fun_Oinj__on(w,v,u,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,w,u,x),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(w,z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),c_Hilbert__Choice_Oinv__into(v,w,u,x))),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(c_Hilbert__Choice_Oinv__into(v,w,u,x),x3),x4,z,x1))**.
% 299.92/300.52 52200[0:SpL:584.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(c_COMBS(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),w,x,y,z),hAPP(c_Com_Ocom_OBODY,x1)),tc_Hoare__Mirabelle_Otriple(u)),x2),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x1))),hAPP(w,hAPP(c_Com_Ocom_OBODY,x1))),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x2,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,x1)),hAPP(w,hAPP(c_Com_Ocom_OBODY,x1))),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 39350[0:SpL:533.0,449.0] || hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__1(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),y,z))),v_sko__Hoare__Mirabelle__Xtriple__valid__def2__3(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),y,z)))* -> c_Hoare__Mirabelle_Otriple__valid(z,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w))),t_a).
% 299.92/300.52 48336[0:SpL:205.1,224.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),z,x),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),y),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),y),z),x1),z,x) -> .
% 299.92/300.52 49288[0:SpL:21893.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)),x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_Com_Opname,y),u,w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_Com_Opname,y)))*.
% 299.92/300.52 49287[0:SpL:21267.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)),x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x),tc_Com_Opname,y),u,w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x),tc_Com_Opname,y)))*.
% 299.92/300.52 49828[0:Rew:49662.2,49564.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(w,x1),x2),v,x1,tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),y,z),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,v,x1,tc_fun(u,tc_bool)),y),x))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(v,w)),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,v,x1,tc_fun(u,tc_bool)),y),x),y,z).
% 299.92/300.52 49829[0:Rew:49662.2,49557.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x,y) -> hBOOL(hAPP(hAPP(c_in(y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x1))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,y),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),x1),x),w))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),z),x1),x),w),x,y).
% 299.92/300.52 51892[0:SpL:11177.1,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x)),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),w,x)) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),u)),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(u,x1),x2,x,y))**.
% 299.92/300.52 52547[0:SpL:8415.2,624.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)))) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,x,y,w),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),v_x)),hAPP(c_Hilbert__Choice_Oinv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),v_x))*.
% 299.92/300.52 52576[0:MRR:52575.2,49657.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oinsert(y,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))* c_Fun_Oinj__on(c_COMBK(y,x,z),x1,z,x) -> equal(x1,c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))) equal(hAPP(c_Hilbert__Choice_Oinv__into(x1,c_COMBK(y,x,z),z,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oinsert(y,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),w,x,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Fun_Ocomp(w,c_COMBK(y,x,z),x,u,z),z,u),v))*.
% 299.92/300.52 52659[0:SpL:8415.2,623.0] || equal(v_Procs,v_x) equal(c_Set_Oinsert(v_x,tc_Com_Opname),c_in(u)) hBOOL(hAPP(v_x,hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)))) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Fun_Othe__inv__into(z,x,y,w),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),v_x)),hAPP(c_Fun_Othe__inv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),v_x))*.
% 299.92/300.52 52689[0:MRR:52688.2,49657.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oinsert(y,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))))))* c_Fun_Oinj__on(c_COMBK(y,x,z),x1,z,x) -> equal(x1,c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))) equal(hAPP(c_Fun_Othe__inv__into(x1,c_COMBK(y,x,z),z,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oinsert(y,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),w,x,u),v)),hAPP(c_Fun_Othe__inv__into(x1,c_Fun_Ocomp(w,c_COMBK(y,x,z),x,u,z),z,u),v))*.
% 299.92/300.52 48406[0:SpL:486.1,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),x1,x),c_HOL_Ominus__class_Ominus(x2,hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),tc_fun(x1,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),hAPP(y,v)),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(z,tc_bool)),x1),x2),x1,x) -> .
% 299.92/300.52 48957[0:SpL:24914.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)))* -> hBOOL(hAPP(x,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,x,u)),w)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),tc_Com_Opname,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x)),x,u)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),tc_Com_Opname,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),v_x))))*.
% 299.92/300.52 49471[0:SpR:465.1,225.1] || c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),z,x,y) -> hBOOL(hAPP(hAPP(c_in(x),v),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(x1,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))) hBOOL(hAPP(hAPP(c_in(y),hAPP(c_Fun_Ofun__upd(u,v,w,x,y),x1)),hAPP(c_Set_Oimage(u,x,y),c_HOL_Ominus__class_Ominus(z,hAPP(c_Set_Oinsert(x1,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Fun_Ofun__upd(u,v,w,x,y),hAPP(c_Set_Oinsert(x1,x),z),x,y).
% 299.92/300.52 49831[0:Rew:49662.2,49493.3] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),z,x1,x2) -> hBOOL(hAPP(hAPP(c_in(x2),u),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),x1,x2),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,w,y),u),x1),z))))* c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(x,w,y),u),x1),z),x1,x2).
% 299.92/300.52 50774[0:SpR:622.0,9268.0] || -> hBOOL(c_HOL_Ouminus__class_Ouminus(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool))),tc_bool)) equal(hAPP(c_Set_Oinsert(v_x,t_a),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)))**.
% 299.92/300.52 51108[0:SpL:21893.0,472.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v_x),c_Hilbert__Choice_Oinv__into(y,w,x,u),tc_Com_Opname,z)),hAPP(c_Set_Oimage(w,x,u),y)))* equal(hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v_x)) -> equal(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v_x),c_Hilbert__Choice_Oinv__into(y,w,x,u),tc_Com_Opname,z))*.
% 299.92/300.52 51107[0:SpL:21267.0,472.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Hilbert__Choice_Oinv__into(y,w,x,u),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v_x),tc_Com_Opname,z)),hAPP(c_Set_Oimage(w,x,u),y)))* equal(hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v_x)) -> equal(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Hilbert__Choice_Oinv__into(y,w,x,u),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v_x),tc_Com_Opname,z))*.
% 299.92/300.52 51260[0:SpL:21893.0,462.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),tc_Com_Opname,y)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 51259[0:SpL:21267.0,462.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),tc_Com_Opname,y)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 51544[0:Res:13.2,195.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,y,tc_fun(w,tc_bool))* c_lessequals(z,c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),tc_fun(w,tc_bool))* c_Fun_Oinj__on(x1,c_HOL_Ominus__class_Ominus(v,x,tc_fun(w,tc_bool)),w,x2)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x1,w,x2),c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool))),hAPP(c_Set_Oimage(x1,w,x2),z),tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(x1,w,x2),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(u,y,tc_fun(w,tc_bool)),z,tc_fun(w,tc_bool))))**.
% 299.92/300.52 51707[0:Res:651.0,233.2] || c_Finite__Set_Ofinite(v_x,u) c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oimage(v,u,w),tc_Com_Opname,tc_fun(w,tc_bool)),w) c_lessequals(hAPP(c_Set_Oimage(x,w,u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oimage(v,u,w),tc_Com_Opname,tc_fun(w,tc_bool))),v_x,tc_fun(u,tc_bool))* c_Fun_Oinj__on(v,v_x,u,w) c_Fun_Oinj__on(x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oimage(v,u,w),tc_Com_Opname,tc_fun(w,tc_bool)),w,u) -> equal(c_Finite__Set_Ocard(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_Set_Oimage(v,u,w),tc_Com_Opname,tc_fun(w,tc_bool)),w),c_Finite__Set_Ocard(v_x,u)).
% 299.92/300.52 51702[0:Res:376.0,233.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(w,x),hAPP(c_Set_Oimage(y,v,x),u)),x) c_lessequals(hAPP(c_Set_Oimage(z,x,v),hAPP(c_Set_Oinsert(w,x),hAPP(c_Set_Oimage(y,v,x),u))),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(y,u,v,x) c_Fun_Oinj__on(z,hAPP(c_Set_Oinsert(w,x),hAPP(c_Set_Oimage(y,v,x),u)),x,v) -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,x),hAPP(c_Set_Oimage(y,v,x),u)),x),c_Finite__Set_Ocard(u,v)).
% 299.92/300.52 51957[0:SpL:9935.1,459.0] || c_lessequals(c_Orderings_Otop__class_Otop(tc_bool),hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,w,x)),tc_bool)* equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,w,x),c_Orderings_Otop__class_Otop(tc_bool)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(u,x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),x1),x2,x,y))**.
% 299.92/300.52 51913[0:SpL:353.0,459.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(c_Set_Oinsert(w,v),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(w,v),c_Set_Oinsert(u,v),x,y))),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(w,v),c_Set_Oinsert(u,v),x,y))** -> equal(hAPP(c_Set_Oinsert(w,v),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oinsert(u,v),y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),c_Set_Oinsert(w,v))),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(c_Set_Oinsert(w,v),x2),x3,y,z))**.
% 299.92/300.52 51907[0:SpL:8385.1,459.0] || equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,tc_Com_Opname),u,v,w)),v_Procs) equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,tc_Com_Opname),u,v,w)),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,tc_Com_Opname),u,v,w))** -> equal(hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(u,w,v,x),tc_fun(x,w),tc_fun(x,v),v),hAPP(c_COMBB(y,w,tc_fun(x,w),v),c_Set_Oinsert(v_x,tc_Com_Opname))),z,x1,v,x)),c_List_Ofoldl(y,hAPP(c_Set_Oinsert(v_x,tc_Com_Opname),z),x1,w,x))**.
% 299.92/300.52 51900[0:SpL:586.0,459.0] || equal(hAPP(u,hAPP(v,hAPP(w,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_COMBB(v,x,y,z),w),x1,x2)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_COMBB(v,x,y,z),w),x1,x2))** -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_COMBB(v,x,y,z),w),x2,x1,x3),tc_fun(x3,x2),tc_fun(x3,x1),x1),hAPP(c_COMBB(x4,x2,tc_fun(x3,x2),x1),u)),x5,x6,x1,x3)),c_List_Ofoldl(x4,hAPP(u,x5),x6,x2,x3))**.
% 299.92/300.52 51899[0:SpL:585.0,459.0] || equal(hAPP(u,hAPP(hAPP(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_COMBC(v,w,x,y),z),x1,x2)),z)),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_COMBC(v,w,x,y),z),x1,x2))** -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_COMBC(v,w,x,y),z),x2,x1,x3),tc_fun(x3,x2),tc_fun(x3,x1),x1),hAPP(c_COMBB(x4,x2,tc_fun(x3,x2),x1),u)),x5,x6,x1,x3)),c_List_Ofoldl(x4,hAPP(u,x5),x6,x2,x3))**.
% 299.92/300.52 51888[0:SpL:328.1,459.0] || c_lessequals(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y),w,tc_fun(v,tc_bool))* equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x,y),hAPP(u,w)) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),u)),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(u,x2),x3,y,z))**.
% 299.92/300.52 71789[7:SpL:71455.1,459.0] || equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,t_a),u,v,w)),v_x) equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,t_a),u,v,w)),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,t_a),u,v,w))** -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(u,w,v,x),tc_fun(x,w),tc_fun(x,v),v),hAPP(c_COMBB(y,w,tc_fun(x,w),v),c_Set_Oinsert(v_x,t_a))),z,x1,v,x)),c_List_Ofoldl(y,hAPP(c_Set_Oinsert(v_x,t_a),z),x1,w,x))**.
% 299.92/300.52 83895[0:SpL:5899.0,459.0] || equal(hAPP(u,hAPP(c_COMBS(v,w,x,y,z),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_COMBS(v,w,x1,x2,x3),x4,x5))),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_COMBS(v,w,x1,x2,x3),x4,x5))** -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_COMBS(v,w,x1,x2,x3),x5,x4,x6),tc_fun(x6,x5),tc_fun(x6,x4),x4),hAPP(c_COMBB(x7,x5,tc_fun(x6,x5),x4),u)),x8,x9,x4,x6)),c_List_Ofoldl(x7,hAPP(u,x8),x9,x5,x6))**.
% 299.92/300.52 86474[0:SpL:86109.1,459.0] || equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,t_a),u,v,w)),v_Procs) equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,t_a),u,v,w)),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,t_a),u,v,w))** -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(u,w,v,x),tc_fun(x,w),tc_fun(x,v),v),hAPP(c_COMBB(y,w,tc_fun(x,w),v),c_Set_Oinsert(v_x,t_a))),z,x1,v,x)),c_List_Ofoldl(y,hAPP(c_Set_Oinsert(v_x,t_a),z),x1,w,x))**.
% 299.92/300.52 49282[0:SpL:24914.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)),x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_Com_Opname,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x)),u,w)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),tc_Com_Opname,y),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),v_x))))*.
% 299.92/300.52 50169[0:SpR:21893.0,620.1] || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x),c_Set_Oimage(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x),c_Set_Oimage(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x),u,v,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),tc_fun(w,tc_bool),tc_fun(w,tc_bool)))**.
% 299.92/300.52 50168[0:SpR:21267.0,620.1] || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x),tc_Com_Opname,x),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x),tc_Com_Opname,x),u,v,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),tc_fun(w,tc_bool),tc_fun(w,tc_bool)))**.
% 299.92/300.52 51258[0:SpL:24914.0,462.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),tc_Com_Opname,y),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),v_x))),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 51658[0:Rew:6.0,51657.4] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_lessequals(w,hAPP(c_Set_Oinsert(v,u),x),tc_fun(u,tc_bool))* c_lessequals(y,x,tc_fun(u,tc_bool))* c_Fun_Oinj__on(z,x,u,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,u,x1),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(z,u,x1),y),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,u,x1),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),y),tc_fun(u,tc_bool))))**.
% 299.92/300.52 51687[0:SpL:158.0,233.2] || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(u,v,w),x),w) c_Finite__Set_Ofinite(y,z) c_lessequals(hAPP(c_Set_Oimage(c_Fun_Ocomp(x1,u,w,z,v),v,z),x),y,tc_fun(z,tc_bool))* c_lessequals(hAPP(c_Set_Oimage(x2,z,w),y),hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool))* c_Fun_Oinj__on(x1,hAPP(c_Set_Oimage(u,v,w),x),w,z)* c_Fun_Oinj__on(x2,y,z,w) -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),x),w),c_Finite__Set_Ocard(y,z)).
% 299.92/300.52 51925[0:SpL:299.2,459.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(hAPP(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x,y)),w,u)* equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),v,x,y),w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(v,y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x2),x3,y,z))**.
% 299.92/300.52 51905[0:SpL:2097.1,459.0] || hBOOL(hAPP(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v,w),u,x,y)),v))* equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v,w),u,x,y)),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v,w),u,x,y)) -> equal(hAPP(c_Set_Oinsert(v,w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(u,y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),c_Set_Oinsert(v,w))),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(c_Set_Oinsert(v,w),x2),x3,y,z))**.
% 299.92/300.52 51987[0:Rew:9.0,51964.1,9.0,51964.1] || equal(hAPP(u,hAPP(v,hAPP(w,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Fun_Ocomp(u,v,x,y,z),w,x1,x2)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Fun_Ocomp(u,v,x,y,z),w,x1,x2))** -> equal(hAPP(u,hAPP(v,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(w,x2,x1,x3),tc_fun(x3,x2),tc_fun(x3,x1),x1),hAPP(c_COMBB(x4,x2,tc_fun(x3,x2),x1),c_Fun_Ocomp(u,v,x,y,z))),x5,x6,x1,x3))),c_List_Ofoldl(x4,hAPP(u,hAPP(v,x5)),x6,x2,x3))**.
% 299.92/300.52 52167[0:SpL:21893.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Obody,v_x),c_Com_Obody,tc_Com_Opname,w))),x),tc_Hoare__Mirabelle_Otriple(u)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Com_Obody,v_x),c_Com_Obody,tc_Com_Opname,w))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52166[0:SpL:21267.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Obody,hAPP(c_Com_Obody,v_x),tc_Com_Opname,w))),x),tc_Hoare__Mirabelle_Otriple(u)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Com_Obody,hAPP(c_Com_Obody,v_x),tc_Com_Opname,w))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52581[0:MRR:52580.3,20734.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(c_Set_Oimage(x2,w,z),u))) c_Fun_Oinj__on(x2,u,w,z) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,w,y),u),c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),hAPP(c_Hilbert__Choice_Oinv__into(u,x2,w,z),x1)),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,w,y),u),c_Fun_Ocomp(x2,c_Hilbert__Choice_Oinv__into(v,x,w,y),w,z,y),y,z),x1))*.
% 299.92/300.52 52694[0:MRR:52693.3,20734.1] || c_lessequals(u,v,tc_fun(w,tc_bool)) c_Fun_Oinj__on(x,v,w,y) hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(c_Set_Oimage(x2,w,z),u))) c_Fun_Oinj__on(x2,u,w,z) -> equal(hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,w,y),u),c_Hilbert__Choice_Oinv__into(v,x,w,y),y,w),hAPP(c_Fun_Othe__inv__into(u,x2,w,z),x1)),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,w,y),u),c_Fun_Ocomp(x2,c_Hilbert__Choice_Oinv__into(v,x,w,y),w,z,y),y,z),x1))*.
% 299.92/300.52 58731[0:SpL:497.0,15629.0] || hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),w)))*.
% 299.92/300.52 59239[0:SpL:497.0,15857.0] || hBOOL(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))) -> hBOOL(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),x)))*.
% 299.92/300.52 79385[0:SpR:21268.0,617.1] || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,tc_fun(x,tc_bool)),y),u,z),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(hAPP(c_Set_Oinsert(x1,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,tc_fun(x,tc_bool)),y),u,z),v,w,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(x,tc_bool)),y),c_Set_Oinsert(x1,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)))**.
% 299.92/300.52 80578[0:SpR:21894.0,617.1] || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,tc_fun(x,tc_bool)),y),c_Set_Oimage(v,w,tc_fun(x,tc_bool)),u,z),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(hAPP(c_Set_Oinsert(x1,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,tc_fun(x,tc_bool)),y),c_Set_Oimage(v,w,tc_fun(x,tc_bool)),u,z),v,w,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(x,tc_bool)),y),c_Set_Oinsert(x1,x),tc_fun(x,tc_bool),tc_fun(x,tc_bool)))**.
% 299.92/300.52 94284[0:Res:14491.3,233.2] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || hBOOL(hAPP(v,hAPP(c_Set_Oimage(w,x,u),y)))* c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_Finite__Set_Ofinite(y,x) c_Finite__Set_Ofinite(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),u) c_lessequals(hAPP(c_Set_Oimage(z,u,x),c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool))),y,tc_fun(x,tc_bool))* c_Fun_Oinj__on(w,y,x,u) c_Fun_Oinj__on(z,c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),u,x) -> equal(c_Finite__Set_Ocard(y,x),c_Finite__Set_Ocard(c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),u)).
% 299.92/300.52 48401[0:SpL:161.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,tc_fun(v,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(w,y,tc_fun(v,tc_bool))),z,u),c_HOL_Ominus__class_Ominus(x1,hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)),z),c_Orderings_Obot__class_Obot(tc_fun(z,tc_bool))),tc_fun(z,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_HOL_Ominus__class_Ominus(w,y,tc_fun(v,tc_bool))),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(x,y,tc_fun(v,tc_bool)),z),x1),z,u) -> .
% 299.92/300.52 48400[0:SpL:162.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Ovimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),z))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),y)),x1,u),c_HOL_Ominus__class_Ominus(x2,hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(v,w,x),z),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),tc_fun(x1,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Ovimage(v,w,x),y)),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(v,w,x),z),x1),x2),x1,u) -> .
% 299.92/300.52 48399[0:SpL:507.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Set_Oimage(v,w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y)),x1,u),c_HOL_Ominus__class_Ominus(x2,hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(v,w,x),z),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),tc_fun(x1,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(v,w,x),z),x1),x2),x1,u) -> .
% 299.92/300.52 50509[0:SpL:223.1,274.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) equal(hAPP(c_Set_Oinsert(x,y),z),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x1,v,x,u,y),u,y),w))* -> hBOOL(hAPP(hAPP(c_in(y),x),z))* hBOOL(hAPP(hAPP(c_in(y),x),hAPP(c_Set_Oimage(x1,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))))* equal(z,hAPP(c_Set_Oimage(x1,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))*.
% 299.92/300.52 51106[0:SpL:24914.0,472.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* hBOOL(hAPP(hAPP(c_in(u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Hilbert__Choice_Oinv__into(y,w,x,u),tc_Com_Opname,z),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v_x))),hAPP(c_Set_Oimage(w,x,u),y)))* equal(hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v_x)) -> equal(v,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Hilbert__Choice_Oinv__into(y,w,x,u),tc_Com_Opname,z),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v_x)))*.
% 299.92/300.52 51876[0:SpL:297.2,459.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y),u)* equal(hAPP(w,c_List_Osko__List__Xfoldl__apply__inv__1__1(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y)),c_List_Osko__List__Xfoldl__apply__inv__1__1(w,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y)) -> equal(hAPP(w,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),w)),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(w,x2),x3,y,z))**.
% 299.92/300.52 51873[0:SpL:331.0,459.0] || equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w,x)),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),w,x)) -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),u)),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(u,x1),x2,x,y))**.
% 299.92/300.52 52449[0:SpL:21893.0,228.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),v_x),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),x),y),z),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSemi(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),v_x),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),tc_Com_Opname,x1),y)),z),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 52448[0:SpL:21267.0,228.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),v_x),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),x),y),z),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSemi(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),v_x),tc_Com_Opname,x1),y)),z),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 52553[0:SpL:584.0,624.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(v,w,u),x,y,z),hAPP(c_Set_Oimage(x1,x2,w),x3)))* c_Fun_Oinj__on(x1,x3,x2,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x1,x2,w),x3),w,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x3,x1,x2,w),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x1,x2,w),x3),v,w,u),hAPP(c_Set_Oimage(x1,x2,w),x3))),hAPP(c_Hilbert__Choice_Oinv__into(x3,c_Fun_Ocomp(v,x1,w,u,x2),x2,u),hAPP(c_Set_Oimage(x1,x2,w),x3)))*.
% 299.92/300.52 52665[0:SpL:584.0,623.0] || hBOOL(hAPP(c_COMBS(c_in(u),c_Set_Oimage(v,w,u),x,y,z),hAPP(c_Set_Oimage(x1,x2,w),x3)))* c_Fun_Oinj__on(x1,x3,x2,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x1,x2,w),x3),w,u) -> equal(hAPP(c_Fun_Othe__inv__into(x3,x1,x2,w),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x1,x2,w),x3),v,w,u),hAPP(c_Set_Oimage(x1,x2,w),x3))),hAPP(c_Fun_Othe__inv__into(x3,c_Fun_Ocomp(v,x1,w,u,x2),x2,u),hAPP(c_Set_Oimage(x1,x2,w),x3)))*.
% 299.92/300.52 64220[0:SpR:497.0,646.1] || c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_Com_Opname,w),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))),v_x)**.
% 299.92/300.52 64387[0:SpR:497.0,645.1] || c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_Com_Opname,w),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))),v_x)**.
% 299.92/300.52 80282[0:SpL:21268.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y)))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),z,x1),u,w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),z,x1)))*.
% 299.92/300.52 80274[0:SpL:21268.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),z,x1),u,w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),z,x1)))*.
% 299.92/300.52 79617[0:SpR:21268.0,465.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1),w,x2)))* equal(hAPP(c_Set_Oimage(x,u,z),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1),w,x2)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1))**.
% 299.92/300.52 81477[0:SpL:21894.0,489.1] || hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v,u,w)))* hBOOL(hAPP(hAPP(c_in(w),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y)))* -> hBOOL(hAPP(u,x))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),z,x1),u,w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),z,x1)))*.
% 299.92/300.52 81469[0:SpL:21894.0,484.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(u,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)))* hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z,x1),u,w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z,x1)))*.
% 299.92/300.52 80811[0:SpR:21894.0,465.1] || -> hBOOL(hAPP(hAPP(c_in(u),v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1),c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w,x2)))* equal(hAPP(c_Set_Oimage(x,u,z),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1),c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),w,x2)),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,y,u,z),u,z),x1))**.
% 299.92/300.52 89563[7:SpL:78590.1,459.0] || equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,t_a),u,v,w)),c_Set_Oinsert(v_x,t_a)) equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,t_a),u,v,w)),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,t_a),u,v,w))** -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(u,w,v,x),tc_fun(x,w),tc_fun(x,v),v),hAPP(c_COMBB(y,w,tc_fun(x,w),v),c_Set_Oinsert(v_x,t_a))),z,x1,v,x)),c_List_Ofoldl(y,hAPP(c_Set_Oinsert(v_x,t_a),z),x1,w,x))**.
% 299.92/300.52 90354[4:SpL:78660.1,459.0] || equal(hAPP(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,t_a),u,v,w)),v_x),v_x)** equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,t_a),u,v,w)),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,t_a),u,v,w)) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(u,w,v,x),tc_fun(x,w),tc_fun(x,v),v),hAPP(c_COMBB(y,w,tc_fun(x,w),v),c_Set_Oinsert(v_x,t_a))),z,x1,v,x)),c_List_Ofoldl(y,hAPP(c_Set_Oinsert(v_x,t_a),z),x1,w,x))**.
% 299.92/300.52 41805[0:SpL:465.1,199.0] || hBOOL(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,x,z),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oimage(c_Fun_Ofun__upd(u,x1,x2,v,w),v,w),y,x,z))))* c_Fun_Oinj__on(y,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,z) -> hBOOL(hAPP(hAPP(c_in(v),x1),hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,x,z),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Set_Oimage(c_Fun_Ofun__upd(u,x1,x2,v,w),v,w),y,x,z))))* hBOOL(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,x1,x2,v,w),v,w),x3))*.
% 299.92/300.52 41795[0:SpL:71.2,199.0] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Fun_Othe__inv__into(v,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,y),u,z),x,w,y)),v))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,y),v,u,z) hBOOL(c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Fun_Othe__inv__into(v,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,y),u,z),x,w,y)) c_Fun_Oinj__on(x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,y) -> hBOOL(hAPP(c_Fun_Othe__inv__into(v,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,y),u,z),x1))*.
% 299.92/300.52 41794[0:SpL:373.2,199.0] || hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Hilbert__Choice_Oinv__into(v,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,y),u,z),x,w,y)),v))* c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,y),v,u,z) hBOOL(c_ATP__Linkup_Osko__Hilbert__Choice__Xinj__transfer__1__1(c_Hilbert__Choice_Oinv__into(v,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,y),u,z),x,w,y)) c_Fun_Oinj__on(x,c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,y) -> hBOOL(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,y),u,z),x1))*.
% 299.92/300.52 42482[0:SpL:465.1,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Set_Oimage(c_Fun_Ofun__upd(w,x,y,z,x1),z,x1),x2,x3)),hAPP(c_Set_Oimage(w,z,x1),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Set_Oimage(c_Fun_Ofun__upd(w,x,y,z,x1),z,x1),x2,x3)))* -> hBOOL(hAPP(hAPP(c_in(z),x),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,c_Set_Oimage(c_Fun_Ofun__upd(w,x,y,z,x1),z,x1),x2,x3)))* equal(hAPP(c_Set_Oimage(u,x2,x3),v),hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(w,x,y,z,x1),z,x1),x2,x3),v)).
% 299.92/300.52 42441[0:SpL:465.1,315.0] || equal(hAPP(c_Set_Oimage(u,v,w),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(x,c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),x1,x2,x3)),hAPP(x1,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(x,c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),x1,x2,x3)))* -> hBOOL(hAPP(hAPP(c_in(v),y),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(x,c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),x1,x2,x3)))* equal(hAPP(c_Set_Oimage(c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),x2,x3),x),hAPP(c_Set_Oimage(x1,x2,x3),x)).
% 299.92/300.52 47646[0:SSi:47581.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(w,x))* hBOOL(hAPP(hAPP(c_in(v),x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,hAPP(c_Set_Oinsert(z,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool))))* -> hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,w,v)))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),w,v)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool))))*.
% 299.92/300.52 48096[0:SSi:48031.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(w,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(x,w,v)))* hBOOL(hAPP(hAPP(c_in(v),y),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z,hAPP(c_Set_Oinsert(x,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool))))* -> hBOOL(hAPP(w,y))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),w,v)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),z,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool))))*.
% 299.92/300.52 49168[0:SpL:21893.0,239.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,x,u),v_x),c_Set_Oimage(w,x,u),tc_Com_Opname,y),z,tc_fun(x,tc_bool)) c_Fun_Oinj__on(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,x,u),v_x),c_Set_Oimage(w,x,u),tc_Com_Opname,y),x,u) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(w,x,u),v_x),c_Set_Oimage(w,x,u),tc_Com_Opname,y),w,x,u),v)),z))*.
% 299.92/300.52 49167[0:SpL:21267.0,239.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),v_x),tc_Com_Opname,y),z,tc_fun(x,tc_bool)) c_Fun_Oinj__on(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),v_x),tc_Com_Opname,y),x,u) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),v_x),tc_Com_Opname,y),w,x,u),v)),z))*.
% 299.92/300.52 49832[0:Rew:49662.2,49565.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),z,x1,x2) -> hBOOL(hAPP(hAPP(c_in(x2),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),x1,x2),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)),x1),z))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(y,v)),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,u,tc_fun(x,tc_bool)),x1),z),x1,x2).
% 299.92/300.52 50166[0:SpR:24914.0,620.1] || -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x)),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,tc_fun(w,tc_bool)),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x)),u,v,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(w,tc_bool)),v_x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),tc_fun(w,tc_bool),tc_fun(w,tc_bool)))**.
% 299.92/300.52 51908[0:SpL:9493.1,459.0] || equal(hAPP(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,t_a),u,v,w)),v_x),c_Orderings_Otop__class_Otop(tc_bool))** equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,t_a),u,v,w)),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v_x,t_a),u,v,w)) -> equal(hAPP(c_Set_Oinsert(v_x,t_a),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(u,w,v,x),tc_fun(x,w),tc_fun(x,v),v),hAPP(c_COMBB(y,w,tc_fun(x,w),v),c_Set_Oinsert(v_x,t_a))),z,x1,v,x)),c_List_Ofoldl(y,hAPP(c_Set_Oinsert(v_x,t_a),z),x1,w,x))**.
% 299.92/300.52 51906[0:SpL:8498.1,459.0] || equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v,w),u,x,y)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))) equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v,w),u,x,y)),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(v,w),u,x,y))** -> equal(hAPP(c_Set_Oinsert(v,w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(u,y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),c_Set_Oinsert(v,w))),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(c_Set_Oinsert(v,w),x2),x3,y,z))**.
% 299.92/300.52 52219[0:SpL:338.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),hAPP(c_Com_Ocom_OBODY,x)),y),tc_Hoare__Mirabelle_Otriple(u)),z)),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),z),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),w),hAPP(c_Com_Ocom_OBODY,x)),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52217[0:SpL:317.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x,tc_Hoare__Mirabelle_Otriple(u)),hAPP(c_Set_Oinsert(y,x),z)),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x,tc_Hoare__Mirabelle_Otriple(u)),z),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52165[0:SpL:24914.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Obody,tc_Com_Opname,w),hAPP(c_Com_Obody,v_x)))),x),tc_Hoare__Mirabelle_Otriple(u)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Com_Obody,tc_Com_Opname,w),hAPP(c_Com_Obody,v_x)))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52446[0:SpL:24914.0,228.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),v_x),x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),x),y),z),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSemi(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),tc_Com_Opname,x1),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),v_x)),y)),z),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 58699[0:SpL:622.0,15629.0] || hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool)))) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),w)))*.
% 299.92/300.52 59207[0:SpL:622.0,15857.0] || hBOOL(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),v,u,tc_fun(t_a,tc_bool)))) -> hBOOL(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__Xbex__Un__1__3(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,u,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),x)))*.
% 299.92/300.52 80280[0:SpL:21268.0,462.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),z,x1)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 81475[0:SpL:21894.0,462.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Com_Ocom_OBODY,x)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),y),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),z,x1)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 42490[0:SpL:533.0,315.0] || equal(hAPP(u,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),z,x1)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v,u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),z,x1))))* -> equal(hAPP(c_Set_Oimage(u,z,x1),v),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)),z,x1),v)).
% 299.92/300.52 42449[0:SpL:533.0,315.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),y,z,x1))),hAPP(y,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),y,z,x1)))* -> equal(hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),z,x1),x),hAPP(c_Set_Oimage(y,z,x1),x)).
% 299.92/300.52 50420[0:SpR:223.1,71.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),x1))* c_Fun_Oinj__on(c_Set_Oinsert(x2,z),x1,x,x3) -> equal(hAPP(c_Fun_Othe__inv__into(x1,c_Set_Oinsert(x2,z),x,x3),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,x2,u,z),u,z),w)),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))*.
% 299.92/300.52 50419[0:SpR:223.1,373.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),x1))* c_Fun_Oinj__on(c_Set_Oinsert(x2,z),x1,x,x3) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Set_Oinsert(x2,z),x,x3),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,x2,u,z),u,z),w)),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))*.
% 299.92/300.52 51760[0:SSi:51734.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(x,v) c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z),w) c_lessequals(hAPP(c_Set_Oimage(x1,w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)),x,tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,x,v,w) c_Fun_Oinj__on(x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z),w,v) -> equal(c_Finite__Set_Ocard(x,v),c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z),w)).
% 299.92/300.52 51761[0:SSi:51731.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_lessequals(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(x,v) c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),y),w) c_lessequals(hAPP(c_Set_Oimage(x1,w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),y)),x,tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,x,v,w) c_Fun_Oinj__on(x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),y),w,v) -> equal(c_Finite__Set_Ocard(x,v),c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),z),y),w)).
% 299.92/300.52 51991[0:Rew:586.0,51966.1,586.0,51966.1] || equal(hAPP(u,hAPP(v,hAPP(w,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_COMBB(u,x,y,z),v),w,x1,x2)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_COMBB(u,x,y,z),v),w,x1,x2))** -> equal(hAPP(u,hAPP(v,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(w,x2,x1,x3),tc_fun(x3,x2),tc_fun(x3,x1),x1),hAPP(c_COMBB(x4,x2,tc_fun(x3,x2),x1),hAPP(c_COMBB(u,x,y,z),v))),x5,x6,x1,x3))),c_List_Ofoldl(x4,hAPP(u,hAPP(v,x5)),x6,x2,x3))**.
% 299.92/300.52 51992[0:Rew:585.0,51965.1,585.0,51965.1] || equal(hAPP(hAPP(u,hAPP(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_COMBC(u,w,x,y),z),v,x1,x2))),z),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_COMBC(u,w,x,y),z),v,x1,x2))** -> equal(hAPP(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(v,x2,x1,x3),tc_fun(x3,x2),tc_fun(x3,x1),x1),hAPP(c_COMBB(x4,x2,tc_fun(x3,x2),x1),hAPP(c_COMBC(u,w,x,y),z))),x5,x6,x1,x3)),z),c_List_Ofoldl(x4,hAPP(hAPP(u,x5),z),x6,x2,x3))**.
% 299.92/300.52 52178[0:SpL:584.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),hAPP(x,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w)))),tc_Hoare__Mirabelle_Otriple(u)),y),hAPP(c_Set_Oinsert(hAPP(c_COMBS(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),x,z,x1,x2),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),hAPP(x,hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w)))),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 64190[0:SpR:622.0,646.1] || c_Fun_Oinj__on(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Fun_Othe__inv__into(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,w),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))),v_x)**.
% 299.92/300.52 64357[0:SpR:622.0,645.1] || c_Fun_Oinj__on(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v_Procs,tc_Com_Opname,w) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,w),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))),v_x)**.
% 299.92/300.52 80238[0:SpL:21268.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(y,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,y,u)),w)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),z,x1),y,u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),z,x1)))*.
% 299.92/300.52 81433[0:SpL:21894.0,483.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x)))* -> hBOOL(hAPP(y,v))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(w,y,u)),w)) hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z,x1),y,u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),z,x1)))*.
% 299.92/300.52 49007[0:SSi:48927.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(hAPP(c_in(v),w),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,hAPP(c_Set_Oinsert(y,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool))))* -> hBOOL(hAPP(z,w))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(y,z,v)),y))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xball__Un__1__3(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),z,v)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool))))*.
% 299.92/300.52 49833[0:Rew:49662.2,49495.2] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),x1),hAPP(c_Set_Oimage(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),y,z),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),x1),y),x))))* c_Fun_Oinj__on(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(u,v,w),x1),y),x),y,z).
% 299.92/300.52 52574[0:MRR:52544.2,9371.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(v),x),y)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Set_Oimage(u,v,w),y),w,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(y,u,v,w),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,v,w),y),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x)),hAPP(c_Hilbert__Choice_Oinv__into(y,c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),u,w,v,v),v,v),x))*.
% 299.92/300.52 52687[0:MRR:52656.2,9371.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(v),x),y)) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Set_Oimage(u,v,w),y),w,v) -> equal(hAPP(c_Fun_Othe__inv__into(y,u,v,w),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,v,w),y),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x)),hAPP(c_Fun_Othe__inv__into(y,c_Fun_Ocomp(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),u,w,v,v),v,v),x))*.
% 299.92/300.52 80273[0:SpL:21268.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)),x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),z,x1),u,w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),z,x1)))*.
% 299.92/300.52 80259[0:SpL:21268.0,228.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),y),z),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSemi(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),x2,x3),z)),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 81468[0:SpL:21894.0,488.1] || hBOOL(hAPP(u,v))* hBOOL(hAPP(hAPP(c_in(w),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y)))* -> hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(x,u,w)),x)) hBOOL(hAPP(hAPP(c_in(w),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z,x1),u,w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),z,x1)))*.
% 299.92/300.52 81454[0:SpL:21894.0,228.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),y),z),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSemi(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x2,x3),z)),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 49165[0:SpL:24914.0,239.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),v_x))) c_lessequals(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,x,u),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,x,u),v_x)),z,tc_fun(x,tc_bool)) c_Fun_Oinj__on(w,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,x,u),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,x,u),v_x)),x,u) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(w,x,u),tc_Com_Opname,y),hAPP(c_Set_Oimage(w,x,u),v_x)),w,x,u),v)),z))*.
% 299.92/300.52 49332[0:SSi:49252.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,tc_fun(v,tc_bool)) hBOOL(hAPP(w,x))* hBOOL(hAPP(hAPP(c_in(v),x),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,hAPP(c_Set_Oinsert(z,tc_fun(v,tc_bool)),u),tc_fun(v,tc_bool),tc_fun(v,tc_bool))))* -> hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(z,w,v)),z))* hBOOL(hAPP(hAPP(c_in(v),c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool)),w,v)),c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),y,u,tc_fun(v,tc_bool),tc_fun(v,tc_bool))))*.
% 299.92/300.52 49834[0:Rew:49662.2,49556.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x1))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),y,z),hAPP(c_Set_Oinsert(x1,y),x))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),hAPP(c_Set_Oinsert(x1,y),x),y,z).
% 299.92/300.52 51878[0:SpL:181.1,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Ovimage(c_COMBK(v,w,x),x,w),y,z),hAPP(u,c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool)))) -> hBOOL(hAPP(hAPP(c_in(w),v),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Ovimage(c_COMBK(v,w,x),x,w),y,z)))* equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Ovimage(c_COMBK(v,w,x),x,w),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),u)),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(u,x3),x4,z,x1))**.
% 299.92/300.52 52002[0:Obv:51920.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oimage(u,v,w),x,y,z),tc_fun(z,x),tc_fun(z,y),y),hAPP(c_COMBB(x1,x,tc_fun(z,x),y),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v))),x2,x3,y,z)),c_List_Ofoldl(x1,hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),x2),x3,x,z))**.
% 299.92/300.52 52460[0:SpL:21893.0,228.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),v_x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),v_x),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),tc_Com_Opname,y)),z),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSemi(x,z)),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.92/300.52 52459[0:SpL:21267.0,228.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),v_x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),v_x),tc_Com_Opname,y)),z),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSemi(x,z)),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.92/300.52 80270[0:SpL:21268.0,472.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Hilbert__Choice_Oinv__into(y,w,x,u),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),x1),z,x2)),hAPP(c_Set_Oimage(w,x,u),y)))* equal(hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),x1))* -> equal(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Hilbert__Choice_Oinv__into(y,w,x,u),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),x1),z,x2))*.
% 299.92/300.52 81465[0:SpL:21894.0,472.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y)))* hBOOL(hAPP(hAPP(c_in(u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),x1),c_Hilbert__Choice_Oinv__into(y,w,x,u),z,x2)),hAPP(c_Set_Oimage(w,x,u),y)))* equal(hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),v),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),x1))* -> equal(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(y,w,x,u),x1),c_Hilbert__Choice_Oinv__into(y,w,x,u),z,x2))*.
% 299.92/300.52 83134[0:SpL:5924.0,459.0] || equal(hAPP(u,hAPP(hAPP(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2),x3,x4)),w)),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_COMBS(v,c_COMBK(w,x,y),z,x1,x2),x3,x4))** -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_COMBS(v,c_COMBK(w,x,y),z,x1,x2),x4,x3,x5),tc_fun(x5,x4),tc_fun(x5,x3),x3),hAPP(c_COMBB(x6,x4,tc_fun(x5,x4),x3),u)),x7,x8,x3,x5)),c_List_Ofoldl(x6,hAPP(u,x7),x8,x4,x5))**.
% 299.92/300.52 83451[0:SpL:5961.0,459.0] || equal(hAPP(u,hAPP(v,hAPP(w,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_COMBS(c_COMBK(v,x,y),w,z,x1,x2),x3,x4)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_COMBS(c_COMBK(v,x,y),w,z,x1,x2),x3,x4))** -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_COMBS(c_COMBK(v,x,y),w,z,x1,x2),x4,x3,x5),tc_fun(x5,x4),tc_fun(x5,x3),x3),hAPP(c_COMBB(x6,x4,tc_fun(x5,x4),x3),u)),x7,x8,x3,x5)),c_List_Ofoldl(x6,hAPP(u,x7),x8,x4,x5))**.
% 299.92/300.52 38517[0:Rew:21893.0,38485.3] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,v),v_x),c_Set_Oimage(u,v,v),tc_Com_Opname,w),v) c_lessequals(hAPP(c_Set_Oimage(u,v,v),v_x),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,v),v_x),c_Set_Oimage(u,v,v),tc_Com_Opname,w),tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,v),v_x),c_Set_Oimage(u,v,v),tc_Com_Opname,w),v,v) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,v),v_x),c_Set_Oimage(u,v,v),tc_Com_Opname,w),hAPP(c_Set_Oimage(u,v,v),v_x)).
% 299.92/300.52 38518[0:Rew:21267.0,38484.3] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,v),hAPP(c_Set_Oimage(u,v,v),v_x),tc_Com_Opname,w),v) c_lessequals(hAPP(c_Set_Oimage(u,v,v),v_x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,v),hAPP(c_Set_Oimage(u,v,v),v_x),tc_Com_Opname,w),tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,v),hAPP(c_Set_Oimage(u,v,v),v_x),tc_Com_Opname,w),v,v) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,v),hAPP(c_Set_Oimage(u,v,v),v_x),tc_Com_Opname,w),hAPP(c_Set_Oimage(u,v,v),v_x)).
% 299.92/300.52 48402[0:SpL:323.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x),y,v,tc_fun(z,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,v,tc_fun(z,tc_bool))),x1,u),c_HOL_Ominus__class_Ominus(x2,hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,tc_fun(z,tc_bool)),x1),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))),tc_fun(x1,tc_bool)))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(z,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,y,v,tc_fun(z,tc_bool))),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x,y,v,tc_fun(z,tc_bool)),x1),x2),x1,u) -> .
% 299.92/300.52 51958[0:SpL:11177.1,459.0] || equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,w,x)),c_Orderings_Otop__class_Otop(tc_bool)) equal(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,w,x)),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),u,w,x))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(u,x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v))),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v),x1),x2,x,y))**.
% 299.92/300.52 51877[0:SpL:188.1,459.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_List_Osko__List__Xfoldl__apply__inv__1__1(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z)))* equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(w,c_Set_Ovimage(c_COMBK(v,u,x),x,u),y,z),hAPP(w,c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)))) -> equal(hAPP(w,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Ovimage(c_COMBK(v,u,x),x,u),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),w)),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(w,x3),x4,z,x1))**.
% 299.92/300.52 51869[0:SpL:445.1,459.0] || equal(hAPP(u,hAPP(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Fun_Ofun__upd(v,w,x,y,z),x1,x2))),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Fun_Ofun__upd(v,w,x,y,z),x1,x2))** -> equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Fun_Ofun__upd(v,w,x,y,z),x1,x2),w) equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Fun_Ofun__upd(v,w,x,y,z),x2,x1,x3),tc_fun(x3,x2),tc_fun(x3,x1),x1),hAPP(c_COMBB(x4,x2,tc_fun(x3,x2),x1),u)),x5,x6,x1,x3)),c_List_Ofoldl(x4,hAPP(u,x5),x6,x2,x3))**.
% 299.92/300.52 52457[0:SpL:24914.0,228.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),v_x),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),tc_Com_Opname,y),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),v_x))),z),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSemi(x,z)),x1),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.92/300.52 80175[0:SpL:21268.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Com_Obody,hAPP(c_Com_Obody,x),w,y))),z),tc_Hoare__Mirabelle_Otriple(u)),x1),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Com_Obody,hAPP(c_Com_Obody,x),w,y))),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 79386[0:SpR:21268.0,620.1] || -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,tc_fun(x,tc_bool)),y),u,z),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(v,w,tc_fun(x,tc_bool)),y),u,z),v,w,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(x,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),tc_fun(x,tc_bool),tc_fun(x,tc_bool)))**.
% 299.92/300.52 81370[0:SpL:21894.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Com_Obody,x),c_Com_Obody,w,y))),z),tc_Hoare__Mirabelle_Otriple(u)),x1),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x))),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_Com_Obody,x),c_Com_Obody,w,y))),z),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 80579[0:SpR:21894.0,620.1] || -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,tc_fun(x,tc_bool)),y),c_Set_Oimage(v,w,tc_fun(x,tc_bool)),u,z),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,tc_fun(x,tc_bool)),y),c_Set_Oimage(v,w,tc_fun(x,tc_bool)),u,z),v,w,tc_fun(x,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(v,w,tc_fun(x,tc_bool)),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),x1),tc_fun(x,tc_bool),tc_fun(x,tc_bool)))**.
% 299.92/300.52 49835[0:Rew:49662.2,49560.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),x,y,z) -> hBOOL(hAPP(hAPP(c_in(z),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x1),w,tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),y,z),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(x1,w,tc_fun(u,tc_bool)),y),x))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_HOL_Ominus__class_Ominus(v,w,tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(c_HOL_Ominus__class_Ominus(x1,w,tc_fun(u,tc_bool)),y),x),y,z).
% 299.92/300.52 49836[0:Rew:49662.2,49559.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),y,z,x1) -> hBOOL(hAPP(hAPP(c_in(x1),hAPP(c_Set_Ovimage(v,u,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x2))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),z,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(v,u,w),x2),z),y))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Ovimage(v,u,w),x)),hAPP(c_Set_Oinsert(hAPP(c_Set_Ovimage(v,u,w),x2),z),y),z,x1).
% 299.92/300.52 49837[0:Rew:49662.2,49558.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),y,z,x1) -> hBOOL(hAPP(hAPP(c_in(x1),hAPP(c_Set_Oimage(v,w,u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),x2))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),z,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(v,w,u),x2),z),y))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,u),x)),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(v,w,u),x2),z),y),z,x1).
% 299.92/300.52 49991[0:SpR:497.0,317.0] || -> equal(hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),w,x),hAPP(c_Set_Oinsert(v_x,w),y)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),x),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),w,x),y)))*.
% 299.92/300.52 49990[0:SpR:497.0,99.1] || c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),w,x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))),v_x)**.
% 299.92/300.52 49989[0:SpR:497.0,438.1] || c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),w,x),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v))),v_x)**.
% 299.92/300.52 50411[0:SpR:223.1,2098.1] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> c_Hoare__Mirabelle_Ohoare__valids(x,hAPP(c_Set_Oimage(y,u,tc_Hoare__Mirabelle_Otriple(t_a)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),t_a) equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(x,hAPP(c_Set_Oimage(y,u,tc_Hoare__Mirabelle_Otriple(t_a)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))),u,tc_Hoare__Mirabelle_Otriple(t_a)),u,tc_Hoare__Mirabelle_Otriple(t_a)),w),hAPP(c_Set_Oimage(y,u,tc_Hoare__Mirabelle_Otriple(t_a)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))))**.
% 299.92/300.52 51540[0:Res:326.2,195.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,y,tc_fun(w,tc_bool))* c_lessequals(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),tc_fun(w,tc_bool))* c_Fun_Oinj__on(x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),v),y),w,x2)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x1,w,x2),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x)),hAPP(c_Set_Oimage(x1,w,x2),z),tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(x1,w,x2),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x),z,tc_fun(w,tc_bool))))**.
% 299.92/300.52 51713[0:Res:362.1,233.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(v,x) c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(y,x,z),u,tc_fun(z,tc_bool)),z) c_lessequals(hAPP(c_Set_Oimage(x1,z,x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(y,x,z),u,tc_fun(z,tc_bool))),v,tc_fun(x,tc_bool))* c_Fun_Oinj__on(y,v,x,z) c_Fun_Oinj__on(x1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(y,x,z),u,tc_fun(z,tc_bool)),z,x) -> equal(c_Finite__Set_Ocard(v,x),c_Finite__Set_Ocard(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(w,c_Set_Oimage(y,x,z),u,tc_fun(z,tc_bool)),z)).
% 299.92/300.52 51937[0:SpL:544.1,459.0] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x)),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x1),x2,x,y))**.
% 299.92/300.52 51936[0:SpL:543.1,459.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x)),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x1),x2,x,y))**.
% 299.92/300.52 51914[0:SpL:317.0,459.0] || equal(hAPP(c_Set_Oinsert(hAPP(u,v),w),hAPP(c_Set_Oimage(u,x,w),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oimage(u,x,w),c_Set_Oinsert(v,x),y,z))),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oimage(u,x,w),c_Set_Oinsert(v,x),y,z))** -> equal(hAPP(c_Set_Oimage(u,x,w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oinsert(v,x),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),c_Set_Oimage(u,x,w))),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(c_Set_Oimage(u,x,w),x3),x4,z,x1))**.
% 299.92/300.52 52237[0:Rew:21893.0,52203.1] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),tc_Com_Opname,y)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52238[0:Rew:21267.0,52202.1] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),tc_Com_Opname,y)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52540[0:SpL:393.1,624.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))) c_Fun_Oinj__on(x,y,z,x1) c_Fun_Oinj__on(c_COMBK(w,u,x1),hAPP(c_Set_Oimage(x,z,x1),y),x1,u) -> equal(hAPP(c_Set_Oimage(x,z,x1),y),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))) equal(hAPP(c_Hilbert__Choice_Oinv__into(y,x,z,x1),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,z,x1),y),c_COMBK(w,u,x1),x1,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(y,c_Fun_Ocomp(c_COMBK(w,u,x1),x,x1,u,z),z,u),v))*.
% 299.92/300.52 52652[0:SpL:393.1,623.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oinsert(w,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))))) c_Fun_Oinj__on(x,y,z,x1) c_Fun_Oinj__on(c_COMBK(w,u,x1),hAPP(c_Set_Oimage(x,z,x1),y),x1,u) -> equal(hAPP(c_Set_Oimage(x,z,x1),y),c_Orderings_Obot__class_Obot(tc_fun(x1,tc_bool))) equal(hAPP(c_Fun_Othe__inv__into(y,x,z,x1),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,z,x1),y),c_COMBK(w,u,x1),x1,u),v)),hAPP(c_Fun_Othe__inv__into(y,c_Fun_Ocomp(c_COMBK(w,u,x1),x,x1,u,z),z,u),v))*.
% 299.92/300.52 49950[0:SpR:497.0,21893.0] || -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_Com_Opname,w)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)))**.
% 299.92/300.52 49944[0:SpR:497.0,21267.0] || -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),tc_Com_Opname,w)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)))**.
% 299.92/300.52 51539[0:Res:399.1,195.0] || c_lessequals(u,v,tc_fun(w,tc_bool))* c_lessequals(x,hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),v),tc_fun(w,tc_bool))* c_Fun_Oinj__on(y,hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),v),w,z)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(y,w,z),hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),u)),hAPP(c_Set_Oimage(y,w,z),x),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,w,z),c_HOL_Ominus__class_Ominus(hAPP(c_COMBC(c_in(w),w,tc_fun(w,tc_bool),tc_bool),u),x,tc_fun(w,tc_bool))))**.
% 299.92/300.52 51712[0:Res:84.1,233.2] || c_lessequals(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),x),y,tc_fun(w,tc_bool)),z,tc_fun(w,tc_bool))* c_Finite__Set_Ofinite(x,v) c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z),w) c_lessequals(hAPP(c_Set_Oimage(x1,w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z)),x,tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,x,v,w) c_Fun_Oinj__on(x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z),w,v) -> equal(c_Finite__Set_Ocard(x,v),c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),z),w)).
% 299.92/300.52 51889[0:SpL:329.1,459.0] || c_lessequals(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y),tc_fun(w,tc_bool))* equal(hAPP(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y)),c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x,y)) -> equal(hAPP(v,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),v)),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(v,x2),x3,y,z))**.
% 299.92/300.52 51868[0:SpL:393.1,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oimage(c_COMBK(v,w,x),x,w),y,z),hAPP(u,hAPP(c_Set_Oinsert(v,w),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))))) -> equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oimage(c_COMBK(v,w,x),x,w),y,z),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))) equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oimage(c_COMBK(v,w,x),x,w),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),u)),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(u,x3),x4,z,x1))**.
% 299.92/300.52 52239[0:Rew:24914.0,52201.1] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),tc_Com_Opname,y),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x))),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),v_x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52552[0:SpL:21893.0,624.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)))) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,x,y,w),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,x1))),hAPP(c_Hilbert__Choice_Oinv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,x1)))*.
% 299.92/300.52 52551[0:SpL:21267.0,624.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)))) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,x,y,w),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,x1))),hAPP(c_Hilbert__Choice_Oinv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,x1)))*.
% 299.92/300.52 52664[0:SpL:21893.0,623.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)))) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Fun_Othe__inv__into(z,x,y,w),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,x1))),hAPP(c_Fun_Othe__inv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_in(u),v_x),c_in(u),tc_Com_Opname,x1)))*.
% 299.92/300.52 52663[0:SpL:21267.0,623.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)))) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Fun_Othe__inv__into(z,x,y,w),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,x1))),hAPP(c_Fun_Othe__inv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_in(u),hAPP(c_in(u),v_x),tc_Com_Opname,x1)))*.
% 299.92/300.52 80277[0:SpL:21268.0,228.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),y),z,x1)),x2),x3),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSemi(x,x2)),x3),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.92/300.52 81472[0:SpL:21894.0,228.0] || c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),y),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v) c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),y),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),x),z,x1)),x2),x3),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),w),c_Com_Ocom_OSemi(x,x2)),x3),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v).
% 299.92/300.52 702[0:Res:589.0,592.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v_x)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v_x))),hAPP(v_Q,v_x)),t_a).
% 299.92/300.52 49993[0:SpR:497.0,118.0] || -> equal(c_Fun_Ocomp(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_Fun_Ofun__upd(w,x,v_x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),w,z,x1,y),x,hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),y,x1))*.
% 299.92/300.52 49981[0:SpR:497.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)),v,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)),u,y),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),x))),v_x)**.
% 299.92/300.52 49980[0:SpR:497.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)),v,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)),u,y),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),x))),v_x)**.
% 299.92/300.52 49956[0:SpR:497.0,24914.0] || -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),tc_Com_Opname,w),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)))),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)))**.
% 299.92/300.52 50844[0:SpR:622.0,317.0] || -> equal(hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),w,x),hAPP(c_Set_Oinsert(v_x,w),y)),hAPP(c_Set_Oinsert(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),x),hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),w,x),y)))*.
% 299.92/300.52 50843[0:SpR:622.0,99.1] || c_Fun_Oinj__on(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Fun_Othe__inv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),w,x),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))),v_x)**.
% 299.92/300.52 50842[0:SpR:622.0,438.1] || c_Fun_Oinj__on(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),w,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),w,x),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool)))),v_x)**.
% 299.92/300.52 51623[0:Res:247.4,195.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(tc_fun(u,tc_bool),tc_bool))* c_lessequals(x,c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* c_Fun_Oinj__on(y,c_Finite__Set_Olinorder__class_OMax(v,tc_fun(u,tc_bool)),u,z)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,tc_bool),tc_bool))) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(y,u,z),c_Finite__Set_Olinorder__class_OMax(w,tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(y,u,z),x),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(c_Finite__Set_Olinorder__class_OMax(w,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))))**.
% 299.92/300.52 51622[0:Res:248.4,195.0] class_Orderings_Olinorder(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,tc_fun(u,tc_bool)) c_lessequals(w,v,tc_fun(tc_fun(u,tc_bool),tc_bool))* c_lessequals(x,c_Finite__Set_Olinorder__class_OMin(w,tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* c_Fun_Oinj__on(y,c_Finite__Set_Olinorder__class_OMin(w,tc_fun(u,tc_bool)),u,z)* -> equal(w,c_Orderings_Obot__class_Obot(tc_fun(tc_fun(u,tc_bool),tc_bool))) equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(y,u,z),c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(y,u,z),x),tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(y,u,z),c_HOL_Ominus__class_Ominus(c_Finite__Set_Olinorder__class_OMin(v,tc_fun(u,tc_bool)),x,tc_fun(u,tc_bool))))**.
% 299.92/300.52 51954[0:SpL:328.1,459.0] || c_lessequals(hAPP(u,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,x,y)),w,tc_fun(v,tc_bool))* equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),u,x,y),w) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(u,y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x2),x3,y,z))**.
% 299.92/300.52 51930[0:SpL:297.2,459.0] class_Lattices_Oupper__semilattice(u) || c_lessequals(v,hAPP(w,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y)),u)* equal(hAPP(w,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y)),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w,x,y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(w,y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v))),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x2),x3,y,z))**.
% 299.92/300.52 51921[0:SpL:131.0,459.0] || equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Ovimage(v,y,w),c_Set_Ovimage(u,w,x),z,x1)),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Ovimage(v,y,w),c_Set_Ovimage(u,w,x),z,x1))** -> equal(hAPP(c_Set_Ovimage(v,y,w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Ovimage(u,w,x),x1,z,x2),tc_fun(x2,x1),tc_fun(x2,z),z),hAPP(c_COMBB(x3,x1,tc_fun(x2,x1),z),c_Set_Ovimage(v,y,w))),x4,x5,z,x2)),c_List_Ofoldl(x3,hAPP(c_Set_Ovimage(v,y,w),x4),x5,x1,x2))**.
% 299.92/300.52 51919[0:SpL:158.0,459.0] || equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,v,w,x,y),y,x),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oimage(u,w,x),c_Set_Oimage(v,y,w),z,x1)),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oimage(u,w,x),c_Set_Oimage(v,y,w),z,x1))** -> equal(hAPP(c_Set_Oimage(u,w,x),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oimage(v,y,w),x1,z,x2),tc_fun(x2,x1),tc_fun(x2,z),z),hAPP(c_COMBB(x3,x1,tc_fun(x2,x1),z),c_Set_Oimage(u,w,x))),x4,x5,z,x2)),c_List_Ofoldl(x3,hAPP(c_Set_Oimage(u,w,x),x4),x5,x1,x2))**.
% 299.92/300.52 83168[0:Rew:5924.0,83124.1,5924.0,83124.1] || equal(hAPP(hAPP(u,hAPP(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_COMBS(u,c_COMBK(w,x,y),z,x1,x2),v,x3,x4))),w),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_COMBS(u,c_COMBK(w,x,y),z,x1,x2),v,x3,x4))** -> equal(hAPP(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(v,x4,x3,x5),tc_fun(x5,x4),tc_fun(x5,x3),x3),hAPP(c_COMBB(x6,x4,tc_fun(x5,x4),x3),c_COMBS(u,c_COMBK(w,x,y),z,x1,x2))),x7,x8,x3,x5)),w),c_List_Ofoldl(x6,hAPP(hAPP(u,x7),w),x8,x4,x5))**.
% 299.92/300.52 83478[0:Rew:5961.0,83443.1,5961.0,83443.1] || equal(hAPP(u,hAPP(v,hAPP(w,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_COMBS(c_COMBK(u,x,y),v,z,x1,x2),w,x3,x4)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_COMBS(c_COMBK(u,x,y),v,z,x1,x2),w,x3,x4))** -> equal(hAPP(u,hAPP(v,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(w,x4,x3,x5),tc_fun(x5,x4),tc_fun(x5,x3),x3),hAPP(c_COMBB(x6,x4,tc_fun(x5,x4),x3),c_COMBS(c_COMBK(u,x,y),v,z,x1,x2))),x7,x8,x3,x5))),c_List_Ofoldl(x6,hAPP(u,hAPP(v,x7)),x8,x4,x5))**.
% 299.92/300.52 83885[0:SpL:5899.0,459.0] || equal(hAPP(c_COMBS(u,v,w,x,y),hAPP(z,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_COMBS(u,v,x1,x2,x3),z,x4,x5))),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_COMBS(u,v,x1,x2,x3),z,x4,x5))** -> equal(hAPP(c_COMBS(u,v,x1,x2,x3),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(z,x5,x4,x6),tc_fun(x6,x5),tc_fun(x6,x4),x4),hAPP(c_COMBB(x7,x5,tc_fun(x6,x5),x4),c_COMBS(u,v,x1,x2,x3))),x8,x9,x4,x6)),c_List_Ofoldl(x7,hAPP(c_COMBS(u,v,x1,x2,x3),x8),x9,x5,x6))**.
% 299.92/300.52 38519[0:Rew:24914.0,38482.3] || c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,v),tc_Com_Opname,w),hAPP(c_Set_Oimage(u,v,v),v_x)),v) c_lessequals(hAPP(c_Set_Oimage(u,v,v),v_x),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,v),tc_Com_Opname,w),hAPP(c_Set_Oimage(u,v,v),v_x)),tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,v),tc_Com_Opname,w),hAPP(c_Set_Oimage(u,v,v),v_x)),v,v) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,v),tc_Com_Opname,w),hAPP(c_Set_Oimage(u,v,v),v_x)),hAPP(c_Set_Oimage(u,v,v),v_x)).
% 299.92/300.52 51536[0:Res:232.1,195.0] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_lessequals(x,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)) c_Fun_Oinj__on(z,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),y),tc_fun(w,tc_bool)),w,x1) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,w,x1),hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(y,tc_fun(v,tc_bool)))),hAPP(c_Set_Oimage(z,w,x1),x),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,w,x1),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(u,v,w),c_HOL_Ouminus__class_Ouminus(y,tc_fun(v,tc_bool))),x,tc_fun(w,tc_bool))))**.
% 299.92/300.52 52550[0:SpL:24914.0,624.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)))) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(z,x,y,w),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,x1),hAPP(c_in(u),v_x)))),hAPP(c_Hilbert__Choice_Oinv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,x1),hAPP(c_in(u),v_x))))*.
% 299.92/300.52 52546[0:SpL:158.0,624.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(x1,x2,z),x3)))))* c_Fun_Oinj__on(x1,x3,x2,z) c_Fun_Oinj__on(c_Fun_Ocomp(w,y,x,u,z),hAPP(c_Set_Oimage(x1,x2,z),x3),z,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x3,x1,x2,z),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x1,x2,z),x3),c_Fun_Ocomp(w,y,x,u,z),z,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(x3,c_Fun_Ocomp(c_Fun_Ocomp(w,y,x,u,z),x1,z,u,x2),x2,u),v))*.
% 299.92/300.52 52662[0:SpL:24914.0,623.0] || hBOOL(hAPP(hAPP(c_in(u),v_x),hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)))) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Fun_Othe__inv__into(z,x,y,w),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,x1),hAPP(c_in(u),v_x)))),hAPP(c_Fun_Othe__inv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_in(u),tc_Com_Opname,x1),hAPP(c_in(u),v_x))))*.
% 299.92/300.52 52658[0:SpL:158.0,623.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(x1,x2,z),x3)))))* c_Fun_Oinj__on(x1,x3,x2,z) c_Fun_Oinj__on(c_Fun_Ocomp(w,y,x,u,z),hAPP(c_Set_Oimage(x1,x2,z),x3),z,u) -> equal(hAPP(c_Fun_Othe__inv__into(x3,x1,x2,z),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x1,x2,z),x3),c_Fun_Ocomp(w,y,x,u,z),z,u),v)),hAPP(c_Fun_Othe__inv__into(x3,c_Fun_Ocomp(c_Fun_Ocomp(w,y,x,u,z),x1,z,u,x2),x2,u),v))*.
% 299.92/300.52 80488[0:Rew:21268.0,80220.1] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),z,x1)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 81683[0:Rew:21894.0,81415.1] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),z,x1)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 49982[0:SpR:497.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),x)),y),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)),u,y),v)),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)),u,y),v))**.
% 299.92/300.52 50846[0:SpR:622.0,118.0] || -> equal(c_Fun_Ocomp(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Fun_Ofun__upd(w,x,v_x,y,z),z,x1,y),c_Fun_Ofun__upd(c_Fun_Ocomp(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),w,z,x1,y),x,hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),y,x1))*.
% 299.92/300.52 50834[0:SpR:622.0,71.2] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,x,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v,u,y) -> equal(hAPP(c_Fun_Othe__inv__into(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,x,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),u,y),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),w,x,tc_fun(t_a,tc_bool)))),v_x)**.
% 299.92/300.52 50833[0:SpR:622.0,373.2] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) c_Fun_Oinj__on(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,x,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),v,u,y) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,x,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),u,y),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),w,x,tc_fun(t_a,tc_bool)))),v_x)**.
% 299.92/300.52 51701[0:Res:341.0,233.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(y,v,w),u)),w) c_lessequals(hAPP(c_Set_Oimage(z,w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(y,v,w),u))),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(y,u,v,w) c_Fun_Oinj__on(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(y,v,w),u)),w,v) -> equal(c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oimage(y,v,w),u)),w),c_Finite__Set_Ocard(u,v)).
% 299.92/300.52 51700[0:Res:342.0,233.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(x,v,w),u)),y),w) c_lessequals(hAPP(c_Set_Oimage(z,w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(x,v,w),u)),y)),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(x,u,v,w) c_Fun_Oinj__on(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(x,v,w),u)),y),w,v) -> equal(c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(x,v,w),u)),y),w),c_Finite__Set_Ocard(u,v)).
% 299.92/300.52 51973[0:SpL:338.0,459.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Set_Oinsert(w,u),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(w,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,y))),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(w,u),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,y))** -> equal(hAPP(c_Set_Oinsert(w,u),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),c_Set_Oinsert(w,u))),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(c_Set_Oinsert(w,u),x2),x3,y,z))**.
% 299.92/300.52 51902[0:SpL:131.0,459.0] || equal(hAPP(u,hAPP(c_Set_Ovimage(v,w,x),hAPP(c_Set_Ovimage(y,x,z),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Ovimage(c_Fun_Ocomp(y,v,x,z,w),w,z),x1,x2)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Ovimage(c_Fun_Ocomp(y,v,x,z,w),w,z),x1,x2))** -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Ovimage(c_Fun_Ocomp(y,v,x,z,w),w,z),x2,x1,x3),tc_fun(x3,x2),tc_fun(x3,x1),x1),hAPP(c_COMBB(x4,x2,tc_fun(x3,x2),x1),u)),x5,x6,x1,x3)),c_List_Ofoldl(x4,hAPP(u,x5),x6,x2,x3))**.
% 299.92/300.52 51901[0:SpL:158.0,459.0] || equal(hAPP(u,hAPP(c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(y,z,w),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oimage(c_Fun_Ocomp(v,y,w,x,z),z,x),x1,x2)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oimage(c_Fun_Ocomp(v,y,w,x,z),z,x),x1,x2))** -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oimage(c_Fun_Ocomp(v,y,w,x,z),z,x),x2,x1,x3),tc_fun(x3,x2),tc_fun(x3,x1),x1),hAPP(c_COMBB(x4,x2,tc_fun(x3,x2),x1),u)),x5,x6,x1,x3)),c_List_Ofoldl(x4,hAPP(u,x5),x6,x2,x3))**.
% 299.92/300.52 80290[0:SpL:21268.0,239.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) c_lessequals(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),y),z,x1),x2,tc_fun(x,tc_bool)) c_Fun_Oinj__on(w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),y),z,x1),x,u) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(w,x,u),y),z,x1),w,x,u),v)),x2))*.
% 299.92/300.52 79890[0:SpR:497.0,21268.0] || -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),w,x)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)))**.
% 299.92/300.52 81485[0:SpL:21894.0,239.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),y))) c_lessequals(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(w,x,u),y),c_Set_Oimage(w,x,u),z,x1),x2,tc_fun(x,tc_bool)) c_Fun_Oinj__on(w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(w,x,u),y),c_Set_Oimage(w,x,u),z,x1),x,u) -> hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(w,x,u),y),c_Set_Oimage(w,x,u),z,x1),w,x,u),v)),x2))*.
% 299.92/300.52 81084[0:SpR:497.0,21894.0] || -> equal(hAPP(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),u)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),w,x)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),u),v)))**.
% 299.92/300.52 49914[0:SpR:497.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)),u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),w),x))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)),u,tc_fun(y,tc_bool))))*.
% 299.92/300.52 50392[0:SpR:223.1,246.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),y) -> hBOOL(hAPP(hAPP(c_in(y),z),hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))))* equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,z,u,y),u,y),w),y),c_Suc(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(x,u,y),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),y)))*.
% 299.92/300.52 50802[0:SpR:622.0,21893.0] || -> equal(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,w)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))))**.
% 299.92/300.52 50796[0:SpR:622.0,21267.0] || -> equal(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),tc_Com_Opname,w)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))))**.
% 299.92/300.52 51941[0:SpL:536.1,459.0] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y))),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x2),x3,y,z))**.
% 299.92/300.52 51940[0:SpL:535.1,459.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y))),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),x,y))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w))),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x2),x3,y,z))**.
% 299.92/300.52 52577[0:Rew:465.1,52534.4,465.1,52534.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1)))) c_Fun_Oinj__on(c_Fun_Ofun__upd(y,x2,x3,z,x),x1,z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> hBOOL(hAPP(hAPP(c_in(z),x2),x1)) equal(hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Fun_Ofun__upd(y,x2,x3,z,x),z,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Fun_Ocomp(w,c_Fun_Ofun__upd(y,x2,x3,z,x),x,u,z),z,u),v))*.
% 299.92/300.52 52690[0:Rew:465.1,52646.4,465.1,52646.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1)))) c_Fun_Oinj__on(c_Fun_Ofun__upd(y,x2,x3,z,x),x1,z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> hBOOL(hAPP(hAPP(c_in(z),x2),x1)) equal(hAPP(c_Fun_Othe__inv__into(x1,c_Fun_Ofun__upd(y,x2,x3,z,x),z,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,u),v)),hAPP(c_Fun_Othe__inv__into(x1,c_Fun_Ocomp(w,c_Fun_Ofun__upd(y,x2,x3,z,x),x,u,z),z,u),v))*.
% 299.92/300.52 49838[0:Rew:49662.2,49561.1] || c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),y,z,x1) -> hBOOL(hAPP(hAPP(c_in(x1),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),v),x2),w,x,tc_fun(u,tc_bool))),hAPP(c_Set_Oimage(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),z,x1),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,w,x,tc_fun(u,tc_bool)),z),y))))* c_Fun_Oinj__on(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,w,x,tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(x2,w,x,tc_fun(u,tc_bool)),z),y),z,x1).
% 299.92/300.52 50835[0:SpR:622.0,475.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(c_Set_Oinsert(hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),x,w,tc_fun(t_a,tc_bool))),y),hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),u,y),v)),hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(x,w,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),u,y),v))**.
% 299.92/300.52 50808[0:SpR:622.0,24914.0] || -> equal(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),tc_Com_Opname,w),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))))),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))))**.
% 299.92/300.52 51971[0:SpL:317.0,459.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oinsert(x,v),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(hAPP(u,x),w),c_Set_Oimage(u,v,w),y,z))),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(hAPP(u,x),w),c_Set_Oimage(u,v,w),y,z))** -> equal(hAPP(c_Set_Oinsert(hAPP(u,x),w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oimage(u,v,w),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),c_Set_Oinsert(hAPP(u,x),w))),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(c_Set_Oinsert(hAPP(u,x),w),x3),x4,z,x1))**.
% 299.92/300.52 51885[0:SpL:104.0,459.0] || equal(hAPP(u,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),x,y),tc_fun(w,tc_bool)),tc_fun(w,tc_bool))),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),x,y))** -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(v,tc_fun(w,tc_bool))),y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),u)),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(u,x2),x3,y,z))**.
% 299.92/300.52 50431[0:SpR:223.1,244.2] || hBOOL(hAPP(hAPP(c_in(u),v),w)) -> hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(z,u,x),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool)))))* equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(z,u,x),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),x),c_HOL_Ozero__class_Ozero(tc_nat)) equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(z,v,y,u,x),u,x),w),x),c_Suc(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(z,u,x),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),x)))*.
% 299.92/300.52 50766[0:SpR:622.0,410.0] || -> equal(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oinsert(v_x,u),v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,x,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),u,tc_fun(y,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(y,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),w,x,tc_fun(t_a,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,x,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),u,tc_fun(y,tc_bool))))*.
% 299.92/300.52 51763[0:MRR:51711.4,9371.1] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool)),v) c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),w) c_lessequals(hAPP(c_Set_Oimage(y,w,v),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool))),c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool)),tc_fun(v,tc_bool))* c_Fun_Oinj__on(y,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),w,v) -> equal(c_Finite__Set_Ocard(c_HOL_Ouminus__class_Ouminus(x,tc_fun(v,tc_bool)),v),c_Finite__Set_Ocard(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(u,v,w),x),tc_fun(w,tc_bool)),w)).
% 299.92/300.52 51883[0:SpL:537.1,459.0] class_Lattices_Olattice(u) || equal(hAPP(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y,z)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y,z))** -> equal(hAPP(v,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),v)),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(v,x3),x4,z,x1))**.
% 299.92/300.52 51882[0:SpL:534.1,459.0] class_Lattices_Oupper__semilattice(u) || equal(hAPP(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),x),c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y,z)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(v,hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),y,z))** -> equal(hAPP(v,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x)),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),v)),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(v,x3),x4,z,x1))**.
% 299.92/300.52 52003[0:Obv:51918.2] || c_lessequals(c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(u,v,w,x),x,w),c_Set_Oimage(v,w,x),y,z),u,tc_fun(w,tc_bool)) c_Fun_Oinj__on(v,u,w,x) -> equal(hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(u,v,w,x),x,w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oimage(v,w,x),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),c_Set_Oimage(c_Hilbert__Choice_Oinv__into(u,v,w,x),x,w))),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(c_Set_Oimage(c_Hilbert__Choice_Oinv__into(u,v,w,x),x,w),x3),x4,z,x1))**.
% 299.92/300.52 52723[0:Res:526.1,592.0] || hBOOL(hAPP(v_Procs,u)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,u)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u))),hAPP(v_Q,u)),t_a)*.
% 299.92/300.52 80093[0:SpL:21268.0,624.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1)))) c_Fun_Oinj__on(y,x1,z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x1,y,z,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_in(u),hAPP(c_in(u),v),x2,x3))),hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Fun_Ocomp(w,y,x,u,z),z,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_in(u),hAPP(c_in(u),v),x2,x3)))*.
% 299.92/300.52 80092[0:SpL:21268.0,623.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1)))) c_Fun_Oinj__on(y,x1,z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> equal(hAPP(c_Fun_Othe__inv__into(x1,y,z,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_in(u),hAPP(c_in(u),v),x2,x3))),hAPP(c_Fun_Othe__inv__into(x1,c_Fun_Ocomp(w,y,x,u,z),z,u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_in(u),hAPP(c_in(u),v),x2,x3)))*.
% 299.92/300.52 81288[0:SpL:21894.0,624.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1)))) c_Fun_Oinj__on(y,x1,z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x1,y,z,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(c_in(u),v),c_in(u),x2,x3))),hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Fun_Ocomp(w,y,x,u,z),z,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(c_in(u),v),c_in(u),x2,x3)))*.
% 299.92/300.52 81287[0:SpL:21894.0,623.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1)))) c_Fun_Oinj__on(y,x1,z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> equal(hAPP(c_Fun_Othe__inv__into(x1,y,z,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(c_in(u),v),c_in(u),x2,x3))),hAPP(c_Fun_Othe__inv__into(x1,c_Fun_Ocomp(w,y,x,u,z),z,u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(c_in(u),v),c_in(u),x2,x3)))*.
% 299.92/300.52 50046[0:SpL:497.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),x,u),y)))* c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u)* -> hBOOL(hAPP(hAPP(c_in(x),v_x),y)).
% 299.92/300.52 50502[0:SpL:223.1,224.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) hBOOL(hAPP(hAPP(c_in(x),hAPP(c_Set_Oimage(c_Fun_Ofun__upd(y,v,z,u,x1),u,x1),w)),hAPP(c_Set_Oimage(c_Set_Oinsert(z,x1),x2,x),c_HOL_Ominus__class_Ominus(x3,hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(y,u,x1),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),x2),c_Orderings_Obot__class_Obot(tc_fun(x2,tc_bool))),tc_fun(x2,tc_bool)))))* c_Fun_Oinj__on(c_Set_Oinsert(z,x1),hAPP(c_Set_Oinsert(hAPP(c_Set_Oimage(y,u,x1),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),x2),x3),x2,x) -> .
% 299.92/300.52 51541[0:Res:82.0,195.0] || c_lessequals(u,hAPP(c_Set_Oimage(v,w,x),c_HOL_Ominus__class_Ominus(y,z,tc_fun(w,tc_bool))),tc_fun(x,tc_bool)) c_Fun_Oinj__on(x1,hAPP(c_Set_Oimage(v,w,x),c_HOL_Ominus__class_Ominus(y,z,tc_fun(w,tc_bool))),x,x2) -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(x1,x,x2),c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(v,w,x),y),hAPP(c_Set_Oimage(v,w,x),z),tc_fun(x,tc_bool))),hAPP(c_Set_Oimage(x1,x,x2),u),tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(x1,x,x2),c_HOL_Ominus__class_Ominus(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(v,w,x),y),hAPP(c_Set_Oimage(v,w,x),z),tc_fun(x,tc_bool)),u,tc_fun(x,tc_bool))))**.
% 299.92/300.52 51703[0:Res:7539.0,233.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(w,x),hAPP(c_Set_Oinsert(y,x),hAPP(c_Set_Oimage(z,v,x),u))),x) c_lessequals(hAPP(c_Set_Oimage(x1,x,v),hAPP(c_Set_Oinsert(w,x),hAPP(c_Set_Oinsert(y,x),hAPP(c_Set_Oimage(z,v,x),u)))),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(z,u,v,x) c_Fun_Oinj__on(x1,hAPP(c_Set_Oinsert(w,x),hAPP(c_Set_Oinsert(y,x),hAPP(c_Set_Oimage(z,v,x),u))),x,v) -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,x),hAPP(c_Set_Oinsert(y,x),hAPP(c_Set_Oimage(z,v,x),u))),x),c_Finite__Set_Ocard(u,v)).
% 299.92/300.52 51886[0:SpL:339.0,459.0] || equal(hAPP(u,hAPP(c_Set_Oinsert(v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),x)),y,z)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),x)),y,z))** -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oinsert(v,w),x)),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),u)),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(u,x3),x4,z,x1))**.
% 299.92/300.52 52216[0:SpL:55.1,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),y),z,tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(u)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x)),z)) c_Hoare__Mirabelle_Ohoare__derivs(c_HOL_Ominus__class_Ominus(y,z,tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 79859[0:SpR:622.0,21268.0] || -> equal(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),w,x)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))))**.
% 299.92/300.52 81053[0:SpR:622.0,21894.0] || -> equal(hAPP(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(u,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),w,x)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,tc_fun(t_a,tc_bool))))**.
% 299.92/300.52 82091[0:SSi:81977.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Set_Oimage(x,v,w),y,z,x1),u),w) c_lessequals(hAPP(c_Set_Oimage(x2,w,v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Set_Oimage(x,v,w),y,z,x1),u)),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(x,u,v,w) c_Fun_Oinj__on(x2,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Set_Oimage(x,v,w),y,z,x1),u),w,v) -> equal(c_Finite__Set_Ocard(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_Set_Oimage(x,v,w),y,z,x1),u),w),c_Finite__Set_Ocard(u,v)).
% 299.92/300.52 49984[0:SpR:497.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),x),y))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),y)),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),x)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),y)),u,tc_fun(w,tc_bool)))**.
% 299.92/300.52 52526[0:SpL:317.0,624.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oinsert(hAPP(y,z),x),hAPP(c_Set_Oimage(y,x1,x),x2)))))* c_Fun_Oinj__on(y,hAPP(c_Set_Oinsert(z,x1),x2),x1,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,x1,x),hAPP(c_Set_Oinsert(z,x1),x2)),x,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oinsert(z,x1),x2),y,x1,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(y,x1,x),hAPP(c_Set_Oinsert(z,x1),x2)),w,x,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oinsert(z,x1),x2),c_Fun_Ocomp(w,y,x,u,x1),x1,u),v))*.
% 299.92/300.52 52638[0:SpL:317.0,623.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oinsert(hAPP(y,z),x),hAPP(c_Set_Oimage(y,x1,x),x2)))))* c_Fun_Oinj__on(y,hAPP(c_Set_Oinsert(z,x1),x2),x1,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,x1,x),hAPP(c_Set_Oinsert(z,x1),x2)),x,u) -> equal(hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oinsert(z,x1),x2),y,x1,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(y,x1,x),hAPP(c_Set_Oinsert(z,x1),x2)),w,x,u),v)),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oinsert(z,x1),x2),c_Fun_Ocomp(w,y,x,u,x1),x1,u),v))*.
% 299.92/300.52 52724[0:Res:8375.1,592.0] || equal(c_Orderings_Otop__class_Otop(tc_fun(tc_Com_Opname,tc_bool)),v_Procs) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,v)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,v))),hAPP(v_Q,v)),t_a)*.
% 299.92/300.52 50870[0:SpL:622.0,284.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,tc_fun(t_a,tc_bool)))),hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),x,u),y)))* c_Fun_Oinj__on(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),x,u)* -> hBOOL(hAPP(hAPP(c_in(x),v_x),y)).
% 299.92/300.52 51945[0:SpL:338.0,459.0] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(u,v),x,y))),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_Set_Oinsert(u,v),x,y))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oinsert(u,v),y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w))),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x2),x3,y,z))**.
% 299.92/300.52 51932[0:SpL:181.1,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Ovimage(c_COMBK(u,v,w),w,v),x,y,z),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool))) -> hBOOL(hAPP(hAPP(c_in(v),u),hAPP(x,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Ovimage(c_COMBK(u,v,w),w,v),x,y,z))))* equal(hAPP(c_Set_Ovimage(c_COMBK(u,v,w),w,v),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(x,z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),c_Set_Ovimage(c_COMBK(u,v,w),w,v))),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(c_Set_Ovimage(c_COMBK(u,v,w),w,v),x3),x4,z,x1))**.
% 299.92/300.52 52222[0:SpL:21893.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),v_x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) -> c_Hoare__Mirabelle_Ohoare__derivs(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),v_x),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 52221[0:SpL:21267.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),v_x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) -> c_Hoare__Mirabelle_Ohoare__derivs(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),v_x),tc_Com_Opname,y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 52561[0:Res:168.0,624.0] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(y,hAPP(c_Set_Oimage(u,w,x),v),x,tc_Hoare__Mirabelle_Otriple(t_a)) -> c_Hoare__Mirabelle_Ohoare__valids(z,hAPP(c_Set_Oimage(y,x,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oimage(u,w,x),v)),t_a) equal(hAPP(c_Hilbert__Choice_Oinv__into(v,u,w,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,w,x),v),y,x,tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(z,hAPP(c_Set_Oimage(y,x,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oimage(u,w,x),v))))),hAPP(c_Hilbert__Choice_Oinv__into(v,c_Fun_Ocomp(y,u,x,tc_Hoare__Mirabelle_Otriple(t_a),w),w,tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(z,hAPP(c_Set_Oimage(y,x,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oimage(u,w,x),v)))))**.
% 299.92/300.52 52545[0:SpL:465.1,624.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1)))) c_Fun_Oinj__on(y,x1,z,x) c_Fun_Oinj__on(c_Fun_Ofun__upd(w,x2,x3,x,u),hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> hBOOL(hAPP(hAPP(c_in(x),x2),hAPP(c_Set_Oimage(y,z,x),x1))) equal(hAPP(c_Hilbert__Choice_Oinv__into(x1,y,z,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(y,z,x),x1),c_Fun_Ofun__upd(w,x2,x3,x,u),x,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(x1,c_Fun_Ocomp(c_Fun_Ofun__upd(w,x2,x3,x,u),y,x,u,z),z,u),v))*.
% 299.92/300.52 52673[0:Res:168.0,623.0] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(y,hAPP(c_Set_Oimage(u,w,x),v),x,tc_Hoare__Mirabelle_Otriple(t_a)) -> c_Hoare__Mirabelle_Ohoare__valids(z,hAPP(c_Set_Oimage(y,x,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oimage(u,w,x),v)),t_a) equal(hAPP(c_Fun_Othe__inv__into(v,u,w,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,w,x),v),y,x,tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(z,hAPP(c_Set_Oimage(y,x,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oimage(u,w,x),v))))),hAPP(c_Fun_Othe__inv__into(v,c_Fun_Ocomp(y,u,x,tc_Hoare__Mirabelle_Otriple(t_a),w),w,tc_Hoare__Mirabelle_Otriple(t_a)),v_sko__Hoare__Mirabelle__Xhoare__valids__def__3(z,hAPP(c_Set_Oimage(y,x,tc_Hoare__Mirabelle_Otriple(t_a)),hAPP(c_Set_Oimage(u,w,x),v)))))**.
% 299.92/300.52 52657[0:SpL:465.1,623.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1)))) c_Fun_Oinj__on(y,x1,z,x) c_Fun_Oinj__on(c_Fun_Ofun__upd(w,x2,x3,x,u),hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> hBOOL(hAPP(hAPP(c_in(x),x2),hAPP(c_Set_Oimage(y,z,x),x1))) equal(hAPP(c_Fun_Othe__inv__into(x1,y,z,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(y,z,x),x1),c_Fun_Ofun__upd(w,x2,x3,x,u),x,u),v)),hAPP(c_Fun_Othe__inv__into(x1,c_Fun_Ocomp(c_Fun_Ofun__upd(w,x2,x3,x,u),y,x,u,z),z,u),v))*.
% 299.92/300.52 50837[0:SpR:622.0,486.1] || hBOOL(hAPP(hAPP(c_in(u),v_x),v)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),y,x,tc_fun(t_a,tc_bool)))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(y,x,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),u,tc_fun(w,tc_bool))),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(y,x,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),u,tc_fun(w,tc_bool)))**.
% 299.92/300.52 51931[0:SpL:188.1,459.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(w,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Ovimage(c_COMBK(v,u,x),x,u),w,y,z))))* equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Ovimage(c_COMBK(v,u,x),x,u),w,y,z),c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool))) -> equal(hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(w,z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),c_Set_Ovimage(c_COMBK(v,u,x),x,u))),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(c_Set_Ovimage(c_COMBK(v,u,x),x,u),x3),x4,z,x1))**.
% 299.92/300.52 51910[0:SpL:445.1,459.0] || equal(hAPP(u,hAPP(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Fun_Ofun__upd(u,w,x,y,z),v,x1,x2))),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Fun_Ofun__upd(u,w,x,y,z),v,x1,x2))** -> equal(hAPP(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Fun_Ofun__upd(u,w,x,y,z),v,x1,x2)),w) equal(hAPP(c_Fun_Ofun__upd(u,w,x,y,z),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(v,x2,x1,x3),tc_fun(x3,x2),tc_fun(x3,x1),x1),hAPP(c_COMBB(x4,x2,tc_fun(x3,x2),x1),c_Fun_Ofun__upd(u,w,x,y,z))),x5,x6,x1,x3)),c_List_Ofoldl(x4,hAPP(c_Fun_Ofun__upd(u,w,x,y,z),x5),x6,x2,x3))**.
% 299.92/300.52 52214[0:SpL:24914.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),v_x),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) -> c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),v_x)),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 78672[4:Res:78665.1,592.0] || equal(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs),v_x) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,u)),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,u))),hAPP(v_Q,u)),t_a)*.
% 299.92/300.52 80489[0:Rew:21268.0,80033.3] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,w),hAPP(c_Set_Oimage(v,w,w),x),u,y),w) c_lessequals(hAPP(c_Set_Oimage(v,w,w),x),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,w),hAPP(c_Set_Oimage(v,w,w),x),u,y),tc_fun(w,tc_bool))* c_Fun_Oinj__on(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,w),hAPP(c_Set_Oimage(v,w,w),x),u,y),w,w) -> equal(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,w),hAPP(c_Set_Oimage(v,w,w),x),u,y),hAPP(c_Set_Oimage(v,w,w),x)).
% 299.92/300.52 81684[0:Rew:21894.0,81228.3] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,w),x),c_Set_Oimage(v,w,w),u,y),w) c_lessequals(hAPP(c_Set_Oimage(v,w,w),x),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,w),x),c_Set_Oimage(v,w,w),u,y),tc_fun(w,tc_bool))* c_Fun_Oinj__on(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,w),x),c_Set_Oimage(v,w,w),u,y),w,w) -> equal(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,w),x),c_Set_Oimage(v,w,w),u,y),hAPP(c_Set_Oimage(v,w,w),x)).
% 299.92/300.52 51659[0:SSi:51611.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_fun(u,tc_bool)),v),w))* c_Finite__Set_Ofinite(w,tc_fun(u,tc_bool)) c_lessequals(x,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y,w,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),tc_fun(u,tc_bool))* c_Fun_Oinj__on(z,c_Finite__Set_Ofold(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),y,w,tc_fun(u,tc_bool),tc_fun(u,tc_bool)),u,x1)* -> equal(c_HOL_Ominus__class_Ominus(hAPP(c_Set_Oimage(z,u,x1),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y)),hAPP(c_Set_Oimage(z,u,x1),x),tc_fun(x1,tc_bool)),hAPP(c_Set_Oimage(z,u,x1),c_HOL_Ominus__class_Ominus(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y),x,tc_fun(u,tc_bool))))**.
% 299.92/300.52 51739[0:Res:49.2,233.2] class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_lessequals(hAPP(c_Set_Oimage(v,w,u),x),c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),tc_fun(u,tc_bool)) c_Finite__Set_Ofinite(x,w) c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(v,w,u),x),tc_fun(u,tc_bool)),u) c_lessequals(hAPP(c_Set_Oimage(y,u,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(v,w,u),x),tc_fun(u,tc_bool))),x,tc_fun(w,tc_bool))* c_Fun_Oinj__on(v,x,w,u) c_Fun_Oinj__on(y,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(v,w,u),x),tc_fun(u,tc_bool)),u,w) -> equal(c_Finite__Set_Ocard(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(v,w,u),x),tc_fun(u,tc_bool)),u),c_Finite__Set_Ocard(x,w)).
% 299.92/300.52 51710[0:Res:19747.0,233.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oimage(x,v,y),u),tc_fun(y,tc_bool)),tc_fun(y,tc_bool)),y) c_lessequals(hAPP(c_Set_Oimage(z,y,v),c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oimage(x,v,y),u),tc_fun(y,tc_bool)),tc_fun(y,tc_bool))),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(x,u,v,y) c_Fun_Oinj__on(z,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oimage(x,v,y),u),tc_fun(y,tc_bool)),tc_fun(y,tc_bool)),y,v) -> equal(c_Finite__Set_Ocard(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oimage(x,v,y),u),tc_fun(y,tc_bool)),tc_fun(y,tc_bool)),y),c_Finite__Set_Ocard(u,v)).
% 299.92/300.52 51705[0:Res:1145.0,233.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_Set_Oimage(w,v,x),u),y,z),tc_Com_Opname,tc_fun(x,tc_bool)),x) c_lessequals(hAPP(c_Set_Oimage(x1,x,v),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_Set_Oimage(w,v,x),u),y,z),tc_Com_Opname,tc_fun(x,tc_bool))),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(w,u,v,x) c_Fun_Oinj__on(x1,c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_Set_Oimage(w,v,x),u),y,z),tc_Com_Opname,tc_fun(x,tc_bool)),x,v) -> equal(c_Finite__Set_Ocard(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(v_Procs,c_COMBK(hAPP(c_Set_Oimage(w,v,x),u),y,z),tc_Com_Opname,tc_fun(x,tc_bool)),x),c_Finite__Set_Ocard(u,v)).
% 299.92/300.52 51768[0:Rew:22010.1,51697.6] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v) c_Finite__Set_Ofinite(y,w) c_lessequals(hAPP(c_Set_Oimage(u,v,w),v_x),y,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Oimage(z,w,v),y),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(u,v,w),v_x),c_Set_Oimage(u,v,w),tc_Com_Opname,x),v,w)* c_Fun_Oinj__on(z,y,w,v) -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),v_x),w),c_Finite__Set_Ocard(y,w)).
% 299.92/300.52 51769[0:Rew:21384.1,51696.6] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v) c_Finite__Set_Ofinite(y,w) c_lessequals(hAPP(c_Set_Oimage(u,v,w),v_x),y,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Oimage(z,w,v),y),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(u,v,w),v_x),tc_Com_Opname,x),v,w)* c_Fun_Oinj__on(z,y,w,v) -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),v_x),w),c_Finite__Set_Ocard(y,w)).
% 299.92/300.52 52220[0:SpL:223.1,461.0] || hBOOL(hAPP(hAPP(c_in(u),v),w)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(x,v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(y),z),hAPP(c_Com_Ocom_OBODY,x1)),x2),u,tc_Hoare__Mirabelle_Otriple(y)),u,tc_Hoare__Mirabelle_Otriple(y)),w),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(y),z),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,x1))),x2),tc_Hoare__Mirabelle_Otriple(y)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(y),tc_bool))),y)* -> c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(x,u,tc_Hoare__Mirabelle_Otriple(y)),c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oinsert(v,u),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))),tc_fun(u,tc_bool))),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(y),z),hAPP(c_Com_Ocom_OBODY,x1)),x2),tc_Hoare__Mirabelle_Otriple(y)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(y),tc_bool))),y)*.
% 299.92/300.52 51955[0:SpL:329.1,459.0] || c_lessequals(u,hAPP(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v,x,y)),tc_fun(w,tc_bool))* equal(hAPP(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v,x,y)),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),v,x,y)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(v,y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u))),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),u),x2),x3,y,z))**.
% 299.92/300.52 51909[0:SpL:393.1,459.0] || equal(c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oimage(c_COMBK(u,v,w),w,v),x,y,z),hAPP(c_Set_Oinsert(u,v),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)))) -> equal(hAPP(x,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oimage(c_COMBK(u,v,w),w,v),x,y,z)),c_Orderings_Obot__class_Obot(tc_fun(w,tc_bool)))** equal(hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(x,z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),c_Set_Oimage(c_COMBK(u,v,w),w,v))),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(c_Set_Oimage(c_COMBK(u,v,w),w,v),x3),x4,z,x1))**.
% 299.92/300.52 52537[0:SpL:158.0,624.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(x1,x2,z),x3)))))* c_Fun_Oinj__on(c_Fun_Ocomp(y,x1,z,x,x2),x3,x2,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(c_Fun_Ocomp(y,x1,z,x,x2),x2,x),x3),x,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(x3,c_Fun_Ocomp(y,x1,z,x,x2),x2,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(c_Fun_Ocomp(y,x1,z,x,x2),x2,x),x3),w,x,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(x3,c_Fun_Ocomp(w,c_Fun_Ocomp(y,x1,z,x,x2),x,u,x2),x2,u),v))*.
% 299.92/300.52 52529[0:SpL:158.0,624.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(c_Fun_Ocomp(y,z,x1,x,x2),x2,x),x3))))* c_Fun_Oinj__on(y,hAPP(c_Set_Oimage(z,x2,x1),x3),x1,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,x1,x),hAPP(c_Set_Oimage(z,x2,x1),x3)),x,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(z,x2,x1),x3),y,x1,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(y,x1,x),hAPP(c_Set_Oimage(z,x2,x1),x3)),w,x,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(z,x2,x1),x3),c_Fun_Ocomp(w,y,x,u,x1),x1,u),v))*.
% 299.92/300.52 52582[0:Rew:205.1,52530.4,205.1,52530.3] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(z,v,x),x1))) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Set_Oimage(u,v,w),x1),w,v) c_Fun_Oinj__on(z,x1,v,x) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,v,w),x1),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),hAPP(c_Hilbert__Choice_Oinv__into(x1,z,v,x),y)),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,v,w),x1),c_Fun_Ocomp(z,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),v,x,w),w,x),y))*.
% 299.92/300.52 52649[0:SpL:158.0,623.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(x1,x2,z),x3)))))* c_Fun_Oinj__on(c_Fun_Ocomp(y,x1,z,x,x2),x3,x2,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(c_Fun_Ocomp(y,x1,z,x,x2),x2,x),x3),x,u) -> equal(hAPP(c_Fun_Othe__inv__into(x3,c_Fun_Ocomp(y,x1,z,x,x2),x2,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(c_Fun_Ocomp(y,x1,z,x,x2),x2,x),x3),w,x,u),v)),hAPP(c_Fun_Othe__inv__into(x3,c_Fun_Ocomp(w,c_Fun_Ocomp(y,x1,z,x,x2),x,u,x2),x2,u),v))*.
% 299.92/300.52 52641[0:SpL:158.0,623.0] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(c_Fun_Ocomp(y,z,x1,x,x2),x2,x),x3))))* c_Fun_Oinj__on(y,hAPP(c_Set_Oimage(z,x2,x1),x3),x1,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,x1,x),hAPP(c_Set_Oimage(z,x2,x1),x3)),x,u) -> equal(hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(z,x2,x1),x3),y,x1,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(y,x1,x),hAPP(c_Set_Oimage(z,x2,x1),x3)),w,x,u),v)),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(z,x2,x1),x3),c_Fun_Ocomp(w,y,x,u,x1),x1,u),v))*.
% 299.92/300.52 52695[0:Rew:205.1,52642.4,205.1,52642.3] || c_Fun_Oinj__on(u,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),v,w) hBOOL(hAPP(hAPP(c_in(x),y),hAPP(c_Set_Oimage(z,v,x),x1))) c_Fun_Oinj__on(c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),hAPP(c_Set_Oimage(u,v,w),x1),w,v) c_Fun_Oinj__on(z,x1,v,x) -> equal(hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,v,w),x1),c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),w,v),hAPP(c_Fun_Othe__inv__into(x1,z,v,x),y)),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,v,w),x1),c_Fun_Ocomp(z,c_Hilbert__Choice_Oinv__into(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),u,v,w),v,x,w),w,x),y))*.
% 299.92/300.52 80304[0:SpL:21268.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) -> c_Hoare__Mirabelle_Ohoare__derivs(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),y),z,x1),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 81499[0:SpL:21894.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u) -> c_Hoare__Mirabelle_Ohoare__derivs(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),y),c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),z,x1),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 50047[0:SpL:497.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_in(t_a),v_x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),v),w))),hAPP(c_Set_Oimage(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v_x,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(t_a,tc_bool)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),v)),hAPP(c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),w)),hAPP(c_Set_Oinsert(v_x,x),y),x,u) -> .
% 299.92/300.52 51771[0:Rew:34029.1,51694.6] || c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v) c_Finite__Set_Ofinite(y,w) c_lessequals(hAPP(c_Set_Oimage(u,v,w),v_x),y,tc_fun(w,tc_bool)) c_lessequals(hAPP(c_Set_Oimage(z,w,v),y),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),tc_fun(v,tc_bool))* c_Fun_Oinj__on(u,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(u,v,w),tc_Com_Opname,x),hAPP(c_Set_Oimage(u,v,w),v_x)),v,w)* c_Fun_Oinj__on(z,y,w,v) -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(u,v,w),v_x),w),c_Finite__Set_Ocard(y,w)).
% 299.92/300.52 51944[0:SpL:542.0,459.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x)),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w,x)) -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,w,y),tc_fun(y,x),tc_fun(y,w),w),hAPP(c_COMBB(z,x,tc_fun(y,x),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v))),x1,x2,w,y)),c_List_Ofoldl(z,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x1),x2,x,y))**.
% 299.92/300.52 52738[0:Res:48989.1,592.0] || -> hBOOL(hAPP(u,v_x)) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Xball__Un__1__3(v_Procs,u,tc_Com_Opname))),t_a)*.
% 299.92/300.52 52743[0:MRR:52727.2,3591.0] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname)))),hAPP(v_Q,c_Finite__Set_Olinorder__class_OMin(v_Procs,tc_Com_Opname))),t_a).
% 299.92/300.52 52744[0:MRR:52726.2,3591.0] class_Orderings_Olinorder(tc_Com_Opname) || c_Finite__Set_Ofinite(v_Procs,tc_Com_Opname) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname)))),hAPP(v_Q,c_Finite__Set_Olinorder__class_OMax(v_Procs,tc_Com_Opname))),t_a).
% 299.92/300.52 50871[0:SpL:622.0,224.0] || hBOOL(hAPP(hAPP(c_in(u),hAPP(hAPP(c_in(t_a),v_x),c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),w,v,tc_fun(t_a,tc_bool)))),hAPP(c_Set_Oimage(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),x,u),c_HOL_Ominus__class_Ominus(y,hAPP(c_Set_Oinsert(v_x,x),c_Orderings_Obot__class_Obot(tc_fun(x,tc_bool))),tc_fun(x,tc_bool)))))* c_Fun_Oinj__on(c_Complete__Lattice_Ocomplete__lattice__class_OSUPR(hAPP(c_Set_Oimage(w,v,tc_fun(t_a,tc_bool)),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool))),c_COMBC(c_in(t_a),t_a,tc_fun(t_a,tc_bool),tc_bool),tc_fun(t_a,tc_bool),tc_fun(t_a,tc_bool)),hAPP(c_Set_Oinsert(v_x,x),y),x,u) -> .
% 299.92/300.52 51770[0:SSi:51736.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,y,z,x1),hAPP(c_Set_Oimage(x2,v,w),u)),w) c_lessequals(hAPP(c_Set_Oimage(x3,w,v),hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,y,z,x1),hAPP(c_Set_Oimage(x2,v,w),u))),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(x2,u,v,w) c_Fun_Oinj__on(x3,hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,y,z,x1),hAPP(c_Set_Oimage(x2,v,w),u)),w,v) -> equal(c_Finite__Set_Ocard(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x,y,z,x1),hAPP(c_Set_Oimage(x2,v,w),u)),w),c_Finite__Set_Ocard(u,v)).
% 299.92/300.52 52739[0:Res:49314.1,592.0] || hBOOL(hAPP(u,v_x)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Xbex__Un__1__2(v_Procs,u,tc_Com_Opname))),t_a)*.
% 299.92/300.52 77383[0:Res:2399.2,233.2] class_Orderings_Olinorder(tc_fun(u,tc_bool)) class_OrderedGroup_Olordered__ab__group__add(tc_fun(u,tc_bool)) || c_Finite__Set_Ofinite(v,w) c_Finite__Set_Ofinite(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(x,w,u),v),tc_fun(u,tc_bool)),u) c_lessequals(hAPP(c_Set_Oimage(y,u,w),c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(x,w,u),v),tc_fun(u,tc_bool))),v,tc_fun(w,tc_bool))* c_Fun_Oinj__on(x,v,w,u) c_Fun_Oinj__on(y,c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(x,w,u),v),tc_fun(u,tc_bool)),u,w) -> c_lessequals(c_HOL_Ozero__class_Ozero(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(x,w,u),v),tc_fun(u,tc_bool)) equal(c_Finite__Set_Ocard(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(x,w,u),v),tc_fun(u,tc_bool)),u),c_Finite__Set_Ocard(v,w)).
% 299.92/300.52 51879[0:SpL:465.1,459.0] || equal(hAPP(u,hAPP(c_Set_Oimage(v,w,x),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oimage(c_Fun_Ofun__upd(v,y,z,w,x),w,x),x1,x2))),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oimage(c_Fun_Ofun__upd(v,y,z,w,x),w,x),x1,x2))** -> hBOOL(hAPP(hAPP(c_in(w),y),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,c_Set_Oimage(c_Fun_Ofun__upd(v,y,z,w,x),w,x),x1,x2)))* equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oimage(c_Fun_Ofun__upd(v,y,z,w,x),w,x),x2,x1,x3),tc_fun(x3,x2),tc_fun(x3,x1),x1),hAPP(c_COMBB(x4,x2,tc_fun(x3,x2),x1),u)),x5,x6,x1,x3)),c_List_Ofoldl(x4,hAPP(u,x5),x6,x2,x3))**.
% 299.92/300.52 51968[0:SpL:131.0,459.0] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(c_Set_Ovimage(x,w,y),hAPP(z,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z,x1,x2)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),z,x1,x2))** -> equal(hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(z,x2,x1,x3),tc_fun(x3,x2),tc_fun(x3,x1),x1),hAPP(c_COMBB(x4,x2,tc_fun(x3,x2),x1),c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y))),x5,x6,x1,x3)),c_List_Ofoldl(x4,hAPP(c_Set_Ovimage(c_Fun_Ocomp(x,u,w,y,v),v,y),x5),x6,x2,x3))**.
% 299.92/300.52 51967[0:SpL:158.0,459.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(c_Set_Oimage(x,y,v),hAPP(z,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z,x1,x2)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),z,x1,x2))** -> equal(hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(z,x2,x1,x3),tc_fun(x3,x2),tc_fun(x3,x1),x1),hAPP(c_COMBB(x4,x2,tc_fun(x3,x2),x1),c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w))),x5,x6,x1,x3)),c_List_Ofoldl(x4,hAPP(c_Set_Oimage(c_Fun_Ocomp(u,x,v,w,y),y,w),x5),x6,x2,x3))**.
% 299.92/300.52 51887[0:SpL:533.0,459.0] || equal(hAPP(u,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y,z)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(u,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),y,z))** -> equal(hAPP(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x)),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),u)),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(u,x3),x4,z,x1))**.
% 299.92/300.52 52000[0:Rew:104.0,51948.1,104.0,51948.1] || equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(v,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),v,x,y)),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))),v,x,y))** -> equal(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(v,y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),c_HOL_Ouminus__class_Ouminus(u,tc_fun(w,tc_bool))))),x2,x3,x,z),tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),c_List_Ofoldl(x1,c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,x2,tc_fun(w,tc_bool)),tc_fun(w,tc_bool)),x3,y,z))**.
% 299.92/300.52 52930[0:SpL:337.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v))* c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),hAPP(x,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(y,u)),tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.92/300.52 71125[0:Res:7568.0,233.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(y,v,x),u)),z)),x) c_lessequals(hAPP(c_Set_Oimage(x1,x,v),hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(y,v,x),u)),z))),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(y,u,v,x) c_Fun_Oinj__on(x1,hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(y,v,x),u)),z)),x,v) -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),hAPP(c_Set_Oimage(y,v,x),u)),z)),x),c_Finite__Set_Ocard(u,v)).
% 299.92/300.52 71335[0:Res:7538.0,233.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(y,w),hAPP(c_Set_Oimage(z,v,w),u))),w) c_lessequals(hAPP(c_Set_Oimage(x1,w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(y,w),hAPP(c_Set_Oimage(z,v,w),u)))),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(z,u,v,w) c_Fun_Oinj__on(x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(y,w),hAPP(c_Set_Oimage(z,v,w),u))),w,v) -> equal(c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(c_Set_Oinsert(y,w),hAPP(c_Set_Oimage(z,v,w),u))),w),c_Finite__Set_Ocard(u,v)).
% 299.92/300.52 72150[0:Res:7830.0,233.2] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(z,v,x),u))),x) c_lessequals(hAPP(c_Set_Oimage(x1,x,v),hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(z,v,x),u)))),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(z,u,v,x) c_Fun_Oinj__on(x1,hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(z,v,x),u))),x,v) -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oinsert(w,x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(x,tc_bool)),y),hAPP(c_Set_Oimage(z,v,x),u))),x),c_Finite__Set_Ocard(u,v)).
% 299.92/300.52 51972[0:SpL:475.1,459.0] || hBOOL(hAPP(hAPP(c_in(u),v),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(hAPP(w,v),x),c_Set_Oimage(w,u,x),y,z)))* equal(hAPP(c_Set_Oimage(w,u,x),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(hAPP(w,v),x),c_Set_Oimage(w,u,x),y,z)),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oinsert(hAPP(w,v),x),c_Set_Oimage(w,u,x),y,z))** -> equal(hAPP(c_Set_Oinsert(hAPP(w,v),x),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oimage(w,u,x),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),c_Set_Oinsert(hAPP(w,v),x))),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(c_Set_Oinsert(hAPP(w,v),x),x3),x4,z,x1))**.
% 299.92/300.52 80490[0:Rew:79546.1,80035.6] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),u,z),w) c_Finite__Set_Ofinite(x1,x) c_lessequals(hAPP(c_Set_Oimage(v,w,x),y),x1,tc_fun(x,tc_bool)) c_lessequals(hAPP(c_Set_Oimage(x2,x,w),x1),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),u,z),tc_fun(w,tc_bool))* c_Fun_Oinj__on(v,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(v,w,x),hAPP(c_Set_Oimage(v,w,x),y),u,z),w,x)* c_Fun_Oinj__on(x2,x1,x,w) -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(v,w,x),y),x),c_Finite__Set_Ocard(x1,x)).
% 299.92/300.52 81685[0:Rew:80739.1,81230.6] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),u,z),w) c_Finite__Set_Ofinite(x1,x) c_lessequals(hAPP(c_Set_Oimage(v,w,x),y),x1,tc_fun(x,tc_bool)) c_lessequals(hAPP(c_Set_Oimage(x2,x,w),x1),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),u,z),tc_fun(w,tc_bool))* c_Fun_Oinj__on(v,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(v,w,x),y),c_Set_Oimage(v,w,x),u,z),w,x)* c_Fun_Oinj__on(x2,x1,x,w) -> equal(c_Finite__Set_Ocard(hAPP(c_Set_Oimage(v,w,x),y),x),c_Finite__Set_Ocard(x1,x)).
% 299.92/300.52 51951[0:SpL:532.0,459.0] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,y))),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),x,y))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),y,x,z),tc_fun(z,y),tc_fun(z,x),x),hAPP(c_COMBB(x1,y,tc_fun(z,y),x),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w))),x2,x3,x,z)),c_List_Ofoldl(x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x2),x3,y,z))**.
% 299.92/300.52 52563[0:Res:171.2,624.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),u) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(c_Hilbert__Choice_Oinv__into(z,x,y,w),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),u))),hAPP(c_Hilbert__Choice_Oinv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),u)))*.
% 299.92/300.52 52562[0:Res:172.2,624.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),u) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(c_Hilbert__Choice_Oinv__into(z,x,y,w),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),u))),hAPP(c_Hilbert__Choice_Oinv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),u)))*.
% 299.92/300.52 52583[0:Rew:21893.0,52539.3,21893.0,52539.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),v_x)))) c_Fun_Oinj__on(y,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(y,z,x),v_x),c_Set_Oimage(y,z,x),tc_Com_Opname,x1),z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),v_x),x,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(y,z,x),v_x),c_Set_Oimage(y,z,x),tc_Com_Opname,x1),y,z,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(y,z,x),v_x),w,x,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(y,z,x),v_x),c_Set_Oimage(y,z,x),tc_Com_Opname,x1),c_Fun_Ocomp(w,y,x,u,z),z,u),v))*.
% 299.92/300.52 52584[0:Rew:21267.0,52538.3,21267.0,52538.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),v_x)))) c_Fun_Oinj__on(y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(y,z,x),v_x),tc_Com_Opname,x1),z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),v_x),x,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(y,z,x),v_x),tc_Com_Opname,x1),y,z,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(y,z,x),v_x),w,x,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(y,z,x),v_x),tc_Com_Opname,x1),c_Fun_Ocomp(w,y,x,u,z),z,u),v))*.
% 299.92/300.52 52675[0:Res:171.2,623.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),u) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(c_Fun_Othe__inv__into(z,x,y,w),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),u))),hAPP(c_Fun_Othe__inv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),c_Finite__Set_Olinorder__class_OMin(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),u)))*.
% 299.92/300.52 52674[0:Res:172.2,623.0] class_Orderings_Olinorder(u) || c_Finite__Set_Ofinite(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),u) c_Fun_Oinj__on(x,z,y,w) c_Fun_Oinj__on(v,hAPP(c_Set_Oimage(x,y,w),z),w,u) -> equal(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),c_Orderings_Obot__class_Obot(tc_fun(u,tc_bool))) equal(hAPP(c_Fun_Othe__inv__into(z,x,y,w),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(x,y,w),z),v,w,u),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),u))),hAPP(c_Fun_Othe__inv__into(z,c_Fun_Ocomp(v,x,w,u,y),y,u),c_Finite__Set_Olinorder__class_OMax(hAPP(c_Set_Oimage(v,w,u),hAPP(c_Set_Oimage(x,y,w),z)),u)))*.
% 299.92/300.52 52696[0:Rew:21893.0,52651.3,21893.0,52651.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),v_x)))) c_Fun_Oinj__on(y,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(y,z,x),v_x),c_Set_Oimage(y,z,x),tc_Com_Opname,x1),z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),v_x),x,u) -> equal(hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(y,z,x),v_x),c_Set_Oimage(y,z,x),tc_Com_Opname,x1),y,z,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(y,z,x),v_x),w,x,u),v)),hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(y,z,x),v_x),c_Set_Oimage(y,z,x),tc_Com_Opname,x1),c_Fun_Ocomp(w,y,x,u,z),z,u),v))*.
% 299.92/300.52 52697[0:Rew:21267.0,52650.3,21267.0,52650.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),v_x)))) c_Fun_Oinj__on(y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(y,z,x),v_x),tc_Com_Opname,x1),z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),v_x),x,u) -> equal(hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(y,z,x),v_x),tc_Com_Opname,x1),y,z,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(y,z,x),v_x),w,x,u),v)),hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(y,z,x),v_x),tc_Com_Opname,x1),c_Fun_Ocomp(w,y,x,u,z),z,u),v))*.
% 299.92/300.52 51998[0:Rew:537.1,51943.2,537.1,51943.2] class_Lattices_Olattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(x,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y,z)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y,z))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(x,z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))),x3,x4,y,x1))),c_List_Ofoldl(x2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x3)),x4,z,x1))**.
% 299.92/300.52 51999[0:Rew:534.1,51942.2,534.1,51942.2] class_Lattices_Oupper__semilattice(u) || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),hAPP(x,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y,z)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)),x,y,z))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(x,z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),w)))),x3,x4,y,x1))),c_List_Ofoldl(x2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(u),w),x3)),x4,z,x1))**.
% 299.92/300.52 52734[0:Res:27441.0,592.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,v,hAPP(v,v_x),tc_Com_Opname,w))),t_a)*.
% 299.92/300.52 52731[0:Res:27381.0,592.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(v,v_x),v,tc_Com_Opname,w))),t_a)*.
% 299.92/300.52 52585[0:Rew:24914.0,52536.3,24914.0,52536.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),v_x)))) c_Fun_Oinj__on(y,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(y,z,x),tc_Com_Opname,x1),hAPP(c_Set_Oimage(y,z,x),v_x)),z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),v_x),x,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(y,z,x),tc_Com_Opname,x1),hAPP(c_Set_Oimage(y,z,x),v_x)),y,z,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(y,z,x),v_x),w,x,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(y,z,x),tc_Com_Opname,x1),hAPP(c_Set_Oimage(y,z,x),v_x)),c_Fun_Ocomp(w,y,x,u,z),z,u),v))*.
% 299.92/300.52 52698[0:Rew:24914.0,52648.3,24914.0,52648.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),v_x)))) c_Fun_Oinj__on(y,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(y,z,x),tc_Com_Opname,x1),hAPP(c_Set_Oimage(y,z,x),v_x)),z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),v_x),x,u) -> equal(hAPP(c_Fun_Othe__inv__into(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(y,z,x),tc_Com_Opname,x1),hAPP(c_Set_Oimage(y,z,x),v_x)),y,z,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(y,z,x),v_x),w,x,u),v)),hAPP(c_Fun_Othe__inv__into(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(y,z,x),tc_Com_Opname,x1),hAPP(c_Set_Oimage(y,z,x),v_x)),c_Fun_Ocomp(w,y,x,u,z),z,u),v))*.
% 299.92/300.52 52001[0:Rew:339.0,51949.1,339.0,51949.1] || equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),hAPP(x,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),x,y,z)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)),x,y,z))** -> equal(hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(x,z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Oinsert(u,v),w)))),x3,x4,y,x1))),c_List_Ofoldl(x2,hAPP(c_Set_Oinsert(u,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),w),x3)),x4,z,x1))**.
% 299.92/300.52 52737[0:Res:31533.0,592.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x)))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x))))),hAPP(v_Q,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,v,tc_Com_Opname,w),hAPP(v,v_x)))),t_a)*.
% 299.92/300.52 52736[0:Res:27443.0,592.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBK(v,w,x),v,tc_Com_Opname,y))),t_a)*.
% 299.92/300.52 52735[0:Res:28312.0,592.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),v_x,tc_Com_Opname,v))),t_a)*.
% 299.92/300.52 52733[0:Res:27383.0,592.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v,c_COMBK(v,w,x),tc_Com_Opname,y))),t_a)*.
% 299.92/300.52 52732[0:Res:28009.0,592.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,v_x,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v))),t_a)*.
% 299.92/300.52 52564[0:Res:468.0,624.0] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(y,hAPP(c_Set_Oimage(u,w,x),v),x,z) -> equal(hAPP(c_Set_Oimage(x1,z,x2),hAPP(c_Set_Oimage(y,x,z),hAPP(c_Set_Oimage(u,w,x),v))),hAPP(c_Set_Oimage(x3,z,x2),hAPP(c_Set_Oimage(y,x,z),hAPP(c_Set_Oimage(u,w,x),v)))) equal(hAPP(c_Hilbert__Choice_Oinv__into(v,u,w,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(u,w,x),v),y,x,z),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(y,x,z),hAPP(c_Set_Oimage(u,w,x),v)),x1,x3,z,x2))),hAPP(c_Hilbert__Choice_Oinv__into(v,c_Fun_Ocomp(y,u,x,z,w),w,z),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(y,x,z),hAPP(c_Set_Oimage(u,w,x),v)),x1,x3,z,x2)))*.
% 299.92/300.52 52676[0:Res:468.0,623.0] || c_Fun_Oinj__on(u,v,w,x) c_Fun_Oinj__on(y,hAPP(c_Set_Oimage(u,w,x),v),x,z) -> equal(hAPP(c_Set_Oimage(x1,z,x2),hAPP(c_Set_Oimage(y,x,z),hAPP(c_Set_Oimage(u,w,x),v))),hAPP(c_Set_Oimage(x3,z,x2),hAPP(c_Set_Oimage(y,x,z),hAPP(c_Set_Oimage(u,w,x),v)))) equal(hAPP(c_Fun_Othe__inv__into(v,u,w,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(u,w,x),v),y,x,z),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(y,x,z),hAPP(c_Set_Oimage(u,w,x),v)),x1,x3,z,x2))),hAPP(c_Fun_Othe__inv__into(v,c_Fun_Ocomp(y,u,x,z,w),w,z),c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(hAPP(c_Set_Oimage(y,x,z),hAPP(c_Set_Oimage(u,w,x),v)),x1,x3,z,x2)))*.
% 299.92/300.52 53354[0:Res:31543.0,592.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x)))),hAPP(v_Q,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_bool),v_x),tc_Com_Opname,v),v_x))),t_a)*.
% 299.92/300.52 64690[0:Res:27986.0,592.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_bool),c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),tc_Com_Opname,w))),t_a)*.
% 299.92/300.52 64710[0:Res:27987.0,592.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_bool),c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),tc_Com_Opname,w))),t_a)*.
% 299.92/300.52 64730[0:Res:28288.0,592.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Orderings_Otop__class_Otop(tc_bool),tc_Com_Opname,w))),t_a)*.
% 299.92/300.52 64750[0:Res:28289.0,592.0] || -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(u,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Orderings_Obot__class_Obot(tc_fun(v,tc_bool)),c_Orderings_Obot__class_Obot(tc_bool),tc_Com_Opname,w))),t_a)*.
% 299.92/300.52 52728[0:Res:468.0,592.0] || -> equal(hAPP(c_Set_Oimage(u,tc_Com_Opname,v),v_Procs),hAPP(c_Set_Oimage(w,tc_Com_Opname,v),v_Procs)) hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(x,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v_Procs,u,w,tc_Com_Opname,v))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v_Procs,u,w,tc_Com_Opname,v)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__cong__1__1(v_Procs,u,w,tc_Com_Opname,v))),t_a)*.
% 299.92/300.52 80491[0:Rew:21268.0,80316.3,21268.0,80316.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1)))) c_Fun_Oinj__on(y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(y,z,x),x1),x2,x3),z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(y,z,x),x1),x2,x3),y,z,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(y,z,x),x1),x2,x3),c_Fun_Ocomp(w,y,x,u,z),z,u),v))*.
% 299.92/300.52 80492[0:Rew:21268.0,80315.3,21268.0,80315.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1)))) c_Fun_Oinj__on(y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(y,z,x),x1),x2,x3),z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> equal(hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(y,z,x),x1),x2,x3),y,z,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,u),v)),hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),c_Set_Oimage(y,z,x),hAPP(c_Set_Oimage(y,z,x),x1),x2,x3),c_Fun_Ocomp(w,y,x,u,z),z,u),v))*.
% 299.92/300.52 81686[0:Rew:21894.0,81511.3,21894.0,81511.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1)))) c_Fun_Oinj__on(y,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(y,z,x),x1),c_Set_Oimage(y,z,x),x2,x3),z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> equal(hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(y,z,x),x1),c_Set_Oimage(y,z,x),x2,x3),y,z,x),hAPP(c_Hilbert__Choice_Oinv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,u),v)),hAPP(c_Hilbert__Choice_Oinv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(y,z,x),x1),c_Set_Oimage(y,z,x),x2,x3),c_Fun_Ocomp(w,y,x,u,z),z,u),v))*.
% 299.92/300.52 81687[0:Rew:21894.0,81510.3,21894.0,81510.2] || hBOOL(hAPP(hAPP(c_in(u),v),hAPP(c_Set_Oimage(w,x,u),hAPP(c_Set_Oimage(y,z,x),x1)))) c_Fun_Oinj__on(y,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(y,z,x),x1),c_Set_Oimage(y,z,x),x2,x3),z,x) c_Fun_Oinj__on(w,hAPP(c_Set_Oimage(y,z,x),x1),x,u) -> equal(hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(y,z,x),x1),c_Set_Oimage(y,z,x),x2,x3),y,z,x),hAPP(c_Fun_Othe__inv__into(hAPP(c_Set_Oimage(y,z,x),x1),w,x,u),v)),hAPP(c_Fun_Othe__inv__into(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x2,tc_bool)),hAPP(c_Set_Oimage(y,z,x),x1),c_Set_Oimage(y,z,x),x2,x3),c_Fun_Ocomp(w,y,x,u,z),z,u),v))*.
% 299.92/300.52 75625[0:SSi:75497.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),hAPP(c_Set_Oimage(z,v,w),u))),w) c_lessequals(hAPP(c_Set_Oimage(x1,w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),hAPP(c_Set_Oimage(z,v,w),u)))),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(z,u,v,w) c_Fun_Oinj__on(x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),hAPP(c_Set_Oimage(z,v,w),u))),w,v) -> equal(c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),y),hAPP(c_Set_Oimage(z,v,w),u))),w),c_Finite__Set_Ocard(u,v)).
% 299.92/300.52 76093[0:SSi:75951.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Finite__Set_Ofinite(u,v) c_Finite__Set_Ofinite(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(y,v,w),u)),z)),w) c_lessequals(hAPP(c_Set_Oimage(x1,w,v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(y,v,w),u)),z))),u,tc_fun(v,tc_bool))* c_Fun_Oinj__on(y,u,v,w) c_Fun_Oinj__on(x1,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(y,v,w),u)),z)),w,v) -> equal(c_Finite__Set_Ocard(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(y,v,w),u)),z)),w),c_Finite__Set_Ocard(u,v)).
% 299.92/300.52 52181[0:SpL:21893.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),v_x),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),tc_Com_Opname,x)),tc_Hoare__Mirabelle_Otriple(u)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),v_x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),v_x),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),tc_Com_Opname,x)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52180[0:SpL:21267.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),v_x),tc_Com_Opname,x)),tc_Hoare__Mirabelle_Otriple(u)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),v_x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),v_x),tc_Com_Opname,x)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52179[0:SpL:24914.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),tc_Com_Opname,x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),v_x))),tc_Hoare__Mirabelle_Otriple(u)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),v_x),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),tc_Com_Opname,x),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),v_x))),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 51933[0:SpL:465.1,459.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(x,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),x,x1,x2))),c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),x,x1,x2))** -> hBOOL(hAPP(hAPP(c_in(v),y),hAPP(x,c_List_Osko__List__Xfoldl__apply__inv__1__1(c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),x,x1,x2))))* equal(hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(x,x2,x1,x3),tc_fun(x3,x2),tc_fun(x3,x1),x1),hAPP(c_COMBB(x4,x2,tc_fun(x3,x2),x1),c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w))),x5,x6,x1,x3)),c_List_Ofoldl(x4,hAPP(c_Set_Oimage(c_Fun_Ofun__upd(u,y,z,v,w),v,w),x5),x6,x2,x3))**.
% 299.92/300.52 53318[0:SpL:337.0,506.0] || c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u).
% 299.92/300.52 51953[0:SpL:162.0,459.0] || equal(hAPP(c_Set_Ovimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),x),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x)),c_Set_Ovimage(u,v,w),y,z))),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x)),c_Set_Ovimage(u,v,w),y,z))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x)),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Ovimage(u,v,w),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x)))),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),hAPP(c_Set_Ovimage(u,v,w),x)),x3),x4,z,x1))**.
% 299.92/300.52 51952[0:SpL:507.0,459.0] || equal(hAPP(c_Set_Oimage(u,v,w),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(v,tc_bool)),x),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x)),c_Set_Oimage(u,v,w),y,z))),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x)),c_Set_Oimage(u,v,w),y,z))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x)),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(c_Set_Oimage(u,v,w),z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x)))),x3,x4,y,x1)),c_List_Ofoldl(x2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(w,tc_bool)),hAPP(c_Set_Oimage(u,v,w),x)),x3),x4,z,x1))**.
% 299.92/300.52 80227[0:SpL:21268.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),y),x,z)),tc_Hoare__Mirabelle_Otriple(u)),x1),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),y),x,z)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 81422[0:SpL:21894.0,461.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),y),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x,z)),tc_Hoare__Mirabelle_Otriple(u)),x1),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),y),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Com_Ocom_OBODY,w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),y),hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),v),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,w))),x,z)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 74541[7:Rew:71835.1,74359.2] || equal(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_Set_Oinsert(v_x,t_a)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),x),v_x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,v_x,u).
% 299.92/300.52 52004[0:Rew:533.0,51950.1,533.0,51950.1] || equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),hAPP(x,c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,y,z)))),c_List_Osko__List__Xfoldl__apply__inv__1__1(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)),x,y,z))** -> equal(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),c_List_Ofoldl(hAPP(c_COMBB(c_COMBB(x,z,y,x1),tc_fun(x1,z),tc_fun(x1,y),y),hAPP(c_COMBB(x2,z,tc_fun(x1,z),y),hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),w)))),x3,x4,y,x1))),c_List_Ofoldl(x2,hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(u,tc_bool)),w),x3)),x4,z,x1))**.
% 299.92/300.52 53332[0:Rew:8415.2,53289.3] || equal(v_Procs,v_x) equal(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),x),v_x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,v_x,u).
% 299.92/300.52 80005[0:SpL:21268.0,592.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(tc_Com_Opname),hAPP(c_in(tc_Com_Opname),u),w,x))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(tc_Com_Opname),hAPP(c_in(tc_Com_Opname),u),w,x)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),c_in(tc_Com_Opname),hAPP(c_in(tc_Com_Opname),u),w,x))),t_a)*.
% 299.92/300.52 81200[0:SpL:21894.0,592.0] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v_Procs)) -> hBOOL(hAPP(hAPP(c_in(tc_Hoare__Mirabelle_Otriple(t_a)),v_n(v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(t_a),tc_bool)),v_G),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_a),tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),tc_Com_Opname),v_P),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a))),v_Q,tc_Com_Opname,tc_fun(t_a,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_a)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(t_a)),v_Procs))))* c_Hoare__Mirabelle_Otriple__valid(v,hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_a),hAPP(v_P,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(tc_Com_Opname),u),c_in(tc_Com_Opname),w,x))),hAPP(c_Option_Othe(tc_Com_Ocom),hAPP(c_Com_Obody,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(tc_Com_Opname),u),c_in(tc_Com_Opname),w,x)))),hAPP(v_Q,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(w,tc_bool)),hAPP(c_in(tc_Com_Opname),u),c_in(tc_Com_Opname),w,x))),t_a)*.
% 299.92/300.52 74538[7:Rew:73901.1,74380.3] || equal(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v),w))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(v_x,c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),y,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),w)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(v_x,hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),y,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),w),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(v_x,v),hAPP(c_Com_Ocom_OBODY,v)),hAPP(y,v)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 74539[7:Rew:71835.1,74381.2] || equal(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),c_Set_Oinsert(v_x,t_a)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(v_x,c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(v_x,hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(v_x,c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u).
% 299.92/300.52 52939[0:Rew:8915.2,52895.4] || equal(v_Procs,v_x) equal(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v),w))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(v_x,c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),y,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),w)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(v_x,hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),y,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),w),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(v_x,v),hAPP(c_Com_Ocom_OBODY,v)),hAPP(y,v)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 52897[0:SpL:3229.1,504.1] || equal(u,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),w),x))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),y),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(u,v_x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),z,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),x)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(u,v_x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),z,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),x),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(v_x,w)),hAPP(c_Com_Ocom_OBODY,w)),hAPP(z,w)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 53329[0:Rew:8415.2,53283.3] || equal(v_Procs,v_x) equal(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(v_x,c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(v_x,hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(v_x,c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u).
% 299.92/300.52 680[0:Res:589.0,504.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_Procs)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_Procs),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),hAPP(w,v_x)),hAPP(c_Com_Ocom_OBODY,v_x)),hAPP(x,v_x)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u).
% 299.92/300.52 52922[0:SpL:331.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),hAPP(x,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(y,u)),tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.92/300.52 52936[0:SpL:328.1,504.1] || c_lessequals(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),y,tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),z),x))* c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),hAPP(v,z)),hAPP(c_Com_Ocom_OBODY,z)),hAPP(w,z)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 52931[0:SpL:538.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v)),z),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(z,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),hAPP(x,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(y,u)),tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.92/300.52 52938[0:SpL:584.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),z,x1,x2),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),hAPP(x,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(y,u)),tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.92/300.52 52941[0:SSi:52926.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v)) c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v),w) -> c_Hoare__Mirabelle_Ohoare__derivs(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v),tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),hAPP(x,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(y,u)),tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.92/300.52 74540[7:Rew:73901.1,74226.3] || equal(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Set_Oinsert(v_x,t_a)) c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(v_x,w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(v_x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,y,v_x,z,x,w)),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,y,v_x,z,x,w))),hAPP(x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,y,v_x,z,x,w))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),z,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.92/300.52 52910[0:SpL:3229.1,504.1] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),w),x))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),y),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),z,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),x)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),y),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),z,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),x),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(v_x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(y,w)),hAPP(c_Com_Ocom_OBODY,w)),hAPP(z,w)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 52903[0:SpL:3229.1,504.1] || equal(u,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v))) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),y),v_x)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),z),hAPP(u,v_x)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(z,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(w,y)),hAPP(c_Com_Ocom_OBODY,y)),hAPP(x,y)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 52890[0:SpL:3229.1,504.1] || equal(u,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v))) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),y),v_x)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),z),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x)),hAPP(u,v_x),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(z,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(w,y)),hAPP(c_Com_Ocom_OBODY,y)),hAPP(x,y)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 53285[0:SpL:3229.1,506.0] || equal(u,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),w),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(u,v_x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(u,v_x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),v_x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y),v).
% 299.92/300.52 74376[7:SpL:71835.1,504.1] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v),w))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(v_x,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),y,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),w)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),y,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),w),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v_x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),hAPP(x,v)),hAPP(c_Com_Ocom_OBODY,v)),hAPP(y,v)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 74187[7:SpL:71835.1,504.1] || equal(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),x),v_x)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),y),v_x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),hAPP(v,x)),hAPP(c_Com_Ocom_OBODY,x)),hAPP(w,x)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 74186[7:SpL:71835.1,504.1] || equal(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_Set_Oinsert(v_x,t_a)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),x),v_x)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),y),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x)),v_x,u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),hAPP(v,x)),hAPP(c_Com_Ocom_OBODY,x)),hAPP(w,x)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 52976[0:SpL:3229.1,457.1] || equal(u,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)))* c_Finite__Set_Ofinite(v_x,t_a) c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(u,v_x),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,v,x1,x,w))),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,v,x1,x,w))),hAPP(x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,v,x1,x,w))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),z),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x1,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),t_b)*.
% 299.92/300.52 52970[0:SpL:3229.1,457.1] || equal(u,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a)) c_Finite__Set_Ofinite(v,t_a) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(u,v_x),x,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),y,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(w,z,v_x,x1,y,x))),hAPP(x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(w,z,v_x,x1,y,x))),hAPP(y,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(w,z,v_x,x1,y,x))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),z),x,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x1,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v),t_b)*.
% 299.92/300.52 73981[7:SpL:71835.1,457.1] || equal(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),c_Set_Oinsert(v_x,t_a))** c_Finite__Set_Ofinite(v_x,t_a) c_Hoare__Mirabelle_Ohoare__derivs(x,v_x,t_b) -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(u,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x,y,u,z,w,v))),hAPP(v,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x,y,u,z,w,v))),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x,y,u,z,w,v))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),z,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),t_b)*.
% 299.92/300.52 52982[0:Rew:8915.2,52968.4] || equal(v_Procs,v_x) equal(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(v_x,w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(v_x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,y,v_x,z,x,w)),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,y,v_x,z,x,w))),hAPP(x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,y,v_x,z,x,w))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),z,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.92/300.52 53130[0:SpL:3229.1,458.2] || equal(u,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)))* c_Finite__Set_Ofinite(v_x,t_a) c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(z,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,v,x1,x,w))),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,v,x1,x,w))),hAPP(x1,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,v,x1,x,w))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(u,v_x),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),z),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x1,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),t_b)*.
% 299.92/300.52 53124[0:SpL:3229.1,458.2] || equal(u,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a)) c_Finite__Set_Ofinite(v,t_a) c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(w,x,v_x,y,z,x1))),hAPP(x1,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(w,x,v_x,y,z,x1))),hAPP(y,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(w,x,v_x,y,z,x1))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(u,v_x),x1,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),z,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(w,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),x),x1,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),y,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v),t_b)*.
% 299.92/300.52 74251[7:SpL:71835.1,458.2] || equal(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Set_Oinsert(v_x,t_a)) c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,v_x,x,y,z))),hAPP(z,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,v_x,x,y,z))),hAPP(x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,v_x,x,y,z))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(v_x,z,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),y,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),z,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.92/300.52 73982[7:SpL:71835.1,458.2] || equal(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),c_Set_Oinsert(v_x,t_a))** c_Finite__Set_Ofinite(v_x,t_a) c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(y,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x,y,u,z,w,v))),hAPP(v,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x,y,u,z,w,v))),hAPP(z,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x,y,u,z,w,v))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(x,v_x,t_b) -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),z,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),t_b)*.
% 299.92/300.52 52932[0:SpL:104.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v))* c_Hoare__Mirabelle_Ohoare__derivs(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(w,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(x),tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(x))),tc_Com_Opname),y),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(x))),z,tc_Com_Opname,tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(x)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(x)),v),tc_fun(tc_Hoare__Mirabelle_Otriple(x),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(x),tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(x),tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(x))),tc_Com_Opname),y),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(x))),z,tc_Com_Opname,tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(x)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(x)),v),x)* -> c_Hoare__Mirabelle_Ohoare__derivs(c_HOL_Ouminus__class_Ouminus(w,tc_fun(tc_Hoare__Mirabelle_Otriple(x),tc_bool)),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(x),hAPP(y,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(z,u)),tc_Hoare__Mirabelle_Otriple(x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(x),tc_bool))),x)*.
% 299.92/300.52 52908[0:SpL:8415.2,504.1] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),v),w))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(v_x,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),y,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),w)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),y,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),w),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v_x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),hAPP(x,v)),hAPP(c_Com_Ocom_OBODY,v)),hAPP(y,v)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 52901[0:SpL:8415.2,504.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),x),v_x)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),y),v_x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),hAPP(v,x)),hAPP(c_Com_Ocom_OBODY,x)),hAPP(w,x)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 52888[0:SpL:8415.2,504.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_Set_Oinsert(v_x,tc_Com_Opname)) hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),x),v_x)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),y),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x)),v_x,u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(u),hAPP(v,x)),hAPP(c_Com_Ocom_OBODY,x)),hAPP(w,x)),tc_Hoare__Mirabelle_Otriple(u)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool))),u)*.
% 299.92/300.52 52933[0:SpL:339.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(x)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(x),tc_bool)),y),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(x),tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(x))),tc_Com_Opname),z),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(x))),x1,tc_Com_Opname,tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(x)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(x)),v))),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(x),tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(x))),tc_Com_Opname),z),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(x))),x1,tc_Com_Opname,tc_fun(x,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(x)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(x)),v),x)* -> c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(w,tc_Hoare__Mirabelle_Otriple(x)),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(x),hAPP(z,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(x1,u)),tc_Hoare__Mirabelle_Otriple(x)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(x),tc_bool))),x)*.
% 299.92/300.52 52974[0:SpL:8415.2,457.1] || equal(v_Procs,v_x) equal(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),c_Set_Oinsert(v_x,tc_Com_Opname))** c_Finite__Set_Ofinite(v_x,t_a) c_Hoare__Mirabelle_Ohoare__derivs(x,v_x,t_b) -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(u,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x,y,u,z,w,v))),hAPP(v,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x,y,u,z,w,v))),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x,y,u,z,w,v))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),z,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),t_b)*.
% 299.92/300.52 53128[0:SpL:8415.2,458.2] || equal(v_Procs,v_x) equal(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),c_Set_Oinsert(v_x,tc_Com_Opname))** c_Finite__Set_Ofinite(v_x,t_a) c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(y,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x,y,u,z,w,v))),hAPP(v,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x,y,u,z,w,v))),hAPP(z,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x,y,u,z,w,v))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(x,v_x,t_b) -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),z,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),t_b)*.
% 299.92/300.52 53122[0:SpL:8415.2,458.2] || equal(v_Procs,v_x) equal(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,v_x,x,y,z))),hAPP(z,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,v_x,x,y,z))),hAPP(x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,v_x,x,y,z))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(v_x,z,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),y,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),z,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.92/300.52 53310[0:SpL:331.0,506.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u).
% 299.92/300.52 52934[0:SpL:533.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),x),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),y),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),z),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),x1,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v))),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),z),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),x1,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),x),y),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),hAPP(z,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(x1,u)),tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.92/300.52 53324[0:SpL:328.1,506.0] || c_lessequals(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),y,tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)) c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u).
% 299.92/300.52 53319[0:SpL:538.0,506.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x)),y),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u).
% 299.92/300.52 53326[0:SpL:584.0,506.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_COMBS(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x,y,z),x1),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x1),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x1),u).
% 299.92/300.52 53331[0:SSi:53314.0,559.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,561.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,560.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,557.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,558.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,554.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,556.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,552.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,551.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,549.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,555.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1,550.0,580.0,582.0,581.0,578.0,579.0,575.0,577.0,574.0,573.0,572.0,570.0,576.0,571.1] || c_Hoare__Mirabelle_Ohoare__derivs(c_Orderings_Otop__class_Otop(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u) -> c_Hoare__Mirabelle_Ohoare__derivs(c_HOL_Ouminus__class_Ouminus(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u)*.
% 299.92/300.52 53298[0:SpL:3229.1,506.0] || equal(u,c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(u,v_x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(v_x,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y),v).
% 299.92/300.52 53291[0:SpL:3229.1,506.0] || equal(u,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v))) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),y),hAPP(u,v_x)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x),v).
% 299.92/300.52 53278[0:SpL:3229.1,506.0] || equal(u,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v))) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),y),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x)),hAPP(u,v_x),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x),v).
% 299.92/300.52 74377[7:SpL:71835.1,506.0] || equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),c_Set_Oinsert(v_x,t_a)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(v_x,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v_x,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u).
% 299.92/300.52 74358[7:SpL:71835.1,506.0] || equal(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_Set_Oinsert(v_x,t_a)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x)),v_x,u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),u).
% 299.92/300.52 53320[0:SpL:104.0,506.0] || c_Hoare__Mirabelle_Ohoare__derivs(c_HOL_Ouminus__class_Ouminus(c_HOL_Ominus__class_Ominus(u,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y),tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(c_HOL_Ouminus__class_Ouminus(u,tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y),v).
% 299.92/300.52 53296[0:SpL:8415.2,506.0] || equal(v_Procs,v_x) equal(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(v_x,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v_x,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u).
% 299.92/300.52 53276[0:SpL:8415.2,506.0] || equal(v_Procs,v_x) equal(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_Set_Oinsert(v_x,tc_Com_Opname)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x)),v_x,u)* -> c_Hoare__Mirabelle_Ohoare__derivs(x,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),u).
% 299.92/300.52 53321[0:SpL:339.0,506.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(v)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),w),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),y,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),z))),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),y,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),z),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oinsert(u,tc_Hoare__Mirabelle_Otriple(v)),w),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),y,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),z),v).
% 299.92/300.52 53322[0:SpL:533.0,506.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),w),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),y,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),z))),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),y,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),z),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),w),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),y,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),z),u).
% 299.92/300.52 52914[0:SpL:524.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v)) c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),hAPP(x,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(y,u)),tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.92/300.52 52935[0:SpL:507.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),v))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),z),v)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),z),hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),hAPP(x,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(y,u)),tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.92/300.52 52937[0:SpL:329.1,504.1] || c_lessequals(u,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y),tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))* hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),z),y))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(w,z)),hAPP(c_Com_Ocom_OBODY,z)),hAPP(x,z)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 53302[0:SpL:524.0,506.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),u).
% 299.92/300.52 53323[0:SpL:507.0,506.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Com_Opname,tc_bool)),x),y)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),y),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),v),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),w,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),y),u).
% 299.92/300.52 53325[0:SpL:329.1,506.0] || c_lessequals(u,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y),tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(u,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),y),v).
% 299.92/300.52 53342[0:Rew:21893.0,53295.1] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,y)),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),u).
% 299.92/300.52 53343[0:Rew:21267.0,53294.1] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),tc_Com_Opname,y)),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),u).
% 299.92/300.52 53344[0:Rew:24914.0,53293.1] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,y),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x))),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),u).
% 299.92/300.52 80498[0:Rew:21268.0,80300.1] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),y)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),y),z,x1)),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),y),u).
% 299.92/300.52 81693[0:Rew:21894.0,81495.1] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),y)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(z,tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),y),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),z,x1)),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),y),u).
% 299.92/300.52 52983[0:Rew:22345.0,52973.2] || c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,y,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),tc_Com_Opname,z),x1,x,w))),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,y,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),tc_Com_Opname,z),x1,x,w))),hAPP(x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,y,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),tc_Com_Opname,z),x1,x,w))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x1,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.92/300.52 52984[0:Rew:21716.0,52972.2] || c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),tc_Com_Opname,z),x1,x,w))),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),tc_Com_Opname,z),x1,x,w))),hAPP(x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,y,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),tc_Com_Opname,z),x1,x,w))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x1,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.92/300.52 53127[0:SpL:21893.0,458.2] || c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),tc_Com_Opname,x),y,z,x1))),hAPP(x1,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),tc_Com_Opname,x),y,z,x1))),hAPP(y,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),tc_Com_Opname,x),y,z,x1))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),x1,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),z,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),x1,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),y,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.92/300.52 53126[0:SpL:21267.0,458.2] || c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),tc_Com_Opname,x),y,z,x1))),hAPP(x1,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),tc_Com_Opname,x),y,z,x1))),hAPP(y,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),tc_Com_Opname,x),y,z,x1))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),x1,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),z,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),x1,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),y,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.92/300.52 52985[0:Rew:34472.0,52971.2] || c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v_x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,y,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),tc_Com_Opname,z),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x)),x1,x,w))),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,y,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),tc_Com_Opname,z),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x)),x1,x,w))),hAPP(x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,y,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),tc_Com_Opname,z),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x)),x1,x,w))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x1,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.92/300.52 53125[0:SpL:24914.0,458.2] || c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),tc_Com_Opname,x),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x)),y,z,x1))),hAPP(x1,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),tc_Com_Opname,x),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x)),y,z,x1))),hAPP(y,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),tc_Com_Opname,x),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x)),y,z,x1))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v_x),x1,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),z,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),x1,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),y,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.92/300.52 80497[0:Rew:80367.0,80174.2] || c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),x,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),y,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,z,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),x1,x2),x3,y,x))),hAPP(x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,z,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),x1,x2),x3,y,x))),hAPP(y,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,z,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),x1,x2),x3,y,x))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),z),x,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x3,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.92/300.52 81692[0:Rew:81562.0,81369.2] || c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),x,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),y,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,z,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),x1,x2),x3,y,x))),hAPP(x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,z,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),x1,x2),x3,y,x))),hAPP(y,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,z,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x1,tc_bool)),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),x1,x2),x3,y,x))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),z),x,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x3,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.92/300.52 80199[0:SpL:21268.0,458.2] || c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),x,z),x1,x2,x3))),hAPP(x3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),x,z),x1,x2,x3))),hAPP(x1,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),x,z),x1,x2,x3))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),x3,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x2,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),x3,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x1,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.92/300.52 81394[0:SpL:21894.0,458.2] || c_Finite__Set_Ofinite(u,t_a) c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),x,z),x1,x2,x3))),hAPP(x3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),x,z),x1,x2,x3))),hAPP(x1,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(v,w,c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(x,tc_bool)),hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),x,z),x1,x2,x3))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),y),x3,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x2,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),w),x3,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x1,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u),t_b)*.
% 299.92/300.52 52907[0:SpL:21893.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,y)))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),z),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,y)),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(z,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(w,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(x,u)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 52906[0:SpL:21267.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x),tc_Com_Opname,y)))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),z),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x),tc_Com_Opname,y)),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(z,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(w,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(x,u)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 52905[0:SpL:24914.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,y),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x))))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),z),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,y),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x))),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(z,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(w,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(x,u)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 52980[0:SpL:21893.0,457.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),tc_Com_Opname,x),t_a) c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),t_b) -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(u,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),hAPP(v,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),z),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x1,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),tc_Com_Opname,x)),t_b)*.
% 299.92/300.52 52979[0:SpL:21267.0,457.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),tc_Com_Opname,x),t_a) c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),t_b) -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(u,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),hAPP(v,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),z),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x1,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),tc_Com_Opname,x)),t_b)*.
% 299.92/300.52 53134[0:SpL:21893.0,458.2] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),tc_Com_Opname,x),t_a) c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(z,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),hAPP(v,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),hAPP(x1,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),t_b) -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),z),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x1,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),tc_Com_Opname,x)),t_b)*.
% 299.92/300.52 53133[0:SpL:21267.0,458.2] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),tc_Com_Opname,x),t_a) c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(z,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),hAPP(v,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),hAPP(x1,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),t_b) -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),z),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x1,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),tc_Com_Opname,x)),t_b)*.
% 299.92/300.52 52978[0:SpL:24914.0,457.1] || c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),tc_Com_Opname,x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x)),t_a) c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),t_b) -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(u,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),hAPP(v,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),z),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x1,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),tc_Com_Opname,x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x))),t_b)*.
% 299.92/300.52 53132[0:SpL:24914.0,458.2] || c_Finite__Set_Ofinite(hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),tc_Com_Opname,x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x)),t_a) c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(z,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),hAPP(v,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),hAPP(x1,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(y,z,u,x1,w,v))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x),t_b) -> c_Hoare__Mirabelle_Ohoare__derivs(y,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),z),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x1,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),tc_Com_Opname,x),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),u),v,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),w,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),v_x))),t_b)*.
% 299.92/300.52 80135[0:SpL:21268.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),z),v,x1)))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),x2),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),z)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),z),v,x1)),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(x2,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),hAPP(x,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(y,u)),tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.92/300.52 81330[0:SpL:21894.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),z),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v,x1)))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),x2),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),z)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),z),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v,x1)),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(x2,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),hAPP(x,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(y,u)),tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.92/300.52 80036[0:SpL:21268.0,457.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),y),u,z),t_a) c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),y),t_b) -> c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x1,x2,v,x3,x,w))),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x1,x2,v,x3,x,w))),hAPP(x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x1,x2,v,x3,x,w))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),x2),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x3,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),y),u,z)),t_b)*.
% 299.92/300.52 81231[0:SpL:21894.0,457.1] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),y),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u,z),t_a) c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),y),t_b) -> c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(v,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x1,x2,v,x3,x,w))),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x1,x2,v,x3,x,w))),hAPP(x,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x1,x2,v,x3,x,w))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),x2),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x3,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),y),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u,z)),t_b)*.
% 299.92/300.52 80037[0:SpL:21268.0,458.2] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),y),u,z),t_a) c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(x2,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x1,x2,v,x3,x,w))),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x1,x2,v,x3,x,w))),hAPP(x3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x1,x2,v,x3,x,w))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),y),t_b) -> c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),x2),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x3,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),y),u,z)),t_b)*.
% 299.92/300.52 81232[0:SpL:21894.0,458.2] || c_Finite__Set_Ofinite(c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),y),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u,z),t_a) c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(t_b),hAPP(x2,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x1,x2,v,x3,x,w))),hAPP(w,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x1,x2,v,x3,x,w))),hAPP(x3,v_sko__Hoare__Mirabelle__Xfinite__pointwise__1(x1,x2,v,x3,x,w))),tc_Hoare__Mirabelle_Otriple(t_b)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(t_b),tc_bool))),t_b)* c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),y),t_b) -> c_Hoare__Mirabelle_Ohoare__derivs(x1,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),x2),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x3,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(u,tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),y),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(t_b),tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),t_a),v),w,t_a,tc_Com_Ocom,tc_fun(tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b))),x,t_a,tc_fun(t_b,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(t_b)),t_a,tc_Hoare__Mirabelle_Otriple(t_b)),u,z)),t_b)*.
% 299.92/300.52 52894[0:SpL:21893.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,y)))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),z),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,y))),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(z,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(w,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(x,u)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 52893[0:SpL:21267.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x),tc_Com_Opname,y)))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),z),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x),tc_Com_Opname,y))),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(z,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(w,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(x,u)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 52892[0:SpL:24914.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,y),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x))))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool)),z),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,y),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x)))),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(v),tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v))),x,tc_Com_Opname,tc_fun(v,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(v)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(v)),v_x),v)* -> c_Hoare__Mirabelle_Ohoare__derivs(z,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(v),hAPP(w,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(x,u)),tc_Hoare__Mirabelle_Otriple(v)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(v),tc_bool))),v)*.
% 299.92/300.52 80134[0:SpL:21268.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),z),v,x1)))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),x2),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),z),v,x1))),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),z),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(x2,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),hAPP(x,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(y,u)),tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.92/300.52 81329[0:SpL:21894.0,504.1] || hBOOL(hAPP(hAPP(c_in(tc_Com_Opname),u),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),z),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v,x1)))* c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool)),x2),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),c_ATP__Linkup_Osko__Set__XimageE__1__1(c_Orderings_Otop__class_Otop(tc_fun(v,tc_bool)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),z),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),v,x1))),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(w),tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),tc_Com_Opname),x),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w))),y,tc_Com_Opname,tc_fun(w,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(w)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(w)),z),w)* -> c_Hoare__Mirabelle_Ohoare__derivs(x2,hAPP(c_Set_Oinsert(hAPP(hAPP(hAPP(c_Hoare__Mirabelle_Otriple_Otriple(w),hAPP(x,u)),hAPP(c_Com_Ocom_OBODY,u)),hAPP(y,u)),tc_Hoare__Mirabelle_Otriple(w)),c_Orderings_Obot__class_Obot(tc_fun(tc_Hoare__Mirabelle_Otriple(w),tc_bool))),w)*.
% 299.92/300.52 53282[0:SpL:21893.0,506.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,y))),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_ATP__Linkup_Osko__Set__XimageE__1__1(v_Procs,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,y)),u).
% 299.92/300.52 53281[0:SpL:21267.0,506.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),tc_Com_Opname,y))),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),u)* -> c_Hoare__Mirabelle_Ohoare__derivs(v,hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),c_ATP__Linkup_Osko__Set__Ximage__iff__1__1(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),v_x),tc_Com_Opname,y)),u).
% 299.92/300.52 53280[0:SpL:24914.0,506.0] || c_Hoare__Mirabelle_Ohoare__derivs(hAPP(hAPP(c_Lattices_Oupper__semilattice__class_Osup(tc_fun(tc_Hoare__Mirabelle_Otriple(u),tc_bool)),v),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),c_Com_Ocom_OBODY,tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),hAPP(c_Hilbert__Choice_Oinv__into(v_Procs,c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,tc_Hoare__Mirabelle_Otriple(u)),tc_Com_Opname,y),hAPP(c_Set_Oimage(c_COMBS(c_COMBS(hAPP(c_COMBB(c_Hoare__Mirabelle_Otriple_Otriple(u),tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_fun(tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),tc_Com_Opname),w),hAPP(c_COMBB(c_Option_Othe(tc_Com_Ocom),tc_Option_Ooption(tc_Com_Ocom),tc_Com_Ocom,tc_Com_Opname),c_Com_Obody),tc_Com_Opname,tc_Com_Ocom,tc_fun(tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(u))),x,tc_Com_Opname,tc_fun(u,tc_fun(tc_Com_Ostate,tc_bool)),tc_Hoare__Mirabelle_Otriple(Cputime limit exceeded (core dumped)
%------------------------------------------------------------------------------